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THE RR LYRAE VARIABLE STARS IN

THE GLOBULAR CLUSTER M15

By

Nancy Ann Silbermann

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

1994

ABSTRACT

THE R LYRAE VARIABLE STARS IN THE

GLOBULAR CLUSTER M15

By

Nancy Ann Silbermann

The globular cluster M15 is a canonical Oosterhofl' type II globular cluster. The RR
Lyrae variable stars within M15 have previously been used to determine the age of
the cluster as well as the absolute magnitude of the variables. These previous studies
have relied on photographic photometry. With the recent advances in electronic
cameras (CCD’s), it is now possible to obtain higher quality photometry in a much
shorter time. These new cameras challenge observers to make new analyses of RR

Lyrae stars in globular clusters.

To that end, new CCD photometry is presented of RR Lyrae variable stars
in the globular cluster M15. This photometry, mainly in V and R, with some
additional B and I, is used to construct lightcurves of 44 RR Lyraes and 1 Cepheid
(VI) in M15. One new RR Lyrae star was discovered and is tentatively named
v113. Using the new (V-R) colors and Kurucz’s stellar models, the blue and red
edges of the instability strip are found to be at log Tefl' = 3.875 and log Tet! ~ 3.81,
repectively. The transition line between the fundamental and first overtone mode
pulsators is found to be at log Ten = 3.839. There is no overlap in (V-R) between the
fundamental and first overtone mode variables. From pulsation theory and these

observations, the absolute magnitude of the RR Lyrae stars in M15 is MV 2 +0.33

:l: 0.12, for an RR Lyrae mass of 0.75MQ. With Mv = +0.33, the age of M15 is
12.6 x 109 years. However, due to the still present uncertainties in R Lyrae mass
and the Te“ scale calibration, the absolute magnitude of the M15 RR Lyrae stars

still remains significantly uncertain.

We have also investigated the period changes of 49 RR Lyrae variable stars in
the globular cluster M15 using observations spanning almost a century. Some of
the variables have been too sparsely observed over that time interval for reliable
period changes to be determined. Others, which have been well observed, show a
wide range of period change behavior. We find a significant excess of increasing
over decreasing periods. The median rate of period change, +0.03 days / million
years, agrees with the theoretical prediction of Lee. This implies that most M15
RR Lyrae stars are evolving from blue to red through the instability strip. However,
it is not certain whether there are sufficient blue horizontal branch stars in M15 to
sustain the M15 RR Lyrae population at the observed rate of period change. The
dispersion in the rate of period change for R Lyraes of Bailey type ab is greater
than for those of type cd. The origin of that difference in period change behavior

is without adequate explanation.

For my mother and father, at last.

iv

ACKNOWLEDGMENTS

I would like to thank my Ph.D. advisor, Horace Smith, for everything. Without
his patience and understanding I would not be where I am today. I will not forget
those observing nights, that pig smell, those Open Houses (the mosquitos!), and of

course, the ice cream.

Thanks also to Jeff Kuhn, Haosheng Lin, and Ed Loh for maintaining the MSU
and WIRO (MOPE) CCD’s and software (our friend STARGAZEl). A special
thanks to Peter Stetson for his time when I was at DAO and for DAOPHOT and
DAOPHOT II: TNG, and Jim Hesser for allowing me to use the facilities at DAO.
A special thanks go to the MSU gang: Debbie Benedict, Xania Scheick, Larry
Bendler and Ron Wilhelm. A special thanks also to the WIRO gang: Earl Spillar,
Tim Titus, Leisa Townsley and Tom Edwards. I would also like to thank my other
Ph.D. committee members: Ed Loh, Tim Beers, Wayne Repko, and Mike Dubson.

This research used the resources of SIMBAD. This research would not have
been possible without the support of the National Science Foundation Grant

AST9015728.

 

TABLE OF CONTENTS

LIST OF TABLES .............................. , .......................... ix

LIST OF FIGURES ....................................................... x
1. INTRODUCTION ...................................................... 1
PART I

2. EQUIPMENT & OBSERVATIONS

2.1 MSU ................................................................. 11
2.2 WIRO ............................................................... 14
3. DATA REDUCTION ...................... 18
4. CONVERSION TO THE STANDARD SYSTEM .................. 22

5. TRANSFORMING THE VARIABLE STAR
PHOTOMETRY TO THE STANDARD SYSTEM .............. 39

6. NEW PERIODS AND LIGHTCURVES ............................ 42

7. ANALYSIS

7.1. Mean Magnitudes and Colors ......................................... 83
7.2 Radial Dependencies ................................................. 84
7.3 Comparison of < V > with Bingham et a1. ........................... 89
7.4 The Color-Magnitude Diagram of the Horizontal Branch .............. 91
7.5 Amplitude vs < V > and < V — R > ................................. 93
7.6 Period vs Amplitude Diagrams ....................................... 93

vi

7.7 Color vs Period Relations ............................................ 97
7.8 Mean Magnitude vs Period Relations ................................ 100

7.9 Summary ........................................................... 104

8. CONVERSION TO PHYSICAL PARAMETERS

8.1 Effective Temperature and Reddening ............................... 106

8.2 The Absolute Magnitude of the RR Lyrae Stars ..................... 112

8.3 The Distance to M15 ................................................ 118

8.4 The Age of M15 .................................................... 118
PART II.

9. PERIOD CHANGES
9.1 Introduction ........................................................ 120
9.2 The Data

9.2.1 Grouping of the Observations . . . .................... 121
9.2.2 The Problem of Gaps in the Observational Record ................ 124
9.3 The Phase Diagrams ................................................ 125

9.4 Period Changes
9.4.1 Parameterizing the Period Changes .............................. 125
9.4.2 Comments on Individual Variables ............................... 141

9.5 Discussion

9.5.1 The Excess of Increasing Periods ................................. 145
9.5.2 Interpretation of the Period Changes ............................. 149
9.5.3 Period Changes as a Function of Bailey Type ..................... 155
10. CONCLUSION ...................................................... 158
11. FUTURE WORK ................................................... 160

vii

APPENDICES

Appendix A MSU And WIRO Photometry of M15 Variables .............. 162
Appendix B Dates and Phases of Maxima for the M15 Variables ........... 212

LIST OF REFERENCES ............................................... 220

viii

LIST OF TABLES

Table 4.1: Summary of Comparison of Photometric Data ..................... 38
Table 6.1: Parameters of M15 Variables ...................................... 80
Table 8.1: Reddening Determinations for M15 .............................. 107
Table 8.2: mbol and Tag for M15 RR Lyraes ................................. 109
Table 8.3: mbol and Te“ for Non-variables ................................... 110
Table 9.1: Groupings of M15 Observations .................................. 122
Table 9.2: Periods for M15 RR Lyrae Stars ................................. 123
Table 9.3: Rate of Period Change for RR Lyrae Variables in M15 ........... 139
Table 9.4: Mean Rates of Period Change .................................... 148
Table A.1: MSU V Photometry of M15 Variables ........................... 163
Table A.2: MSU R Photometry of M15 Variables ........................... 187
Table A.3: WIRO B Photometry of M15 Variables .......................... 205
Table A.4: WIRO V Photometry of M15 Variables .......................... 206
Table A.5: WIRO R Photometry of M15 Variables .......................... 207
Table A.6: WIRO I Photometry of M15 Variables ........................... 208
Table A.7: WIRO B Photometry of M15 Variables - Northwest Field ........ 209
Table A.8: WIRO V Photometry of M15 Variables - Northwest Field ........ 209
Table A.9: WIRO R Photometry of M15 Variables - Northwest Field ........ 210
Table A.10: WIRO I Photometry of M15 Variables - Northwest Field ........ 210
Table A.11: Photometry for HB N on-variable Stars ......................... 211
Table B.1: Dates and Phases of Maxima .................................... 212

ix

Figure 1.1:
Figure 1.2:
Figure 1.3:
Figure 1.4:
Figure 1.5:
Figure 2.1:
Figure 2.2:
Figure 4.1:
Figure 4.2:
Figure 4.3:
Figure 4.4:
Figure 4.5:

Figure 4.6:

Figure 4.7:

Figure 4.8:

Figure 4.9:

LIST OF FIGURES

Position of RR Lyrae Stars on the Horizontal Branch .............. 2
Location of Bailey Types in the Instability Strip ................... 4
Differences in Horizontal Branch Morphology ...................... 6
Direction of Evolution Determining Pulsation Mode ............... 9
Typical MSU V CCD Frame of M15 .............................. 13
V CCD Frame of the WIRO M15 South Field .................... 16
V CCD Frame of the WIRO M15 Northwest Field ................ 17
WIRO B-V vs V Color-Magnitude Diagram ..................... 25
WIRO V-R vs V Color-Magnitude Diagram ..................... 26
WIRO V—I vs V Color-Magnitude Diagram ...................... 27
Comparison of V Photometry: Buonanno et al. and MSU ........ 29

Comparison of V and (B-V) Photometry:

Buonanno et al. and WIRO ...................... 31
Comparison of V and (V-R) Photometry:

MSU and WIRO South Field .................... 33
Comparison of V and (V—R) Photometry:

MSU and WIRO Northwest Field ................ 34
Comparison of V and (B-V) Photometry:

Battistini et al. and WIRO Northwest Field ...... 35
Comparison of V and (B—V) Photometry:

Battistini et al. and WIRO South Field .......... 36

Figure 6.1: Lightcurves for the Variables in M15 ............................. 43
Figure 7.1: V vs Radius For the Variables .................................... 85
Figure 7.2: (V — Rh,“ vs Radius For the Variables .......................... 87
Figure 7.3: (V - Rh,“ vs Radius For Uncrowded Variables .................. 88
Figure 7.4: Comparison of Variable Star Photometry With Bingham et al. . . . 90
Figure 7.5: Color-Magnitude Diagram of the Horizontal Branch in M15 ....... 92
Figure 7.6: Mean Magnitude vs V Amplitude for the RR Lyrae Stars ......... 94
Figure 7.7: Mean Color vs V Amplitude for the RR Lyrae Stars .............. 95
Figure 7.8: Log Period vs V Amplitude for the RR Lyrae Stars ............... 96
Figure 7.9: Color vs Log Period for the RR Lyrae Stars ...................... 98
Figure 7.10: Color vs log P’ for the RR Lyrae Stars .......................... 99
Figure 7.11: Color vs log Po for the RR Lyrae Stars ......................... 101
Figure 7.12: Color vs log P6 for the RR Lyrae Stars ......................... 102
Figure 7.13: Log Period vs Mean V Magnitude for the RR Lyrae Stars ...... 103
Figure 8.1: Te“ vs mbol for the Horizontal Branch Stars ..................... 111
Figure 8.2: log Te“ vs log P6 for the RR Lyrae Stars ......................... 113
Figure 8.3: Comparison of Estimates of My for the RR Lyrae Stars ......... 115
Figure 8.4: Te“ vs mbol for (V—K) Data .................................... 117
Figure 9.1: Phase Diagrams for the RR Lyrae Stars in M15 ................. 126
Figure 9.2: Histogram of Beta for M15 RR Lyrae Stars ...................... 146
Figure 9.3: Histogram of Alpha for M15 RR Lyrae Stars .................... 147
Figure 9.4: (B—V) vs V Indicating Period Changes of RR Lyrae Stars ....... 152
Figure 9.5: (V—R) vs V Indicating Period Changes of RR Lyrae Stars ....... 153

xi

CHAPTER 1

INTRODUCTION

RR Lyrae variable stars have been studied for almost one hundred years, begin-
ning in the 1890’s with Solon Bailey’s photographic investigations of variable stars
in globular star clusters. Today some 2,000 RR Lyrae stars have been discovered
within globular clusters, while some 7,000 have been identified in the field popula-
tion of the Galaxy. In the course of the last century, much has been learned about
the physical properties of these variable stars and the instability strip they occupy.
We know that RR Lyrae stars vary in brightness because of radial pulsations of their
tenuous outer envelopes. These pulsations are driven by the alternate damming and
releasing of the radiative energy flux by the helium second ionization zone and the
hydrogen ionization zone in the outer layers of the star. These zones act as valves,
trapping the heat at maximum compression and releasing heat at maximum radius.
This process gives the atmosphere a kick which can allow pulsations to continue for

millions of years.

RR Lyrae stars are in the horizontal branch stage of evolution, deriving energy
from the fusion of helium to carbon in their cores and from fusion of hydrogen to
helium in shells surrounding the central cores. Not all horizontal branch stars are
R Lyrae stars. RR Lyraes occur only when the horizontal branch crosses a well-
defined instability strip (Figure 1.1). The existence of high and low temperature
limits to RR Lyrae pulsation is easy to understand qualitatively, though quantitative

limits are harder to achieve. If the star is too hot, the ionization zones which drive

 

    
   

 

 

 

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Asymptotic Giant
Branch
RR Lyrae Stars Bed Giant
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Mv +2 — V
Horizontal ('— SUbQISHts
Branch
+4 ..
Main
+6 - Sequence
0.0 0.4 0.8 1 .2 1 .e

(53“V5c,

Figure 1.1: Position of RR Lyrae Stars on the I
Horizontal Branch.

the pulsation will be too high in the stellar atmosphere. The low density high in
the atmosphere means that there is not enough material in the ionization zones to
effectively dam the flow of energy. If the star is too cool, then the energy flux is
carried to the surface by convection, and the ionization zones again lose their roles

as valves.

Not all RR Lyrae stars pulsate in the same radial mode. As was discovered by
Schwarzschild (1940), some (Bailey type RRab) pulsate in the fundamental mode,
while others (RRc) pulsate in the first overtone mode. The fundamental mode is
simply a breathing mode - the outer atmosphere of the star expands and contracts in
unison. The first overtone mode occurs when a node develops - the region outside
the node moves in the opposite direction to the region within the node. More
recently, it has been discovered that some RR Lyrae stars pulsate simultaneously
in the first overtone and fundamental radial modes (type RRd). In these double

mode RR Lyraes, the first overtone mode is usually dominant.

The Bailey types are not scattered randomly throughtout the instability strip.
Rather, there is a distinct order to the strip. RRab stars populate the red side of
the instability strip, while RRc variables populate the blue side. RRd stars tend
to be in between. Figure 1.2 shows the horizontal branch of the RR. Lyrae-rich
globular cluster M3. The RRab stars are indicated by crosses, the RRc stars are
the open circles, and the non-variable stars are filled circles. The exact boundaries
of the instablility strip, and the divisions between these types in the HR diagram

will be subjects of this study.

In globular clusters, the size of the population of RR Lyrae stars varies consid-
erably from cluster to cluster. Some clusters contain over one hundred RR Lyrae

stars; others contain none. This depends not only upon the size of the cluster

 

 

 

 

 

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Figure 1.2: Location of Bailey Types in the Instability Strip.

population as a whole, but on its horizontal branch morphology. Some clusters have
only a stubby red horizontal branch. Others have distributions of horizontal branch
stars which are very blue in color. A globular cluster with only a small red stubby
horizontal branch may have plenty of horizontal branch stars, but no RR Lyraes
because the horizontal branch lies entirely to the red of the instability strip. A glob-
ular cluster with a well populated horizontal branch in the region Of the instability
strip may have many RR Lyraes, although it may have no more horizontal branch
stars than the first cluster we considered (Figure 1.3). In general, metal-rich globu-
lar clusters have redder horizontal branches then metal-poor globular clusters. Thus
metallicity is the first parameter governing horizontal branch morphology. Globular
clusters which contain significant numbers of RR Lyrae stars are generally metal-
poor, having [Fe / H] < —l.0. These globular clusters fall into two distinct groups,
based primarily upon the mean period of their RRab stars. This phenomenon was
first observed by Oosterhoff (1939, 1944). The mean period of RRab variables in
an Oosterhoff type I cluster is < Pub > = 0.55 days, while in an Oosterhoff type
II cluster < Pab >=0.65 days. Although recent studies have shown something of a
continuum in < Pub > within each group, the basic dichotomy still holds. There are
other differences between Oosterhoff type I and type 11 clusters. In type I clusters,
fewer than 20% of the RR Lyraes are RRc and RRd stars, whereas in type II clus-
ters that fraction can grow to 50%. The Oosterhoff phenomenon is correlated with
metallicity. Oosterhoff type I clusters, are moderately metal deficient, at [Fe/ H] =
-1.5, whereas Oosterhoff type II clusters are very metal-poor, near [Fe/ H] = —2.
M15, the subject of this thesis investigation, is believed to have an [Fe/H] value
near —2 or slightly below (Butler 1975, Zinn 1985).

It does not appear as though metallicity alone can account for the different

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properties of RR Lyrae stars in Oosterhoff I and II clusters. Perhaps this should not
be surprising, since it is known that horizontal branch morphology is not perfectly
correlated with metallicity. Two clusters of the same [Fe / H], as for example M3 and
M13, may have different color distributions of horizontal branch stars. A second
parameter besides [Fe/ H] is needed to explain horizontal branch morphology. The
nature of this second parameter may have a bearing upon the origin of the Oosterhoff
dichotomy. Many culprits have been fingered as the second parameter: differences
in mass or luminosity of the stars, helium abundance, abundance of CNO elements
to iron, and' rotation. Recently, Lee, Demarque, and Zinn (1990) have championed
age as the second parameter: if two globular clusters have equal [Fe / H] but different
ages, the older cluster will have the bluer horizontal branch. I will address some

testable aspects of the Lee, Demarque, and Zinn scenario in Chapter 9.

This study of RR Lyrae variables in the Ooserhoff type II cluster M15 will be
divided into two main parts. The first part presents new photometric observations
of variable and non-variable stars in M15. These photometric observations will
be used to fix the stars in the color-magnitude diagram, and to investigate the
pulsational properties of the RR Lyrae stars. Some of the questions to be addressed

in this part of the study are:

(i) Is the vertical spread in the M15 horizontal branch real, or attributable en-
tirely to observational error? Stellar evolution theory (e.g. Sweigart 1991) predicts
that, as a horizontal branch stars evolves, it will move off the zero-age horizontal
branch (ZAHB) and become brighter. The initial direction of evolution, whether to
the red or blue, depends upon the mass and chemical composition of the stars. Ul-
timately, the horizontal branch stars must evolve to the red to join the asymptotic

red giant branch. Is this evolution off the ZAHB, expected to be about 0.1-0.2 mag

in V, detectable?

(ii) What are the boundaries to the M15 instability strip? And where within the
strip are the different Bailey types located? Obtaining mean colors (hence surface
temperatures) for RR Lyrae stars is more difficult than for nonvariables. There
is debate over the best way to average colors over the light cycle to arrive at the
equilibrium value (Carney et al. 1992, Sandage 1993). Carney et al. in particular
have argued that non-LTE effects and flux redistributions during rising light can
distort the emitted spectrum of RRab variables. This distortion is believed tO be
strongest at shorter wavelengths. V-R colors may thus have some advantage over

B—V colors in this regard.

(iii) Related to the above questions is the issue of what determines pulsational
properties within the instability strip. Is there a sharp break in color between RRcd
and RRab pulsators? Some theorists (e.g. van Albada 8.: Baker 1973, Stellingwerf
& Bono 1993) have proposed the existance of a hysteresis zone: a zone in which
direction of evolution determines whether a star pulsates in the fundamental or first
overtone mode. Figure 1.4 shows a schematic of this. If the variables are evolving
to the blue, the RRab stars will retain their fundamental mode of pulsation as they
cross the hysteresis (H) zone. If the variables are evolving to the red, the RRc stars
will cross through the hysteresis zone, reaching the red boundary of the hysteresis
zone before switching pulsation modes. It is of interest, then, to see whether RRcd
and RRab variables overlap in color. It is also of general interest to determine how
pulsational properties, such as period or amplitude, change with location in the

instability strip.

(iv) The pulsational properties of RR Lyrae stars depend upon luminosity and

mass. The M15 data and stellar pulsation theory will be used to estimate the

log L/Le—b

 

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______L_

 

 

 

 

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Figure 1 .4 :

~<— log To

Direction of Evolution Deter-lining
Pulsation node

10

absolute magnitude of the RR Lyrae stars and the age of Ml5.

The second part of the study will search for period changes among the RR Lyrae
variables, using almost a century of observations. The basic pulsation equation,
Pfi = constant, tells us that a small change in the density of a star will be
reflected in a change in its pulsation period. This affords a method of investigating
the evolution of an R Lyrae variable star through the HR. diagram which is much

more sensitive than any other.

The metal-poor cluster M15 was selected for investigation for several reasons.
It is an archetypal Oosterhoff type II cluster, which has been well-observed by pho-
tographic methods (most recently by Sandage, Katem, S: Sandage 1981 (SKS) and
by Bingham et al. 1984). It is well placed in the sky for observation from Michigan
and is rich in RR Lyrae variables (more than 100 are known). Published color-
magnitude diagrams show M15 to have a well-populated blue horizontal branch,

but a much sparser population of red horizontal branch stars.

A major difference between the present study and earlier work has been the
use of CCD’s (charged-coupled devices) rather than photographic plates to obtain
the observations. CCD’s have high quantum efficiencies, up to 85% in V and R,
compared to the 1% for photographic plates. The red sensitivity of CCD’s is useful
in this instance, where there are reasons to be suspicious of colors involving blue
wavelengths. CCD’s are linear over a large dynamic range: that is, the signal is
directly proportional to the number of photons captured, facilitating interpretation
of the data. CCD frames can also be analyzed much more rapidly than photographic
plates, if you know a computer god who has already labored to bring forth the basic

software necessary to perform the reductions.

PART I

CHAPTER 2

EQUIPMENT 8: OBSERVATIONS

2.1 MSU

Most of the M15 data were obtained using the 24” telescope at Michigan State
University. This telescope, located on the southern agricultural part of campus,
downwind from the Swine Teaching and Research Facility, is of Ritchey-Chretien
design, manufactured by Boller & Chivens. The primary has a focal ratio Of f/ 3.0
and at the cassegrain focus, where the camera sits, the combined primary and

secondary focal ratio is f / 8.0. The telescope is not guided.

The telescope is controlled by a 286 IBM PC, thrOugh an A / D converter on a
rather ancient Raytheon, and the camera is controlled by a 386 IBM PC. The two
PC ’3 are linked together and small movements of the telescope can be made via the
386 IBM PC. Initially CCD data were stored on 9-track tapes and taken back to the
Physics-Astronomy building for analysis. In November 1991 the 9-track tape drive
at the observatory died, facilitating transfer to a recently installed 8mm exabyte
tape drive. At the Physics-Astronomy building, data reduction was done on two
computers, GRUS, a 3100 VAXstation and CORVUS, a 3200 VAXstation. There is
no timing device (ie. clock) at the observatory and we did not trust the computer
clock. All time measurements were made from a wristwatch, which was set to the

correct time by calling the local time phone number.

All the MSU data were Obtained using a charged coupled device, or CCD. The

11

l2

CCD system is a Photometrics, Ltd Slow Scan CCD Camera System, with a Ford
Aerospace/SAIC 1024 x 1024 pixel CCD chip. This camera was extremely reliable
with a typical readout noise of ~18 electrons. The combined telescope and CCD
system provides a scale of 0.7 arc seconds per pixel, giving a total field of view of
almost 12 arc minutes square. Due to the modest seeing conditions at this site and
the desire to not fill up all available disk space, the pixels were usually binned 2 x
2 before readout, resulting in 472 x 472 pixel CCD frames. Binning a square of 2
x 2 pixels into 1 ”superpixel” before readout increases the signal to noise in each
superpixel compared to unbinned pixels. There is however, a loss of resolution when
binning. Since we rarely obtain 0.7 arc second seeing in Michigan, this was not a
problem. The typical temperature of the CCD when obtaining data was between

-100° C and —110° C.

M15 Was Observed at MSU from July thru December 1991 and July thru October
1992. The globular cluster was centered in the field of the CCD. Exposure time for
all the frames was 10 minutes. As the CCD is not very sensitive to blue wavelengths,
only V and R frames were obtained at MSU. Figure 2.1 shows a typical MSU CCD
frame. During every night of observation a set of flats and darks was taken. New
flats were necessary every night due to the transient nature of dust particles on the
window of the CCD. Whenever possible sky flats were obtained, otherwise dome
flats had to be used. Sky flats were taken during evening twilight by pointing the
telescope at zenith with the drive off and exposing the CCD from 3 to as many as 8
seconds to Obtain enough counts in the frame. The required number of flats could
usually be obtained before stars began to appear in the CCD frames. For dome
flats the telescope was pointed at the dome, which is white. Usually 3 flats in each

color were taken and averaged together. The CCD was very consistent in the

 

Figure 2.1: Typical 118!) V 00]) rule of I15

14

amount Of dark current produced. NO noticable differences, aside from a slight
increase in (rare) cosmic ray hits, were seen in darks of 2 seconds to 10 minutes in
length. As a result, a reasonable exposure time of 2 minutes was used for the darks.
Usually 2 darks were taken on each night and averaged to give a final average dark.
The CCD frames were then flat-fielded by subtracting the average dark from the

data frame then dividing the resultant picture by the normalized average flat.

2.2 WIRO

Additional CCD data of M15 were obtained at the Wyoming Infrared Obser-
vatory (WIRO). WIRO has a 2.3m telescope with a primary focus beam of f/2.1.
An optical RCA 337 x 527 pixel CCD camera was used. This CCD is rather old,
having a readout noise of ~100 electrons. The CCD sits at primary focus and has a
scale of 1.23 arc seconds per pixel which gives a 6.4 x 10.4 are minute field of view.
The data from this CCD are not binned before readout. The CCD was controlled,

and data aquired, using a VAXstation II (SUBARU).

Preliminary observations of Ml5 at W IRO were made in September 1991. These
observations, in B, V, and R, were made with the center of the cluster centered in
the CCD field, just like the MSU data. Analysis of this data showed excessive
saturation of the center of the cluster in V and R. Also, the corrector lens for the
camera was not perfectly aligned along the Optical axis causing an elongation of the
stars in one part of the frame. It was concluded that much better photometry of
M15 could be obtained by offsetting the cluster center to the edge, or slightly off, of
the CCD frames, and careful alignment of the corrector lens would have to be done
in order to obtain useful data. The 1991 WIRO data were deemed inferior and not

used.

Another set of observations of M15 were made at WIRO on 14/ 15 thru 17/18

15

July 1993. The temperature of the CCD remained very steady, at approximately
152 K during the entire run. Two fields around M15, a south field and a northwest
field (Figures 2.2 and 2.3), were Observed using B, V, R, and I filters. The B frames
were 3 minute exposures while the V, R, and 1 frames were 2 minute exposures.
A series of sky flats and darks were also taken during the run. The flats were
median filtered to produce median flats for all the filters. This CCD produced
consistent darks with exposures from 5 seconds to at least 7 minutes. The darks
were also median filtered to reduce the number of cosmic ray residuals in the final
”average” dark. The CCD data were first saved on disk and then, at the end of the
run, transferred to DAT tape and brought back to Michigan State University for

analysis. The data were reduced on the same computers as the MSU data.

16

 

Figure 2.2: CCD Franc of the WIRO H15 South Field

 

 

‘1».

Figure 2.3: CCD Free of the WIRO H15 Northwest Field

CHAPTER 3
DATA REDUCTION

Over 200 CCD frames of M15 in V and R were obtained using the MSU
0.6m telescope. Of these, 162 V and 129 R were deemed usable for this project.
The July 1993 WIRO observing run yielded 16 south field and 14 northwest field
CCD frames in B, V, R, and I. All but one of the south B field frames were
deemed useable for this study. The profile-fitting photometry computer programs
DAOPHOT and DAOPHOT II: The Next Generation (Stetson 1987) were used to
obtain instrumental photometry for approximately 2200 stars per CCD frame, the
actual number of stars per frame depending on seeing conditions and amount of

moonlight during the observations.

Since this whole project depends on accurate photometry of the variables I will
go into some detail on how I proceeded. DAOPHOT is a master program. In
DAOPHOT, one resides in a “command shell” where various commands can be
given to manipulate the CCD data, such as OPTIONS, SKY, FIND, PHOT, PSF,
etc. Upon running DAOPHOT, several parameters (OPTIONS) required to reduce
the CCD images are displayed. Some of the more important parameters are: the
full width half-maximum (FWHM) of a typical object you are interested in, the
fitting radius (the radius used to define the profile of the star, for profile-fitting
photometry), the radius of the point spread function, the maximum data value
for the detector (the point where non-linear effects begin), and whether the point

spread function varies across the field or not. For the MSU data, a FVVHM of 2.5

18

19

pixels was used for all the CCD frames. A psf radius of 8 pixels was determined
to be best for the 472 x 472 frames and 11 pixels for the 1024 x 1024 frames. The
maximum good data value was determined to be about 15,500 ADU, and a fitting
radius of 2.0 pixels was used. No evidence for a varying point spread function was
found in the CCD frames. For the WIRO data, a FWHM of 2.5 pixels was also
used for all the frames. A psf radius of 8 pixels was used and the maximum good
data value was determined to be at 20,000 ADU. A fitting radius of 2.0 pixels was
used and the point spread function was determined to be constant across the CCD

frames.

Once these parameters have been set, a CCD frame can be reduced. The
approximate sky value for each CCD frame is determined by running SKY. The
sky value is used to determine an accurate threshold for finding stars to avoiding
spurious false detections. Next, the stars on the frame are located using FIND.
Then, using an aperture radius of 1.5 pixels, aperture” photometry is obtained for
all the stars in the frame using PHOT. Since the stars in the frame are relatively
crowded, profile-fitting photometry must be used to obtain accurate photometry.
Several relatively isolated stars in the frame are chosen to define the point spread
function (psf) of the frame. The same psf stars were not always chosen for all the
frames, as sometimes a nearby cosmic ray hit, nearby bad column, or other defect
rendered one or more of them inferior. Approximately 9 stars were used to define
the point spread function for each frame. The routine PSF then calculates the point
spread function Of the frame using the aperture photometry of these psf stars. Then
the profile- fitting routine ALLSTAR uses the calculated point spread function and
the magnitudes given by PHOT to derive final instrumental magnitudes for all the
stars in the CCD frame. Typical running times of ALLSTAR on GRUS were 40—60

20

minutes per frame. On CORVUS the running time was 15-20 minutes per frame.
Both computers could reduce a given frame faster if no one else was using up the
CPU time (i.e. at night). Each MSU CCD frame was reduced separately, producing
a list of star numbers and instrumental magnitudes for each frame. After all the
MSU frames had been reduced, it was discovered that a better way would have been
to use a common star list for all the frames. In this way, the same star in all the
frames would have the same star number. This would have greatly simplified the
reductions yet to be performed. It was too late to do this for the MSU data but

this technique was used for the 1993 WIRO data.

Part of the MSU data was reduced at the Dominon Astrophysical Observatory
(DAO) using DAOPHOT II. This upgrade, as implemented at DAO, is more
computer intensive than DAOPHOT I at MSU. In DAOPHOT II the user instructs
the software how many psf stars to search for. The user then decides which of the
potential psf stars to use. This makes the chore of displaying each CCD frame and
searching for good psf stars obsolete. Also, the CCD frames are passed through the
FIND routine three times, ensuring that over 90% of the stars actually in the frame
are found. However, there was one problem with the CCD frames reduced at DAO.
For a given real star, the photometry list sometimes indicated two stars, one of
which was several magnitudes fainter than the other. This was found to be due to
the multiple passes through FIND. Once a star was found by FIND and subtracted
out, some residual light would be left over where the center of the star was located.
The next pass through FIND would see this bright spot and tag it as a star. The
result - two stars in the same location when there really is only one. Luckily, this
problem only occured with the brightest stars in the frames - the photometry for

the variables did not have this problem.

21

During the first year of data aquisition, preliminary instrumental lightcurves of
the variables were made. This required picking out the same star on different frames
and scaling the magnitudes to a fiducial frame. The same stars in different CCD
frames were matched up via the computer program DAOMATCH. The computer
program DAOMASTER is then used. This program cross-identifies all the stars
on each frame to produce a variety of master lists, such as: mean magnitudes for
each star, corrected magnitudes for each star for each frame, and raw magnitudes for
each star for each frame. For the instrumental lightcurves, corrected magnitudes are
needed. DAOMASTER corrects magnitudes from all other frames to the fiducial
frame by applying additive constants to all the other frames. F iducial V and R
frames were chosen from the first year of data and, using DAOMASTER, data files
containing all the magnitudes, corrected to the fiducial frames, of all the stars in all
the frames were produced. This provided easy access to the photometry of each star
in the field. A Fortran program was written to read in the “corrected magnitudes”
data file and extract the data of any given star. Due to the (large) number of MSU
CCD frames, 10 of these “corrected magnitude” data files were constructed for the
V frames and 7 for the R frames. Only one “corrected magnitude” data. file for each

band was necessary for the WIRO data.

CHAPTER 4

CONVERSION TO THE STANDARD SYSTEM

Before the photometry can be used further, it must be converted to the stan—
dard magnitude system. This is done by obtaining observations of standard stars
on photometric nights. Landolt (1973, 1992) standards were used. His B and V
photometry is on the usual Johnson system but his R is on the Cousins system.
Photometric nights are a rare occurrence in mid-Michigan. Photometry was Ob-
tained for standard stars on 2 nights in 1991 and 3 nights in 1992. On only one of
those nights each year were data on M15 also obtained. Due to the larger range
of airmass and larger number of observations for the 1992 standards, they were
deemed superior to the 1991 standards. Therefore only the 1992 standards were
used to convert the MSU data to the standard system. On that photometric night
in 1992, 5 V and 6 R M15 frames were obtained. Of those, 3 V and 4 R frames
were chosen as best for use in converting the MSU instrumental magnitudes to the

standard system.

For the July 1993 WIRO run, observations of standard stars were obtained on
two nights. Four B, V, R, and I M15 frames from the last night of observing (the
second night of standards) were used to convert the WIRO instrumental magni—
tudes to the standard system. Conversion to the standard system was achieved
using several computer programs (DAOGROW, COLLECT, CCDSTD, CCDAVE,
FINAL) created by Peter Stetson (1990, 1992). These programs use observations of

standard stars and a library of standard magnitudes for the stars to convert a given

22

23

instrumental magnitude system to the standard magnitude system. A very elemen-
tary way of describing an instrumental magnitude system would be: observations
of stars + telescope + instrument. Several stars in the field of M15 were chosen
as “local standards” to convert the M15 frames to the standard system. First,
curves of growth were calculated, via DAOGROW, for the standards. A curve of
growth is a graph showing the differences in aperture photometry from increasing
concentric radii around a star. It is used to determine the star’s true instrumental
magnitude. The trick is to go out to a large enough radius so the the difference
in magnitudes between two consecutive apertures approaches zero, indicating ~
all the light has been collected from the star.. But you cannot go out too far or
noise (Poisson and/or contributions due to nearby faint stars) will creep into the
calculations of the final magnitudes. For both the MSU and W'IRO data, 9 radii
were used, with the smallest radius being 1.5 pixels and the largest radius being
22 pixels. DAOGROW then extrapolates the total instrumental magnitudes out to

twice the largest aperture used.

Next, the form of the transformation equations to be used to convert the instru-
mental magnitudes to standard magnitudes must be chosen. Various forms of the
equations were tried. CCDSTD then calculates the coefficients of these equations.
Only those terms with coeflicient errors significantly smaller then the coefficients
themselves were kept. For the MSU data the conversion equations are:

v = V + 6.966 - 0.1949(V-R) + 0.2619X
r = R + 7.190 - 0.3053(V-R) + 0.2148X

with X = (airmass -- 1.25), v and r are the observed instrumental magnitudes,
and V and R are the calculated standard magnitudes. The V and R. magnitudes

are calculated by iterating these equations. For the W IRO data the conversion

24

equations are:
b = B + 3.196 - 0.2820(B-V) + 0.0243(B — V)? + 0.2500);
v = v + 3.052 - 0.0729(B-V) + 0.1400x
r = R + 3.793 - 0.2781(V-R) + 0.0700):
i = I + 4.428 + 0.0500):

with X = (airmass - 1.25), b, v, r, and i being the Observed instrumental magni-
tudes, and B, V, R, and I the calculated standard magnitudes. The airmass coef-
ficient terms for the WIRO data were provided by Ed Loh (1994). If the airmass
terms are not forced, the calculated values are almost the same as those provided by
Loh. Again the B, V, R, and I magnitudes are iteratively calculated using the above
equations. Once suitable equations were found and the coefficients determined, the
local standards in the field of M15 were used to convert all the stars in the field to

the standard system using FINAL.

Nine V and R MSU frames were converted to the standard system in order
to construct a V vs V—R color-magnitude diagram (CMD) of M15. Likewise, 4
B, V, R, and I WIRO frames of each of the two fields were also converted to the
standard system to construct WIRO CMDs of Ml5. The W IRO CMDs are shown
in Figures 4.1 - 4.3. These diagrams were constructed by adding the photometry
from the south and northwest fields. Only stars lying Z 120 arcseconds from the
center of the cluster are shown in the figures. No attempt was made to remove
duplicate photometry of stars that appeared in both fields, as the overlap is only
about 10 pixels. These diagrams were constructed to ascertain whether the CCD
photometry agrees with previous studies of this cluster and to provide a population
of non-variable horizontal branch stars to compare with the variables. These figures

show a well populated blue horizontal branch, curving to fainter magnitudes as one

25

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28

goes far to the blue. There is a slight suggestion of a red horizontal branch with
the gap between the red and blue horizontal branches most prominent in the B—V
vs V diagram. This gap is due to the removal of the variables from the CMDs.
As the CMDs were created from only 4 frames in each band, the mean magnitudes
and colors for the variables were not correct so they were removed. There is also a
scattering of stars above the horizontal branch, to the blue of the top of the giant
branch. These are probably foreground stars, as well as a few asymptotic giant
branch stars of M15. The population of stars redward of the giant branch and main
sequence are probably foreground stars as well. There is also the likelihood that a
small fraction of the stars have photometry that is in error. That is, whether due

to a cosmic ray hit, a nearby bad column or whatever, the photometry is incorrect.

The photometry for the stars in the MSU and “7 IRO CMDs was compared
to the photometry from previous studies of Ml5. In particular, Buonanno et al.
(1983) obtained U, B, and V photographic photometry, based on Sandage’s (1970)
photoelectric standards, for 657 stars in the field of M15. As a check on the MSU
photometric system, Figure 4.4 shows the difference between Buonanno et al.’s V
and my V for 46 stars, plotted against Buonanno et al.’s V. At this point I was
unsure how good the comparison would be so I chose to use Buonanno et al.’s
photometry as a standard of reference. For relatively bright stars, the difference
between the two sets is quite small. However, as one goes fainter than V ~ 17.1
mag, AV begins to get quite large. Buonanno does claim accurate photometry
down to B ~ 18.6 mag. I estimate the limiting magnitude for the MSU data at
V ~ 18.0 mag. So the deviation in AV at fainter magnitudes is probably due to
larger errors in one or the other sets of photometry as the limiting magnitude is

approached. Looking at Figure 4.4, I would conservatively estimate that the point

29

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30

where the photometry starts to deteriorate is at V ~ 17.1 mag. Using only those
stars determined by Buonanno et al. to have V S 17.1 mag (33 stars), the mean
difference is AV 2 0.000 :t 0.007. SO, for the brighter stars, the MSU V magnitudes
appear to be on the same photometric system as that of Buonanno et al. to within

about $0.01 mag.

Next is a check on the WIRO photometric system. The top diagram in Figure
4.5 shows AV between Buonanno et al. and the WIRO photometry, plotted against
Buonanno et al.’s V. Limiting the comparison to those stars with V3,,“ S 17.1
mag, the mean differences are: K17”: 0.000 :1: 0.010 for the south W IRO field (31
stars) and -A_V = +0.028 i: 0.009 for the northwest field (23 stars). The bottom
diagram in Figure 4.5 shows A(B — V) for the same stars. The mean differences are:
A—(BTTF) = —0.033 :i: 0.006 for the south WIRO field and 'A—(BTVS = -0.031 :1:
0.006 for the northwest WIRO field. If I assume the Buonanno et al. photometry is
good, the m for the northwest WIRO field is due in most part to an Offset
in WIRO V, and the X7377) for the south field is due to an offset in WIRO B.
Durrell & Harris (1993) found good agreement between their CCD photometry and
Buonanno et al.’s, but did find a mean difference in A(B — V) = —0.011. They also
found a mean difference Of AV = 0.012 between Sandage’s photoelectric standards,
on which the Buonanno et al. photometry is based, and their CCD photometry. So
part of the difference between Buonanno et al.’s photometry and mine may be due

to real errors in Buonanno’s photometry.

As another check, the MSU and WIRO photometry systems were compared.
Unfortunately, there is a large difference in the range of magnitudes covered by the

two systems. The brighter stars in the MSU frames, the ideal ones to use, were

saturated in the WIRO frames. Fainter stars in the MSU frames had to be used.

31

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Also, a good half of M15 field in the northwest W IRO frames falls outside the field of
the MSU frames. This severely limited the number of relatively isolated stars needed
to make the comparison in that field. Figure 4.6, shows AV and A(V — R) for the
south WIRO field, again plotted against Buonanno et al.’s V. For the 29 stars with
V3,... 3 17.1 mag, 737 = —0.004 i 0.007 and m = —0.010 :1: 0.008. For the
northwest field, Figure 4.7, ‘57 = —0.015 i 0.000 and 37173723 = —0.009 :i: 0.007,
for 14 stars. There appears to be a slight gradient in both the AV and A(V - R)
vs < V > diagrams for the northwest field, but with only 14 stars it is hard to tell

if it is real.

Battistini et al. (1985) also published U, B, and V photographic photometry
for 923 stars in M15 but their photometric errors for individual stars are slightly
larger, being S 0.1mag in both V and B—V. Figure 4.8 shows the difference in V
and (B—V) between the northwest WIRO field and Battistini et al., plotted against
WIRO V. The mean differences are (for 34 stars): A7 = —0.041 :1: 0.008 and
m = +0050 :1: 0.011. Figure 4.9 shows the south W IRO field comparison.
The mean differences are: AV = —0.047 :1: 0.007 and A—(B—TV) = +0.030 :i: 0.009,
for 43 stars. As the WIRO photometry agrees fairly well with the MSU photometry,
only the WIRO comparison was made. Considering the large error bars on Battistini
et al.’s data, I give this comparison less weight than that with Buonanno et al.’s

data.

More recent work on M15 has been done by Durrell and Harris (1993). They
Obtained B and V CCD photometry of 6222 stars in 4 wide fields around M15 and
831 stars in one deep field further out from the cluster center. They produced a
B-V vs V CMD that ranged from 14 to 24th mag in V. They then used this data

to construct a fiducial sequence for M15. Overlaying this sequence with my W IRO

33

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CMD, I found (by eye) good agreement to i0.015 mag in (B-V) and i0.015 in V.

In summary, my MSU photometric system appears to agree well with previously
published work, to within AV = $0.01. The errors for the WIRO data, appear to
be a little larger, but they are only at the 20 level. Therefore I decided not to add
any corrections to the WIRO data. A summary of the comparison of photometric

data is given in Table 4.1.

38

Table 4.1. Comparison of Photometric Data

 

 

 

Systems Quantity Differences No. of Stars
MSU — South WIRO AV -0.004 :t 0.007 29
MSU - South WIRO A(V-R) -0.010 :t 0.008 29
MSU - NW WIRO AV -0.015 :1: 0.009 14
MSU - NW WIRO A(V-R) -0.009 :t 0.007 14
Buonanno - MSU AV +0000 1 0.007 33
Buonanno - South WIRO AV 0.000 :t 0.010’ 31
Buonanno - South WIRO A(B.V) —0.033 :l: 0.006 31
Buonanno - NW WIRO AV +0.028 :l: 0.009 23
Buonanno — NW WIRO A(B-V) -0.03l :L- 0.006 23
South WIRO - Battistini AV —0.047 :i: 0.007 43
South WIRO - Battistini A(B-V) +0.030 i 0.009 43
NW WIRO - Battistini AV —-0.041 :h 0.008 32
NW WIRO - Battistini A(B-V) +0.050 d: 0.011 33

 

 

CHAPTER 5
Transforming the Variable Star Photometry
to the Standard System

Once the good agreement between our photometric system and prior work was
established, the photometry of the variable stars had to be converted to the standard
system. Since I already had instrumental magnitudes shifted to a fiducial frame, I
decided to shift the fiducial frame to the standard system, as opposed to shifting all
291 frames to the standard system - an impossible task. One problem in converting
the variables’ photometry is that the color of a variable can change significantly over
its light cycle. This means “simultaneous” observations in each color are necessary
to accurately convert the magnitudes. While the W IRO data have sequential B,
V, R, and I frames only 2 or 3 minutes apart from one another, the MSU data do
not. Sometimes only V frames or only R frames were taken on a given night. More
often, 3 V and then 3 R frames were taken in a sequence, but each exposure was 10
minutes long meaning that there would be at least 30 minutes between a. V and an
R measurement. For some of the variables, such as the RRab’s, their magnitudes

might vary significantly in that time.

Fortunately, most of the variables have excellent phase coverage over their light
cycle. So I used the variables’ lightcurves to obtain the needed instrumental v—r
colors which could then be put in the conversion equations. First, the variables’
v and r magnitudes were sorted by increasing phase, and any magnitude whose

error, as given by DAOPHOT, was larger than 0.10 magnitude was removed at

39

40

this time. Then, the magnitudes were averaged in each 0.05 phase bin. A bin
size of 0.05 was chosen as not too small to have too few points to average and not
so big that the magnitude changed significantly across the bin. The averaged v
and r magnitudes for each phase bin were subtracted giving a v-r color for each
bin. The observed v or r magnitude and the corresponding binned v—r color are
then used in the transformation equations to derive standard system magnitudes.
Occasionally there is a variable that has a gap in phase coverage. In that case, a

color is interpolated from colors on either side of the gap.

While this method is not perfect, it is a reasonable way to accurately convert all
the photometry taking into account color variations over a variable’s light cycle. If
we look at the coefficients for (V—R) in the MSU transformation equations we see
that even if our average v—r color in a phase bin is off by 0.05 mag, the corresponding
error in V is 0.01 mag and 0.015 mag in R. A final list of photometry for each
variable was produced by removing any magnitude whose error as determined by
DAOPHOT was greater than 0.05 mag. The typical error in a single observation,
as given by DAOPHOT, for the remaining photometry is i002 — 0.03 mag. Some
of the variables had few photometry points left after the 0.05 mag error cutoff. To
get a better idea of the lightcurves for these variables, the cutoff was left at 0.1
mag. These crowded variables are v6, v7, v20, v29 (R. only), v32, v65, v67, v74,
and v97. For the WIRO data things were much easier, as B, V, R, and I frames
were taken in sets. A fiducial frame in each color was chosen and all the other
magnitudes of each color were shifted to the fiducial frames, just as for the MSU
data. Only one south field B frame was seriously contaminated by clouds. The
photometry for this frame was interpolated from the b magnitudes of the frame

before and frame after. This way, the interpolated b magnitude could be used in

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41

the v transformation equation for the needed (B—V ) color. Standard magnitudes
were then calculated for the variables using the same method as for the MSU data

- iterating the transformation equations.

Next, the WIRO photometry for the variables was added to the MSU photome-
try. Unfortunately, the two sets of variable star photometry did not match up. The
MSU data appeared to be sytematically brighter than the W IRO data. Local stan-
dards were used to correct for this difference. Using 15 stars, mean instrumental
MSU v and r magnitudes were calculated. These magnitudes were then transformed
to the standard system using the MSU equations producing standard V and R mag-
nitudes. These magnitudes were then compared to their magnitudes in the MSU
CMD. As noted above, the CMDs for the MSU and WIRO systems are consistent.
An average shift of 0.0581 mag in V and 0.0407 mag in R was found between the
MSU CMD and the transformation equation conversion. Thus, the difference in the
MSU and WIRO photometry for the variables was really an inconsistency between
the MSU variable star conversion routine and the MSU C MD. This difference is
thought to be due to the fiducial frames used for the MSU variable photometry.
These fiducial frames were not taken on a photometric night. As a result small
errors due to thin clouds may be the culprit. Once this shift in V and R was added

to the MSU data, both sets of data matched up.

CHAPTER 6

NEW PERIODS AND LIGHTCURVES

Acceptable photometry was obtained for 45 variables in M 15. Periods for
the variables were determined using the phase dispersion minimization routine by
Stellingwerf (1978). Initial new periods were determined using the 1991 MSU data.
After collecting the second year of MSU data, new refined periods for the variables
were determined. These periods were used in creating the lightcurves and thus the
sequence of phases for determining the instrumental colors, v—r, used in convert-
ing the instrumental magnitudes to the standard system. After both the MSU and
WIRO data were converted to the standard system and added together, new refined
periods were again determined for those variables for which we have WIRO data.
The final lightcurves are given in Figure 6.1. The MSU and WIRO photometry for
the variables is given in Appendix A. For those variables having a cutoff in error
of 0.1 mag, any photometry with an error as given by DAOPHOT > 0.05 mag is
marked with a colon. This photometry should be given lower weight than the pho-
tometry with errors less than 0.05 mag. Photometric parameters for the variables
are given in Table 6.1. In the course of this research a new RR Lyrae variable was
found in M15 and tentatively named v113. A finder chart for the variable is given
in Figure 2.1 and the position is (x = +6, y = —257) measured in arcseconds from

the cluster center, where +x is east and +y is north.

42

 

 

 

 

 

 

 

 

 

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80

Table 6.1. Parameters of M15 Variables

 

 

 

Period Epoch of Max Int Mag Int. Mag Radius
Var Type (days) 244848000+ < V > < V > (V-R) (V-R) (arcsec) AV
1 Cep 1.437712 660.312 14.996 14.944 0.360 0.339 121 0.95
2 ab 0.68430 660.131 15.585 15.573 0.359 0.355 172 0.56
3 c 0.388746 660.293 15.823 15.809 0.252 0.247 252 0.50
4 c 0.313587 660.108 15.902 15.880 0.205 0.196 199 0.65
5 c 0.384215 660.120 15.789 15.777 0.267 0.262 235 0.52
6 ab 0.665967 660.253 15.875: 15.845: 0.207: 0.207: 80 0.80
7 c 0.367557 660.342 15.687: 15.674: 0.342: 0.337: 74 0.75
8 ab 0.64625 660.287 15.880: 15.842: 0.400: 0.381: 127 0.90
9 ab 0.715277 660.437 15.759 15.735 0.326 0.319 140 0.80
10 c 0.386382 660.293 15.894 15.879 0.273 0.268 126 0.58
11 c 0.343267 660.085 15.828 15.806 0.205 0.196 174 0.65
13 ab 0.57491 660.169 15.896 15.861 0.319 0.306 144 1.05
14 c 0.38201 660.228 15.893 15.881 0.265 0.261 270 0.50
15 ab 0.583453 660.101 15.911 15.871 0.309 0.295 315 1.25
17 d 0.428907 660.302 15.866 15.854 0.280 0.275 139 0.42
18 c 0.367737 660.051 15.821 15.807 0.221 0.217 127 0.60
19 ab 0.57228 660.514 15.901 15.845 0.296 0.283 195 1.30
20 ab 0.697021 660.657 15.811: 15.777: 0.126: 0.115: 82 1.10
22 ab 0.72013 660.467 15.723 15.692 0.306 0.292 334 0.95
23 ab 0.632680 660.170 15.772 15.758 0.327 0.323 320 0.70
24 c 0.369693 660.013 15.769: 15.755: 0.297: 0.290: 107 0.68
25 ab 0.66532 660.496: missed maximum 303 —
29 ab 0.57493 660.457 15.978: 15.931: 0.422: 0.398: 268 1.25
30 d 0.405997 660.354 15.683 15.673 0.272 0.268 165 0.50
31 d 0.408154 660.319 15.870 15.860 0.269 0.266 270 0.43
32 ab 0.60547 660.205 15.733: 15.704: 0.321: 0.310: 119 1.10
35 c 0.38400 660.326 15.929 15.912 0.275 0.268 167 0.57
38 c 0.375265 660.140 15.812 15.795 0.237 0.230 146 0.64
39 d 0.389563 660.192 15.779 15.772 0.265 0.262 126 0.45
40 c 0.37735 660.362 15.882 15.870 0.262 0.259 176 0.58
42 c 0.360166 660.112 15.893 15.871 0.269 0.260 230 0.67
44 ab 0.59558 660.141 15.749: 15.718: 0.255: 0.239: 91 0.80
49 ab 0.65518 660.638 15.142: 15.128: 0.217: 0.212: 171 0.75
50 c 0.298060 660.266 15.922: 15.898: 0.201: 0.191: 193 0.70
51 d 0.396935 660.353 15.763: 15.755: 0.276: 0.272: 92 0.30
52 ab 0.57564 660.403 15.932 15.896 0.305 0.291 194 1.01
53 d 0.414108 660.130 15.784 15.775 0.231 0.229 145 0.40
54 d 0.399542 660.223 15.708: 15.700: 0.268: 0.268: 89 0.40
65 ab 0.718196 660.525 15.623: 15.614: 0.270: 0.266: 109 0.53
66 c 0.37935 660.346 15.890 15.878 0.282 0.279 132 0.55
67 d 0.404627 660.230 15.969: 15.962: 0.218: 0.216: 87 0.60
74 c 0.29601 660.164 16.007: 15.974: 0.371: 0.350: 93 0.80
97 ab 0.696336 660.008 15.897: 15.877: 0.177: 0.172: 85 0.70
99 c 0.290808 660.213 15.811: 15.808: 0.158: 0.157: 198 0.35
113 c 0.40603 660.375 15.698 15.696 0.220 0.219 257 0.22

 

 

81

Notes on individual variables:

v1 - A cepheid variable. Photometry is reported for this variable but since I am

only studying the RR Lyrae stars, v1 will not appear in any of the analyses.

v2 - Somewhat brighter in < V > than the other RR Lyraes. Our value of < V > is
~ 0.1 mag brighter than Bingham et al.’s value. Our lightcurve is more symmetric

and has less scatter than Bingham et al.’s.

v6 - This variable has a near neighbor. Messy lightcurve. Points included in

lightcurve have errors < 0.1 mag.

v7 - This variable has a near neighbor. Messy lightcurve. Points included in

lightcurve have errors < 0.1 mag.

v8 - This variable has a near neighbor. Points included in lightcurve have errors <

0.1 mag.
v12 - Too crowded in MSU frames - only WIRO data.

v15 - Irregular lightcurve - probable Blazhko star. [The Blazhko effect is a secondary

periodicity, typically tens of days in length].
v17 - A double mode variable according to Bingham et al.

v20 - Crowded. Messy lightcurve. Points included in lightcurve have errors < 0.1

mag.
v25 - Missed maximum in both V and R.

v29 - This variable has a near neighbor. Points included in lightcurve have errors

< 0.1 mag.
v30 - A double mode variable according to Bingham et a1.

v31 - A double mode variable according to Bingham et a1.

82

v32 - This variable has a near neighbor. Messy lightcurve. Points included in

lightcurve have errors < 0.1 mag.

v39 - A double mode variable according to Bingham et al.

v40 - Considerable scatter in lightcurve. Perhaps it is a double mode variable?
v44 — Messy lightcurve.

v49 - Unusually bright for an RR Lyrae in this cluster - double star according to
Bingham et al. & SKS.

v50 - Points included in lightcurve have errors < 0.1 mag.
v51 - A double mode variable according to Bingham et al.
v53 - A double mode variable according to Bingham et a1.
v54 - A double mode variable according to Bingham et a1.

v65 - This variable has a near neighbor. Messy lightcurve. Points included in

lightcurve have errors < 0.1 mag.

v67 - A double mode variable according to Bingham et al. Messy lightcurve. Points

included in lightcurve have errors < 0.1 mag.

v7 4 - Points included in lightcurve have errors < 0.1 mag.

v97 - Messy lightcurve. Points included in lightcurve have errors < 0.1 mag.
v99 - Some scatter in lightcurve.

v113 - period alias problems, P = 0.40603 days preferred over P = 0.288556 days.

CHAPTER 7

ANALYSIS

7.1 Mean Magnitudes and Colors

Once good lightcurves were produced for the variables, mean magnitudes need-
ed to be calculated. Ideally, one would like to obtain a < V > for the variables that
could then be compared to the < V > of non-variables in the horizontal branch.
Unfortunately, as the variables change in magnitude, there is some debate as to
how to average over the light cycle to obtain an equivalent non-variable < V >.
The most common mean V magnitude used is intensity averaged V (< V >im) but
there is no consensus on how to average the colors. Some people prefer magnitude
averaged colors while others prefer intensity averaged colors. Others apply ampli-
tude corrections. For this analysis, both intensity averaged and magnitude averaged
< V >’s and colors were calculated for the variables and are given in Table 6.1.
[Note: Whenever I am discussing a mean magnitude or color in general, I will use
< V > or < V — R >. Otherwise, an intensity averaged V magnitude is designated
by < V >1,“ and a magnitude averaged V magnitude by < V >mag. Mean colors are
[< V > - < R >]im for intensity averaged V-R and < V - R >mag for magnitude

averaged V—R.]

Interpolated lightcurves were used to calculate the mean quantities. Each
lightcurve was binned by 0.05 phase and a mean magnitude for each phase bin

was calculated. Then, the Numerical Recipes (Press et. a1. 1986) routines SPLINE

83

84

and SPLINT were used to interpolate magnitudes every 0.01 phase. These inter-
polated lightcurves were checked by eye with the actual lightcurves. For any stray
points, a correction by hand to the file containing the magnitudes at every 0.05
phase bin and then re-interpolating was sufficient to correct the error. Gaps in
the lightcurves were handled the same way. The magnitudes in these interpolated
lightcurves were then averaged to obtain < V >mas and < V - R >mag. Intensity
averaged magnitudes were determined by transforming each magnitude to an in-
tensity, then averaging all the points and converting the mean intensity back into
a magnitude. [< V > — < R >]im colors were determined by first calculating
< V >im and < R >im and subtracting the two. While this method worked well
for most of the variables, several of the variables had poor lightcurves or large gaps
in the lightcurves. The mean quantities for these variables are suspect and are
indicated as such by a colon next to the number in Table 6.1. For those variables
with good phase coverage, I estimate the random error in < V > to be 21:0.02 mag,

and the error in (V—R) to be 21:0.02 — 0.03 mag.

7.2 Radial dependencies

Figure 7.1 shows < V >im of the variables as a function of the distance from
the cluster center. The RRab stars are indicated by filled circles, the RRc’s by
open circles and the RRd’s are indicated by crosses. There is some suggestion of
increased scatter for stars at radii < 120 are seconds. This is quite possibly due to
the increased crowding at one goes to smaller radii. Those variables that lie less
than 120 arc seconds from the center of the cluster therefore have photometry that
is suspect. There are over 40 known RR Lyrae variables in M15 that lie less than
120 arc seconds from the center of the cluster. Due to extreme crowding of the

stars, photometry has been very difficult to obtain for these stars. Unfortunately,

E

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owing to the poor seeing conditions in Michigan, the effects of crowding in the
center were compounded. Inside 100 arc seconds, the stars are badly blended in
the CCD frames. It was decided not to try to obtain photometry of these stars.
Indeed, for those few variables just inside 100 arc seconds (v20, v44, v51. v54, v67,
and v74) for which photometry was tried, results indicate much poorer photometry
than for the RR Lyrae stars further out. With the WIRO data, we wanted to obtain
photometry for stars several magnitudes fainter than the horizontal branch to allow
comparison with previous work on M15 (Buonnanno et al. 1983, Durrell & Harris
1993). Therefore the exposure times were longer than necessary just to get the RR
Lyrae stars. As a result, the center region of M15 is saturated in the CCD frames.

Photometry for the inner RR Lyrae stars was not attempted with the W IRO data.

Figure 7.2 shows < V — R >mag as a function of distance from the cluster center.
There appears to be a strong color dependence for the RR ab’s. However, this effect
is not thought to be real, but to be a consequence of the crowding problem described
above. The four RRab stars less than 100 are seconds from the center, v6, v20, v44,
and v97, all show contamination in their lightcurves. There are near neighbors to
these variables which, especially in the MSU data, degrade the photometry. The
color of a nearby star will most likely be at least somewhat different and probably
redder (contaminating the sky around the variable) than the color of the variable
star itself. The photometric color obtained for a crowded variable may well be in
error. Therefore, the colors for v6, v20, v44, and v97 are not to be trusted. If
we exclude those variables with poor lightcurves and near neighbors we get Figure
7.3. The color dependence on radius for the RRab stars has now disappeared. The
figure for the RRcd stars however, shows a very slight gradient of about 0.03 mag.

However, since the innermost 2 stars are RRd variables. which probably are

87

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actually redder then most RRc stars, this slight gradient. may not be a consequence
of photometric error. Rather than correct for an effect that may not be real, no

corrections were made to the data.
7 .3 Comparison of < V > with Bingham et al.

Out of the 44 RR Lyrae stars for which I have photometry, 31 of them I would
classify as “good”. That is, the lightcurve is clean (no scattered points) and well
sampled in phase, leading to accurate values of < V > and < V — R >. These 31
variables are v2, v3, v4, v5, v9, v10, v11, v13, v14, v15, v17, v18, v19, v22, v23,
v30, v31, v35, v38, v39, v40, v42, v52, v53, v66, and v113 — with VB, v24, v44,
v51, and v54 having slightly greater uncertainties. These 5 variables with slightly
greater uncertainties are represented in the diagrams as smaller symbols, and are

given less weight.

Figure 7.4 shows the comparison of my < V >im. and Bingham et al.’s final
corrected < V > (from Table 8 in Bingham et a1. 1984) for 30 of the variables. The
filled circles are RRab variables, the open circles are RRc’s and the crosses are RRd
variables. Bingham et al.’s work is the most recent in depth look at the RR Lyrae
population in M15. They obtained data from new B and V photographic plates of
M15 and added to this re-reduced B and V Mt. Wilson data from SKS’s study. In
all, 62 RR Lyrae were investigated. They found strong correlations in < V > and
< B -- V > with cluster radius as well as a small north-south gradient in < B — V >.
The correlation in radius was due to crowding effects as one approached the center
of the cluster. Because of these contaminations in the data, Bingham et al. had to
apply a correction to these values for the variables lying within approximately 120
arc seconds from the cluster center. From the error bars given in Bingham et al.’s

color-magnitude diagram of the horizontal branch (their Figure 14), the error in

90

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91

their mean < V > measurements for the variables is :1: 0.03 or 0.04 mag. In my
Figure 7.4, nineteen of the thirty variables fall within A < V >= :l:0.04 mag
zone. Four of the eleven variables outside the zone have more uncertain colors
(smaller symbols). For my data, the typical internal error for < V >im for those
variables with good phase coverage is :l: 0.02 mag. Therefore, I feel that I am in
overall excellent agreement with Bingham et al.’s photometry, though significant

differences exist for some variables.
7.4 The Color-Magnitude Diagram of the Horizontal Branch

Figure 7.5 is a color magnitude diagram of the horizontal branch of M15. The
variables in the figure are the 31 good ones. Again, as in all the figures, RRab
variables are indicated by filled circles, RRc variables by open circles and RRd
variables are indicated by crosses. Non-variable stars are indicated by the + symbol.
The photometry of the non-variable stars is from the \YIRO CMDs and is given
in Table A.11 in Appendix A. The variables are spread across the gap between
the non-variable stars with some overlap between the variable and non-variable
stars. The non-variable stars that are mixed in with the variables have been tested
for variability. The photometry for some of the stars showed some scatter, but
none were found to be definitely variable. Some of these stars could be field stars
superimposed on the cluster. The RRd’s are mixed in with the RRc’s but tend to
concentrate to the cooler (red) edge of the RRc domain. The RRab’s appear to be
grouped separately from those other two groups. There is a spread in < V >im, of
about 0.35 mag, including v2, which is slightly brighter than the other variables.
There is a slight hint of increased (redder) color for the brighter RRab stars but not
for the RRc and RRd stars. The blue edge of the instability strip is at < V —R >mag

= 0.19. The red edge of the strip is at < V — R >maLg = 0.37, with no reddening

92

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correction made. The implications of this diagram will be discussed further in

Chapter 8.
7.5 Amplitude vs < V > and < V — R >

Figure 7.6 shows < V > vs V amplitude, A.., for the 31 good variables. The top
diagram shows < V >th while the bottom diagram uses < V >mag. Both of these
show considerable scatter, but both indicate an increase in amplitude as < V >
gets fainter for the RRab stars. This may be also true for the RRc’s but with only
one RRc star (v113) with < V >< 15.75, the trend is very uncertain. The double
mode variables appear to have the smallest amplitudes in this sample, excluding
v113. This is no doubt due to their double mode nature. Stars that pulsate in more
than one mode will have pulsation amplitudes less than single mode (fundamental
or first overtone) amplitudes due to the modal mixing. The RRd stars show no
correlation between < V > and amplitude. There also appears to be essentially
no difference between the top and bottom figure. That is, there is no difference

between using < V >1,“ and < V >mag.

Figure 7.7 shows < V — R > vs .4.1 for the 31 good variables. Again, the top
diagram is for [< V > — < R >]im and the bottom diagram is for < V — R >mag.
Both diagrams indicate a strong correlation for the RRab stars. That is, as one
goes to the red, the amplitude of the variables decreases. The effect is either very

small or absent for the RRc and RRd variables (except for v113).

7 .6 Period vs Amplitude Diagrams

Figure 7.8 shows the period vs amplitude relations for 42 variables with reliable
amplitudes. It is easier to obtain accurate amplitudes of the variables than to obtain
accurate mean magnitudes or colors. All you need is a well-defined minimum and

maximum in the lightcurve. Thus I have more than 31 variables with reliable

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- u 1
L .
1 1 1 1 l 1 1 1 l 1 1 1 1 l 1 1 1J l 1 1 1 J l 1 1 1 1
-0.5 -0.4 -0.3 '0.8 '0.1
Log P
1 1 r 1 1 1 r l I In 1 1 l 1 I 1 1 I rm 1 1 l I l Ij
: -
I. '0 .I
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1 1 1 1 l 1 1 1 l 1 1 1 1 l 1 L 1 1 l 1 1 1 1 l 1 14 1
-0.5 -0.4 -0.3 -0.8 -0.1
L09 Pg'

97

amplitudes. The top diagram shows log P vs AV while the bottom figure shows the
fundamentalized reduced period, log P6, vs Av. The reduced period of a variable is
the period it would be expected to have were it at the mean < V > magnitude of
all the variables. This has the effect of removing the scatter due to each variable
having a different mean V magnitude. Following Bingham et al., the reduced period
is given by:

log P’ = log P + 0.336(< V > —‘<_V_§).

The mean < V > for the variables was found using only the 31 good variables
and is 15.817 mag. Also, the periods of the first overtone mode (P1) variables
are often converted to their fundamental mode equivalent P0 to better observe the
transition zone between the fundamental mode and first overtone mode pulsators.
The relation between Po and P1 is log P0 = log P1 + 0.125 (Bingham et al. 1984).
Because the reduced period depends on < V >, only the 31 variables with good
< V > measurements are plotted in this figure. There appears to be a strong
correlation between amplitude and period for the RRab variables. The RRd stars
show little variation but then they occupy only a small region in period. The RRc
stars are a bit harder to judge. Their amplitude appears to decrease at longer
periods but v99, a much shorter period variable, also has a low amplitude. Does
this mean the relation turns over at the shortest periods, perhaps at the blue edge

of the instability strip?

7 .7 Color vs Period Relations

Figure 7.9 shows log P vs [< V > - < R >lim and < V — R >mag. The RRd
stars are plotted using their first overtone period only. The RRab are well isolated
from the RRc and RRd stars. [Hereafter, if I am talking about both BBC and RRd

stars I will use the notation RRcd to mean both groups of stars] There appears to

98

 

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Color vs Log Period for the RR Lyrae Stars

0.8

Figure 7.9

99

 

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Color vs Log P' for the RR Lyrae Stars

Figure 7.10

100

be only a small overlap in log P between the BBC and RRd stars. There is a
hint of decreasing color as one goes to shorter periods for the RRc stars. Using
reduced periods for all the variables I get Figure 7.10. The RRab stars are now
more tightly clumped together, but the RRds are now scattered over the RRc’s
region. The hint of decreasing color with shorter period is still present for the RRc
stars. Fundamentalizing the RRcd periods we get Figure 7.11. The gap between the
RRab and RRcd stars has closed up. A small overlap in period now exists between
the RRab and RRd stars. The decrease in color with shorter period for the BBC is
still present. Using reduced periods, and fundamentalizing the RRcds we get Figure
7.12. Again the gap between the RRabs and RRcds has closed up. The RRd stars
are scattered throughout the RRC stars. But, we now notice that there appears to

be a linear relation, with some scatter, between log P6 and < V — R >.
7 .8 Mean Magnitude vs Period Relations

Figure 7.13 shows log P vs < V >im for the 31 good variables. Again the RRd
stars are plotted using only their first overtone period. The top diagram shows log
P vs < V >im while the bottom diagram shows the fundamentalized period, log Po
vs < V >. The figures show that, in general, the different RR Lyrae types fall
into three well defined groups, with the RRab stars showing a correlation between
< V >int and period. The RRc stars show considerable more spread then the RRab
stars for a given period so I am more uncertain whether a real correlation exists for
that group. The RRd stars show no correlation in the figures, but again they cover
a small period range. It appears that the spread in < V > among the variables
is real - approximately 0.35 mag for the RRab stars and approximately 0.25 mag
for the RRcd stars. From the last section, the tighter correlation between reduced

periods and < V — R > strengthens the conclusion that the spread in < V > is real.

101

 

 

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Color vs Log Po for the RR Lyrae Stars

Figure 7.11:

102

 

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Figure 7.12

103

 

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Figure 7.13: Log Period vs lean Magnitude for the RR Lyrae Stars

104

7.9 Summary

Now that you have been inundated with all of these figures, what do they tell
us? For the RRab stars, as you go to the blue, their amplitudes increase. Thus,
those RRab stars found at the blue edge of the fundamental mode zone will have the
highest amplitudes. This trend is nonexistent for the RRcd stars. The amplitude
and period of the RRab and RRc stars are also well correlated. The longer the
period of the variable, the lower its amplitude. This is true for both fundamental
mode and first overtone pulsators but there is no correlation with the double mode

variables. However, the RRd stars cover only a small range in period.

The color-magnitude diagram for the variables indicates the blue edge of the
instability strip is at < V - R >= 0.19:}:0025 mag. The red edge is at < V—R >~
0.37i0.05 mag (both uncorrected for reddening). This assumes the instability strip
cuts vertically through the horizontal branch which is probably not completely true
(see Chapter 8). The blue edge of the fundamental mode zone (line between first
overtone and fundamental mode pulsators) is at < V — R >= 0.28 :h 0.018 mag.

There appears to be a real height to the horizontal branch of A < V >~ 0.35 mag.

There is a strong correlation between < V — R > color and period for the
variables. That is, as one goes to the red, the period of the variables increases. There
is no overlap in color between RRab and RRcd variables using intensity averaged
< V — R > colors or magnitude averaged < V — R > but the gap between types
is smaller using the magnitude averaged colors. The tightest color-period diagram
is Figure 7.12 — < V — R > vs log P6. This correlation is an expected consequence
of the pulsation equation, Pf = constant, provided that all RR Lyrae stars have

about the same mass.

There is a correlation between period and mean magnitude for the RRab stars.

That is, as you go to longer periods, the stars become brighter. There is a hint
of this trend with the RRc stars. One would again expect a correlation between

< V > and period because of the pulsation equation.

CHAPTER 8

CONVERSION TO PHYSICAL PARAMETERS

8.1 Effective Temperature and Reddening

Before the observed quantities, < V > and < V - R >, for the variables, can
compared to theoretical models, and to the RR Lyrae variables in other clusters,
they must be converted to real physical quantities. One of the most important of
these is effective temperature or Ten. Accurate effective temperatures are necessary
for a direct comparison between observations and theoretical stellar evolutionary
models for both variables and non-variables. This is important for determining
the precise location of the red and blue edges of the instability strip as well as for

determining the location of different zones within the strip.

Before effective temperatures can be calculated, the reddening of MlS must be
determined. Reddening is a term used to describe the shift in color due to differential
absorption by interstellar dust of light of different wavelengths. Interstellar dust
preferentially scatters light of shorter wavelengths. Reddening is severest toward
the Galactic plane. Reddening is smallest towards the Galactic poles, for there we
are looking perpendicular to the plane of our Galaxy in which most of the dust is
concentrated. The most common expression used to describe reddening is E(B—V), '
or the reddening of the (B—V) color. Several published estimates of the reddening
to MIB are listed in Table 8.1. The exact value is still somewhat uncertain. I adopt

the value E(B-—V) =0.08 i 0.02. I considered redctermining the reddening for M15

106

107

Table 8.1. Reddening Determinations for MlS

 

 

 

Method E(B-V) Reference
UBV photometry 0.12 Sandage (1969)
Integrated light 0.08 Zinn (1980)
Comparison with M3 0.08 Sandage, Katem, & Sandage (1981)
Far Ultraviolet photometry 0.10 :l: 0.02 van Albada et al. (1981)
Integrated DDO photometry 0.05 i 0.05 Bica & Pasteriza (1983)
UBV Photometry 0.08 Buonanno (1983)
UV spectra of M15 0.08 Nesci (1983)
Sturch’s (1966) Method 0.11 Bingham et al. (1984)
IUE spectra of UV bright stars < 0.08 Cacciari et al. (1984)
Bingham’s data 0.10 :1: 0.02 Caputo et al. (1984)
UBV photometry of 9 field stars 0.11 :1: 0.04 F ahlman et al. (1985)
Comparison with M92 0.10 Stetson & Harris (1988)
Comparison with M92 0.098 :1: 0.01 Durrell & Harris (1993)

 

 

108

by the method of Sturch (1966) [revisited by Blanco 1992], which depends on the
(B—V) colors of RRab variables between phases 0.5 and 0.8. This was abandoned
because too few RRab stars had adequate B coverage in that phase interval. As
no one has done (V—R) work on this cluster before, there is no previous E(V—R)
for this cluster. From Cardelli et al. (1989), I adopt E(B—V)/E(V-R) =0.74 or
E(V—R)=0.06.

The < V —- R > colors of the variables were then de-reddened using

<V—R>o =<V—R>—E(V-R).

Next, the theoretical stellar atmosphere models by Kurucz (1979) were used to
find Tag and the bolometric corrections (BC) for the variables. The bolometric
correction is added to V for the variables to obtain a bolometric magnitude. Using
a micoturbulence of 2.0 (the only choice), and an [M/ H] = -2.0, I interpolated
Kurucz’s models between his calculated gravities of log g = 2.5 and log g = 3.0
to obtain a sequence of models with log g = 2.75, appropriate for RR Lyrae stars.
These models were then used to calculate Tea and BC’s for the variables and a
selection of fairly isolated, nonvariable horizontal branch stars near the instability
strip, given in Tables 8.2 and 8.3. Figure 8.1 shows the Te“ vs mbol diagram for
the variables (usual symbols) and the nonvariables (+ symbol). This figure looks
similar to Figure 7.5, the CMD of the horizontal branch (as it shouldl). Many of the
blue horizontal branch stars are not in figure 31 because their < V— R > colors were
too blue for the particular Kurucz models used. As I am interested in those stars
closest to the edges of the instability strip, these very blue stars are not necessary
for this analysis. The blue edge of the instability strip at the level of the horizontal
branch is at about Te}; = 7500 (log Tea = 3.875) but the red edge is a little more

ambiguous. V 2 lies further redward and is brighter than the other

109

Table 8.2. mbo. and Tea for Ml5 RR Lyraes

 

 

 

Var mbo. Tefl'
2 15.412 6570
3 15.698 7110
4 15.794 7430
5 15.657 7030
8 15.680 6330
9 15.603 6740
10 15.760 6970
11 15.720 7430
13 15.742 6760
14 15.763 7040
15 15.762 6840
17 15.729 6950
18 15.710 7320
19 15.757 6860
22 15.576 6840
23 15.614 6730
24 15.624 6860
30 15.550 6990
31 15.737 7000
35 15.794 6970
38 15.694 7210
39 15.649 7040
40 15.753 7050
42 15.761 7000
44 15.624 7080
51 15.601 6960
52 15.785 68-10
53 15.670 7240
54 15.576 7010

.7 2 6940
113 15.586 7320

 

 

110

Table 8.3. mbol and Tefl' for Non-variables

 

 

 

Star mbol Tefl'
1 15.455 7150
2 15.382 6050
3 15.401 6500
4 15.680 7550
5 15.508 6190
6 15.501 6170
7 15.560 6670
8 15.632 7730
9 15.631 7400
10 15.592 6710
11 15.654 6070
12 15.919 7530
13 15.701 6370
14 15.831 7700
15 15.318 63:50
16 15.352 6170
17 15.508 6420

 

 

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112

variables, making the decision harder. One must also remember that there is no
law that says the instability strip must be vertical through the horizontal branch.
Indeed, many models indicate that the instability strip does have a slope through
the horizontal branch. In fact, the circumstance that both v99 and v113 have low
amplitudes suggests that the blue edge of the first overtone zone may become cooler
as luminosity increases. The location of v2 suggests that it may be more evolved

than other variables in the cluster.

The effective temperature of the variables can be used with their periods to
derive another physical quantity: the mass-to-light ratio of the RR Lyrae stars.
From van Albada 8.: Baker (1971), the period of the fundamental mode of pulsation,
P0, is given by

log P0 = 11.50 — 0.68 log .7)! + 0.84logL - 3.4810g Teg,

where M is the mass of the star in solar units and L is the bolometric luminosity.
Since the variables change in brightness and temperature as they go through a
cycle of pulsation. these quantities refer to mean values of L and Teff- Thus for
each variable, if we know T eff and Po, we can calculated an M / L ratio. Even better,
if there is a straight line correlation between log Po and log Tag for the variables,
a mean M/L ratio of all of them can be calculated. Figure 8.2 shows log Teg vs
log P6. There is indeed a strong correlation. The above equation predicts a line of
slope -3.48 in this diagram (shown). Fitting a line of slope —3.48 to the data, I
get log[11'I 0‘81 / L] = —1.93 i 0.05 (assuming a generous error in Tag of 21:200 K).

8.2 The Absolute Magnitude of the RR Lyrae Stars

At this time, two of the most fundamental physical quantities of RR Lyrae stars
are still somewhat uncertain: their mass and their absolute magnitude. Published

determination of RR Lyrae masses range from 0.5 to 0.8 1119, while published

113

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114

absolute magnitudes range from Alv=0.0 to 1.0 or even fainter. One of the most
recent determinations of RR Lyrae masses comes from an investigation of double
mode RR Lyrae stars by Cox (1993) who employs the revised OPAL opacities.
He found a mass of 0.75 [Hg for the double mode variables in Oosterhoff type 11
clusters. Using this mass and log 11! 0'81 / L = —1.93, we get log L = 1.83. Using

MVbol - Metal = -2-5108 LRRbol/LGbala

and a bolometric magnitude of the sun of 4.76 we get My“; = 0.188. Using the
mean BC for the 31 good variables, —0.139, we get an absolute magnitude for the
RR Lyrae of A/Iv=+0.33 mag. Cox (1994), applying the method of Cox, Hudson,
& Clancy (1983) to our RR Lyrae data, obtains the slightly fainter value of Mbol =
+0.29, corresponding to .Mv = +0.43. Walker (1992) also obtained 114v = +0.44 for
metal-poor RR. Lyrae stars in the Large Magellanic Cloud (LMC), using a distance

modulus for the LMC tied to observations of the ring around SN 1987A.

These magnitudes are brighter than those found from recent Baade-Wesselink
solutions or from the most recent statistical parallax analyses. From Baade-
Wesselink analyses of nearby field RR. Lyrae stars, Carney et al. (1992) obtained
114v = 0.16[Fe/H] + 1.02, implying Alv = + 0.71 for [Fe/H] = -2.1. The statistical
parallax solution of Layden et al. ( 1994) obtained Mv = +0.74 :1: 0.12 for halo
RR Lyraes of < [F e / H ] > = —1.6. Similar values were found by Layden et al. for
halo samples of slightly greater or lower metallicity. Figure 8.3 shows some recent
estimates of the absolute magnitude of RR Lyrae stars. The filled circles are Mv
estimates from my data (van Albada S: Baker (1971) equation and Cox’s (1994)
estimate). The cross is VValker’s (1992) LMC estimate. The open circles are from
statistical parallax measurements (Layden et a1 1994). The solid line is from Carney

et al. (1992) and the dashed line is from Sandage (1993). Our bright Ml5

115

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RR Lyrae absolute magnitudes accord better with the AA; — [Fe/ H] calibration of

Sandage (1993).

These discrepancies are unfortunate, because a relatively small uncertainty in
Mv can have important consequences, for example, in calculating the ages of the
globular clusters. An uncertainty of :1:0.1 mag in Adv translates into an uncertainty

of about :1: 1.5 Gyr in the cluster age (see section 8.4).

The absolute magnitude can be put back into the pulsation equations to de-
termine what mass the RR Lyrae stars should have, if their absolute magnitudes
are ~ +0.71 mag. Using my determinations of the the RR Lyrae BC in M15 and
1149501 = 4.76, I get A! R R = 0.48.M®. This is significantly different from the mass
found by Cox (1993) and in fact is comparable to theoretical calculations of the

core mass for RR. Lyrae stars. \Ve thus arrive at a contradiction.

Can plausible systematic errors in our Te“ scale reconcile the values for absolute
magnitude? Considering uncertainties in reddening and photometric calibration,
our Teff scale might be uncertain by :t 150K. (This does not include errors in the
Kurucz models). Let us assume that our Teff scale could be in error by i200K.
Incorporating this uncertainty, we find 111v = +0.33 i 0.12, an error bar insufficient
to close the gap with values near +0.7. To eliminate the discrepancy would require
temperatures cooler by about 500K. Work done by Longmore et al. (1990) using
V-K colors indicates a shift in this direction. Using the Longmore et al. Te“
calibration and K magnitudes, our values of < V >in11 and E(V—K) = 0.23, I place
the M15 RR Lyraes in the HR diagram as shown in Figure 8.4. The Te“ scale is
400K cooler than that obtained from the V—R data. However, several of Longmore
et al.’s RR Lyraes have only one or two measurements in the K band. That is not

as bad as it sounds, because in the K band, the RR. Lyraes have amplitudes of only

117

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~0.2 mag. Even so, their data should be considered as only approximate. A second
problem is that the Longmore et al. calibration produces an instability strip cooler

than theorists of stellar pulsation prefer.

8.3 The Distance to M15

Previous published values of the distance modulus to M15 vary from 15.03
to 15.40. Using < V >= 15.817 for the RR Lyrae variables, a V absorption of
3.2E(B-V), and an absolute magnitude of Alv = +0.33, I obtain a distance modulus
of 15.23 :1: 0.09 (distance of 11kpc). Using 114v = +0.71 I get a distance modulus of
14.85 :1: 0.09 (distance of 9kpc). Until the absolute magnitude of RR Lyrae stars is
better determined, the distance to M15 will remain somewhat uncertain using this

method.

8.4 The Age of M15

One of the largest controversies in astronomical research is the age of the glob-
ular clusters in the Galaxy. There are two opposing camps: one favors a relatively
short time in which most of the globular clusters formed, while the other camp
favors globular cluster formation over an extended time period. RR Lyrae stars
have become central to this controversy. Using Iben’s (1971) interpolation formula

for cluster age in units of 109 years, t9,

logtg = 1.42 — 1.1 log LTO — 0.59(1" — 0.3) — 0.14(3 + log Z)

where LTo is the main sequence turnoff luminosity, Y is the helium abundance, and
Z is the metal abundance. To determine the main sequence turnoff luminosity, I

will use:

mv(RR) — mv(TO) = —2.5log[LRR/LT0]

where mv(RR) is the apparent mean magnitude for the RR Lyrae stars, mv(TO) is

the apparent magnitude at the main sequence turnoff, and LRR and LTO are their

119

respective luminosities. From Durrell S: Harris (1993), mv(TO) = 19.40 :1: 0.03;
mv(RR) = 15.817 i 0.03 and log LRR = 1.83 i 0.05 from my work, and with
bolometric corrections from Kurucz’s models (—0.139 for the RR Lyrae, —0.251 for
the turnoff stars) I obtain log LTD 2 0.44 :1: 0.05. Using a helium abundance of Y
= 0.23 and a log Z = —3.9 in the above equation, the result is log t9 = 1.10 :1: 0.04
or 12.6 x 109 years. If however, the absolute magnitude of the RR Lyrae stars
is +0.71, log LRR = 1.68 which gives log LTO = 0.30. Using this log LTD in the
above equation, log t9 = 1.26 or 18.2 x 109 years. We see that the ages of the
globular clusters, using this method, depend strongly on the absolute magnitude
of the RR Lyrae stars. Until better estimates are available for Mv this method is
better suited to determine the relative ages of the globular clusters (as SKS does)

than their absolute ages.

PART II

CHAPTER 9

PERIOD CHANGES

9.1 Introduction

We can determine the period of an RR Lyrae star or Cepheid far more accurately
than we can determine any of its other properties. The potential of period changes

in these stars was recognized long ago by Eddington (1918):

“It would be of great interest to determine the change in period (if any) of these
stars, some of which have been under observation for many years; because this would
give a means of measuring a very slight change of density, and so determine the

rate of stellar evolution and the length of life of a star.”

In the case of the RR Lyrae stars, this potential to reveal the speed and direction
of evolution in the HR diagram has been partly, but perhaps not completely,
frustrated. It has become clear that evolutionary period changes in R Lyrae
stars are overlain by “noisy” period changes of ill-understood origin. Sweigart &
Renzini (1979) attributed this apparent noise to mixing events associated with the
semiconvective zone of the stellar core. Stothers (1980) attributed the noisy period
changes to hydromagnetic effects. Whatever the origin, this period change noise
means that the evolutionary rate of period change can not certainly be determined
from observations of any individual RR Lyrae star, even should those observations
span nearly a century. If true evolutionary period changes are to be revealed, then

period change results from many RR Lyrae stars must be combined to average out

120

121

the period change noise. The R Lyrae stars in R Lyrae-rich globular clusters
are obvious objects of interest in this connection. This provides the motivation for
our period study of RR Lyrae variables in the globular cluster M15, for which the

observational baseline extends over nearly a century.
9.2 The Data

9.2.1 Grouping of the Observations

The approach adopted in this paper follows that of Wesselink (1974) which was
also used by Smith & Sandage (1981). Since the study of Smith 8; Sandage, six new
groups of observations have become available, giving a total of 20 possible epochs of
observation. The identity of these 20 groups, the interval of Julian Date spanned by
their observations, the number of observations within each group, and the reference

to the paper reporting those observations are given in Table 9.1.

For groups 1-6 and 9-14 observed times of maximum light were taken from Smith
& Sandage when the variable under consideration was discussed in their paper. If
the variable was not discussed by Smith & Sandage, then times of maximum light
for these groups were determined as in Smith & Sandage. For groups 7, 8, and
18 lightcurves were plotted according to the adopted period (Table 9.2) and the
mean epoch of maximum light for each group was determined from the lightcurves.
Epochs of maximum light for groups 15 and 16 were adopted without modification
from Bingham et al. (1984) and Filippenko & Simon (1981), respectively. The
Gordenko et al. (1984) paper did not list individual observations for the stars they
studied, and epochs of maximum for groups 17 and 19 were adopted unchanged

from their paper.

122

Table 9.1. Groupings of M15 Observations

 

 

 

No. of
Group JD Interval Year Observations Reference

1 2413770 — 14212 1896/7 9 Bailey (1919)

2 2420724 -- 21113 1915/6 49 Bailey (1919)

3 2421157 - 22162 1916/9 24 Wemple (1932), Levy (1933)

4 2424381 - 24474 1925 46 Notni & Oleak (1958), Fritze (1963)
Bronkalla (1960)

5 2426543 - 26959 1931/2 52 Wemple (1932), Levy (1933)

6 2427334 - 27384 1933 26 Notni & Oleak (1958), Fritze (1963)
Bronkalla (1960)

7 2429107 - 29187 1938 93 Barlai (1989)

8 2433858 - 33895 1951 94 Barlai (1989)

9 2434973 — 35052 1954 166 Mannino (1956a,b), Grubissich (1956)
Nobili (1957)

10 2435302 — 35407 1955 34 Mannino (1956a,b), Grubissich (1956)
Nobili (1957)

11 2436136 — 36840 1957/9 163 Sandage, Katem, & Sandage (1981)

12 2437089 - 37905 1960/2 66 Maltarova & Akimova (1965)

13 2437913 - 37966 1962 84 Makarova 85 Akimova (1965)

14 2439356 — 40153 1966/8 47 Wesselink (1974)
Smith & Wesselink (1977)

15 2441981 - 44168 1973/9 98 Bingham et al. (1984)

16 2442989 - 43723 1976/8 198 Filippenko & Simon (1981)

17 2444052 - 44219 1979 233 Gardenko et al. (1984)

18 2444136 — 44220 1979 41 Chu et al. (1982)

19 2444811 — 44824 1981 49 Gardenko et al. (1984)

20 2448446 - 49186 1991/3 178 Silbermann & Smith (1994)

 

 

123

Table 9.2. Periods for M15 RR Lyrae Stars

 

 

Variable Adopted Period Current Period

 

2 0.6842702 0.684273
3 0.3887407 0.388743
4 0.313575 0.313576
5 0.384214 0.384216
6 0.665971 0.665968
7 0.367561 0.367567
8 0.646245 0.646243
9 0.71528277 0.715286
10 0.386391 0.386391
11 0.3432526 0.343267:
12 0.592848 0.592850
13 0.574961 0.574921
14 0.382001 0.382004
15 0.5835200 0.583540
17 0.4288967 0.428897
18 0.3677382 0.367742
19 0.5723027 0.572309
20 0.6969598 0.696947
22 0.7201462 0.720167
23 0.632700 0.632680
24 0.3697032 0.369703
25 0.665329 0.665329
26 0.402270 0.402270
28 0.670648 0.670648
29 0.574975 0.574977
30 0.405980 0.405980
31 0.408178 0.408178
32 0.605400 0.605401
35 0.383997 0.383997
36 0.6241424 -

38 0.375274 0.375270
39 0.389572 0.389573
40 0.377330 0.377339
41 0.6452282 —

42 0.3601746 0.360181
43 0.395993 -

44 0.5955543 0.595566
49 0.6552054 0.655193
50 0.2980583 0.298060
51 0.3969545 0.396954
52 0.575624 0.575636
53 0.414125 0.414126
54 0.3995683 0.399567
57 0.3492988 -

65 0.7183491 0.718196
66 0.379348 0.379350
67 0.404613 0.404609
74 0.296071 0.2960 1:
97 0.696333 0.696332

 

 

124

The epochs of maximum for group 20 were taken from the photometric study
in Part I (hereafter referred to as Silbermann & Smith (1994)). This study is based
upon new CCD observations of the variables. The bulk of these observations were
obtained with the 0.6 m telescope at Michigan State University during 1991—1992.
For many variables, the MSU observations were supplemented by a limited number
of observations obtained in 1993 at the Wyoming Infrared Observatory. Although
data were taken in several bandpasses, the phases of maximum are based mainly
upon observations in the V passband. The number of observations reported for this
epoch refers only to those in the V passband. One star, V12, was too crowded to be
measured on the MSU frames but could be measured on the WIRO frames. More

details of these observations are reported in Silbermann & Smith.

9.2.2 The Problem of Gaps in the Observational Record

Gaps in the observational record occasionally cause difficulties in the determi-
nation of the rates of period change. Usually, the rates of period change for M15
RR Lyrae stars are small enough relative to the spacing in time between groups of
observations that the number of cycles elapsed between successive recorded epochs
of maximum light is known. However, for some variables alternative cycle counts
are possible between two epochs of maximum light. The period changes derived for
such stars will depend upon which cycle count is used. These cycle count ambigu-
ities are most severe for stars with observational records having large gaps or for
stars showing especially large rates of period change. Sometimes, scattered obser-
vations not included within any of the groups of Table 9.1 can help to decide which
of two alternative cycle counts is correct. In other cases, a decision between the
alternatives is not possible based on the available observations. There is then no

remedy, other than discovering new observations in the historical record. We reiter-

125

ate the exhortation of Smith & Sandage that more or less continuous observations
should be maintained for RR Lyrae stars in clusters like M15, so that in the future

period changes can be derived without uncertainty from this cause.

9.3 The Phase Diagrams

Phases of maximum light were calculated for each epoch from the formula

Phase = (J De - 2400000) / period

where the period is that adopted in column (1) of Table 9.2. Uncertainties were
assigned each phase of maximum. These were taken from Smith 82. Sandage when
they were available in that paper. Otherwise, the uncertainties were estimated
based upon the lightcurve for each group of observations. Individual observations
were not published for groups 17 and 19. For these groups, it was assumed that the
uncertainties in the phases of maximum light were typical of those determined for
other groups of photographic observations. Mean epochs and phases of maximum
light are given in Table R1 in Appendix B. Diagrams plotting the phases of
maximum light versus Julian Date were constructed for each variable. These are

shown in Figure 9.1.
9.4 Period Changes

9.4.1 Parameterizing the Period Changes

The phase diagram of a variable which is undergoing a slow but constant rate of
period change is well described by a parabola. The rate of period change deduced
from the phase diagram is often parameterized by fitting a parabola to the diagram
to determine 6, the rate of period change in days/ million years. This is a useful
approach which will be followed here. However, it is necessary to add a few words

of caution. As others have pointed out, and as is apparent from Figure 9.1,

126

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Table 9.3. Rate of Period Change For RR Lyrae Variables in M15

139

 

 

 

(Parabola) (Line)
ID Type Period 6 a x2 x2
2 ab 0.684 +0.32 :1: 0.04 +0.47 :1: 0.07 1.9 5.1
3 c 0.389 +0.05 :1: 0.01 +0.13 :1: 0.02 0.4 1.2
4 c 0.314 +0.01 :1: 0.01 +0.03 :1: 0.04 1.9 1.9
5 c 0.384 +0.04 :1: 0.01 +0.10 i 0.04 0.3 0.8
6 ab 0.666 -0.06 :1: 0.05 -0.09 :1: 0.07 0.4 0.5
7 c 0.368 +0.13 :h 0.02 +0.36 :h 0.06 1.8 5.5
8 ab 0.646 —0.04 :1: 0.02 -0.06 :1: 0.03 0.6 0.8
9 ab 0.715 +0.13 :1: 0.04 +0.18 :1; 0.06 0.2 0.8
10 c 0.386 —0.05 :t 0.01 -0.14 :1: 0.04 1.9 2.7
11 c 0.343 decrease — —
12 ab 0.593 increase - —
13 ab 0.575 -0.66 :1: 0.03 -1.15 :1: 0.05 0.5 39.8
14 c 0.382 0.00 :1: 0.01 0.00 :1: 0.03 1.2 1.2
15 ab 0.584 erratic — --
17 d 0.429 +0.06 :1: 0.03 +0.14 :h 0.08 2.4 2.5
18 c 0.368 +0.08 :t 0.02 +0.21 :1: 0.04 0.5 2.2
19 ab 0.572 +0.18 :1: 0.02 +0.31 :1: 0.04 1.1 4.5
22 ab 0.720 +0.76 :1: 0.04 +1.06 :1: 0.05 6.5 33.6
23 ab 0.633 -0.21 :1: 0.03 -0.33 :1: 0.04 4.4 8.2
24 c 0.370 +0.01:1: 0.03 +0.03 :1: 0.10 3.7 3.2
25 ab 0.665 +0.01 :1: 0.03 +0.02 :1: 0.06 0.2 0.2
26 d 0.402 +0.17 :1: 0.02 +0.42 :1: 0.05 1.0 9.0
28 ab 0.671 +0.03 :1: 0.05 +0.04 :h 0.06 0.2 0.2
29 ab 0.575 —0.06 :1: 0.04 -0.10 :1: 0.07 2.0 2.0
30 d 0.406 0.00 :1: 0.02 0.00 :1: 0.05 2.1 1.9
31 d 0.408 +0.02 :1: 0.02 +0.05 :t 0.05 1.0 1.0
32 ab 0.605 +0.18 :1: 0.04 +0.30 :t 0.07 0.8 3.2
35 c 0.384 +0.03 :h 0.01 +0.08 :1: 0.03 2.3 2.3
38 c 0.375 -0.15 :t 0.01 —0.40 :1: 0.03 3.9 11.5
39 d 0.390 —0.02 :h 0.02 -0.05 :1: 0.05 1.5 1.5
40 c 0.377 +0.14 :h 0.02 +0.38 :1: 0.04 2.8 9.5
42 c 0.360 +0.12 :1: 0.01 +0.33 :h 0.03 5.5 14.7
43 c 0.396 +0.16 :h 0.02 +0.40 :1: 0.05 8.6 11.7
44 ab 0.596 increase - -
51 d 0.397 +0.02 :1: 0.02 +0.05 :1: 0.05 2.2 2.0
52 ab 0.576 +0.44 :1: 0.03 +0.76 :1: 0.05 0.3 16.7
53 d 0.414 +0.10 :1: 0.03 +0.25 :1: 0.06 1.1 2.4
54 d 0.400 +0.07 :1: 0.02 +0.17 :1: 0.05 1.0 2.1
66 c 0.379 +0.03 :1: 0.02 +0.07 :1: 0.05 1.1 1.2

 

 

140

the phase diagrams are not always well described by parabolae. Sometimes, the
period changes seem so abrupt that the phase diagrams are better described by two
or more straight lines than by a parabolic curve. In our discussion of the overall
period changes of the M15 RR Lyrae stars, we will frequently make use of the 6
values determined for each variable. The goodness of the parabolic fit will, however,

be addressed in the discussions of individual variables.

Period change results are tabulated in Table 9.3. The variable is identified in
column (1) according to its number in the catalog of Sawyer Hogg (1973). Its type,
ab, c or d, is indicated in column (2). The period of the star is given in column (3).
The rate of period change, fl, calculated in days/ million years, is listed in column
(4), along with its mean error. Values of ,6 were determined by fitting a weighted
least squares parabola to the phases of maximum in Table 3.1. The reduced x2
value of the parabolic fit is given in column (5). For comparison, column (6) gives
the value of the reduced x2 for a single straight line least squares fit to the same
data points. Column (7) restates the parabolic fit in terms of a = (1 / P)(dP /dt),

where the interval dt is again taken as one million years.

Only variables with nine or more observed epochs are included in Table 9.3.
Several of the variables have observations reported for only five to six epochs. Period
changes can be derived for these variables only if the period has changed little over
the span of the observations. These variables are not included in Table 9.3. However,
phase diagrams for these variables are given in Figure 9.1 and they are included in

the discussion of individual variables.

The last few points in the phase diagram have been used to estimate the current
period of each-variable. These are listed in column (2) of Table 9.2. For a few stars,

reliable current periods could not be determined by this method. In those cases,

141

the current period is the period found by Silbermann & Smith from their 1991-1993
data. These periods are marked with a colon and are good to about 1 part in

100,000.

9.4.2 Comments on Individual Variables

V2. 19 is positive, but the phase diagram suggests that the actual period changes

may have a more erratic pattern.

V3. A parabola gives a good fit to the phase diagram, but a straight line does

almost as well. A real period change is possible but not certain.

V4. No overall period change is evident, but the phase diagram raises the possibility
of a period increase near JD 2,430,000 followed by a period decrease near JD

2,438,000.
V5. A period increase is likely but not certain.
V6. A period decrease is possible but not certain.

V7. The phasing of the first Bailey epoch (group 1) is uncertain. As noted by
Smith & Sandage, there is evidence for the phasing depicted in Figure 1 based upon
Bailey’s scattered meaurements made between the observations of groups 1 and 2.
However, this evidence is not conclusive. The parabolic fit was made excluding
group 1. The phase diagram for V7 nonetheless shows significant evidence for a

period increase.
V8. There is only marginal evidence for a period decrease.

V9. The evidence for a small period increase is not conclusive, although the

parabolic fit produces a considerable smaller reduced X2 value.

V10. The period decrease depends mainly on epoch 1.

142

V11. Different cycle counts are possible, as shown in Figure 9.1. However, a period

decrease of some sort seems likely.

V12. Alternative cycle counts for groups 1 and 2 are possible. Nevertheless, a
period increase of some sort seems likely. [For group 20, only WIRO photometry of
V12 was obtained. Therefore HJ D of maximum for this group is 49185.713 and the

phase of maximum is 1.13 :t 0.1.]

V13. The variable with the largest rate of period decrease. The phase diagram is

well fit by a parabola, but three line segments would also give a good fit.

V14. There is no evidence for an overall period change, but some fluctuations in

period are possible.

V15. This star exhibits a strong Blazhko effect. As noted by Barlai (1977) the star
may have experienced very large period changes near JD 2,421,000 the nature of
which is difiicult to unravel (Smith & Sandage 1981). The phase diagram since JD
2,432,000 can be described by an abrupt period decrease near JD 2,438,000 followed

by a period increase near JD 2,446,000.

V17. Smith & Sandage interpreted this star as showing a large period increase,
although they noted the possibility of a cycle count error. We now suggest that a

period near 0.428897 with little or no period change is a more likely alternative.
V18. A period increase for this star now seems likely.
V19. A period increase is likely.

V20. A small period decrease with B = -0.25 d: 0.07 is possible, but the small

number of epochs makes this interpretation uncertain. Not included in Table 9.3.

V22. A large period increase is certain. The phase diagram is better fit by two

straight lines than by a parabola.

143

V23. The parabolic fit indicates an overall period decrease, but the phase diagram
suggests a more complicated pattern: a period increase near JD 2,430,000 and a

larger period decrease near JD 2,443,000.

V24. Only nine epochs are available for this variable and a cycle count error cannot

be excluded. However, our favored interpretation shows no period change.
V25. No significant period change.

V26. A period increase is likely. The phase diagram is reasonably well fit by either

a parabola or two straight lines.
V28. No significant evidence for a period change.

V29. The parabolic fit indicates a possible though not certain period decrease.
The parabola does not provide a good fit to the, admitted rather uncertain, point

of group 1.

V30. The phase diagram shows some scatter about a straight line, but no significant

evidence for a period change.
V31. There is no significant evidence for a period change.

V32. A period increase is likely. Both a parabola and two straight lines provide a

reasonable fit to the phase diagram.

V35. The evidence for a period increase depends most strongly on the inability of

a straight line to fit the group 1 point in the phase diagram.

V36. With only five epochs, no definitive interpretation of the phase diagram is
possible. Not included in Table 9.3.

V38. An overall period decrease is probable, but a fit with three straight lines is

superior to a parabola. A period increase is likely near JD 2,428,000 followed by a

144

period decrease near JD 2,438,000.

V39. The evidence for a period decrease is weak.

V40. Neither a straight line nor a parabola provide a good fit to the phase diagram.
A cycle count error for group 1 is possible. An overall period increase is possible,
but the phase diagram suggests that a more complicated sequence of period changes

may have occurred.
V41. Only three epochs. Not included in Table 9.3.

V42. A period increase is likely, although there could be a cycle count error for
group 1.

V43. Neither a parabola nor a straight line provide a good fit to the phase diagram.

A period increase seems most likely.

V44. A period increase is likely but there could be a cycle count error in the placing

of group 1. The fits have been made omitting that group.

V49. The six epochs are not sufficient to unambiguously indicate the period changes

of this star. A constant period seems unlikely. Not included in Table 9.3.

V50. The six epochs for this star can be well fit with a straight line, but cycle

count ambiguities are possible. Not included in Table 9.3.
V51. The evidence for a period change is not significant.
V52. A large period increase is certain. The phase diagram is well fit by a parabola.

V53. A period increase is likely, although the phasing of the group 1 point may be

off by a cycle. Epoch 1 was omitted in fitting the line and parabola.

V54. The evidence for a period increase is marginal.

145

V57. N o reliable period change could be determined from the five observed epochs.
Not included in Table 9.3.

V65. The four epochs are too few for a reliable period change determination. Not

included in Table 9.3.
V66. The evidence for a period decrease is marginal.

V67. The four epochs show no evidence for a period change but are too few for

certain results. Not included in Table 9.3.

V74. Only five observed epochs. Not included in Table 9.3.

V97. The five epochs show no evidence for a period change, but are too few in

number for certain results. Not included in Table 9.3.
9.5 Discussion

9.5.1 The Excess of Increasing Periods

A striking aspect of Table 9.3 is' the excess number of stars with positive values
of 6 relative to negative values. The first issue to be addressed is whether this
excess is significant. Of the stars listed in Table 9.3, about 16 show unequivocal
evidence of having undergone a period change, based upon the phase diagrams of
Figure 9.1. Eleven of these 16 stars show an overall period increase, while 4 show a
period decrease while in one case, V15, the changes are erratic. For the remainder,
the phase diagram by itself does not provide unassailable evidence for a changing
period. However, the distribution of the values of ,3 and a for these additional
stars do not scatter evenly about zero, but show a preponderance of positive values.
Unless this is an artifact, attributable to some bias of which we are unaware, this
distribution provides statistical evidence for an excess of period increases among

the M15 RR Lyrae stars which have relatively small values of 6. Histograms of the

146

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148

Table 9.4. Mean Rates of Period Changes

 

 

 

Mean Median
Type n < 6 > s.d. < a > s.d. 6 a
ab 13 +0.08 :1: 0.10 :1: 0.34 +0.11 :1: 0.16 :t 0.54 +0.03 +0.04
cd 22 +0.05 :1: 0.02 :t 0.07 +0.12 :1: 0.04 :1: 0.19 +0.03 +0.09
c 15 +0.05 :t 0.02 :t 0.09 +0.13 :1: 0.06 :1: 0.23 — -
d 7 +0.04 :t 0.02 :1: 0.04 +0.09 :1: 0.04 :1: 0.10 -

All 35 +0.06 :1: 0.04 :1: 0.21 +0.12 :1: 0.06 :1: 0.35 +0.03 +0.08

 

 

149

rates of period for both 5 and a are plotted in Figures 9.2 and 9.3 (hatched area

indicate RRcd’s, open area indicate RRab’s).

Mean and. median rates of period change are listed in Table 9.4 for the variables
belonging to the various Bailey types, and also for the entire sample. The formal
uncertainties of the mean values tend to be determined by the existence of several
outlying stars of very large or small ,6. Even so, the positive mean values of 19 and

a are significant at slightly less than the two sigma level.

A different test of the significance of the excess of increasing periods can be made
based only upon the sign of the {9 value for each star. Excluding the erratic star V15,
we find that, among the remaining 38 variables in Table 9.3, 27 have positive values
of 6 and 9 have negative values. If we distribute equally the two stars with [9 = 0.00,
we end up with 28 positive and 10 negative. This would be an unlikely result, were
positive and negative rates of period change equally likely. Under that hypothesis,
the binomial theorem gives a likelihood of only 0.3 percent of obtaining an excess
of increasing periods as large or greater than that observed. Thus, assuming we are
not biased by any unknown effect, the preponderance of increasing periods would
appear significant. Smith & Sandage, too, found an excess of increasing periods,
but Barlai (1983) had argued for a more nearly equal number of increasing and

decreasing periods.

9.5.2 Interpretation of the Period Changes

If we accept the excess of positive values of [3 as significant, the next question
is why this occurs. Evolution is a plausible explanation. Taken at face value, the
excess of increasing periods implies that the majority of RR Lyrae variables in M15
are evolving across the instability strip from blue to red. Lee, Demarque, &. Zinn

(1990) advanced an explanation for the Oosterhoff dichotomy wherein most RR

150

Lyrae variables in Oosterhoff type II clusters would, in fact, have evolved into the
instability strip from ZAHB locations on the blue horizontal branch (BHB). These
RR Lyrae stars would be evolving from blue to red during the latter stages of their

horizontal branch lifetimes.

Under this scenario, Lee (1991) calculated the expected mean rate of period
change for R Lyrae stars in a globular cluster as a function of the color distribution
of its horizontal branch stars. In the case of M15, Lee predicted a mean rate
of period change, [3 equal to 0.03 days/million years, in excellent agreement with
the observed median rate of period change. Lee’s histogram of theoretical period
changes for M15 variables does not, however, perfectly accord with the observed
histogram. The discrepancy is one that has been noted before in comparisons of
theoretical and observed period changes (e.g. Iben 8: Rood 1970): the theoretical
histogram does not account for the largest period changes observed, in the case of

M15 especially the few large negative values of 6.

Observational studies of RR Lyrae stars in globular clusters have tended to show
< 19> = 0 for Oosterhoff type I clusters and slightly positive values of < B > for
Oosterhoff type 11 clusters (Stagg & Wehlau 1980; Lee 1991; Hazen & Nemec 1992;
Smith 1995). The new period change results are consistent with that pattern. Lee
found this tendency to be in agreement with the predictions of the Lee, Demarque,
& Zinn (1990) model, in which the excess of positive fl’s among the RR Lyraes of

the Oosterhoff type 11 clusters is a consequence of their redward evolution.

Two additional questions may be asked, however, which also may shed light
on whether evolution is responsible for the excess of increasing periods: (1) Is the
observed rate of period change correlated with the position of an R Lyrae star in

the HR diagram? and (2) Are there enough BHB stars in M15 to populate the RR

151

Lyrae instability strip, given the observed mean rate of period change?

To address the first question, we consider two color-magnitude diagrams for M15
RR Lyrae stars. Figure 9.4 depicts the rate of period change as a function of the
color—magnitude data in Table 8 of Bingham et al. (1984). This color-magnitude
diagram is based upon observations by Sandage, Katem, & Sandage (1981), as
well as observations by Bingham et al. (1984). In this diagram, < V > is an
intensity weighted time average, while (B-V) is the combination of magnitude and
intensity weighted colors which Bingham et al. considered to best match the colors
which the RR Lyrae stars would have were they not variables. The open circles
represent variables with period increases and the filled circles are variables with
period decreases. The larger symbols indicate an a > 0.18 and the smaller symbols
indicate an a < 0.18. A second color-magnitude diagram is shown in Figure 9.5.
It is based upon the V and R observations of Silbermann & Smith (1994). In this
diagram, < V > and < R > are both intensity weighted time averages, and the
symbol size indicates the size of 6, as in Figure 9.4. For stars more than 120 are
seconds from the cluster center, the mean difference < V >(Bingham et al.) minus
< V >(Silbermann & Smith) is 0.00 :l: 0.04. Discrepancies are often greater for stars
at radii smaller than 120 are seconds, where crowding and cluster background are
problems. In this region, values of < V > can differ by as much as 0.1 mag. Partly,
these differences arise because Bingham et al. apply a correction for background

light to these innermost stars, while Silbermann & Smith do not.

Figure 9.4 suggests that the brighter envelope of RR Lyrae stars have a strong
tendency toward increasing periods. The four brightest RR Lyrae stars in this
diagram all have relatively large rates of period increase. The general pattern is

similar, though perhaps not quite so clear, from Figure 9.5.

152

 

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Figure 9.4:

153

 

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(V—R) vs V Indicating Period Changes of an Lyrae Stars

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Figure 9.5:

154

The brighter RR Lyraes might be expected to be in the most advanced evolu-
tionary state, hence to show the greatest rates of period increase. However, given
the general preponderance of period increases, and the relatively small number of
stars, it is difficult to be certain whether or not the patterns seen in Figures 9.4 and
9.5 are significant. If, using the Bingham et al. magnitudes, we compare the ten
brightest stars with the twenty five fainter stars, we find < a > = +0.19 :1: 0.13 for
the brighter group and +0.09 :1: 0.07 for the fainter, a suggestive but not conclusive

difference.

The second question, whether M15 contains enough BHB stars to populate
the instability strip, we test following the simple approach of Smith & Sandage.
Evolutionary lifetimes for HB stars are about 108 years (Sweigart 1991). At a rate
of period change of 0.03 days / million years, an RR Lyrae star would evolve across
the instability strip in roughly 13 million years. The ratio of RR Lyrae to RHB stars
in M15 is about 5 to 1 (Lee, Demarque, & Zinn 1990)- Let us assign, then, a total
span of about 16 million years for the RR Lyrae and RHB stages of evolution. We
would then expect the BHB progenitor to spend roughly 84 million years to the blue
of the instability strip, giving a ratio of BHB stars to RR Lyraes of about 6.5:1. Of
course, the actual mean rate of period change could be somewhat smaller than 0.03
days / million years. However, if the mean rate were much under 0.015 days / million
years, then, given the uncertainties in our determinations of 5, it would become
dificult to explain the preponderance of positive 6 values. Thus, we would not
expect a BHBzRR ratio smaller than about 3:1.

The observed BHBzRR ratio is a about 3.8:1 (Lee, Demarque, & Zinn), con-
sistent with our prediction but only if we take a lower limit for the mean rate of

period change. Rood (1990) has pointed out another possible problem. To obtain

155

this ratio of 3.8:1, we must include the stars forming the very blue tail of the M15
HB. The origin of these very blue HB stars is unclear, nor is it clear whether they
will eventually evolve through the RR Lyrae instability strip. If the blue tail is
excluded, we are left with a BHB:RR ratio of less than 2:1, significantly smaller

than that needed to feed the instability strip at the observed rate of period change.

Our results, then, do provide significant evidence that we are seeing the mean
evolution of the M15 RR Lyrae stars through the instability strip, a blue-to-red
evolution similar to that predicted by Lee, Demarque, & Zinn. This interpretation
is not, however, free of difficulty. It remains to be seen whether the BHB:RR ratio
problem can be overcome and also whether the Lee, Demarque, & Zinn scenario is

the only one to match the observations.

9.5.3 Period Changes as a Function of Bailey Type

Though there is little evidence for a difference in < a > between RR Lyraes of
Bailey type ab and those of Bailey type cd, there is nonetheless evidence for different
period change behavior between these two groups. In particular, the RRab variables
appear to show a greater range of period changes. As indicated in Table 9.4, the
standard deviations about the mean for the a and 6 values are more than twice as
large for the RRab variables as for the RRcd stars. The wider range in a and 19
for the RRab variables is also evident in the histograms of rate of period change
(Figures 9.2 and 9.3). This difference in period change behavior among the M15
variables was noted earlier by Barlai (in Szeidl 1975) and by Smith & Sandage.

The origin of this difference is unclear. It is surprising to find a difference
in period change behavior which is associated with pulsation mode. Whether
an RR Lyrae star pulsates in the first overtone or fundamental mode depends
upon its location in the instability strip (Schwarzchild 1940; Bingham et al. 1984;

156

Silbermann & Smith 1994). On the other hand, the rate of evolutionary period
change ought not to depend upon pulsation mode per se, but on the degree of
evolution away from the ZAHB. The roughly equal values of < a > for RRab and
RRcd variables indicate that, as a group, the RRab stars are not in a much more
advanced evolutionary state than are the RRcd’s. It is true that the spread in
< V > among the RRab variables does appear to be larger than among the RRcd
variables, which could signify a greater range in degree of evolution away from the

instability strip.

One might seek the cause of the greater spread in < a > values among the RRab
stars by considering the period change ”noise” believed to overlie the evolutioanry
period changes in many stars. However, because this period change noise is itself
without accepted explanation, only tentative conclusions can be obtained by this
approach. Sweigart & Renzini (1979) attributed the period change noise to mixing
events associated with the semi-convective zone in the stellar core. We might
expect that these mixing events would not be associated in a direct manner with
pulsation mode, a phenomenon chiefly of the outer envelope. It is possible that the
frequency of mixing events might be associated with the frequency of occurrence of
so-called ”breathing pulse” instabilities. The very existence of these breathing pulse
instabilities is controversial. Dorman & Rood (1993) regard them as an artifact of
the computer codes used to calculate the evolution of the core. If the pulses do
exist, they would be expected to be increasingly important toward the end of the
HB life of a star. Thus, if we seek to explain the greater spread in rates of period
change among the RRab stars as a consequence of these breathing pulses, we again
would require that the RRab stars be in a significantly more advanced evolutionary

state than the RRcd variables. As we have noted, independent evidence for this is,

157

at best, equivocal.

The RRd variables, which pulsate simultaneously in the first overtone and
fundamental modes, have posed a severe test for stellar pulsation theory (Cox,
Hodson, & Clancy 1983; Kovacs et al. 1992). It is not known why some Oosterhoff
type II clusters, such as M15 and M68, contain relatively large numbers of RRd
variables whereas others, such as M53 or 1..) Gen contain few or none. The first
overtone periods of the RRd variables are among the longest found in cd pulsators
in M15. It has been suggested that RRd variables might be mode switching. The
period changes of these stars cannot confirm or refute this hypothesis. The rates
of period change observed for the seven RRd variables in this study are similar to
those of the RRc variables (Table 9.4). If the positive mean rates of period change
were taken at face value, then the RRd variables, like most others in M15, would be
evolving from blue to red. Thus, if they are changing modes, they must be changing

from predominantly first overtone to predominantly fundamental pulsation.

CHAPTER 10

CONCLUSION

There appears to be a real spread in the height of the horizontal branch. A
tight log P’ vs < V > diagram indicates the spread is real. The observed spread in
< V > is ~ 0.3 mag, which is slightly larger than the 0.22 mag found by Sandage
(1990). V2 and perhaps v113 appear to be more evolved than the other variables.

Based upon the (V—R) data, the boundaries of the instability strip are: log T.“
= 3.875 for the blue edge and log Teff ~ 3.81 for the red edge. The sparce number
of RR Lyrae towards the red edge means this value is uncertain. The transition line
between the fundamental and first overtone mode variables is at log Teff = 3.839.
The difference between < V — R >in¢ and < V — R >mag for the variables appears
to be quite small. Thus, the difficulty over how to average colors for the variables

may indeed be alleviated by going to longer wavelengths.

There appears to be no overlap in < V - R > between the fundamental and
first overtone mode pulsators. This may suggest that a hysteresis zone does not
exist for M15. However, if all the variables are evolving to the red, the hysteresis
zone would be completely populated by first overtone and double mode variables.

The existence of a hysteresis is therefore not disproven by this investigation.

The absolute magnitude of the RR Lyrae stars was found to be My = +0.33
21:0.12, which is significantly brighter than some estimates. However, the uncertain-

ties in the reddening of M15, the Te“ scale calibration, and the mass of the RR

158

159

Lyrae stars contributes to the uncertainties in Mv. The absolute magnitude and

masses of RR Lyrae stars are not well-determined quantities.

Using Mv = +0.33, the age of M15 is 12.6 x 109 years. However, as noted above,

this depends on physical quantities that are not well-determined for the variables.

The excess of increasing periods among the RR Lyrae stars in M15 is significant.
Though the hypothesis that this excess occurs because most M15 RR Lyraes are
evolving from blue to red through the instability strip is tempting, it is not free
of dificulty. The median rate of period change observed for the M15 RR Lyraes
agrees well with the theoretical prediction of Lee (1991). However, at that rate
of period increase there may not be enough blue horizontal branch stars in M15
to sustain the RR Lyrae population. The strength of this objection depends on
whether stars in the blue tail of the M15 horizontal branch eventually evolve to
become RR Lyrae variables, a matter of considerable uncertainty. If the problem
is real, then something is wrong either with the way the rates of period change are
determined (i.e., a century is too short a span to reveal the actual mean rate of
period change) or with the evolutionary models. The greater dispersion in observed
rates of period change in the RRab variables as compared to the RRcd variables is

without adequate explanation.

CHAPTER 11

FUTURE WORK

A comparison with other globular clusters needs to be made, especially a com-
parison with an Oosterhoff type I cluster like M3. At this time there are several
groups working on various globular clusters using CCD data (ie. Cacciari et al. for
M3). There are no completed, published analyses available yet. As a result I have
decided to postpone a comparison between M15 and M3 in the hope that Cacciari
et al. will publish their data soon. If so, a full analysis will be made between M15
and M3 before this work is published. Very preliminary results from Cacciari et al
(1993) indicate a period shift ratio A log P/ A[Fe / H] = —0.1 which implies a fairly

steep metallicity-luminosity relation, similar to Sandage’s (1993) results.

An analysis of the double mode puslators should also be made. From van Albada
& Baker (1971) the ratio of the fundamental and first overtone pulsation periods
are given by:

log Po/ log P1 = 0.438 — 0.032 log M + 0.014103; L — 0.09 log T,“

where again M is the mass of the star and L is its bolometric luminosity. For a star
pulsating in both the fundamental and first overtone modes, this equations leads
directly to a mass for the star. However, obervational errors in magnitudes and
colors (hence log L and log Tag) are still a problem. An analysis of the double mode

RR Lyrae stars in M15, using the new photometry presented here, has recently been

begun.

160

161

On the theoretical front, better estimates of RR Lyrae masses and their absolute
magnitudes are needed. Their usefulness in age determinations will be limited until
that time. Perhaps more importantly, the different methods used for determining
RR Lyrae masses and their absolute magnitudes should agree more than they
presently do. Part of the problem is errors in reddening of the stars in globular
clusters. Present values are in error by i002 — 0.03, which is enough to seriously
affect the outcome of the above calculations. Also, there is a need for better/ more
realistic stellar models, which in turn may lead to a more accurate color to Tefl’

transformation.

It cannot be stressed too much that accurate and systematic observations of
the RR Lyrae stars in globular clusters should continue. Only by observation will
we be able to determine whether the period changes we see are due to evolution or

some other long-term internal processes in these stars.

APPENDICES

APPENDIX A

This appendix contains the MSU and WIRO photometry of the variables in
M15. The tables also list the frame number and the heliocentric Julian Date of
mid-exposure for each frame. Photometry with error > 0.05 mag but less than 0.1

mag is indicated by a colon. The tables begin on the next page.

162

163

Table A.1 MSU V Photometry of M15 Variables

 

 

 

HJ D
frame 2448000+ v1 v2 v3 v4 v5 v6 v7 v8
1501 446.837 15.25 15.57 15.63 15.70 15.61 — 15.33 15.86
1502 446.845 15.34 15.58 15.58 15.54 15.54 — 15.92: 15.99
1533 452.771 15.31 15.19 15.59 15.88 15.79 16.10 15.83: 16.12
1534 452.780 ‘ 15.25 15.25 15.62 15.79 15.84 - - —
1535 452.822 15.26 15.29 15.76 15.53 15.94 16.16 15.55: 15.28
1536 452.829 15.22 15.34 15.79 15.57 15.92 - 16.10: 15.20
1537 452.838 15.27 15.34 15.83 15.51 15.98 - 16.11: -
1508 453.772 15.10 15.72 16.02 15.51 15.49 15.44 15.36: 15.84
1509 453.781 15.12 15.66 16.01 15.51 15.53 15.32: 15.35: 15.81
1510 453.789 15.08 15.72 15.92 15.56 15.48 15.40 15.18: —
1511 453.830 15.13 15.70 15.71 15.70 — — 15.37 -
1512 453.838 15.13 15.65 15.65 15.76 15.57 15.47: 15.53: -
1513 453.846 15.08 15.71 15.62 15.76 15.58 15.39 15.45: -
1520 454.750 14.37 15.61 15.78 15.68 15.92 — 15.85: 15.38
1522 454.769 14.41 15.48 15.83 15.74 16.01 — 15.74 15.16
1523 454.817 14.42 15.26 16.01 15.98 15.97 16.12: 15.25: 15.34
1525 454.833 14.47 15.27 16.05 16.01 15.91 16.20: 15.32: 15.38
1559 474.726 14.45 15.38 16.05 15.87 15.98 16.25: 15.34 -
1563 474.763 14.44 15.44 16.05 15.50 — — 15.25 -
1565 474.784 14.40 15.43 15.90 15.54 16.01 - 15.80 15.40
1569 474.820 14.40 15.49 15.72 15.64 — — 15.65 15.18
1571 474.837 14.40 15.55 15.66 15.77 15.85 - 16.03: -
1572 475.683 - 15.70 15.59 15.61 15.45 - 15.93: -
1573 475.691 15.27 15.71 15.53 15.55 15.43 — 15.96: 15.82
1574 475.699 15.35 15.72 15.60 15.50 15.45 — 15.76: -
1578 475.733 15.48 15.73 15.72 15.50 15.53 15.69: 15.64: 15.86
1579 475.741 15.40 15.66 15.73 15.56 15.57 - 15.67 —
1580 475.750 15.40 15.70 - 15.58 15.54 15.71 15.34: —
1584 479.657 15.06 15.51 15.75 — 15.79 — 15.91: -
1585 479.665 15.03 15.49 — — 15.82 — 15.84: —
1586 479.673 15.10 15.58 — - 15.80 — - -
1590 479.707 15.09 15.60 15.93 16.06 15.95 - 15.80: -
1591 479.715 15.10 15.61 15.95 16.03 15.91 16.09: 15.64: -
1592 479.724 15.16 15.56 15.98 16.00 15.97 15.68: 15.68: -
1599 480.687 14.39 15.73 15.45 15.80 15.55 - 15.29: 15.46
2501 480.696 14.41 15.71 15.50 15.64 15.51 — 15.62: 15.39
2502 480.704 14.41 15.72 15.52 15.61 15.53 - — 15.48
2506 480.746 14.51 15.69 — 15.53 15.58 - 15.56: 15.58
2507 480.754 14.57 15.61 15.61 15.54 - - 15.65: 15.62
2508 480.763 14.60 15.55 15.63 15.55 15.64 - 15.90: -
2509 481.638 15.03 15.42 15.80 15.74 15.98 — 15.37 15.89
2511 481.655 15.06 15.42 15.89 15.58 15.97 - 15.25: -
2515 481.691 14.93 15.53 15.92 15.55 15.95 - 15.42: —
2516 481.702 14.86 15.56 16.00 15.61 15.96 — 15.44: —
2517 481.710 14.96 15.51 - 15.60 16.00 - 15.42: —

 

Table A.1 (cont’d).

164

 

 

HJ D
frame 2448000+ v1 v2 v3 v4 v5 v6 v7 VS
2521 481.743 14.85 15.60 16.03 15.82 15.96 15.59: 15.52: -
2522 481.751 14.82 15.59 16.02 15.82 15.86 15.45: 15.69: —
2523 481.760 14.80 15.63 15.99 15.79 15.84 15.30 15.67: 16.02
2530 537.523 15.27 15.71 15.66 15.60 - — 15.33: 15.34
2531 537.532 15.39 15.63 15.65 15.62 15.53 - 15.35: -
2532 537.540 15.34 15.66 15.68 15.63 15.53 — 15.60: 15.39
2534 546.573 14.37 15.27 15.90 15.52 15.94 15.99: 15.69 15.32
2535 546.581 14.39 15.28 — 15.54 15.98 15.99: - —
2536 546.615 14.38 15.34 — 15.55 15.95 — 15.51: -
2538 546.630 14.40 15.37 15.97 15.67 — — 15.66 15.48
2542 547.527 15.27 15.63 15.57 15.55 15.51 16.20: 15.50 -
2543 547.536 15.37 15.63 15.57 15.55 15.50 — 15.68: —
2544 547.543 15.34 15.64 15.58 15.56 15.54 16.28: 15.41' —
2545 547.592 15.33 15.72 - 15.78 15.62 16.00: - —
2549 568.542 14.73 15.42 15.53 15.54 15.98 15.84: 15.92: 15.28
2550 568.558 14.78 15.44 15.55 15.57 16.04 16.17' 15.76: 15.31
2551 568.573 14.79 15.45 15.61 15.63 15.91 - 15.64 15.38
2552 568.623 15.00 15.58 15.64 15.84 15.63 — 16.17: —
2553 568.634 15.10 15.52 15.70 15.85 15.57 - 15.76: 15.64
2565 569.627 14.48 15.69 — - — 16.26: 15.51: -
2567 570.489 15.22 15.19 - 15.76 15.93 — 15.78: 15.26
2568 570.497 15.29 — — - 15.89 — 15.83: 15.44
2569 570.531 15.33 15.30 15.55 15.97 15.72 15.84: 15.81: 15.52
2573 570.552 15.34 15.34 15.61 16.01 15.61 - 15.62: -
2574 570.559 15.35 15.36 15.62 15.97 15.58 15.92: 15.80: 15.65
2578 570.602 15.34 15.38 15.69 16.16 15.56 — 15.33: —
2579 570.609 15.27 15.41 15.80 16.16 15.48 - 15.32 -
2580 570.618 15.35 15.44 15.73 — 15.58 - 15.52 15.72
2585 574.560 15.12 15.42 - — - - — -
2586 574.569 15.13 15.36 15.96 15.83 15.82 15.82: — —
2587 574.576 15.15 15.30 15.98 15.82 15.84 — 15.75: —
2597 601.463 - — — — - — — —
2591 601.476 14.50 - 15.96 15.57 15.90 — 15.41: 15.28
2592 601.491 14.50 15.58 16.01 15.55 15.92 — 15.48 15.29
2594 601.507 14.54 — — 15.66 — — 15.21: -
2595 601.517 14.54 15.59 — - — — 15.45 15.37
2598 602.471 14.98 15.72 — 15.76 15.55 - 16.23: -
2599 602.479 14.97 15.75 - — 15.47 - - —
3501 602.487 14.96 - - - 15.59 — 15.71: 15.89
3502 602.495 14.96 15.66 - - 15.53 - 15.80: —
3505 802.799 14.53 — 16.00 15.53 15.81 15.34: - -
3506 802.807 — — 16.07 15.60 15.84 15.43: - 16.05
3507 802.815 14.63 - 16.03 15.60 15.85 15.50: — 16.03
3511 802.848 14.65 — 16.04 15.75 15.93 15.53: — —
3512 802.855 14.67 — 16.03 15.77 15.91 — — 16.09

 

165

Table A.1 (cont’d).

 

 

HJ D
frame 2448000+ v1 v2 v3 v4 v5 v6 v7 VS
3513 802.863 14.69 15.75 16.00 15.84 15.93 15.67 - -
3514 831.774 15.11 15.83 15.66 16.02 15.88 16.00 — —
3515 831.786 15.10 15.77 15.65 16.04 15.84 15.90 16.04: 15.98
3520 831.828 15.17 15.61 15.75 16.19 15.59 15.94 — -
3521 831.837 15.09 15.42 15.76 16.22 15.58 15.92 — -
3522 831.846 15.06 15.35 15.75 16.17 15.55 15.90: — -
3526 833.713 15.46 15.76 15.64 16.17 15.84 15.91 15.74: 15.63
3527 835.725 14.49 - 15.76 15.53 15.53 16.09 15.87 16.02
3528 835.733 14.43 15.74 15.77 15.56 15.53 15.97 — 16.07
3529 835.741 14.41 15.79 15.81 15.57 15.56 16.04 15.78: 16.07
3533 835.774 14.49 15.72 15.94 15.74 15.63 15.94 16.09: 16.12
3534 835.783 14.46 15.72 15.99 15.78 15.61 16.04 15.73: 16.08
3535 835.791 14.48 15.72 15.97 15.80 15.67 15.88 15.78 16.13
3539 835.824 14.57 15.77 16.00 15.92 15.74 15.88 15.78: 16.10
3540 835.831 14.48 15.79 16.02 15.92 15.79 15.95 15.68: -
3541 835.840 14.51 15.83 16.04 15.96 15.82 — 15.86 -
3545 836.712 15.44 15.26 15.84 15.76 15.98 15.32 15.54: 15.28
3546 836.720 15.33 15.25 15.76 15.74 16.00 15.28 15.61: 15.39
3547 836.727 15.37 15.25 15.73 15.78 15.98 15.19 15.56 15.36
3551 836.768 15.20 15.36 15.54 15.93 15.89 15.27 15.45: 15.51
3552 836.776 15.18 15.44 15.54 15.93 15.82 15.34 - 15.45
3553 836.784 15.18 - 15.55 15.97 15.79 15.42 15.73 15.51
3554 839.694 15.07 15.66 15.97 16.20 15.89 15.94 15.33 -
3555 839.702 15.01 15.64 16.01 16.18 15.91 15.89 15.70 16.12
3556 839.760 14.86 15.71 16.06 15.67 15.94 15.90 15.76: 16.10
3560 839.793 14.77 15.78 16.07 15.55 16.02 15.90 15.65 16.15
3561 839.801 14.62 15.76 16.04 15.55 16.06 — 15.80 -
3562 840.681 15.30 15.73 15.55 15.89 15.55 15.62 — 15.58
3563 840.696 15.25 15.70 15.57 15.68 15.53 15.65 15.69: 15.62
3564 840.704 15.27 15.64 15.61 15.63 15.56 15.30 15.58: 15.62
3568 854.648 14.76 15.59 15.57 15.98 15.77 15.89 15.76 16.14
3569 854.657 14.84 15.54 15.57 15.99 15.79 — 15.66: 16.06
3573 857.623 15.08 15.71 16.01 15.76 15.55 16.11: 15.79: 15.94
3574 857.630 15.14 15.70 16.00 15.71 15.56 15.86 15.55: 15.99
3575 857.638 15.07 - 16.02 15.63 15.59 15.81 15.82: 15.94
3576 857.646 15.11 15.70 16.08 15.57 15.65 15.90 15.63 15.97
3577 857.654 15.06 15.71 16.03 15.55 — 15.88 15.61: 16.05
3578 857.662 15.13 15.66 16.03 15.57 15.70 15.96: 15.60: 16.01
3579 857.678 15.16 15.68 15.99 15.57 15.65 16.08: 15.73: 16.00
3580 857.686 15.11 15.72 15.98 15.55 15.67 15.99 15.58 16.05
3581 857.694 15.13 15.70 15.99 15.60 15.66 15.87 15.49: 16.04
3582 857.703 15.15 15.77 15.88 15.65 15.69 15.97 15.70: 16.10
3583 857.719 15.14 15.79 15.75 15.73 15.79 16.12: 15.52 -
3584 857.735 15.16 15.85 15.73 15.81 15.84 15.93: 15.65 16.02
3585 857.744 15.22 15.86 15.69 15.80 15.80 15.87 - —

 

166

Table A.1 (cont’d).

 

11.1 D
frame 2448000+ v1 v2 v3 v4 v5 v6 v7 v8

 

4551 867.607 14.86 15.46 15.80 16.12 15.53 15.86 15.51: 16.24
4552 867.616 14.95 15.48 15.81 16.13 15.53 15.82 15.65: —

4553 867.623 14.93 15.51 15.84 16.09 15.53 15.80 15.60 -

4560 869.672 15.45 15.47 16.04 15.85 15.88 15.76 16.21: 15.33
4561 888.568 15.14 15.76 15.67 16.13 15.96 16.05 15.66 15.70
4562 888.576 15.08 15.85 15.72 - 16.01 16.04 15.44 15.70
4563 888.584 15.03 15.72 , 15.75 16.22 15.98 16.26 15.59 15.74
4564 888.600 15.02 15.65 15.80 16.18 16.00 15.97 15.69: 15.83
4565 888.608 15.01 15.60 15.84 16.21 15.99 16.11 15.54 15.83
4566 888.616 14.99 15.52 15.87 16.18 15.99 16.03 15.28: 15.90
4567 888.623 14.97 15.42 15.90 16.17 16.00 15.77 15.42 15.89
4568 888.640 14.90 15.33 15.94 16.08 15.90 15.47 15.69: 15.88
4569 888.650 14.83 15.29 15.97 16.01 15.89 15.41 15.66 -

4570 888.659 14.83 15.26 15.99 15.90 15.77 15.34 15.78 -

4571 888.667 14.67 15.22 16.06 15.85 15.72 15.26 15.42 15.70
4572 888.702 14.57 15.23 16.05 15.57 15.56 15.35 - 15.93
4589 890.562 14.68 15.72 15.79 15.61 16.01 — 15.67: 15.83
4590 890.570 14.68 15.71 15.84 15.58 15.91 16.18 15.88 15.89
4591 890.578 14.72 15.70 15.87 15.57 - 16.13 15.70 15.83
4592 890.594 14.80 15.79 ‘15.93 15.56 15.79 16.04 15.99 15.90
4593 890.603 14.78 15.74 15.93 15.55 15.73 16.04 15.68: 15.95
4594 890.611 14.83 15.77 15.97 15.57 15.69 15.94 16.20: 16.01
4595 890.618 14.90 15.74 15.98 15.59 15.67 15.98 16.03: 16.07
4596 890.626 14.90 15.71 16.00 15.61 15.64 15.77 16.11: 15.99
5522 896.542 15.12 15.69 15.93 15.53 15.82 16.16: 15.95: 16.07
5523 896.550 15.15 15.69 15.96 15.56 15.81 16.16: 16.01: -

5524 897.530 14.41 15.31 15.68 15.63 15.58 15.72 15.88 15.49

 

167

Table A.1 (cont ’d).

 

 

 

HJD

frame 2448000+ v9 v10 v11 v13 v14 v15 v17 v18
1501 446.837 - 16.09 15.99 15.99 16.01 16.15 — 15.61
1502 446.845 — — 15.92 15.69 16.01 16.16 — 15.62
1533 452.771 15.89 15.59 15.46 15.77 15.63 16.26 15.70 15.84
1534 452.780 — 15.59 15.50 15.81 15.63 - 15.69 —
1535 452.822 — 15.58 15.65 15.93 15.68 16.23 15.78 15.93
1536 452.829 16.01 15.62 15.65 15.91 15.67 16.15 15.91 15.99
1537 452.838 — 15.69 - — 15.68 16.22 15.95 -
1508 453.772 15.41 16.02 15.47 15.21 16.03 16.00 15.91 15.53
1509 453.781 15.37 16.01 15.50 15.13 16.05 15.94 15.97 15.51
1510 453.789 15.37 16.01 15.46 15.17 16.05 15.96 16.00 15.58
1511 453.830 - - 15.52 15.40 — - 16.05 15.63
1512 453.838 15.53 16.05 15.62 15.44 16.02 16.10 15.95 15.67
1513 453.846 — 16.04 15.59 15.49 - 16.15 — 15.73
1520 454.750 15.83 15.64 — 16.14 15.70 15.29 16.02 -
1522 454.769 15.80 15.59 15.62 — 15.70 15.40 15.93 15.92
1523 454.817 — 15.71 15.45 16.01 15.79 15.55 15.75 15.63
1525 454.833 15.92 15.85 15.46 16.02 15.83 15.61 15.67 15.52
1559 474.726 15.83 16.00 15.41 - 15.89 15.80 15.95 15.53
1563 474.763 — 15.74 15.45 — — 15.83 16.04 —
1565 474.784 15.94 15.64 15.60 16.17 15.93 15.94 - 15.63
1569 474.820 15.88 15.55 15.67 16.07 15.98 16.01 16.22 15.80
1571 474.837 15.84 15.54 15.70 16.06 15.96 16.07 16.13 15.79
1572 475.683 15.89 15.73 — 15.44 15.66 15.36 15.96 16.01
1573 475.691 - 15.74 - 15.46 15.63 15.20 16.07 16.11
1574 475.699 15.99 15.82 15.82 15.50 15.56 15.00 16.02 16.09
1578 475.733 16.00 15.85 15.45 15.63 15.52 14.97 15.90 15.99
1579 475.741 - — 15.46 15.68 15.55 15.05 15.89 —
1580 475.750 16.11 15.98 15.51 15.66 15.59 15.11 15.84 15.86
1584 479.657 15.63 16.06 15.83 15.19 15.93 16.15 15.54 15.92
1585 479.665 15.62 - — 15.26 15.90 -- 15.54 15.97
1586 479.673 15.70 16.02 15.92 15.27 15.92 16.15 15.41 15.93
1590 479.707 15.77 16.11 16.00 15.46 16.07 16.23 15.42 16.05
1591 479.715 15.81 16.11 16.06 15.45 15.97 16.19 15.37 16.03
1592 479.724 15.81 - 16.02 15.52 16.08 16.15 15.44 16.06
1599 480.687 - 15.68 15.70 — 15.68 — - 15.77
2501 480.696 15.93 15.76 15.84 16.06 15.65 16.23 15.86 15.77
2502 480.704 - 15.78 15.99 — 15.63 - 15.96 -
2506 480.746 — 15.90 15.97 - 15.66 16.24 15.99 15.94
2507 480.754 - 15.97 — 15.97 15.74 — - 15.87
2508 480.763 — 15.98 - 15.75 15.70 16.27 16.02 15.97
2509 481.638 15.42 16.16 15.65 16.12 - 15.62 - 15.85
2511 481.655 15.43 - 15.73 — 16.08 15.66 - 15.83
2515 481.691 15.49 15.99 15.88 16.16 16.16 15.77 - 15.60
2516 481.702 15.65 16.03 15.90 - 16.14 15.80 - 15.57
2517 481.710 15.57 15.84 15.78 16.15 16.10 15.81 16.14 15.58

 

168

Table A.1 (cont’d).

 

 

HJ D
frame 2448000+ v9 v10 v11 v13 v14 v15 v17 v18
2521 481.743 15.59 15.67 — 16.26 15.96 15.82 16.15 15.67
2522 481.751 15.59 15.63 15.91 16.15 15.96 15.93 16.10 15.64
2523 481.760 15.63 15.64 16.05 16.18 15.86 15.85 16.12 15.70
2530 537.523 15.50 15.82 15.58 -— 16.03 15.88 16.06 16.04
2531 537.532 15.52 15.86 15.61 16.28 15.98 15.72 16.04 15.95
2532 537.540 15.48 - 15.55 -— 15.95 15.70 - 15.83
2534 546.573 16.07 16.09 15.81 16.05 16.20 16.11 15.64 15.94
2535 546.581 16.05 16.12 15.89 15.94 ‘ — 16.10 15.57 15.98
2536 546.615 - 15.99 — 16.21 — — 15.68 16.05
2538 546.630 — — — — - 16.14 15.67 16.04
2542 547.527 15.54 15.73 15.57 15.42 15.70 15.59 15.74 15.58
2543 547.536 - 15.80 15.64 15.45 15.66 15.62 15.74 15.59
2544 547.543 15.56 15.78 15.60 15.51 15.68 15.65 15.75 15.62
2545 547.592 15.59 — 15.75 15.63 15.72 15.70 15.76 15.63
2549 568.542 15.91 16.20 15.80 16.19 15.64 15.67 15.71 15.67
2550 568.558 15.98 16.15 15.94 16.22 15.67 15.69 15.79 15.69
2551 568.573 15.92 16.14 - 16.20 15.70 15.72 15.83 15.76
2552 568.623 15.94 16.03 - -— 15.73 15.82 -— -
2553 568.634 — 15.95 — — 15.78 - 15.89 15.85
2565 569.627 15.44 - - — — — - 15.71
2567 570.489 15.60 16.17 15.66 15.25 15.72 16.06 16.12 16.01
2568 570.497 15.64 16.13 15.57 15.22 15.74 16.04 16.04 15.96
2569 570.531 15.70 16.09 15.58 15.42 15.80 16.08 16.07 16.10
2573 570.552 15.78 16.07 15.66 15.49 15.85 16.06 15.95 16.06
2574 570.559 15.75 16.06 15.72 15.57 15.84 16.10 15.90 16.11
2578 570.602 — 15.79 15.79 15.79 16.06 16.11 15.51 16.11
2579 570.609 15.79 — 15.90 15.80 16.05 16.17 15.49 16.04
2580 570.618 - 15.71 15.87 15.78 - - 15.50 16.01
2585 574.560 15.37 15.61 15.93 15.48 16.06 15.96 — —
2586 574.569 15.32 15.68 15.77 — 16.00 16.00 15.77 —
2587 574.576 15.31 15.76 15.71 15.53 15.98 16.01 15.74 -—
2597 601.463 - 15.95 — 16.18 - - 15.67 15.93
2591 601.476 15.86 15.93 15.78 16.20 15.78 16.19 15.83 16.02
2592 601.491 15.89 15.79 — — 15.81 - 15.84 -
2594 601.507 16.00 — — 15.52 — — — —
2595 601.517 — — - 15.37 15.94 - - -
2598 602.471 15.30 15.98 15.65 — 15.94 15.91 15.74 15.93
2599 602.479 - 16.02 15.70 - 15.89 15.85 - 15.97
3501 602.487 — — 15.70 16.29 15.86 15.87 15.81 -
3502 602.495 15.31 — 15.74 - 15.74 — - -
3505 802.799 15.26 15.89 16.07 15.44 15.75 16.20 15.80 15.67
3506 802.807 15.31 15.80 16.05 15.46 15.75 16.21 15.81 15.70
3507 802.815 15.34 15.78 15.99 15.50 15.75 16.15 15.83 15.70
3511 802.848 15.44 15.63 15.61 15.61 15.88 16.17 15.93 15.77
3512 802.855 15.45 15.65 15.56 15.67 15.90 16.17 15.94 15.80

 

169

Table A.1 (cont’d).

 

 

111 D

frame 2448000+ v9 v10 v11 v13 v14 v15 v17 v18
3513 802.863 15.44 15.65 15.51 15.68 15.91 16.18 15.99 15.83
3514 831.774 15.98 15.85 15.60 16.04 15.60 15.73 16.00 15.53
3515 831.786 15.92 15.76 15.63 16.04 15.64 15.79 15.88 15.54
3520 831.828 15.94 15.67 15.77 16.11 15.74 15.92 15.77 15.59
3521 831.837 15.94 15.64 15.78 16.18 15.76 16.02 15.75 15.59
3522 831.846 15.96 15.62 15.77 16.19 15.81 15.99 15.72 -—
3526 833.713 15.68 15.83 15.98 16.10 15.64 16.22 15.83 15.64
3527 835.725 15.38 15.62 16.03 15.84 15.93 14.97 15.76 16.07
3528 835.733 15.40 15.61 16.04 15.87 15.94 14.99 15.82 15.99
3529 835.741 15.43 15.62 16.05 15.89 15.98 15.07 15.82 16.02
3533 835.774 15.50 15.70 15.86 15.90 16.01 15.33 15.80 15.78
3534 835.783 15.53 15.70 15.82 15.95 16.01 15.35 15.86 15.77
3535 835.791 15.55 15.71 15.66 15.94 16.01 15.40 15.76 15.62
3539 835.824 15.62 15.86 15.45 16.05 16.04 15.57 15.86 15.48
3540 835.831 15.64 15.88 15.43 16.04 16.03 15.59 15.87 15.47
3541 835.840 - 15.88 15.45 16.09 16.06 15.61 15.92 15.49
3545 836.712 15.87 16.09 16.10 15.38 15.63 16.22 15.81 15.86
3546 836.720 15.89 16.10 16.08 15.44 15.64 16.19 15.87 15.91
3547 836.727 15.86 16.12 16.13 15.44 15.61 16.17 15.83 15.91
3551 836.768 15.92 16.05 16.03 15.59 15.66 16.13 15.95 16.05
3552 836.776 16.07 16.09 15.99 15.63 15.64 16.09 16.06 16.00
3553 836.784 15.91 15.98 15.98 15.65 15.68 16.17 16.01 16.05
3554 839.694 15.97 15.90 15.75 15.76 16.06 16.26 15.84 15.95
3555 839.702 15.95 15.98 15.76 15.77 15.96 16.22 15.82 16.00
3556 839.760 15.93 16.11 15.91 15.88 15.66 15.71 15.99 15.99
3560 839.793 16.02 16.08 15.97 15.96 15.57 15.05 16.00 16.01
3561 839.801 16.04 16.08 16.02 15.93 15.58 15.01 16.06 15.86
3562 840.681 15.25 15.75 15.61 15.32 15.92 — 15.93 15.60
3563 840.696 15.29 15.70 15.57 15.24 16.00 16.24 15.96 15.67
3564 840.704 15.29 15.64 15.68 15.26 16.03 16.22 15.90 15.70
3568 854.648 15.90 15.62 16.02 15.81 15.68 16.06 15.76 15.64
3569 854.657 15.91 15.65 15.92 15.79 15.64 16.04 15.77 15.63
3573 857.623 15.90 — 16.04 16.05 16.11 16.18 15.78 15.66
3574 857.630 15.95 16.11 — 16.04 16.13 16.25 15.82 15.76
3575 857.638 15.91 16.09 16.05 16.08 16.07 16.24 15.79 15.72
3576 857.646 15.90 16.00 16.12 16.04 16.08 16.23 15.81 15.78
3577 857.654 15.88 15.98 16.08 — 16.00 16.18 15.82 15.80
3578 857.662 15.95 15.90 16.10 16.10 15.88 16.17 15.80 15.85
3579 857.678 15.99 15.76 16.10 16.07 15.82 16.21 15.79 15.91
3580 857.686 - 15.71 - 16.09 15.78 16.20 15.84 15.93
3581 857.694 15.99 15.67 16.11 16.09 15.70 16.25 15.84 15.91
3582 857.703 16.03 15.69 16.08 16.10 15.68 16.20 15.86 15.94
3583 857.719 16.10 15.62 — 16.12 15.62 16.14 15.91 15.95
3584 857.735 16.09 15.60 15.94 16.15 15.65 16.11 15.90 16.05
3585 857.744 16.05 15.60 - — 15.64 - 15.89 15.97

 

170

Table A.1 (cont’d).

 

 

11.1 D

frame 2448000+ v9 v10 v11 v13 v14 v15 v17 v18

4551 867.607 15.94 16.10 16.05 15.99 15.80 16.10 15.89 15.85
4552 867.616 15.98 16.08 16.09 16.02 15.72 16.07 15.89 15.88
4553 867.623 15.92 16.13 15.99 16.05 15.71 16.04 15.93 15.88
4560 869.672 15.92 15.69 16.07 15.92 15.78 15.64 15.77 15.52
4561 888.568 15.44 15.87 16.07 15.79 16.11 16.04 15.77 15.92
4562 888.576 15.36 15.83 16.07 15.79 16.10 16.04 15.81 15.89
4563 888.584 15.32 15.79 16.10 15.77 16.05 16.04 15.80 15.99
4564 888.600 15.29 15.69 16.07 15.81 15.95 16.02 15.81 15.94
4565 888.608 15.28 15.69 16.01 15.85 15.92 16.05 15.85 15.97
4566 888.616 15.34 15.62 16.01 15.83 15.89 16.02 15.89 15.99
4567 888.623 15.31 15.60 16.00 15.85 15.80 15.97 15.92 16.00
4568 888.640 15.35 15.56 15.86 15.89 15.71 15.97 15.93 16.00
4569 888.650 15.40 15.58 15.72 15.92 15.71 15.96 15.99 15.98
4570 888.659 15.43 15.65 15.67 15.99 15.67 15.97 16.03 16.00
4571 888.667 15.46 15.66 15.64 15.95 15.67 16.00 16.08 16.03
4572 888.702 15.55 15.74 15.43 16.11 15.67 16.08 16.11 15.94
4589 890.562 15.93 15.74 15.99 16.15 15.74 15.52 15.73 15.84
4590 890.570 15.97 15.67 16.00 16.12 15.74 15.49 15.63 15.77
4591 890.578 15.96 15.71 16.02 16.13 15.68 - 15.62 15.68
4592 890.594 15.98 15.73 16.07 16.06 15.69 15.46 15.59 15.61
4593 890.603 16.03 15.72 — 16.02 15.67 15.57 15.62 15.54
4594 890.611 16.01 15.70 16.09 16.05 15.68 15.58 15.55 15.55
4595 890.618 16.01 15.72 16.05 16.04 15.67 15.60 15.54 15.50
4596 890.626 16.03 15.76 16.06 16.07 15.70 15.63 15.57 15.54
5522 896.542 15.40 16.04 15.93 15.58 16.12 15.90 15.62 15.60
5523 896.550 15.41 16.09 15.82 15.67 — — 15.60 15.60
5524 897.530 15.85 15.65 16.14 16.16 15.79 15.73 15.71 15.97

 

171

Table A.1 (cont’d).

 

 

 

II] D
frame 2448000+ v19 v20 v22 v23 v24 v25 v29 v30
1501 446.837 16.14 15.68: 15.65 15.99 15.65 16.05 — 15.41
1502 446.845 — 15.95: 15.61 15.94 - 15.84 — 15.40
1533 452.771 14.94 16.28: 15.80 15.61 15.87 16.11 - 15.81
1534 452.780 14.99 16.22: 15.80 15.65 15.85 — - 15.74
1535 452.822 15.20 — 15.82 15.70 15.82 — - -
1536 452.829 15.27 16.46: 15.85 15.79 15.87 — — 15.49
1537 452.838 15.32 — 15.82 15.70 - — — 15.45
1508 453.772 16.18 15.70: 15.32 15.88 15.60 15.70 - 15.62
1509 453.781 - 15.54 15.23 15.88 15.62 15.74 - 15.61
1510 453.789 16.11 15.69: 15.21 15.87 15.58 15.74 — 15.56
1511 453.830 — 15.80: 15.21 15.94 — 15.84 - 15.63
1512 453.838 16.22 15.99: 15.21 15.91 - 15.87 — 15.61
1513 453.846 16.20 15.77: 15.22 15.82 15.68 15.90 - 15.61
1520 454.750 - 16.20: 15.60 15.73 15.80 — - 15.87
1522 454.769 16.04 16.22: 15.72 15.80 15.64 — — 15.85
1523 454.817 16.21 16.31: — 15.97 15.44 — — -
1525 454.833 16.10 16.29: 15.77 15.90 15.47 — — 15.87
1559 474.726 15.90 15.89: 15.30 15.90 15.69 15.97 - 15.72
1563 474.763 15.92 - 15.43 15.53 — — 14.97 15.59
1565 474.784 15.99 15.99 15.48 15.26 15.46 15.97 15.31 15.53
1569 474.820 16.12 16.07: 15.52 — 15.49 15.47 - 15.61
1571 474.837 16.15 16.09 15.59 — 15.50 15.24 15.44 15.62
1572 475.683 15.04 — 15.75 15.79 15.89 15.67 — 15.42
1573 475.691 15.10 - 15.83 - — 15.70 - 15.48
1574 475.699 15.09 16.35: 15.84 15.86 15.82 15.70 - 15.44
1578 475.733 15.33 16.27: 15.84 15.88 15.87 15.73 16.17 15.55
1579 475.741 15.44 - 15.88 15.90 - 15.73 - 15.56
1580 475.750 15.45 16.36: 15.87 - 15.92 15.76 - 15.61
1584 479.657 14.99 - 15.60 15.92 15.55 15.76 — 15.45
1585 479.665 14.93 — 15.54 - 15.49 15.70 — 15.49
1586 479.673 14.87 15.95: 15.47 15.94 15.56 15.74 — 15.48
1590 479.707 15.07 16.02: 15.15 15.90 15.67 15.74 — 15.55
1591 479.715 15.12 16.02: 15.10 15.81 — 15.77 — 15.54
1592 479.724 15.20 15.85 15.13 - - 15.80 — 15.55
1599 480.687 - - 15.69 - 15.30 16.08 - 15.68
2501 480.696 16.13 16.37: 15.64 15.69 15.43 16.13 — 15.72
2502 480.704 - — 15.72 15.74 15.31 - - 15.69
2506 480.746 - - - 15.90 15.44 16.11 - -
2507 480.754 16.24 - 15.87 — 15.52 16.06 - 15.88
2508 480.763 16.11 16.52: 15.84 15.81 — — - 15.90
2509 481.638 - 15.73: 15.82 15.92 15.89 15.82 15.13 15.58
2511 481.655 16.07 — 15.83 16.09 15.87 - — 15.53
2515 481.691 16.14 15.85: - 16.01 15.91 — — 15.36
2516 481.702 16.23 16.05: — 15.93 - 15.81 — 15.41
2517 481.710 16.11 15.78: 15.89 15.88 —- 15.82 15.51 15.38

 

172

Table A.1 (cont’d).

 

 

11.1 D
frame 2448000+ v19 v20 v22 v23 v24 v25 v29 v30
2521 481.743 16.25 15.89 16.05 15.44 15.70 15.82 -- 15.44
2522 481.751 16.21 15.95: 15.96 15.40 15.69 15.80 15.56 15.45
2523 481.760 - 15.97 16.05 15.35 15.62 15.88 - 15.47
2530 537.523 15.33 15.93: 15.51 15.64 15.99 15.79 15.66 15.76
2531 537.532 15.35 16.29: 15.53 15.64 15.90 15.76 — 15.72
2532 537.540 15.36 — 15.54 15.68 15.93 15.80 — 15.77
2534 546.573 16.14 16.09 —- 15.92 15.51 - 15.38 15.71
2535 546.581 16.03 16.00: - 15.93 15.63 16.23 - 15.67
2536 546.615 15.14 16.22: 15.80 16.02 15.69 16.23 15.37 15.54
2538 546.630 15.04 16.27: 15.59 15.99 15.71 - 15.43 15.58
2542 547.527 16.18 16.14: — 15.41 — 15.84 -— 15.48
2543 547.536 16.18 — 15.43 15.32 16.00 15.73 - 15.44
2544 547.543 16.20 16.29: — 15.32 15.89 15.81 - 15.47
2545 547.592 16.21 16.26: 15.53 15.45 15.52 15.85 - 15.60
2549 568.542 15.80 — — 15.62 15.90 16.12 — 15.77
2550 568.558 15.81 — — 15.65 15.97 16.17 - 15.71
2551 568.573 15.92 — -— 15.74 15.88 16.15 15.29 15.61
2552 568.623 — — — 15.69 15.92 15.58 - 15.58
2553 568.634 — — - 15.81 15.74 15.49 - 15.60
2565 569.627 —- — — 15.71 — — — —
2567 570.489 16.22 16.10 — 15.74 — 16.14 — 15.78
2568 570.497 16.15 — — 15.75 — 16.15 — 15.71
2569 570.531 — 16.30: — 15.81 15.52 16.16 - 15.70
2573 570.552 16.23 16.19: — 15.77 15.50 16.15 — 15.64
2574 570.559 16.20 16.13: — 15.84 — 16.14 - 15.62
2578 570.602 — 16.44: — 15.98 15.57 15.95 — 15.48
2579 570.609 - 16.46: - 15.92 15.59 15.79 - 15.44
2580 570.618 16.09 — - 15.97 15.63 15.71 - 15.53
2585 574.560 16.17 16.06: 15.83 — - 16.11 - —
2586 574.569 — 15.99: 15.96 15.90 — 16.09 — -
2587 574.576 - 15.95 15.92 15.91 — 15.98 - -
2597 601.463 - - - - 15.83 — - 15.72
2591 601.476 16.19 15.39 15.24 15.71 - 15.88 — 15.41
2592 601.491 — 15.57: 15.36 15.70 — 15.82 - 15.44
2594 601.507 - 15.75: — - — — — 15.35
2595 601.517 — 15.59 - 15.72 — — - 15.45
2598 602.471 16.22 16.06: 15.75 - 15.87 16.14 — 15.77
2599 602.479 — - 15.81 — - 16.07 15.62 15.75
3501 602.487 16.09 — 15.77 15.94 15.92 16.16 — 15.85
3502 602.495 - — 15.78 — - - 15.72 15.78 ,
3505 802.799 16.15 16.16: 15.95 15.85 - 15.84 16.22 15.78
3506 802.807 16.16 15.89: 15.96 15.87 15.75 15.68 - -
3507 802.815 16.15 15.94: 15.96 15.84 15.71 15.59 - 15.79
3511 802.848 16.16 15.53 15.97 15.94 15.81 15.31 16.12 -
3512 802.855 16.16 15.43 16.00 15.95 — 15.28 16.17 15.64

 

173

Table A.1 (cont’d).

 

 

HJD

frame 2448000+ v19 v20 v22 v23 v24 v25 v29 v30
3513 802.863 16.17 15.43: 16.01 15.96 15.87 15.26 - -
3514 831.774 15.74 15.99 - 15.59 15.98 15.92 15.15 15.65
3515 831.786 15.79 15.82 - 15.60 16.01 15.96 15.11 15.68
3520 831.828 15.91 15.97 — 15.66 15.97 15.94 15.44 15.70
3521 831.837 15.98 16.15 — 15.70 15.91 16.05 15.49 15.71
3522 831.846 15.95 15.90 — 15.71 15.80 16.07 15.58 15.69
3526 833.713 16.19 15.76 15.95 15.66 15.66 15.81 - 15.60
3527 835.725 15.53 15.52 15.76 15.82 15.73 15.88 16.15 15.45
3528 835.733 15.58 15.53 15.79 15.82 15.78 15.88 16.11 15.46
3529 835.741 15.60 15.49 15.82 15.86 15.78 15.89 16.12 15.47
3533 835.774 15.72 15.57 15.84 15.86 15.96 15.91 15.73 15.51
3534 835.783 15.75 15.64 15.84 15.87 16.01 15.93 15.55 15.57
3535 835.791 15.79 15.72 15.90 15.88 15.96 15.90 15.35 15.55
3539 835.824 15.87 15.64 15.89 15.88 16.02 15.93 15.17 15.58
3540 835.831 15.89 15.68 15.90 15.88 16.05 15.96 15.27 15.58
3541 835.840 15.92 15.67 15.90 15.87 16.02 15.99 - 15.64
3545 836.712 16.18 16.04 15.95 15.51 15.51 16.10 16.37 15.78
3546 836.720 16.06 15.95 15.96 15.49 15.50 16.02 16.41 15.73
3547 836.727 15.92 15.97 15.98 15.49 15.67 15.93 - 15.81
3551 836.768 15.08 15.93 16.04 15.52 — 15.41 16.36 15.85
3552 836.776 15.05 16.18 16.07 15.54 15.60 15.33 — 15.82
3553 836.784 15.09 15.95 16.01 15.57 15.79 15.30 16.44 15.92
3554 839.694 15.30 16.08 15.83 15.87 15.52 15.88 — 15.85
3555 839.702 15.36 16.05 15.74 15.84 15.55 15.86 16.38 15.92
3556 839.760 15.62 15.64 15.31 15.88 15.66 15.94 16.17 15.81
3560 839.793 15.73 15.25 15.30 15.79 15.76 15.94 15.93 15.63
3561 839.801 15.75 15.18 15.33 15.75 15.73 15.97 15.78 15.66
3562 840.681 16.19 15.63 15.63 15.71 - 16.16 16.26 15.52
3563 840.696 16.23 15.77 15.64 15.71 15.97 16.12 16.25 15.50
3564 840.704 16.18 15.72 15.74 15.69 15.89 16.06 16.14 15.60
3568 854.648 15.60 15.71 15.91 15.81 15.98 16.13 16.33 15.88
3569 854.657 15.65 15.84 15.91 15.80 16.02 16.11 16.26 16.02
3573 857.623 15.99 15.95 15.96 15.55 — 15.84 15.67 15.60
3574 857.630 16.07 15.96 16.02 15.63 15.99 15.87 15.54 15.58
3575 857.638 16.06 15.97 16.04 15.61 - 15.88 15.45 15.62
3576 857.646 16.06 16.00 16.07 15.65 — 15.83 15.24 15.51
3577 857.654 16.05 15.91: 16.07 15.63 16.14 15.87 15.22 15.56
3578 857.662 16.10 15.99 16.06 15.63 16.14 15.84 15.18 15.58
3579 857.678 16.13 15.92 16.03 15.65 — 15.89 15.27 15.63
3580 857.686 16.14 16.03 16.00 15.67 16.07 15.90 15.32 15.57
3581 857.694 16.14 16.04 15.96 15.64 - 15.91 15.37 15.57
3582 857.703 16.12 15.93 15.85 15.68 - - 15.38 15.63
3583 857.719 16.20 15.97 15.62 15.66 — — 15.49 15.67
3584 857.735 16.05 16.10: 15.52 15.67 15.75 15.89 15.57 15.65
3585 857.744 16.16 16.04 15.46 15.64 15.73 — 15.66 15.62

 

174

Table A.1 (cont’d).

 

 

11.1 D
frame 2448000+ v19 v20 v22 v23 v24 v25 v29 v30
4551 867.607 16.26 15.99 15.95 15.80 16.01 15.79 16.05 15.96
4552 867.616 16.17 16.00 15.99 15.75 16.13 15.78 16.02 15.85
4553 867.623 16.07 15.74 15.96 15.71 15.98 15.77 16.09 15.99
4560 869.672 16.10 15.97 15.87 15.63 15.58 15.90 15.97 15.93
4561 888.568 16.13 15.33 15.99 15.32 15.72 16.14 16.25 15.40
4562 888.576 16.11 15.26 15.99 15.35 15.73 16.16 16.31 15.49
4563 888.584 16.15 15.22 16.03 15.39 15.75 16.13 16.24 15.44
4564 888.600 16.17 15.20 16.11 15.42 15.84 16.05 16.28 15.51
4565 888.608 16.13 15.17 16.08 15.48 15.86 16.05 16.20 15.64
4566 888.616 16.15 15.20 16.08 15.47 15.79 15.99 16.11 15.60
4567 888.623 16.19 15.26 16.12 15.51 15.84 15.86 15.99 15.58
4568 888.640 16.16 15.27 16.09 15.56 15.96 15.60 15.67 15.59
4569 888.650 16.20 15.48 16.03 15.57 15.97 15.56 15.50 15.63
4570 888.659 16.19 15.52 15.98 15.57 15.98 15.44 15.42 15.66
4571 888.667 16.21 15.54 15.91 15.61 15.99 15.37 15.47 15.67
4572 888.702 16.19 15.47 15.48 15.68 16.03 15.35 — 15.70
4589 890.562 15.19 16.10 15.84 15.62 15.99 16.21 16.03 15.60
4590 890.570 15.11 16.37 15.85 15.66 15.98 16.22 16.07 15.61
4591 890.578 15.10 16.12 15.90 15.68 15.96 16.23 16.08 15.62
4592 890.594 15.13 16.11 15.89 15.70 15.95 16.23 16.10 15.60
4593 890.603 15.19 16.01 15.90 15.72 15.94 16.15 16.15 15.58
4594 890.611 15.22 16.00 15.94 15.69 - 16.08 16.14 15.56
4595 890.618 15.26 15.94 15.94 15.72 . 15.87 15.95 16.15 15.60
4596 890.626 15.29 15.75 15.93 15.75 - 15.75 16.16 15.60
5522 896.542 16.04 15.98 - 16.01 15.99 - 16.18 15.93
5523 896.550 16.02 15.95 16.00 - 15.73 16.26 16.23 15.91
5524 897.530 15.58 16.16 15.44 15.68 15.95 15.91 16.24 15.55

 

175

Table A.1 (cont ’d).

 

 

 

HJD
frame 2448000+ v31 v32 v35 v38 V39 V40 V42 V44
1501 446.837 15.49 15.62: 15.64 - 15.71 15.74 — —
1502 446.845 15.50 15.64: 15.63 — 15.81 15.75 15.70 -
1533 452.771 16.04 15.70: 16.08 15.98 15.93 15.72 15.90 16.07
1534 452.780 15.97 15.65 16.13 — 15.82 15.65 15.94 —
1535 452.822 15.97 15.73 16.09 16.13 15.68 15.56 16.03 -
1536 452.829 — 15.65: — — — 15.50 16.08 -
1537 452.838 15.97 15.76 16.14 16.07 15.68 15.61 — 16.18
1508 453.772 15.82 15.17 15.67 15.52 15.56 15.98 15.54 15.86
1509 453.781 15.77 15.26 15.69 15.58 15.60 15.98 15.60 15.89
1510 453.789 15.86 15.32 15.68 15.63 15.60 16.03 15.62 15.91
1511 453.830 — 15.37 15.78 15.66 15.66 16.06 15.75 -
1512 453.838 15.77 15.39 15.77 15.72 15.66 16.12 15.74 .-
1513 453.846 15.76 15.35 15.81 15.76 15.72 16.08 - -
1520 454.750 15.93 — 16.20 — 15.91 15.72 15.73 15.45
1522 454.769 15.97 15.73: 16.15 — 15.79 15.62 15.56 15.46
1523 454.817 — 15.93: - 15.63 15.53 15.79 15.52 15.65
1525 454.833 16.07 15.90 15.76 15.51 15.42 15.83 15.61 15.59
1559 474.726 15.81 16.18: 16.14 15.50 15.43 — 15.75 16.12
1563 474.763 - 15.68: — 15.42 15.37 — 15.86 -
1565 474.784 15.95 - 15.96 15.57 15.48 — 15.99 -
1569 474.820 16.01 — 15.69 15.59 15.58 15.76 16.06 —
1571 474.837 16.00 15.87: 15.63 15.65 15.58 - 16.09 16.27
1572 475.683 16.10 15.58 15.71 15.93 15.77 — 15.54 15.69
1573 475.691 16.11 15.53: — — 15.75 — 15.52 -
1574 475.699 16.05 15.51 15.79 15.98 15.83 — 15.50 15.75
1578 475.733 16.01 15.69 15.80 16.06 15.84 16.06 15.48 15.80
1579 475.741 — 15.70: — 15.94 — — 15.55 15.84
1580 475.750 15.86 15.69 15.83 16.00 15.83 15.94 15.57 15.80
1584 479.657 15.82 16.05: 16.04 15.54 16.01 15.70 15.55 15.51
1585 479.665 15.97 - 16.17 15.55 15.87 15.71 15.54 15.26
1586 479.673 - 16.01: 16.16 15.57 15.93 15.62 15.60 15.29
1590 479.707 15.96 15.91 16.13 15.67 15.92 15.88 15.60 15.09
1591 479.715 15.96 16.01 16.12 15.68 15.90 15.73 15.61 15.22
1592 479.724 15.98 15.93 16.15 —- 15.87 15.79 15.67 15.18
1599 480.687 15.72 15.72: 15.78 15.74 - - - 15.90
2501 480.696 15.55 - 15.74 15.66 15.72 15.66 15.64 15.92
2502 480.704 15.54 - 15.80 15.59 15.73 15.82 15.58 15.64
2506 480.746 15.50 15.79: 15.86 15.48 15.85 15.54 15.57 15.88
2507 480.754 15.54 16.12: 15.87 15.44 15.89 15.48 15.59 -
2508 480.763 15.62 16.08 15.98 15.49 15.87 — 15.50 15.86
2509 481.638 15.80 15.15 16.24 15.86 - 15.91 - 15.66
2511 481.655 - 15.06: — 16.03 15.83 - 16.08 15.84
2515 481.691 16.01 15.42 16.02 16.03 15.75 — 16.12 15.67
2516 481.702 - 15.50 15.90 16.06 15.69 — - 15.77
2517 481.710 16.02 15.41: 15.84 16.15 15.76 — 16.23 —

 

176

Table A.1 (cont’d).

 

 

HJ D

frame 2448000+ v31 v32 v35 v38 v39 v40 v42 v44
2521 481.743 16.05 15.49: 15.68 16.05 15.68 — 15.95 15.82
2522 481.751 16.01 15.65 15.66 - 15.68 - 15.93 15.76
2523 481.760 16.10 15.67 15.65 15.98 15.77 — 15.81 15.90
2530 537.523 15.77 15.61: 15.81 15.80 15.66 — - 15.56
2531 537.532 15.76 15.49: 15.82 — 15.77 16.07 — 15.72
2532 537.540 15.72 — 15.92 15.79 15.69 — 16.14 15.64
2534 546.573 15.75 15.56: 16.12 — 15.89 — 16.07 —
2535 546.581 15.79 15.59 16.02 15.87 15.91 — 16.13 15.98
2536 546.615 - 15.59 15.81 - 15.97 — 15.78 16.01
2538 546.630 16.03 15.77: 15.78 - 15.94 —- 15.80 16.16
2542 547.527 — 15.94: 15.84 15.61 15.83 15.56 16.14 —
2543 547.536 — 15.90 15.86 15.56 15.86 15.61 16.15 15.81
2544 547.543 15.92 15.89 — 15.58 15.74 15.61 16.20 15.78
2545 547.592 -— 15.56: 16.05 15.59 15.72 15.74 -- 15.28
2549 568.542 15.69 -— 15.65 15.52 15.95 15.96 16.16 15.58
2550 568.558 15.77 15.96: 15.67 15.47 15.87 16.13 15.89 15.63
2551 568.573 - - 15.68 15.50 15.73 15.96 15.86 15.73
2552 568.623 15.95 - 15.79 15.69 15.49 15.82 15.59 —
2553 568.634 15.99 — 15.82 15.67 15.61 15.67 15.65 -
2565 569.627 — 15.84: — - - - - 15.30
2567 570.489 - 15.85: 15.67 15.59 15.87 15.83 15.76 15.87
2568 570.497 — 15.98: 15.59 15.60 15.87 15.74 15.86 16.02
2569 570.531 15.46 15.94 15.73 - 15.76 15.59 15.87 15.97
2573 570.552 15.54 15.96: 15.78 15.78 15.78 15.56 15.95 -
2574 570.559 15.53 15.71: 15.76 15.84 15.75 15.71 16.05 16.04
2578 570.602 15.64 15.17 15.97 15.96 15.73 - 16.19 16.20
2579 570.609 15.72 — 16.00 15.99 15.60 15.68 - -
2580 570.618 - 15.24 15.99 15.90 15.64 15.81 - -
2585 574.560 - 15.80: - - 15.75 — - -
2586 574.569 - 15.93: — 15.55 15.69 - 16.10 -
2587 574.576 - 15.87: 16.12 — 15.74 16.03 — 15.79
2597 601.463 15.69 16.01: — - 15.82 — 15.63 15.61
2591 601.476 15.88 14.98 - — 15.92 - 15.81 15.86
2592 601.491 15.85 14.99 15.97 15.96 15.97 15.60 15.86 16.09
2594 601.507 — 15.27: - — - 15.54 - -
2595 601.517 15.91 15.09 - - - - - -
2598 602.471 15.78 16.04: 15.93 15.88 15.74 16.10 15.59 15.62
2599 602.479 15.77 — -- — 15.70 — - -
3501 602.487 15.85 16.04: 15.95 15.81 15.68 - 15.56 -
3502 602.495 15.92 — — 16.12 15.72 - 15.64 15.72
3505 802.799 15.78 15.92 15.60 — 15.65 16.06 15.71 15.88
3506 802.807 15.79 15.93 15.63 15.70 15.63 16.04 15.72 15.92
3507 802.815 15.82 16.01 15.61 15.72 15.69 16.03 15.71 15.92
3511 802.848 15.81 16.07 15.68 15.83 15.74 16.06 15.86 15.88
3512 802.855 15.81 16.04: 15.72 15.84 15.77 16.06 15.88 15.94

 

177

Table A.1 (cont’d).

 

11.1 D
frame 2448000+ v31 v32 v35 v38 v39 v40 v42 v44

 

3513 802.863 15.84 — 15.76 15.84 15.80 16.05 15.92 15.91
3514 831.774 15.82 15.82 16.13 15.76 15.84 15.95 16.14 15.51
3515 831.786 15.80 15.86 16.13 15.94 15.95 15.92 16.16 15.76

3520 831.828 15.84 15.93 16.15 - 15.87 16.09 15.99 15.59
3521 831.837 15.80 15.91 16.19 15.92 15.93 — 15.97 15.72
3522 831.846 15.85 15.93 16.22 16.02 15.84 - 15.90 15.67

3526 833.713 15.67 16.02 16.14 15.97 15.87 16.10 15.51 15.97
3527 835.725 16.10 16.01 16.06 15.56 15.96 16.08 16.11 15.93
3528 835.733 16.13 16.10 16.05 15.52 15.94 16.02 16.08 15.87
3529 835.741 16.05 16.02 15.97 15.51 15.88 16.01 16.12 15.91
3533 835.774 15.87 15.52 15.74 15.48 15.87 15.73 16.00 15.74
3534 835.783 15.83 15.40 15.72 15.55 15.92 15.67 15.98 15.77
3535 835.791 15.80 15.27 15.68 15.56 15.87 15.61 15.91 15.61
3539 835.824 15.68 15.21 15.61 15.64 15.76 15.60 15.61 15.07
3540 835.831 15.69 15.27 15.62 15.68 15.71 15.60 15.60 15.12
3541 835.840 15.69 15.29 15.65 15.72 15.64 -— 15.58 15.03
3545 836.712 15.74 15.95 15.90 16.00 15.72 15.97 15.95 15.95
3546 836.720 15.77 15.93 15.91 16.00 15.67 16.02 15.93 15.96
3547 836.727 15.80 16.01 15.95 16.05 15.74 15.98 16.00 15.85

 

3551 836.768 15.90 16.00 16.09 15.98 15.73 — 16.04 16.01
3552 836.776 15.88 16.12 16.07 16.07 15.76 — 16.18 16.06
3553 836.784 15.95 16.05 16.10 15.97 15.84 — 16.15 16.00

3554 839.694 16.00 15.89 15.69 16.04 15.58 15.92 16.18 15.87
3555 839.702 16.00 15.87 15.69 16.06 15.53 15.89 16.15 16.10
3556 839.760 16.06 16.03 15.83 16.02 15.47 16.03 15.95 15.98
3560 839.793 15.92 16.10 16.00 — 15.46 — 15.60 15.92
3561 839.801 15.83 16.10 15.97 15.76 15.52 — 15.59 15.86
3562 840.681 15.81 15.17 16.12 15.64 15.90 15.79 15.99 15.36
3563 840.696 15.75 15.31 16.16 15.55 15.76 15.70 16.01 15.50
3564 840.704 15.72 15.26 16.18 15.74 15.84 15.66 16.04 15.48
3568 854.648 15.64 15.44 15.66 15.87 15.69 15.78 15.69 16.25
3569 854.657 15.67 15.41 15.69 15.89 15.70 15.71 15.70 16.04
3573 857.623 15.98 15.13 16.07 15.82 15.76 16.07 16.06 15.93
3574 857.630 15.97 15.19 16.00 15.82 15.74 15.98 16.14 -
3575 857.638 16.02 15.24 15.88 15.81 15.77 15.90 16.11 16.04
3576 857.646 15.98 15.30 15.84 15.85 15.73 15.81 16.13 16.11
3577 857.654 16.04 15.34 15.81 15.89 15.63 15.82 16.14 15.91
3578 857.662 16.09 15.31 15.76 15.92 15.71 15.77 16.12 16.10
3579 857.678 16.06 15.42 15.69 15.99 15.71 15.70 16.14 15.94
3580 857.686 16.06 15.42 15.65 15.93 15.73 15.67 16.17 15.97
3581 857.694 16.10 15.45 15.63 15.99 15.73 15.63 16.13 15.87
13582 857.703 16.10 15.48 15.67 16.03 15.71 15.58 16.15 15.81
3583 857.719 16.12 15.52 15.65 16.03 15.67 15.63 16.12 -
3584 857.735 16.11 15.60 15.66 16.04 15.69 15.68 16.09 15.83
3585 857.744 16.05 15.53 15.71 16.08 15.63 . — - 15.87

 

178

Table A.1 (cont ’d).

 

 

BJD

frame 2448000+ v31 v32 v35 v38 v39 40 v42 v44

4551 867.607 15.66 15.93 16.06 15.61 15.86 15.82 15.67 15.76
4552 867.616 15.58 16.03 16.00 15.58 15.90 15.81 15.68 15.75
4553 867.623 15.54 16.08 15.91 15.53 15.88 15.86 15.73 15.69
4560 869.672 15.83 15.65 15.71 15.89 15.85 16.15 15.73 15.92
4561 888.568 15.72 15.45 15.97 15.93 15.72 16.01 15.90 15.86
4562 888.576 15.79 15.46 16.01 15.93 15.76 15.96 15.93 15.97
4563 888.584 15.78 15.53 16.04 15.92 15.72 15.88 15.94 15.88
4564 888.600 15.83 15.62 16.12 15.77 15.85 15.76 16.01 15.79
4565 888.608 15.86 15.64 16.11 15.63 — 15.72 16.04 15.87
4566 888.616 15.87 15.71 16.08 15.67 15.89 15.67 16.08 15.89
4567 888.623 15.92 15.66 16.14 15.64 15.82 15.62 16.07 15.91
4568 888.640 15.97 15.76 16.15 15.52 15.88 15.67 16.11 15.81
4569 888.650 15.97 15.74 16.16 — 15.93 15.69 16.12 15.89
4570 888.659 16.02 15.85 16.18 — 15.81 15.74 16.19 15.86
4571 888.667 16.07 15.81 16.22 15.41 — 15.79 16.20 15.90
4572 888.702 16.12 15.96 16.26 15.50 16.04 15.82 16.18 15.86
4589 890.562 15.66 15.74 16.16 — 16.00 15.75 15.84 15.91
4590 890.570 15.67 15.89 16.19 - 15.93 15.79 15.77 15.88
4591 890.578 15.66 15.91 16.16 15.69 — 15.77 15.73 15.98
4592 890.594 15.69 15.83 16.15 15.71 16.06 15.80 15.67 15.68
4593 890.603 15.72 15.96 16.16 15.69 - 15.83 15.64 15.45
4594 890.611 15.74 15.92 16.14 15.68 15.97 15.84 15.60 15.32
4595 890.618 15.74 15.88 16.15 15.70 16.13 15.84 15.58 15.30
4596 890.626 15.75 15.98 16.13 — 16.00 15.85 15.61 15.28
5522 896.542 16.00 15.71 15.73 15.56 15.99 15.71 16.10 15.69
5523 896.550 16.00 15.72 15.73 - 15.88 15.69 — 15.58
5524 897.530 15.76 15.52 16.15 - — - 15.87 15.98

 

Table A.1 (cont’d).

179

 

 

 

H] D
frame 2448000+ v49 v50 V51 v52 v53 v54 v65 v66
1501 446.837 15.17 - 15.62 15.23 15.62 15.45 15.69 -
1502 446.845 15.19 - 15.49 15.23 15.66 15.45 15.68 -
1533 452.771 15.25 15.81 15.49 15.91 15.82 15.58 15.68: 15.82
1534 452.780 15.24 - 15.51 15.94 15.79 15.63 15.63 15.78
1535 452.822 15.33 — - 15.96 15.93 — 15.58 15.67
1536 452.829 15.32 - 15.53 16.09 - 15.43 15.69 -
1537 452.838 15.31 - 15.62 16.01 15.91 15.48 15.63 -
1508 453.772 15.06 - 15.90 15.26 15.88 15.58 15.48 15.98
1509 453.781 15.07 — 15.89 15.32 15.89 15.61 15.51: 15.99
1510 453.789 15.10 15.82 15.98 15.35 15.91 15.72 15.46 15.99
1511 453.830 15.10 — - - - — 15.47 -
1512 453.838 15.12 16.00 15.74 15.54 15.67 15.83 15.52 —
1513 453.846 15.13 - 15.73 15.66 15.68 15.78 15.49 16.10
1520 454.750 15.28 — 15.58 16.10 15.45 15.71 15.67: -
1522 454.769 15.27 16.17 15.55 16.05 15.47 15.74 15.77: -
1523 454.817 15.32 — 15.60 16.21 15.59 15.46 15.76: 15.77
1525 454.833 15.28 16.02 15.69 — 15.67 15.43 15.81: 15.91
1559 474.726 15.06 - 15.82 15.97 15.62 15.73 15.66 16.10
1563 474.763 15.16 - — 16.09 — 15.57 15.60 -
1565 474.784 15.10 — 15.94 16.12 15.84 15.53 15.65 -
1569 474.820 15.15 - 15.81 16.07 15.93 15.38 15.69 -
1571 474.837 15.15 15.47 15.95 16.18 — 15.44 15.71 -
1572 475.683 15.25 16.08 15.65 15.49 15.93. 15.52 15.80: 15.73
1573 475.691 15.25 - — 15.53 - - 15.63 15.82
1574 475.699 15.26 - 15.60 15.58 - 15.47 15.68: 15.81
1578 475.733 15.30 15.63 15.57 15.62 15.87 15.55 15.76: 15.91
1579 475.741 15.27 15.47 15.58 15.73 - 15.65 15.63 15.90
1580 475.750 15.31 15.50 15.57 15.73 15.85 15.72 15.75: 15.96
1584 479.657 15.22 15.44 15.68 15.21 15.63 15.43 15.53 16.08
1585 479.665 15.22 — 15.63 15.25 15.69 15.44 15.40 16.14
1586 479.673 15.24 — 15.64 15.34 15.64 15.52 15.51 16.05
1590 479.707 15.31 15.77 15.53 15.47 15.74 15.50 15.54 15.80
1591 479.715 15.30 15.84 15.52 15.50 - 15.55 15.57: -
1592 479.724 15.27 15.84 15.55 15.55 15.78 15.61 15.54: 15.72
1599 480.687 15.17 - — - 15.96 — 15.71: —
2501 480.696 15.11 - 15.78 16.07 15.99 15.78 15.68 -
2502 480.704 15.13 -— — 16.00 15.97 - 15.70: -
2506 480.746 15.20 16.14 — 16.13 15.79 - 15.65 -
2507 480.754 15.21 - 15.83 16.13 15.72 15.45 15.75 -
2508 480.763 15.22 — 15.90 15.84 — 15.51 15.75 16.06
2509 481.638 15.26 -— 15.81 - 15.67 15.40 15.43: —
2511 481.655 15.35 — 15.66 16.12 - 15.44 15.31 —
2515 481.691 15.36 15.61 15.62 16.18 15.73 15.58 15.36 15.65
2516 481.702 15.33 15.59 15.73 16.11 15.73 15.70 15.35 15.66
2517 481.710 15.26 — 15.60 16.17 15.76 15.52 15.34 15.67

 

Table A.1 (cont’d).

180

 

 

HJ D
frame 2448000+ v49 v50 v51 V52 v53 v54 v65 v66
2521 481.743 14.89 — 15.71 16.16 15.69 15.78 15.41 -
2522 481.751 14.83 15.47 15.60 16.20 15.71 15.71 15.42 15.78
2523 481.760 14.80 15.64 15.60 16.14 15.82 15.63 15.41 15.79
2530 537.523 14.93 — 15.95 16.19 15.46 15.48 15.74: 15.74
2531 537.532 14.97 — 15.91 16.22 15.49 15.50 15.68 -
2532 537.540 14.96 - - 16.20 15.45 - 15.73: 15.81
2534 546.573 15.32 — 15.79 15.87 15.87 15.78 15.56 -
2535 546.581 15.23 — 15.78 15.86 '— 15.84 15.58 -
2536 546.615 14.77 — 15.77 15.92 15.74 15.77 15.63 -
2538 546.630 14.66 - 15.85 16.01 15.77 15.65 15.71 —
2542 547.527 15.18 — 15.73 - 15.50 15.46 15.68: 16.03
2543 547.536 15.15 16.13 15.81 16.02 15.61 — 15.82: —
2544 547.543 15.18 16.00 15.66 15.82 15.61 15.44 15.74: 16.20
2545 547.592 15.26 15.51 15.72 15.30 15.65 15.58 15.83: 15.96
2549 568.542 15.23 — 15.88 16.12 15.60 15.77 15.36 15.61
2550 568.558 15.24 — 15.74 16.12 15.61 15.78 15.33 —
2551 568.573 15.28 — 15.68 - 15.51 15.84 15.34 -
2552 568.623 15.30 - 15.54 - 15.45 15.92 15.40 -
2553 568.634 15.25 - 15.46 - 15.55 15.80 15.42 -
2565 569.627 14.92 — — - — — 15.85: —
2567 570.489 15.17 - 15.88 16.11 15.85 15.79 15.66: -
2568 570.497 15.17 — 15.93 16.12 - 15.81 15.72: -—
2569 570.531 15.27 - — 16.23 16.00 — 15.77: 15.78
2573 570.552 15.29 15.51 15.84 16.21 16.00 15.91 - 15.82
2574 570.559 15.27 15.56 15.77 16.02 15.99 15.85 15.85: 15.86
2578 570.602 15.25 - 15.58 15.35 15.95 - 15.69 -
2579 570.609 15.25 - 15.51 15.33 — 15.77 15.61: —
2580 570.618 15.27 - 15.48 15.33 15.92 15.74 15.77 -
2585 574.560 15.28 — 15.65 - — 15.88 15.58 15.82
2586 574.569 15.29 — — 16.26 15.87 - 15.67: 15.82
2587 574.576 15.30 16.09 15.57 — 16.03 — 15.64: 15.73
. 2597 601.463 -— — -— 15.97 15.67 15.81 15.39: 15.91
2591 601.476 15.24 16.09 15.84 16.28 15.70 15.48 15.80 -
2592 601.491 15.27 — 15.95 16.16 15.82 15.50 15.77: —
2594 601.507 15.21 - - - - 15.41 15.82: -
2595 601.517 — — 15.65 — - 15.59 15.72: -
2598 602.471 15.09 15.63 15.68 16.02 15.82 15.81 15.42 16.04
2599 602.479 15.11 - 15.58 15.99 - — 15.35 -
3501 602.487 15.10 15.68 15.72 15.99 15.76 15.90 15.49: -
3502 602.495 15.09 - - - 15.78 — 15.41: -
3505 802.799 14.64 15.78 - 16.01 15.92 - 15.50: 16.09
3506 802.807, 14.63 15.83 15.70 15.96 15.96 15.56 15.47: 16.08
3507 802.815 14.66 15.84 15.72 16.00 16.01 15.53 15.50 16.11
3511 802.848 14.78 16.00 - 16.04 16.04 — 15.50 16.07
3512 802.855 14.81 15.97 15.60 16.06 16.03 15.42 15.53: 16.12

 

Table A.1 (cont’d).

181

 

 

11.1 D

frame 2448000+ v49 v50 v51 v52 v53 V54 v65 v66
3513 802.863 14.83 16.03 15.58 16.10 16.01 15.43 15.68 16.07
3514 831.774 15.10 16.07 15.85 16.07 16.01 15.83 15.79: 15.72
3515 831.786 15.09 16.11 15.70 16.11 15.93 - 15.80 15.71
3520 831.828 15.13 - 15.71 16.04 16.00 15.94 15.91: 15.68
3521 831.837 15.14 16.25 15.66 16.04 16.02 15.88 15.87 -
3522 831.846 15.17 — — 16.04 16.00 — 15.68 15.71
3526 833.713 15.04 15.52 16.01 15.39 15.68 15.64 15.53 15.67
3527 835.725 15.09 16.20 15.87 16.13 15.48 15.66 15.46 15.89
3528 835.733 15.09 16.13 15.96 16.15 15.49 15.80 15.40 15.90
3529 835.741 15.15 16.11 15.95 16.09 15.50 — 15.45 15.91
3533 835.774 15.13 15.92 15.71 16.10 15.55 15.92 15.45 16.02
3534 835.783 15.16 15.77 15.73 16.09 15.60 15.86 15.35 16.03
3535 835.791 15.18 15.69 15.61 16.03 15.59 15.83 15.47: 15.97
3539 835.824 15.18 15.53 15.65 16.04 15.67 15.87 15.46 16.12
3540 835.831 15.19 15.54 15.63 16.04 15.71 15.87 15.56: . 16.09
3541 835.840 15.21 15.51 15.72 16.01 15.79 15.73 15.34 16.09
3545 836.712 15.26 15.58 15.87 15.86 15.91 — 15.79 15.72
3546 836.720 15.24 15.56 15.82 15.89 15.93 15.90 15.49: 15.75
3547 836.727 15.25 15.57 15.82 15.88 15.90 15.81 15.71 15.68
3551 836.768 15.31 15.77 - 15.93 15.94 — 15.85: 15.70
3552 836.776 15.29 15.94 16.01 15.99 - 15.74 15.60 -
3553 836.784 15.24 15.83 15.99 16.05 15.91 15.71 15.77 15.65
3554 839.694 15.12 15.55 15.86 16.07 15.98 15.70 15.74: 15.98
3555 839.702 15.13 15.61 15.74 16.05 15.93 15.63 15.82 15.97
3556 839.760 15.15 15.80 15.62 16.10 15.83 — 15.85 15.73
3560 839.793 15.22 15.85 15.58 16.14 15.77 15.77 15.78 -
3561 839.801 15.20 - 15.64 16.08 15.75 15.90 15.81: 15.73
3562 840.681 15.25 15.94 15.70 15.66 15.50 15.85 15.72 15.88
3563 840.696 15.26 15.94 - 15.73 15.54 15.90 15.57 15.98
3564 840.704 15.24 15.90 15.77 15.79 15.52 15.80 15.55 16.00
3568 854.648 15.01 15.76 15.93 16.04 15.92 15.85 15.68 15.72
3569 854.657 15.00 15.75 16.08 16.04 15.84 16.03 15.47 15.76
3573 857.623 15.27 15.68 - - 15.71 15.65 15.88 15.68
3574 857.630 15.24 15.78 . — 16.22 15.71 — 15.76: 15.68
3575 857.638 15.25 15.83 15.59 16.24 15.66 — 15.89 15.68
3576 857.646 15.22 15.86 15.65 16.17 15.74 — 15.84: 15.71
3577 857.654 15.23 15.83 15.63 16.20 15.74 15.62 15.76: 15.71
3578 857.662 15.24 15.88 15.57 16.18 15.70 - 15.67: 15.71
3579 857.678 15.24 15.91 15.61 16.13 15.71 - 15.72: 15.71
3580 857.686 15.27 15.91 15.75 16.14 15.74 15.76 15.90: 15.76
3581 857.694 15.25 15.93 15.71 16.10 15.77 15.68 15.79: 15.76
3582 857.703 15.27 16.03 15.66 16.07 15.77 15.71 15.92: 15.80
3583 857.719 15.26 - 15.70 16.03 15.71 15.68 15.92: 15.89
3584 857.735 15.28 16.09 15.69 15.95 15.73 15.82 15.98: 15.87
3585 857.744 15.27 — 15.84 15.95 15.72 15.90 15.83: 15.84

 

Table A.1 (cont’d).

182

 

 

HJ D

frame 2448000+ v49 v50 v51 V52 v53 V54 v65 v66
4551 867.607 15.22 16.21 15.71 15.48 15.68 — 15.85 15.85
4552 867.616 15.21 16.15 15.77 15.34 15.66 15.59 15.73 16.00
4553 867.623 15.12 16.10 15.83 15.24 15.69 15.59 15.83 16.00
4560 869.672 14.84 16.16 15.82 16.12 15.51 15.55 15.65 15.92
4561 888.568 15.34 15.59 15.45 15.94 15.91 15.91 15.87: 16.10
4562 888.576 15.31 15.56 15.49 15.93 15.94 15.93 15.63 16.10
4563 888.584 15.26 15.57 15.57 15.97 15.94 15.91 15.77 16.12
4564 888.600 15.04 15.60 15.48 15.99 15.91 15.79 15.85: 16.07
4565 888.608 14.89 15.73 15.48 16.02 15.88 — 15.81: 16.13
4566 888.616 14.81 15.64 15.60 16.01 15.89 15.92 15.77 16.10
4567 888.623 14.72 15.74 15.53 16.04 15.84 15.81 15.83: 16.02
4568 888.640 14.63 15.78 15.68 16.09 15.82 15.88 15.68 15.88
4569 888.650 14.66 15.81 15.68 16.08 15.82 15.92 15.72: 15.86
4570 888.659 14.70 15.79 15.75 16.09 15.73 15.88 15.74 15.74
4571 888.667 14.75 15.76 15.63 16.10 15.71 — 15.56 -
4572 888.702 14.87 16.12 15.60 16.17 15.72 15.61 15.76 15.68
4589 890.562 15.08 - 15.66 16.14 15.92 - 15.71 15.76
4590 890.570 14.95 16.30 15.66 16.18 15.93 — 15.77 15.73
4591 890.578 14.86 16.25 15.61 16.25 15.94 15.88 15.78 15.69
4592 890.594 14.69 16.17 15.62 16.28 15.97 — 15.72 15.69
4593 890.603 14.67 16.11 15.71 16.21 15.98 - 15.68 15.65
4594 890.611 14.67 16.02 15.56 16.13 15.93 15.84 15.76 15.64
4595 890.618 14.68 15.96 15.65 15.83 15.99 16.02 15.81 15.64
4596 890.626 14.71 15.85 15.72 15.60 15.96 15.91 15.81 15.65
5522 896.542 14.79 16.18 15.51 15.83 15.73 15.77 15.89 16.09
5523 896.550 14.83 - 15.64 15.86 15.74 15.99 15.60: 16.04
5524 897.530 15.28 15.62 15.98 15.71 15.69 - 15.39 15.78

 

183

Table A.1 (cont’d).

 

 

 

HJ D
frame 2448000+ V67 v74 v97 v99 v113
1501 446.837 15.87: 15.77 16.01: 15.86 15.56
1502 446.845 15.98: — 15.97: 15.88 15.67
1533 452.771 15.94: — 16.03 15.90 15.65
1534 452.780 15.78: — 15.98 15.92 15.66
1535 452.822 15.74: — 16.07: 15.74 15.59
1536 452.829 15.99 - 16.03 15.72 15.60
1537 452.838 15.96 - 16.12 15.78 15.64
1508 453.772 15.93: - 16.05: 15.75 15.60
1509 453.781 16.00: — 16.03 15.74 15.64
1510 453.789 15.77: 15.89 15.92: 15.83 15.66
1511 453.830 15.43 15.43 15.76: 15.87 -
1512 453.838 15.64: 15.49: 15.69 15.80 15.70
1513 453.846 15.46 15.39 15.54 15.81 -
1520 454.750 15.91: 15.42 15.82 15.89 15.78
1522 454.769 16.06 15.65 15.76 15.88 15.68
1523 454.817 — 15.78: 15.81 15.94 15.58
1525 454.833 16.15: 15.94 15.92 15.82 15.62
1559 474.726 16.26 - 15.92: 15.91 15.59
1563 474.763 15.95: - 15.59 — —
1565 474.784 - - 15.47 15.84 15.52
1569 474.820 16.24: 15.69 15.60 15.86 15.52
1571 474.837 16.01 15.60 15.78 15.81 15.50
1572 475.683 15.70 - 15.96 15.85 15.60
1573 475.691 15.58: - 16.09: — 15.68
1574 475.699 15.97: 15.88: 16.00 15.88 15.65
1578 475.733 15.91 15.47 16.01 15.92 15.68
1579 475.741 15.89 15.49 16.25: 15.87 15.66
1580 475.750 16.02: 15.49 16.08: - -
1584 479.657 - 15.65 15.36 15.71 15.57
1585 479.665 16.13 15.74 15.50 15.71 15.62
1586 479.673 - 15.77 — 15.74 15.58
1590 479.707 15.98: 15.87 15.51: 15.81 15.54
1591 479.715 16.03: 15.96 15.57 15.81 15.58
1592 479.724 - 16.01: 15.65 15.84 15.57
1599 480.687 - — 16.28: - —
2501 480.696 15.94: - 16.27: 15.83 15.81
2502 480.704 15.81: — 16.38: — 15.85
2506 480.746 16.10: — 16.19 15.72 15.78
2507 480.754 16.30: 15.76 16.40: 15.71 15.73
2508 480.763 - 15.51 16.20: 15.67 15.67
2509 481.638 - 15.64 16.08: 15.75 15.69
2511 481.655 - 15.71 15.95: 15.77 15.70
2515 481.691 - 15.48 15.57 15.78 15.64
2516 481.702 15.97: 15.51 15.73: 15.84 15.64
2517 481.710 16.02: 15.73: — 15.82 15.62

 

184

Table A.1 (cont’d).

 

 

HJ D

frame 2448000+ v67 v74 v97 v99 v113
2521 481.743 16.32: - 15.61 15.94 15.62
2522 481.751 16.12' 15.80 15.47 15.93 15.63
2523 481.760 15.91 15.79 15.54 15.91 15.60
2530 537.523 - — 15.74: 15.72 15.84
2531 537.532 16.45: 16.11 15.64: 15.76 15.85
2532 537.540 16.18: — 15.57 15.82 15.85
2534 546.573 15.92: — 15.65: 15.91 15.72
2535 546.581 15.99: — 15.63: 15.96 15.70
2536 546.615 16.17: — 15.82 - 15.69
2538 546.630 16.18: — 15.67 15.97 15.70
2542 547.527 16.20: 16.19 15.94: 15.88 15.59
2543 547.536 — — 16.00: 15.89 15.63
2544 547.543 16.24: — 16.21: 15.91 15.69
2545 547.592 16.16: — 16.34: 15.77 15.70
2549 568.542 16.09: — 16.07 15.86 15.66
2550 568.558 16.25: — 16.06: 15.81 15.67
2551 568.573 — — 16.13: 15.78 15.67
2552 568.623 16.21 — 16.30: 15.78 15.57
2553 568.634 — — 16.25: 15.67 15.61
2565 569.627 — - — - -
2567 570.489 - 15.60 15.88: 15.94 15.81
2568 570.497 — 15.57 15.81: 15.95 15.76
2569 570.531 - — 16.07 15.99 15.67
2573 570.552 — 15.84 16.11: 15.91 15.68
2574 570.559 16.16 15.87 16.06: 15.83 15.68
2578 570.602 - — 16.21: 15.68 15.67
2579 570.609 16.39: — 15.92: 15.68 15.70
2580 570.618 — - 16.04: 15.72 15.65
2585 574.560 - 16.08: 15.96: - 15.74
2586 574.569 16.12 16.03: 15.83 15.82 15.72
2587 574.576 16.16 15.93: 15.86 15.90 15.72
2597 601.463 — — 15.92: — 15.74
2591 601.476 — 16.12 15.53 15.69 15.66
2592 601.491 15.86: - 15.57: 15.74 15.63
2594 601.507 — — - - —
2595 601.517 - - 15.50: — 15.57
2598 602.471 16.00: 15.60 15.84 15.91 15.78
2599 602.479 15.87: 15.70: 15.87 - 15.80
3501 602.487 - 15.73: 15.96: 15.96 15.79
3502 602.495 16.03: 15.70: 15.99: 15.97 -
3505 802.799 - 15.90 15.52 15.87 15.64
3506 802.807 16.12 15.78 15.61: 15.89 15.63
3507 802.815 - 15.68 15.67 15.87 15.65
3511 802.848 - 15.49 15.67 15.83 15.61
3512 802.855 16.24: 15.55 15.70 15.83 15.62

 

185

Table A.1 (cont’d).

 

 

11.1 D
frame 2448000+ v67 v74 v97 v99 V113
3513 802.863 16.37: 15.56 15.69 15.84 15.62
3514 831.774 15.44 16.27: 16.05 15.72 15.64
3515 831.786 15.60 16.37 15.81 15.71 15.65
3520 831.828 15.69 15.78 16.06 15.66 15.74
3521 831.837 15.72 15.71 16.04 15.70 15.74
3522 831.846 15.73 15.70 16.06 15.71 15.76
3526 833.713 16.07 15.91 15.94 15.99 15.59
3527 835.725 15.84 , 15.65 15.83 15.98 15.60
3528 835.733 15.88 15.77 15.92 15.94 15.59
3529 835.741 15.90 15.84 15.85 15.98 15.58
3533 835.774 15.81 15.96 15.63: 15.81 15.61
3534 835.783 15.76 15.94 15.93 15.80 15.60
3535 835.791 15.85 15.98 15.90 15.77 15.58
3539 835.824 15.81 16.15 15.86 15.67 15.61
3540 835.831 15.77 16.26 15.97 15.65 15.61
3541 835.840 15.94 16.13: 16.17 15.63 15.61
3545 836.712 15.64 16.22 15.77: 15.73 15.73
3546 836.720 15.96: 16.27 16.05 15.77 15.74
3547 836.727 15.71 16.23: 15.98 15.75 15.73
3551 836.768 15.84: 16.30: 15.96 15.81 15.77
3552 836.776 15.90 16.28: 15.94: 15.89 15.77
3553 836.784 15.98 16.30 15.79 15.86 15.77
3554 839.694 16.18 16.23 15.48 15.77 15.76
3555 839.702 16.44: 16.25 15.49 15.78 15.74
3556 839.760 16.17 16.28 15.62 15.80 15.67
3560 839.793 16.24 16.09 15.79 15.89 15.60
3561 839.801 15.91 16.01 15.78 15.90 15.61
3562 840.681 15.79 16.16 15.89 15.94 15.65
3563 840.696 15.95 16.07 16.09 15.92 15.68
3564 840.704 15.75 15.83 16.03 15.94 15.69
3568 854.648 16.03 15.74 15.94 15.95 15.81
3569 854.657 16.12 15.60 15.98 15.93 15.77
3573 857.623 15.84 15.67 16.02: 15.83 15.66
3574 857.630 16.03: 15.81 16.06: 15.75 15.71
3575 857.638 16.05: 15.74 16.03: 15.76 15.64
3576 857.646 15.83 15.76 16.06 15.66 15.64
3577 857.654 15.78 15.85: 15.97: 15.65 15.66
3578 857.662 15.90 15.89 15.88 15.62 15.62
3579 857.678 15.99: 15.92 15.77 15.63 15.60
3580 857.686 16.02: 16.13 15.72 15.61 15.63
3581 857.694 15.73 16.06 15.53 15.64 15.65
3582 857.703 15.87 16.05 15.61 15.73 15.63
3583 857.719 15.79 16.28: 15.53 15.75 15.62
3584 857.735 15.91 16.22: 15.51 15.81 15.60
3585 857.744 15.90 16.31: 15.59 15.86 15.63

 

186

Table A.1 (cont’d).

 

HJ D
frame 2448000+ v67 v74 V97 v99 V113

 

4551 867.607 16.15 16.17 15.60 15.72 15.76
4552 867.616 16.01 16.21: 15.63 15.71 15.76
4553 867.623 16.05 16.17 15.64 15.76 15.76
4560 869.672 16.17 16.23 15.53 15.88 15.77
4561 888.568 16.07 16.35: 15.74 15.87 15.63
4562 888.576 16.14 16.36 15.76 15.87 15.65
4563 888.584 16.13 16.46: 15.74 15.81 15.62
4564 888.600 16.16 16.50 15.75 15.82 15.62
4565 888.608 16.10 - 15.77 15.80 15.66
4566 888.616 16.20 16.29 15.81 15.82 15.65
4567 888.623 16.28 16.27: 15.69 15.79 15.68
4568 888.640 16.28: 16.15 15.74 15.82 15.67
4569 888.650 16.23 15.89 15.84 15.81 15.71
4570 888.659 16.22 15.87 15.78 15.84 15.71
4571 888.667 16.13: 15.73 15.87 15.88 15.70
4572 888.702 - 15.83 15.99 15.92 15.74
4589 890.562 16.02 16.14 15.55 15.70 15.64
4590 890.570 15.85 16.29 15.56 15.69 15.67
4591 890.578 15.85 16.26 15.62 15.72 15.65
4592 890.594 15.98 16.04 15.60 15.70 —

4593 890.603 15.96 16.20 15.65 15.73 15.65
4594 890.611 16.04 - 15.61 15.75 15.63
4595 890.618 15.98 16.24 15.60 15.75 15.64
4596 890.626 15.95 16.36 15.62 15.77 15.65
5522 896.542 15.69 16.36: 15.82 15.86 15.79
5523 896.550 15.78 16.37: 15.88 15.85 15.80
5524 897.530 16.00 15.97 15.59 15.74 15.67

 

 

187

Table A.2 MSU R Photometry of M15 Variables

 

 

 

11.1 D
frame 2448000+ v1 v2 v3 v4 v5 v6 v7 VB
1503 446.857 14.97 15.17 15.35 15.44 - — 15.24: -
1504 446.865 14.95 15.15 15.36 15.48 15.31 — — -
1506 449.751 14.79 15.32 15.63 15.60 15.70 15.43: 15.20: —
1507 449.761 14.85 15.36 15.68 15.59 15.69 15.33 15.22: 15.30
1538 452.738 14.92 15.08 15.43 15.88 15.55 15.74: — —
1539 452.747 15.01 15.03 15.38 15.79 15.48 15.65: 15.13: —
1540 452.754 14.94 15.00 15.41 15.79 15.48 15.79: - -
1541 452.789 — 15.01 15.47 15.53 15.53 15.72: 15.72: -
1542 452.797 14.92 15.01 15.48 15.45 15.55 16.14: — -
1544 452.813 - 14.98 15.52 15.43 15.64 15.65: - —
1514 453.755 14.75 15.24 15.75 15.47 15.38 15.49: 15.09: -
1515 453.763 14.74 15.31 15.73 15.41 15.33 15.33: 15.22: 15.48
1516 453.798 14.76 15.28 15.65 15.45 15.29 15.19: - 15.54
1517 453.806 14.74 15.27 15.56 15.53 15.33 15.06: - 15.63
1526 454.711 14.21 15.30 15.32 15.42 15.58 15.75: 15.46: —
1527 454.728 14.23 15.38 15.49 15.41 15.66 15.61 15.79: 15.50
1528 454.735 14.20 15.35 15.49 15.46 15.67 15.56: 15.61: 15.30
1529 454.777 14.21 15.10 15.59 15.59 15.71 15.64: 15.47: 15.03
1530 454.793 14.16 15.09 15.63 15.66 15.69 15.61: 15.29: 15.08
1531 454.809 14.25 15.03 15.66 15.67 15.70 15.73: - 15.18
1552 473.716 — - 15.35 15.90 15.46 15.71: - —
1555 473.768 - 15.36 15.47 15.80 15.31 15.24: 15.63: —
1562 474.754 14.22 15.09 15.79 15.44 15.62 — 15.23: 15.69
1566 474.793 14.21 15.10 15.60 15.44 15.67 - 15.33: 15.09
1568 474.811 14.19 15.13 15.54 15.47 0.07 — 15.15: 15.02
1575 475.707 - - 15.43 15.44 15.29 16.05: — -
1576 475.716 — 15.37 15.49 15.40 15.32 15.74: - 15.60
1577 475.724 14.87 15.35 15.51 15.41 15.35 - 15.44: 15.48
1581 475.759 14.88 15.31 15.51 15.53 15.41 15.36: 15.12: -
1582 475.766 14.83 15.31 15.55 15.52 15.40 15.26: 15.30: -
1583 475.775 14.91 15.33 15.58 15.56 15.41 15.19: 15.41: 15.51
1587 479.682 14.74 15.18 15.59 15.91 15.56 16.09: - 15.60
1588 479.690 14.77 15.18 15.59 15.86 15.60 15.93: 15.57: -
1589 479.698 — - 15.65 15.88 15.63 — - -
1595 479.754 14.84 - 15.73 15.57 15.68 15.13: — -
1597 480.668 14.17 15.31 15.36 15.82 15.34 15.71: 15.19: 15.06
2503 480.714 14.21 15.33 15.37 15.43 15.37 15.74: 15.37: 15.15
2504 480.723 14.24 15.34 15.35 15.44 15.34 - - 15.21
2505 480.738 14.31 15.34 15.39 15.41 15.35 - - 15.29
2512 481.664 14.79 15.11 15.68 15.41 15.64 15.89: 14.93: -
2514 481.682 14.64 15.16 — 15.39 15.69 - 15.29: 15.60
2518 481.718 14.58 15.20 15.70 15.50 15.71 15.67: 15.34: 15.65
2520 481.735 14.57 15.16 15.77 15.56 15.65 15.40: 15.25: —
2525 481.777 14.48 15.25 15.66 15.68 15.47 15.14: 15.42: —
2540 546.597 14.21 15.01 15.71 15.45 15.72 15.53: — -

 

Table A.2 (cont’d).

188

 

 

11.1 D
frame 2448000+ v1 v2 v3 v4 v5 V6 v7 VS
2546 547.552 — 15.28 - 15.44 -— 15.70: 15.36: —
2547 547.560 - 15.31 15.27 15.44 15.43 15.86: — -
2548 547.568 - 15.29 - 15.44 — 15.70: 15.44: —
2557 568.501 14.37 15.02 15.46 15.57 15.69 15.42: 15.59: 15.06
2558 568.510 14.37 15.04 15.42 15.48 15.68 - 15.52 14.90
2559 568.517 14.42 15.03 15.41 15.44 15.68 15.48: 15.34: 14.93
2554 568.582 14.56 15.13 15.38 15.47 15.66 15.59: -- 15.08
2555 568.599 14.56 15.17 15.39 15.57 15.55 15.83: — 15.22
2556 568.615 14.63 15.17 15.44 15.62 15.50 15.77: 15.33: 15.22
2560 569.578 14.29 15.30 15.74 15.73 15.60 -- 15.14: -
2562 569.594 14.22 — 15.67 15.76 - — 15.17: —
2570 570.507 — 14.97 15.31 15.67 15.59 15.42: 15.64: 15.17
2571 570.514 14.82 14.98 15.27 15.68 15.59 15.37: 15.40: —
2575 570.568 15.00 15.10 15.37 15.79 15.34 15.51: - 15.33
2576 570.576 — - 15.41 15.76 15.28 - — —
2577 570.591 14.90 15.08 15.43 15.83 15.30 15.58 15.35: 15.29
2582 574.536 — - 15.63 15.47 - 15.49: — -—
2583 574.544 14.67 - 15.63 15.55 15.49 15.46: - 15.53
2584 574.552 — — 15.65 - 15.52 - — —
3508 802.823 14.27 - 15.75 15.47 15.60 15.43: 15.44: —
3509 802.831 - - 15.72 15.51 15.60 15.32 - -
3510 802.839 — - 15.75 15.51 15.63 15.36: - —
3517 831.803 14.71 15.38 15.47 15.83 15.47 15.99: 15.25: -
3518 831.810 14.65 15.33 15.47 15.87 15.41 15.75: 15.39: 15.55
3519 831.819 - — 15.52 15.90 15.40 15.75: — -
3523 831.854 14.73 15.02 15.54 15.90 15.32 - 15.60: -
3524 831.862 14.73 15.00 15.56 15.91 15.30 16.06: 15.44: «-
3525 831.869 14.77 14.96 15.59 15.88 15.27 15.87: 15.81: 15.64
3530 835.749 14.24 - 15.60 15.48 15.37 — 15.20: -
3531 835.758 14.24 15.41 15.67 15.54 15.36 15.85: 15.24: —
3532 835.766 - — 15.64 15.56 15.38 — 15.65 -
3548 836.743 14.86 — 15.45 15.65 15.67 15.21: -— 15.17
3549 836.751 14.88 - 15.44 15.67 15.68 15.22: 15.29: 15.18
3550 836.758 14.88 15.06 15.41 15.71 15.67 15.25: - -
3557 839.769 14.57 15.33 15.77 15.44 15.70 15.96: 15.15 -
3558 839.777 - 15.31 15.76 15.44 15.70 15.68: -- —
3559 839.785 14.57 — 15.79 15.47 15.68 16.07: 15.37: -
3565 840.713 - - 15.41 15.43 15.31 15.52: 15.21: -
3566 840.721 14.80 15.22 15.41 15.48 15.29 15.60: 15.43 15.35
3567 840.729 14.90 15.16 15.44 15.41 15.34 15.24: 14.99: 15.39
4554 869.589 14.89 15.02 15.56 15.42 15.44 15.66: 15.47: -
4555 869.606 14.95 15.04 15.64 15.43 15.43 15.62: 15.44: 15.61
4556 869.613 14.93 15.08 15.63 15.47 15.44 - - -
4557 869.640 14.91 15.11 15.71 15.58 15.53 - 15.46: -
4558 869.648 14.97 15.14 15.73 15.59 15.54 15.71: 15.48: 15.17

 

Table A.2 (cont’d).

189

 

 

HJ D
frame 2448000+ v1 v2 V3 v4 V5 v6 v7 V8
4559 869.656 14.96 15.15 15.71 15.62 15.55 15.80: — 15.08
4573 889.569 14.80 15.16 — 15.86 15.40 — - 15.70
4574 889.585 14.87 15.20 — 15.82 15.43 — — -
4575 889.593 14.88 15.20 15.49 15.76 15.39 15.68: 15.37: -
4576 889.601 14.85 15.21 15.48 15.72 15.45 - - -
4577 889.609 14.89 15.28 15.45 15.63 15.48 15.73: - —
4578 889.617 — 15.29 15.43 15.55 15.51 15.80: 15.21 -
4579 889.625 14.92 15.27 15.42 15.46 15.52 - - 15.77
4580 889.633 — 15.28 15.42 15.41 15.51 - 15.05: 15.72
4581 889.641 — 15.26 15.42 15.42 15.53 — 15.14: -
4582 889.649 14.91 15.29 15.40 15.39 15.58 16.03: 15.13: -
4583 889.657 14.84 15.27 15.38 15.42 15.60 - 15.05: 15.35
4584 889.666 14.89 15.29 15.40 15.43 15.60 15.79: 15.14: 15.31
4585 889.682 14.91 15.25 15.42 15.44 15.66 15.91: - 15.20
4586 889.689 14.90 15.34 15.43 15.49 15.65 15.89: 15.11: 15.06
4587 889.697 14.88 15.33 15.42 15.51 15.66 15.81: 15.07: 15.04
4588 889.705 — 15.33 15.43 15.53 15.68 16.01: — -
5505 891.560 14.42 15.06 15.37 15.42 15.53 15.55: 15.21: 15.57
5506 891.568 14.39 15.12 — 15.45 15.53 15.61: — -
5507 891.577 14.38 15.11 — 15.53 — — 15.26: —
5508 891.593 14.32 15.13 15.37 15.59 15.62 15.58: 15.34: 15.38
5509 891.601 14.35 15.16 15.40 15.58 15.62 15.58: — 15.30
5525 897.539 - - — 15.53 15.35 15.68: 15.23 15.20
5526 897.546 — 14.95 - — 15.35 — — -
5527 897.562 14.18 — 15.55 15.62 15.34 - - 15.28
5528 897.571 14.20 - 15.59 15.64 15.33 15.65: — —
5529 897.578 - — 15.59 15.68 15.33 15.40: — —
5530 897.594 14.12 — 15.67 15.70 15.35 15.66: 15.52: —
5531 897.602 14.19 - 15.71 15.73 15.34 15.69: - 15.43
5532 897.610 — - 15.71 15.75 15.38 - - -
5533 897.618 - — 15.71 15.77 15.40 15.77: — —
5534 897.626 — - 15.72 15.78 15.40 15.65: — —
5535 897.634 - — 15.75 15.82 15.38 15.78: — 15.46
5536 897.642 14.28 15.13 15.77 15.82 15.42 15.74: 15.28: -
5537 897.650 14.29 - 15.78 15.88 15.45 15.72: 15.46: —
5538 897.658 14.22 - 15.81 15.88 15.47 15.83: 15.38: —
5539 897.666 14.24 — 15.81 15.90 15.47 15.87: — —
5540 897.674 14.30 — 15.82 15.91 15.47 - 15.42: 15.54
5541 897.682 14.25 - 15.79 15.96 15.52 15.98: 15.25: 15.48

 

190

a

Table A.2 (cont’d).

 

 

 

HJD
frame 2448000+ v9 v10 v11 v13 v14 v15 v17 v18
1503 446.857 — - - 15.39 15.81 15.83 15.80 -
1504 446.865 — - 15.55 — - 15.81 15.77 -
1506 449.751 15.55 15.46 15.48 15.04 15.46 15.78 15.37 15.46
1507 449.761 15.50 15.43 15.47 15.02 15.44 15.72 15.41 15.44
1538 452.738 15.69 15.47 15.40 15.38 15.54 15.83 15.42 15.45
1539 452.747 15.59 15.49 15.34 15.43 15.54 15.80 15.39 15.51
1540 452.754 15.62 15.48 15.36 15.56 15.49 15.83 15.49 15.56
1541 452.789 15.61 15.37 15.45 15.49 15.47 15.82 15.48 15.65
1542 452.797 15.60 15.44 — 15.57 15.46 15.84 15.51 15.75
1544 452.813 15.59 15.49 — 15.45 15.45 15.83 15.55 15.69
1514 453.755 15.14 15.71 15.36 15.22 15.74 15.61 15.68 15.36
1515 453.763 15.14 15.77 15.35 15.13 15.72 15.65 15.70 15.36
1516 453.798 15.22 15.77 15.36 15.07 15.77 15.69 15.76 15.38
1517 453.806 15.23 15.77 15.34 15.16 15.83 15.71 15.76 15.45
1526 454.711 15.48 15.52 15.90 -— 15.46 14.90 - 15.83
1527 454.728 15.55 15.51 15.85 15.79 15.43 14.97 15.88 15.76
1528 454.735 15.50 15.40 15.74 15.77 15.43 15.03 15.83 15.83
1529 454.777 15.51 15.43 15.47 15.79 15.50 15.29 15.66 15.71
1530 454.793 15.55 15.49 15.36 15.68 15.53 15.27 15.56 15.62
1531 454.809 15.53 15.49 15.35 15.67 15.55 15.33 15.45 15.54
1552 473.716 15.09 15.44 15.35 15.80 15.74 15.84 15.60 15.58
1555 473.768 15.24 15.53 15.44 15.74 15.46 15.83 15.63 15.72
1562 474.754 15.55 15.49 — 15.61 15.67 15.53 15.78 15.43
1566 474.793 15.57 15.37 15.42 15.75 15.76 15.62 15.72 15.45
1568 474.811 15.57 15.41 15.42 15.77 0.08 15.65 15.90 15.57
1575 475.707 15.62 15.60 15.56 15.32 15.41 14.92 15.74 15.78
1576 475.716 15.74 15.54 15.51 15.34 15.41 14.89 15.72 15.73
1577 475.724 - 15.59 - 15.33 15.41 14.90 15.72 15.73
1581 475.759 15.76 15.66 15.38 15.43 15.42 15.16 15.60 15.54
1582 475.766 15.70 15.72 15.31 15.45 15.43 15.18 15.59 15.52
1583 475.775 - 15.70 15.31 15.49 15.43 15.20 15.55 15.49
1587 479.682 15.35 15.86 15.74 15.19 15.73 15.82 15.24 15.75
1588 479.690 15.44 15.79 - 15.19 15.76 15.87 15.27 15.76
1589 479.698 15.40 15.84 — 15.20 15.70 15.86 15.32 «-
1595 479.754 15.49 15.73 - 15.37 15.75 15.62 15.35 -
1597 480.668 15.63 15.47 15.56 15.76 15.53 15.78 15.60 15.51
2503 480.714 15.73 15.48 15.68 15.85 15.51 15.91 15.73 15.55
2504 480.723 15.61 15.64 15.78 15.79 15.46 15.88 15.60 15.61
2505 480.738 15.67 15.61 15.77 15.88 15.50 15.89 15.63 15.60
2512 481.664 15.20 15.77 15.56 15.71 15.76 15.38 15.76 15.44
2514 481.682 15.21 15.73 15.57 15.72 15.76 15.50 15.73 15.48
2518 481.718 15.24 15.65 15.64 15.78 15.77 15.60 15.75 15.37
2520 481.735 15.29 15.49 — 15.73 15.76 15.50 15.77 15.40
2525 481.777 15.35 15.38 15.70 15.71 15.55 15.61 15.80 15.48
2540 546.597 15.71 15.78 — 15.73 15.87 15.76 15.43 15.73

 

191

Table A.2 (cont’d).

 

 

11.1 D
frame 2448000+ v9 V10 v11 V13 v14 v15 v17 v18
2546 547.552 15.28 15.56 15.51 15.30 15.41 15.33 15.50 15.42
2547 547.560 15.29 15.58 15.54 15.32 15.45 15.38 15.53 15.38
2548 547.568 15.27 - 15.51 15.32 15.47 15.41 15.46 15.40
2557 568.501 15.53 15.73 15.51 15.81 15.53 15.24 15.37 15.37
2558 568.510 15.60 15.67 15.40 15.76 15.54 15.26 15.43 15.31
2559 568.517 15.53 15.79 15.54 15.81 15.49 15.28 15.40 15.43
2554 568.582 15.57 15.78 15.65 15.85 15.44 15.44 15.55 15.50
2555 568.599 15.62 15.82 15.67 15.76 15.47 15.48 15.62 15.66
2556 568.615 15.57 15.73 15.81 15.74 15.56 15.52 15.60 15.64
2560 569.578 15.11 15.59 - 15.69 15.90 15.82 15.75 15.39
2562 569.594 15.02 15.62 15.61 15.66 15.83 15.69 15.73 15.38
2570 570.507 15.36 15.85 15.43 15.09 15.53 15.74 15.78 15.72
2571 570.514 - 15.83 15.45 15.17 15.51 15.74 15.78 15.77
2575 570.568 15.44 15.70 15.56 15.30 15.61 15.73 15.57 15.79
2576 570.576 15.37 15.62 — 15.35 15.63 15.70 15.47 15.80
2577 570.591 15.45 15.56 15.56 15.40 15.65 15.71 15.40 15.82
2582 574.536 15.23 — - 15.13 — 15.58 15.51 -
2583 574.544 15.32 15.44 15.78 15.19 15.85 15.64 15.56 15.73
2584 574.552 -— 15.47 — 15.19 15.79 15.57 - -
3508 802.823 15.15 15.54 15.75 15.25 15.53 15.81 15.60 15.51
3509 802.831 15.08 15.49 15.61 15.31 15.54 15.80 15.61 15.51
3510 802.839 15.16 15.44 15.57 15.29 15.59 15.80 15.61 15.54
3517 831.803 15.56 15.41 15.42 15.73 15.44 15.52 15.59 15.39
3518 831.810 15.62 15.39 15.57 15.70 15.46 15.53 15.54 15.37
‘ 3519 831.819 15.58 15.41 15.58 15.75 15.42 15.54 15.53 15.47
3523 831.854 15.52 15.39 15.62 15.74 15.53 15.66 15.47 15.43
3524 831.862 15.58 15.39 15.65 15.75 15.55 15.67 15.43 15.50
3525 831.869 15.57 15.42 15.73 15.75 15.56 15.67 15.52 15.43
3530 835.749 15.19 15.45 15.76 15.57 15.71 14.93 15.55 15.75
3531 835.758 15.21 15.40 15.73 15.59 15.73 15.05 15.62 15.71
3532 835.766 15.25 15.41 - 15.57 15.77 15.07 15.55 15.67
3548 836.743 15.51 15.79 — 15.23 15.40 15.79 15.61 15.70
3549 836.751 15.57 15.79 15.86 15.29 15.39 15.80 15.66 15.74
3550 ' 836.758 15.55 15.80 15.79 15.32 15.42 15.83 15.64 15.76
3557 839.769 15.62 15.72 15.63 15.61 15.40 15.25 15.78 15.79
3558 839.777 15.63 15.77 15.79 15.54 15.39 15.12 15.75 15.80
3559 839.785 15.66 15.86 15.69 15.59 15.38 14.97 15.77 15.78
3565 840.713 15.11 15.38 15.44 15.06 15.70 15.81 15.68 15.52
3566 840.721 15.24 15.42 15.58 15.17 15.74 15.83 15.68 15.50
3567 840.729 15.14 15.45 15.56 15.13 15.76 15.80 15.69 15.54
4554 869.589 15.44 15.81 15.59 15.43 15.46 15.06 15.48 15.68
4555 869.606 15.50 15.75 15.66 15.48 15.43 15.22 15.47 15.49
4556 869.613 15.49 15.73 15.71 15.52 15.44 15.23 15.48 15.54
4557 869.640 15.49 15.59 15.79 15.55 15.49 15.31 15.54 15.40
4558 869.648 15.53 15.54 15.80 15.56 15.50 15.31 15.51 15.38

 

 

192

Table A.2 (cont’d).

 

HJD
frame 2448000+ v9 v10 v11 v13 V14 v15 v17 v18

 

4559 869.656 15.56 15.52 15.82 15.58 15.49 15.33 15.52 15.38
4573 889.569 — 15.67 15.81 15.09 15.61 15.54 15.65 -

4574 889.585 15.44 15.78 15.81 15.10 15.63 15.55 15.67 15.40
4575 889.593 15.45 15.76 15.84 15.16 15.68 15.57 15.70 15.46
4576 889.601 15.45 15.75 - 15.16 15.72 15.57 15.70 15.47
4577 889.609 15.43 - 15.81 15.21 15.69 15.59 15.64 15.52
4578 889.617 15.34 15.76 15.76 15.24 15.73 15.59 15.72 15.49
4579 889.625 15.48 15.74 15.81 15.28 15.74 15.57 15.64 15.52
4580 889.633 15.55 15.76 15.73 15.28 15.75 15.58 15.61 15.58
4581 889.641 15.47 15.78 15.81 15.31 15.76 15.60 15.61 15.59
4582 889.649 15.49 15.74 15.79 15.32 15.73 15.59 15.58 15.59
4583 889.657 15.51 15.79 15.73 15.34 15.78 15.64 15.55 15.60
4584 889.666 15.51 15.80 15.67 15.38 15.78 15.63 15.54 15.65
4585 889.682 15.50 15.77 15.59 15.38 15.79 15.65 15.49 15.67
4586 889.689 15.56 15.77 15.53 15.41 15.77 15.66 15.45 15.68
4587 889.697 15.52 15.77 15.45 15.45 15.78 15.68 15.45 15.74
4588 889.705 15.56 15.74 15.40 15.44 15.78 15.71 15.47 15.78
5505 891.560 15.17 15.82 15.68 15.69 15.81 15.73 15.51 15.74
5506 891.568 15.16 15.84 15.58 15.70 15.78 15.74 15.51 15.75
5507 . 891.577 15.18 15.83 15.65 15.68 15.80 15.73 15.57 15.76
5508 891.593 15.27 - 15.68 15.69 15.77 15.75 15.53 15.74
5509 891.601 15.27 15.82 15.72 15.74 15.81 15.76 15.59 15.75
5525 897.539 15.51 15.47 15.81 15.82 15.51 15.41 15.43 —

5526 897.546 15.46 15.44 15.77 15.81 15.51 15.34 15.48 15.60
5527 897.562 15.52 15.48 15.76 15.73 15.57 15.29 15.45 15.48
5528 897.571 15.53 15.48 15.68 15.63 15.57 15.27 15.47 15.45
5529 897.578 15.50 - 15.59 15.36 15.65 15.27 15.51 -

5530 897.594 15.54 15.51 15.43 15.23 15.61 15.24 15.55 15.38
5531 897.602 15.54 15.52 15.44 15.09 15.62 15.37 15.55 15.39
5532 897.610 15.55 15.50 15.40 15.09 15.65 15.36 15.56 15.37
5533 897.618 15.55 15.55 15.37 15.09 15.67 15.38 15.60 15.33
5534 897.626 15.59 15.55 15.34 15.10 15.68 15.38 15.59 15.37
5535 897.634 15.60 15.59 15.37 15.09 15.70 15.37 15.64 15.40
5536 897.642 15.61 15.61 15.34 15.11 — 15.35 15.64 15.40
5537 897.650 15.57 15.61 15.33 15.16 15.72 15.36 15.65 15.38
5538 897.658 15.60 15.62 15.39 15.21 15.71 15.39 15.69 15.42
5539 897.666 - 15.67 15.41 15.23 15.75 15.40 15.67 15.46
5540 897.674 15.58 15.69 15.42 15.27 15.73 15.43 15.70 15.47
5541 897.682 — 15.70 15.40 15.26 15.72 15.39 15.73 15.44

 

 

193

Table A.2 (cont’d).

 

 

 

11.1 D
frame 2448000+ v19 V20 v22 V23 v24 V25 v29 v30
1503 446.857 15.90 - 15.31 15.62 15.56 15.48 15.74: 15.21
1504 446.865 15.89 — 15.31 — - — — 15.15
1506 449.751 15.88 15.71 15.45 15.53 15.44 15.38 15.97: 15.37
1507 449.761 15.83 — 15.46 15.55 15.32 15.38 - 15.39
1538 452.738 15.31 - 15.51 15.27 — 15.66 15.55: 15.52
1539 452.747 15.11 - 15.51 15.26 15.37 15.67 — 15.60
1540 452.754 15.00 - 15.50 15.30 15.47 15.73 — 15.58
1541 452.789 14.93 16.09: 15.51 15.38 15.50 15.79 — 15.53
1542 452.797 14.95 - 15.53 15.34 15.54 15.85 — 15.48
1544 452.813 15.03 — 15.56 15.38 - 15.80 - —
1514 453.755 15.85 15.40: 15.25 15.61 15.32 15.45 - 15.36
1515 453.763 15.80 15.48: 15.22 15.56 15.33 15.42 15.67 15.33
1516 453.798 15.82 15.47: 14.99 15.61 15.42 15.49 15.80: 15.37
1517 453.806 15.86 15.48: 15.02 15.62 15.43 15.49 15.75 15.37
1526 454.711 15.66 15.83: 15.24 15.45 15.56 15.73 15.41: 15.49
1527 454.728 15.73 15.93: 15.30 15.41 — 15.73 - 15.59
1528 454.735 15.70 15.80: 15.31 15.44 15.60 15.72 15.34: 15.57
1529 454.777 15.78 15.85: 15.38 15.48 15.41 15.79 - 15.56
1530 454.793 15.86 — 15.40 15.49 15.40 15.77 15.48 15.61
1531 454.809 15.81 15.80: 15.44 15.54 15.27 15.77 15.56 15.59
1552 473.716 15.84 — 15.54 15.39 — 15.42 15.50: -—
1555 473.768 15.88 — 15.64 15.48 15.38 15.46 — —
1562 474.754 15.63 15.72: 15.14 15.39 15.33 15.66 14.91 15.37
1566 474.793 15.73 15.70: 15.22 15.02 15.31 15.48 15.10 15.27
1568 474.811 15.78 - 15.22 15.02 0.07 15.33 15.12: 15.35
1575 475.707 15.09 — 15.47 15.49 15.66 15.44 15.82 15.31
1576 475.716 15.15 - 15.49 15.48 15.54 15.45 15.82 15.34
1577 475.724 15.17 15.94: 15.50 15.51 15.59 15.41 - 15.39
1581 475.759 15.28 - 15.49 15.59 15.57 15.50 — 15.38
1582 475.766 15.34 15.97: 15.52 15.58 15.63 15.48 15.65: 15.40
1583 475.775 15.34 — 15.53 15.56 15.63 15.53 — 15.39
1587 479.682 14.91 15.76: 15.20 15.64 15.44 15.51 15.89: 15.27
1588 479.690 14.95 - 15.03 15.57 15.32 15.53 15.91: 15.30
1589 479.698 14.99 15.63: 15.04 15.58 — 15.44 - -
1595 479.754 15.28 — 15.04 15.63 — 15.53 15.92 -—
1597 480.668 15.89 — 15.27 15.37 15.33 15.78 15.57 15.41
2503 480.714 15.94 - 15.40 15.45 15.20 15.83 15.55: 15.43
2504 480.723 15.87 15.90: 15.43 15.47 15.31 15.80 15.48: 15.54
2505 480.738 15.95 — 15.44 15.49 — 15.80 - 15.57
2512 481.664 15.76 - 15.46 15.64 15.66 15.40 15.04 15.24
2514 481.682 15.82 15.61: 15.57 15.60 - — 15.13: 15.16
2518 481.718 15.80 15.50: 15.64 15.45 15.67 15.48 15.32 15.18
2520 481.735 15.85 15.50: 15.68 15.26 — 15.46 15.39: -
2525 481.777 15.84 15.76: 15.70 15.05 15.31 15.54 15.30: 15.29
2540 546.597 15.27 15.70: — 15.57 15.38 15.89 15.23: 15.32

 

194

Table A.2 (cont’d).

 

 

HJD

frame 2448000+ v19 v20 v22 v23 v24 v25 V29 v30
2546 547.552 15.88 15.75 15.19 15.12 — 15.47 15.71: -
2547 547.560 15.81 15.88: 15.20 15.16 15.34 15.50 15.71: 15.29
2548 547.568 15.83 15.84: 15.23 15.16 - 15.51 15.74: -
2557 568.501 15.41 16.00: - 15.25 15.61 15.73 15.33 15.52
2558 568.510 15.46 16.24: — 15.25 15.60 15.76 15.35: 15.54
2559 568.517 15.44 — — 15.29 15.65 15.76 15.34: 15.48
2554 568.582 15.62 — - 15.33 15.61 15.75 - 15.31
2555 568.599 15.67 - 15.43 15.35 15.58 15.65 - 15.40
2556 568.615 15.67 - 15.48 15.40 15.48 15.42 15.58: 15.31
2560 569.578 15.15 - 15.66 15.63 15.53 15.63 15.14: 15.35
2562 569.594 15.22 15.79: — 15.63 15.63 15.60 15.17: 15.46
2570 570.507 15.86 15.69 - 15.42 15.34 15.75 15.75 15.49
2571 570.514 15.87 15.88: — 15.44 15.32 15.75 15.76: 15.48
2575 570.568 15.93 15.67 - 15.51 15.30 15.80 15.80: 15.30
2576 570.576 15.92 15.77: — 15.49 - 15.78 - 15.34
2577 570.591 16.01 — - 15.50 15.31 15.66 - 15.35
2582 574.536 15.83 15.59: 15.55 15.65 — - - -
2583 574.544 15.78 15.66: 15.55 15.64 15.35 15.78 - 15.56
2584 574.552 - 15.61: 15.59 — — 15.80 15.67: -
3508 802.823 15.81 15.58: 15.58 15.53 — 15.25 15.77: —
3509 802.831 15.82 - 15.62 15.51 15.49 15.20 15.59: 15.48
3510 802.839 15.82 15.32 15.64 15.54 15.56 15.15 - -—
3517 831.803 15.53 16.06: — 15.31 15.57 15.59 14.86: 15.39
3518 831.810 15.52 15.98: — 15.34 15.62 15.61 15.02 15.42
3519 831.819 15.56 15.85: — 15.33 — 15.58 15.01: -
3523 831.854 15.63 — — 15.39 15.51 15.64 15.19: 15.45
3524 831.862 15.64 15.94: - 15.38 15.43 15.64 15.28 15.50
3525 831.869 15.67 15.93: — 15.41 — 15.61 15.24 15.46
3530 835.749 15.38 15.51: 15.45 15.51 15.54 15.51 15.63: 15.24
3531 835.758 15.41 15.44 15.49 15.53 15.51 15.51 - 15.25
3532 835.766 15.41 - 15.55 15.52 15.56 15.57 - -
3548 836.743 15.21 15.77: 15.70 15.22 - 15.37 16.00: 15.53
3549 836.751 15.06 15.89: 15.71 15.23 15.32 15.30 15.84: -—
3550 836.758 14.95 15.83: 15.69 15.23 — 15.25 15.90: -
3557 839.769 15.39 15.60 15.08 15.54 15.33 15.58 15.46: 15.46
3558 839.777 15.43 15.47: 15.08 15.51 — 15.56 15.43: 15.43
3559 839.785 15.44 15.37 15.09 15.53 — 15.56 - -
3565 840.713 15.85 15.68: 15.39 15.41 15.50 15.65 15.58: 15.29
3566 840.721 15.90 - 15.36 15.42 15.56 15.55 15.70: 15.35
3567 840.729 15.76 15.75: 15.36 15.40 15.50 15.39 - 15.26
4554 869.589 15.58 15.89: 15.43 15.20 15.37 15.48 - 15.38
4555 869.606 15.56 15.99: 15.45 15.22 15.28 15.48 - 15.38
4556 869.613 15.62 — 15.47 15.22 15.29 15.50 15.70 15.40
4557 869.640 15.64 - 15.48 15.28 15.29 15.53 15.66: 15.45
4558 869.648 15.68 - 15.51 15.27 15.34 15.51 15.73: 15.50

 

195

Table A.2 (cont’d).

 

 

HJ D

frame 2448000+ v19 v20 v22 v23 v24 v25 V29 v30
4559 869.656 15.72 16.03: 15.52 15.30 15.37 15.51 15.73: 15.54
4573 889.569 15.43 — 15.21 15.56 — 15.48 15.63: 15.53
4574 889.585 15.47 - 15.20 15.54 - 15.49 15.78 15.55
4575 889.593 15.48 - 15.23 15.57 15.28 15.49 15.67: 15.57
4576 889.601 15.53 — 15.23 15.54 15.26 15.53 15.73: 15.55
4577 889.609 15.51 - 15.26 15.53 15.29 15.51 15.77 15.59
4578 889.617 15.53 — 15.27 15.55 15.22 15.52 — 15.53
4579 889.625 15.53 — 15.28 15.54 15.29 15.54 15.74: 15.51
4580 889.633 15.57 15.95: 15.33 15.55 15.33 15.53 — 15.48
4581 889.641 15.60 15.86: 15.34 15.53 15.37 15.52 — 15.49
4582 889.649 15.60 — - 15.54 15.33 15.57 15.61 15.56
4583 889.657 15.65 — 15.34 15.53 15.32 15.58 — 15.38
4584 889.666 15.64 — 15.35 15.52 15.32 15.58 — 15.38
4585 889.682 15.71 - — 15.54 15.45 15.58 — 15.34
4586 889.689 15.69 — '— 15.56 15.44 15.59 - 15.32
4587 889.697 15.73 — — 15.53 15.46 15.59 — 15.30
4588 889.705 15.75 - — 15.56 15.46 15.60 15.64 15.30
5505 891.560 15.82 15.60 15.37 15.57 15.44 15.54 15.20 15.40
5506 891.568 15.85 15.54: — 15.58 15.46 15.52 15.11 15.49
5507 891.577 15.80 15.59 - 15.54 15.51 15.52 15.07 15.53
5508 891.593 15.86 15.48: 15.20 15.56 - 15.53 — 15.54
5509 891.601 15.84 — 15.08 15.55 -— 15.53 15.22 15.56
5525 897.539 15.37 — - 15.33 15.61 -— 15.68 15.32
5526 897.546 15.36 15.94: - 15.34 — 15.47 15.72: 15.33
5527 897.562 15.41 15.90: 15.32 15.37 15.68 15.50 15.65 -
5528 897.571 15.45 15.82 15.32 15.36 — 15.48 15.72 15.41
5529 897.578 15.47 15.79: 15.31 — — 15.50 15.68: -
5530 897.594 15.48 15.60: 15.36 15.37 15.66 15.51 15.73: 15.51
5531 897.602 15.50 15.48 15.37 15.41 - 15.54 15.75 -
5532 897.610 15.52 15.47: 15.39 15.39 — 15.54 15.78: 15.51
5533 897.618 15.54 15.43 15.39 15.41 15.71 15.55 15.69 —
5534 897.626 15.56 15.37: 15.46 15.41 — 15.55 15.63: 15.57
5535 897.634 15.59 15.23 - 15.42 — 15.59 15.74 -
5536 897.642 15.60 15.26 15.47 15.41 15.56 15.52 15.70: 15.60
5537 897.650 15.60 15.17 —— 15.44 15.63 15.57 - -
5538 897.658 15.62 15.20 15.55 15.48 15.48 15.54 - -
5539 897.666 15.65 15.24 15.57 15.47 — 15.59 — -
5540 897.674 15.65 15.23 15.46 15.48 - 15.58 15.71: -
5541 897.682 15.66 15.33: 15.56 15.48 15.30 15.58 15.65: —

 

196

Table A.2 (cont’d).

 

 

 

HJD
frame 2448000+ v31 v32 v35 v38 v39 v40 v42 v44
1503 446.857 15.35 15.72 15.48 15.72 15.59 — 15.56 —
1504 446.865 - - 15.54 15.74 15.46 — - —
1506 449.751 15.50 15.50 15.80 15.61 15.38 15.51 15.39 15.69
1507 449.761 15.57 15.07: 15.92 15.65 15.38 15.41 15.28 -
1538 452.738 — 15.31 15.71 15.56 - 15.72 — -
1539 452.747 15.74 - 15.71 15.60 15.64 15.60 15.57 15.61
1540 452.754 15.75 15.44 15.76 - 15.64 15.62 15.57 15.64
1541 452.789 — 15.22: 15.80 15.78 15.65 15.49 15.68 15.67
1542 452.797 15.76 — 15.84 - 15.60 15.43 15.77 15.70
1544 452.813 15.75 15.55 15.90 — 15.56 15.47 15.80 15.76
1514 453.755 15.56 15.10 15.42 15.35 15.35 15.68 15.40 -
1515 453.763 15.55 14.97 15.40 15.40 15.35 15.72 15.35 15.55
1516 453.798 15.55 15.14 15.51 - 15.38 15.77 15.48 15.60
1517 453.806 15.56 15.13 15.52 15.40 15.40 15.75 15.45 15.67
1526 454.711 15.50 15.57: 15.82 - — — 15.84 15.06
1527 454.728 15.59 15.25: 15.88 — 15.74 15.45 15.75 15.16
1528 454.735 15.59 15.71 15.83 — 15.67 15.38 15.66 15.14
1529 454.777 15.71 15.60 15.82 15.64 15.49 15.46 15.42 15.33
1530 454.793 15.74 15.54 15.79 — 15.45 15.47 15.37 15.32
1531 454.809 15.75 15.60 15.72 15.43 15.36 15.51 15.38 15.28
1552 473.716 15.38 14.87 15.44 15.46 15.49 - 15.74 —
1555 473.768 15.42 14.89 — 15.67 15.64 15.77 15.71 . 15.17
1562 474.754 15.69 15.54: 15.80 15.30 15.25 — 15.59 -
1566 474.793 15.68 — 15.66 15.34 15.32 15.51 15.74 15.68
1568 474.811 15.72 15.40 15.52 15.43 0.06 15.62 15.81 15.44
1575 475.707 15.79 15.31 15.50 - 15.59 15.83 15.37 15.47
1576 475.716 15.78 15.36: 15.55 - 15.59 15.76 15.37 15.58
1577 475.724 15.76 15.27 15.54 15.75 15.62 15.87 15.38 15.54
1581 475.759 15.57 15.41 15.66 15.76 15.58 15.83 15.46 15.59
1582 475.766 15.54 15.43 15.69 15.68 15.72 15.70 15.50 -
1583 475.775 15.48 15.53 15.68 15.68 15.56 15.66 15.51 15.59
1587 479.682 15.65 15.41: 15.89 15.40 15.72 15.52 15.45 15.07
1588 479.690 15.70 15.51 15.81 15.43 15.68 15.58 15.42 15.15
1589 479.698 15.72 15.65: 15.87 - 15.60 15.58 15.40 -
1595 479.754 15.73 15.12 15.79 15.61 15.49 15.63 15.54 —
1597 480.668 15.52 - 15.51 15.64 15.47 15.80 15.71 15.82
2503 480.714 15.41 15.44 15.55 15.39 15.52 15.51 15.42 15.60
2504 480.723 15.38 — 15.57 15.33 15.55 15.44 15.44 15.49
2505 480.738 15.39 15.62 15.62 15.32 15.57 15.39 15.39 15.45
2512 481.664 15.59 15.01 15.80 15.66 15.61 15.79 15.78 15.33
2514 481.682 15.66 15.15: 15.71 - 15.59 15.82 15.83 15.40
2518 481.718 15.70 15.24 15.58 15.69 15.51 15.82 15.79 15.49
2520 481.735 15.79 15.28 15.48 15.74 15.49 15.78 15.72 15.50
2525 481.777 15.81 15.31 15.43 15.72 15.50 15.78 15.44 15.48
2540 546.597 15.57 15.36 15.73 - 15.67 — 15.64 15.57

 

 

197

Table A.2 (cont’d).

 

 

11.1 D

frame 2448000+ v31 V32 v35 v38 v39 v40 v42 v44
2546 547.552 - 15.44 15.60 — 15.54 15.42 15.82 15.25
2547 547.560 15.49 15.47 15.65 15.33 15.51 15.42 15.84 15.18
2548 547.568 15.51 15.46 15.64 - 15.50 15.47 15.87 15.14
2557 568.501 15.40 15.51 15.56 15.54 15.70 15.84 15.84 15.24
2558 568.510 15.42 15.36 15.55 15.42 15.63 15.84 15.86 15.28
2559 568.517 15.47 15.49 15.54 15.47 15.68 15.76 15.81 15.32
2554 568.582 15.54 15.59 15.48 15.35 15.49 15.76 15.47 15.21
2555 568.599 15.60 - 15.51 15.36 15.39 15.68 15.42 15.44
2556 568.615 15.63 - 15.52 15.40 15.32 15.56 15.42 15.45
2560 569.578 15.70 — 15.87 — 15.66 15.71 15.83 15.79
2562 569.594 15.59 15.37 — — 15.64 - 15.88 15.23
2570 570.507 15.26 15.56 15.44 15.49 15.58 15.51 15.55 15.47
2571 570.514 — 15.53 15.50 — 15.55 15.49 15.58 15.56
2575 570.568 15.43 15.32: 15.57 - 15.51 15.47 15.72 15.57
2576 570.576 15.42 15.21 15.59 — 15.45 15.43 15.75 -
2577 570.591 15.44 15.07 15.63 15.63 15.45 15.47 15.75 15.61
2582 574.536 15.55 15.53: 15.82 — - 15.78 15.71 —
2583 574.544 15.47 15.58: - 15.41 15.41 15.82 15.78 15.26
2584 574.552 15.51 15.55: — — - 15.73 15.75 -
3508 802.823 15.55 15.55: 15.44 — 15.41 15.77 15.51 15.64
3509 802.831 15.55 15.41: 15.45 15.54 15.44 15.73 15.50 15.56
3510 802.839 15.58 15.66: 15.47 15.57 15.39 15.77 15.56 15.64
3517 831.803 15.52 15.35 15.81 15.68 15.56 15.65 15.78 15.38
3518 831.810 15.53 15.39 15.84 15.71 15.62 15.68 15.76 15.47
3519 831.819 15.55 15.43 15.84 15.72 15.65 15.66 15.69 15.43
3523 831.854 15.53 - 15.83 15.74 15.63 15.72 15.52 15.47
3524 831.862 15.57 15.55 15.80 15.76 15.52 15.75 15.45 15.54
3525 831.869 15.59 15.55 15.84 15.72 15.52 15.71 15.43 15.51
3530 835.749 15.75 15.67 15.64 15.34 15.65 15.63 15.75 15.63
3531 835.758 15.72 15.40: 15.59 15.33 15.62 15.55 15.74 15.70
3532 835.766 15.69 15.34 15.52 15.34 15.59 15.47 15.67 15.61
3548 836.743 15.58 15.61 15.73 15.74 15.49 15.74 - —
3549 836.751 15.58 15.66 15.73 - 15.47 15.73 15.70 15.54
3550 836.758 15.54 15.63: 15.77 — 15.48 15.76 15.77 -
3557 839.769 15.71 15.53: 15.58 15.71 15.25 15.73 15.55 15.71
3558 839.777 15.75 - 15.62 - 15.33 15.71 15.52 15.74
3559 839.785 15.67 15.54: 15.66 15.75 15.33 15.75 15.49 -
3565 840.713 15.49 15.03 15.81 15.53 15.60 15.34 15.82 15.41
3566 840.721 - 15.13 - — 15.55 15.46 15.74 15.28
3567 840.729 15.45 14.94: 15.72 15.54 15.58 — 15.75 15.43
4554 869.589 15.73 15.59 15.43 15.41 15.58 15.75 15.82 15.59
4555 869.606 15.74 15.70: 15.43 15.49 15.62 15.83 15.91 15.73
4556 869.613 15.76 15.54 15.45 15.49 15.58 15.79 15.78 15.59
4557 869.640 15.62 15.68: 15.43 15.53 15.56 15.82 15.78 15.66
4558 869.648 15.63 15.58 15.46 15.59 15.61 15.79 15.69 15.74

 

198

Table A.2 (cont’d).

 

 

HJ D
frame 2448000+ V31 v32 v35 v38 v39 v40 v42 v44
4559 869.656 15.62 — 15.47 15.57 15.59 15.81 15.64 15.80
4573 889.569 - 15.53 15.44 15.66 15.53 15.75 15.43 15.30
4574 889.585 — 15.65 15.46 — 15.51 15.80 15.44 15.39
4575 889.593 15.60 15.66 15.47 15.69 15.46 15.79 15.47 15.39
4576 889.601 15.61 15.69 15.46 15.71 15.47 15.78 15.50 -
4577 889.609 15.56 15.67 15.47 15.74 15.47 15.82 15.57 15.42
4578 889.617 15.55 15.57: 15.48 15.75 15.44 15.83 15.54 15.49
4579 889.625 15.49 - 15.48 15.73 15.44 15.79 15.57 15.48
4580 889.633 15.46 — 15.48 15.78 15.45 15.82 15.57 -
4581 889.641 15.45 15.62 15.53 15.76 15.48 15.80 15.57 15.52
4582 889.649 15.42 15.46 15.54 15.79 15.45 15.75 15.61 15.58
4583 889.657 15.42 15.16 15.54 15.76 15.41 15.81 15.62 —
4584 889.666 15.40 14.99: 15.55 15.73 15.46 15.80 15.65 15.57
4585 889.682 15.42 14.99 15.58 15.73 15.43 15.78 15.67 15.50
4586 889.689 15.42 14.95 15.60 — 15.46 15.73 15.73 15.57
4587 889.697 15.44 14.93 15.63 15.73 15.44 15.69 15.77 15.63
4588 889.705 15.42 14.95 15.64 15.63 15.42 15.64 15.79 15.59
5505 891.560 15.69 14.97 15.51 15.73 15.36 15.77 15.86 15.60
5506 891.568 - 15.12 15.51 15.71 15.31 15.73 15.89 15.58
5507 891.577 15.67 15.17 15.50 15.72 15.38 15.69 15.86 15.60
5508 891.593 — 15.12 15.58 15.54 15.42 15.60 15.81 15.58
5509 891.601 — 15.17 15.54 15.54 15.38 15.58 15.80 15.57
5525 897.539 — 15.12: 15.77 — 15.52 15.80 15.57 15.55
5526 897.546 — 15.08: 15.77 - 15.54 15.78 15.55 15.65
5527 897.562 15.60 14.93 15.74 15.81 15.54 15.82 15.61 15.58
5528 897.571 15.57 14.97 15.66 15.74 15.59 15.81 15.64 15.61
5529 897.578 15.60 14.92: 15.60 - - - — 15.59
5530 897.594 15.62 14.94 15.54 15.66 15.59 15.79 15.73 -
5531 897.602 15.67 15.10: 15.52 - 15.61 15.75 15.70 15.54
5532 897.610 15.67 15.12 15.50 15.54 15.63 15.72 15.75 15.61
5533 897.618 15.69 15.15 15.48 15.48 15.64 15.70 15.76 -
5534 897.626 15.70 15.20 15.43 15.46 15.61 15.65 15.76 15.62
5535 897.634 15.71 15.20 15.46 - 15.63 15.60 15.78 15.67
5536 897.642 15.75 15.12 15.44 15.42 15.58 15.54 15.83 15.67
5537 897.650 - 15.08: 15.42 15.38 15.68 15.47 15.79 15.57
5538 897.658 15.80 15.33: 15.43 15.42 15.64 15.45 15.83 15.64
5539 897.666 15.76 15.28: 15.45 15.42 15.61 15.42 15.81 15.64
5540 897.674 15.74 15.12: 15.48 15.35 15.62 15.38 15.80 15.66
5541 897.682 15.80 15.26: 15.50 15.41 15.58 15.39 15.80 15.63

 

Table A.2 (cont’d).

199

 

 

 

HJ D
frame 2448000+ v49 v50 V51 v52 V53 V54 v65 v66
1503 446.857 15.01 — 15.29 15.18 15.40 15.20 15.46 15.48
1504 446.865 15.03 - 15.50 15.20 — 15.29 15.43 15.32
1506 449.751 14.80 — 15.60 15.15 15.33 15.46 15.46 —
1507 449.761 14.80 15.82 15.48 15.19 15.30 15.27 15.50 15.42
1538 452.738 15.03 15.97 - 15.46 15.41 — 15.47 15.91
1539 452.747 15.00 - — 15.49 15.51 15.75 15.57 -
1540 452.754 15.04 15.78 — 15.53 15.51 15.75 15.31: 15.74
1541 452.789 15.05 15.47 15.46 15.62 15.63 — 15.47 15.61
1542 452.797 15.11 - 15.65 15.62 15.60 15.56 15.53 -
1544 452.813 15.06 — - 15.68 15.62 — 15.47: 15.56
1514 453.755 14.87 — 15.56 15.11 15.64 15.38 15.28 15.52
1515 453.763 14.88 15.62 15.59 15.08 15.69 15.37 15.24 -
1516 453.798 14.91 15.69 — 15.24 15.62 — 15.27 15.72
1517 453.806 14.90 — 15.48 15.29 15.58 15.43 15.31: 15.77
1526 454.711 — - 15.28 15.86 15.30 — 15.37: —
1527 454.728 15.07 — 15.09 15.82 15.37 — 15.40 15.38
1528 454.735 15.03 - 15.51 15.80 15.34 15.74 15.44 15.36
1529 454.777 15.08 — — 15.71 15.40 15.59 15.48 15.36
1530 454.793 15.10 15.95 15.32 15.75 15.44 15.48 15.47 15.44
1531 454.809 15.09 -— 15.39 15.79 15.45 - 15.49 15.43
1552 473.716 15.06 15.51 — 15.78 15.43 15.46 15.32 -
1555 473.768 15.09 — — 15.68 15.41 — 15.15 -
1562 474.754 14.91 - 15.92 15.65 15.39 15.32 15.39 15.51
1566 474.793 14.92 — 15.74 15.74 15.71 15.37 15.40 —
1568 474.811 14.96 - 15.80 15.76 0.07 15.43 15.45 -
1575 475.707 15.02 15.80 15.47 15.37 15.79 15.43 15.49 15.53
1576 475.716 15.04 - - 15.36 15.75 - 15.40 -
1577 475.724 15.08 - 15.43 15.38 15.72 15.58 15.45 15.53
1581 475.759 15.09 15.47 15.41 15.47 15.61 15.53 15.45 15.85
1582 475.766 15.13 15.44 15.40 15.50 15.51 15.49 15.50 15.56
1583 475.775 15.10 - 15.43 15.51 15.47 15.43 15.52 -
1587 479.682 15.09 - 15.43 15.21 15.44 15.28 15.20 15.67
1588 479.690 15.12 15.52 15.47 15.25 — 15.31 15.20 15.73
1589 479.698 15.09 15.65 — 15.27 15.49 - 15.28: 15.57
1595 479.754 14.95 15.77 — 15.39 15.58 - 15.36: 15.51
1597 480.668 14.90 — 15.61 15.81 15.70 15.53 15.46 15.66
2503 480.714 14.96 — 15.61 15.84 - 15.53 15.43 -
2504 480.723 14.97 — 15.57 15.86 15.71 15.57 15.44: —
2505 480.738 14.96 15.88 15.84 15.88 15.57 15.58 15.44 15.76
2512 481.664 15.11 - 15.49 15.76 15.50 15.28 15.19 15.46
2514 481.682 15.11 15.59 15.44 15.78 15.48 15.51 15.19: 15.45
2518 481.718 14.92 — 15.40 15.81 15.45 15.40 15.17 15.48
2520 481.735 14.76 15.41 15.46 15.82 15.49 - 15.19: 15.56
2525 481.777 14.60 - 15.44 15.79 15.54 15.61 15.23 -
2540 546.597 14.80 - 15.65 15.60 15.54 15.52 15.31 -

 

200

Table A.2 (cont’d).

 

 

11.1 D

frame 2448000+ v49 v50 v51 v52 v53 v54 V65 v66
2546 547.552 14.95 15.71 15.57 15.33 15.37 15.36 15.43: 15.79
2547 547.560 14.99 15.54 15.53 15.24 15.40 15.28 15.37 —
2548 547.568 14.99 15.50 — 15.19 15.35 15.37 15.44: 15.80
2557 568.501 14.92 15.52 15.59 15.64 15.68 15.44 15.31 15.42
2558 568.510 14.96 — 15.48 15.65 - 15.43 15.27 15.39
2559 568.517 14.95 - 15.80 15.64 15.57 15.73 15.26 15.38
2554 568.582 15.02 15.87 15.34 15.73 15.31 15.75 15.13 15.41
2555 568.599 15.04 — 15.35 15.77 15.35 15.42 15.18 —
2556 568.615 15.01 — 15.13 15.79 15.36 15.59 15.15 -
2560 569.578 14.66 — 15.68 15.47 15.59 15.37 15.37 -
2562 569.594 14.64 — 15.67 15.54 15.60 15.51 15.36 15.52
2570 570.507 14.98 — 15.58 15.79 15.65 15.66 15.40 15.47
2571 570.514 15.00 - 15.76 15.86 15.65 — 15.42 15.50
2575 570.568 15.03 15.47 15.41 15.52 15.69 — 15.44: 15.63
2576 570.576 15.02 15.50 — 15.46 15.71 — 15.49: 15.61
2577 570.591 15.02 — 15.51 15.15 15.64 15.57 15.54: 15.62
2582 574.536 15.01 — - 15.77 15.49 — - -
2583 574.544 15.08 — 15.38 15.75 15.54 - 15.29: --
2584 574.552 15.05 — — 15.83 15.60 — - -
3508 802.823 14.54 15.68 — 15.63 15.76 - 15.27: 15.77
3509 802.831 14.59 15.73 15.33 15.64 15.72 15.21 15.26: 15.77
3510 802.839 14.59 - - 15.66 15.77 - 15.27 —
3517 831.803 14.89 - 15.31 15.77 15.69 15.45 15.44 15.34
3518 831.810 14.89 - 15.22 15.76 15.76 15.41 15.41 15.39
3519 831.819 14.88 — 15.27 15.70 15.76 — 15.43 15.31
3523 831.854 14.93 — 15.28 15.81 15.68 - 15.45: 15.49
3524 831.862 14.93 — 15.25 15.84 15.66 15.48 15.42 15.50
3525 831.869 14.94 15.92 15.36 15.81 15.69 15.55 15.53: 15.50
3530 835.749 14.91 — 15.49 15.79 15.39 15.37 15.14 15.64
3531 835.758 14.93 — 15.45 15.79 15.40 15.40 15.13 15.63
3532 835.766 14.91 — 15.33 15.78 15.41 - 15.12 15.62
3548 836.743 15.03 15.47 -— 15.60 15.63 — 15.48: 15.45
3549 836.751 15.09 15.50 — 15.63 15.67 — 15.43: —
3550 836.758 15.02 15.52 - 15.62 15.67 - 15.50: 15.46
3557 839.769 14.97 — 15.27 15.78 15.61 15.39 15.44 15.41
3558 839.777 14.97 15.67 15.26 15.77 15.55 15.43 15.49: 15.43
3559 839.785 15.03 - 15.28 15.73 15.46 15.44 15.48 15.40
3565 840.713 15.00 - 15.51 15.51 15.36 15.48 15.30 15.75
3566 840.721 15.01 - 15.58 15.50 15.34 15.55 15.27 15.75
3567 840.729 14.98 — - 15.51 15.39 15.41 15.21 15.83
4554 869.589 14.90 — 15.27 15.68 15.55 15.24 15.26 -
4555 869.606 14.80 15.77 15.30 15.68 15.48 15.19 15.19 15.84
4556 869.613 14.75 15.73 15.35 15.70 15.39 15.26 15.21 15.79
4557 869.640 14.62 — 15.37 15.75 15.36 15.25 15.23 15.86
4558 869.648 14.61 — 15.37 15.75 15.33 15.25 15.28 -

 

Table A.2 (cont’d).

201

 

 

HJ D

frame 2448000+ v49 v50 v51 v52 v53 v54 v65 V66
4559 869.656 14.63 — 15.40 15.75 15.37 15.24 15.31 -
4573 889.569 14.93 — 15.51 15.31 15.33 15.13 15.26: 15.56
4574 889.585 14.96 15.74 15.56 15.36 15.40 15.25 15.16: 15.51
4575 889.593 14.98 15.81 15.55 15.41 15.43 15.24 15.15 15.65
4576 889.601 15.00 15.75 15.57 15.41 15.43 15.27 15.16: 15.66
4577 889.609 15.01 — 15.56 15.43 15.36 15.23 15.14 15.60
4578 889.617 15.02 — 15.61 15.45 15.44 15.26 15.13 15.71
4579 889.625 15.00 - 15.53 15.46 15.46 15.27 15.19 15.59
4580 889.633 15.02 — 15.60 15.46 15.44 15.34 15.17 15.65
4581 889.641 15.02 — 15.57 15.51 15.46 15.32 15.19 15.68
4582 889.649 15.02 — 15.64 15.50 15.44 15.32 15.17 15.78
4583 889.657 15.03 — 15.54 15.51 15.51 15.29 15.17 15.71
4584 889.666 15.05 — 15.61 15.53 15.49 15.44 15.21 15.61
4585 889.682 15.03 15.93 15.55 15.54 15.54 15.37 15.23 15.74
4586 889.689 15.02 15.88 15.52 15.55 15.52 15.38 15.22 15.79
4587 889.697 15.03 — 15.47 15.60 15.55 15.42 15.25 15.77
4588 889.705 15.04 — 15.48 15.58 15.55 15.46 15.24 15.80
5505 891.560 14.95 — 15.51 15.83 15.58 15.18 15.42 15.75
5506 891.568 14.96 — 15.57 15.86 15.54 15.24 15.48 15.71
5507 891.577 14.98 15.46 15.53 15.84 15.61 15.21 15.44: 15.71
5508 891.593 15.01 15.49 15.56 15.83 - 15.23 15.55: 15.71
5509 891.601 15.01 15.51 15.57 15.85 15.49 15.26 15.51: 15.79
5525 897.539 15.00 15.44 - 15.34 —‘ — 15.14: 15.54
5526 897.546 15.04 15.46 15.59 15.22 — 15.17 - 15.51
5527 897.562 15.01 15.55 — 15.09 — — 15.21: 15.67
5528 897.571 15.05 15.56 — 15.13 15.58 - 15.16: 15.62
5529 897.578 15.02 15.61 - 15.14 -— - — 15.69
5530 897.594 15.05 - — 15.20 15.68 — 15.22 15.68
5531 897.602 15.03 15.64 - 15.22 15.65 - 15.35 15.71
5532 897.610 15.04 -— — 15.26 15.67 — 15.25 15.73
5533 897.618 15.04 15.70 — 15.29 15.67 — 15.25: 15.75
5534 897.626 15.03 15.76 15.59 15.28 15.70 — 15.20 15.76
5535 897.634 15.00 15.75 - 15.33 15.74 — 15.25: 15.75
5536 897.642 15.08 - 15.52 15.33 15.72 15.36 15.28 15.81
5537 897.650 15.06 — 15.48 15.37 15.75 15.32 15.24 15.77
5538 897.658 15.07 - 15.41 15.39 15.76 - 15.31 15.75
5539 897.666 15.08 — - 15.40 15.80 - 15.21 -
5540 897.674 15.06 — 15.31 15.46 15.78 15.33 15.30 15.79
5541 897.682 15.07 - - 15.47 15.80 - 15.34: 15.74

 

202

Table A.2 (cont’d).

 

 

 

111 D
frame 2448000+ v67 v74 v97 v99 V113
1503 446.857 15.98 — — 15.74 15.44
1504 446.865 — — 15.56 15.76 15.44
1506 449.751 15.95: 15.44 15.67: 15.73 15.46
1507 449.761 — 15.36 15.45: 15.69 15.48
1538 452.738 -— — — 15.74 15.55
1539 452.747 15.49 15.49: — 15.68 15.46
1540 452.754 15.43 15.56: 15.71: 15.76 15.47
1541 452.789 15.53 15.61: 16.02: 15.70 15.42
1542 452.797 15.83 15.66: 15.99: 15.70 15.44
1544 452.813 15.69 — 15.83: 15.69 15.44
1514 453.755 15.82 — — 15.60 15.40
1515 453.763 15.72 15.83 — 15.63 15.44
1516 453.798 15.66: 15.56 15.78: 15.63 15.44
1517 453.806 15.57: 15.56 15.61: 15.65 15.46
1526 454.711 15.64: - 15.58: 15.74 15.53
1527 454.728 15.64 15.32: 15.75: 15.75 15.52
1528 454.735 15.59 15.34: 15.47 — 15.52
1529 454.777 15.79 15.41: 15.65: 15.78 15.49
1530 454.793 15.91: 15.63: 15.74: 15.71 15.48
1531 454.809 15.68 15.41: 15.68: 15.70 15.46
1552 473.716 15.79: 15.24: 15.85: 15.62 15.50
1555 473.768 15.52 15.41: 16.10' 15.59 15.57
1562 474.754 — - 15.51 15.72 15.35
1566 474.793 15.84 - 15.49 15.69 15.39
1568 474.811 15.80 15.44: — 15.70 0.08
1575 475.707 15.65 15.57: 15.85: 15.68 15.45
1576 475.716 15.55 15.62: - 15.69 15.42
1577 475.724 15.74: 15.37 - 15.70 15.46
1581 475.759 15.62 15.29 16.02: 15.71 15.50
1582 475.766 15.82: 15.32: 15.94: 15.68 15.51
1583 475.775 15.64 15.32 15.91: 15.67 15.52
1587 479.682 15.69 15.60: 15.40: 15.67 15.44
1588 479.690 - 15.68 — 15.64 15.41
1589 479.698 -— - - 15.64 15.43
1595 479.754 15.46: — 15.43: 15.72 15.44
1597 480.668 — - - 15.74 15.57
2503 480.714 - 15.63: - 15.69 15.58
2504 480.723 15.91: 15.75: 15.75: 15.64 15.55
2505 480.738 15.83: 15.59: 15.81: 15.59 15.53
2512 481.664 15.77 15.31: 15.64: 15.53 15.43
2514 481.682 15.66 15.38 15.75: 15.59 15.40
2518 481.718 15.71: 15.47 - 15.64 15.40
2520 481.735 15.80: 15.43: 15.45: 15.66 15.42
2525 481.777 15.66 15.55 15.66: 15.72 15.40
2540 546.597 15.64: - 15.48: 15.74 15.49

 

203

Table A.2 (cont’d).

 

 

HJ D
frame 2448000+ v67 V74 v97 v99 V113
2546 547.552 - 15.82: 15.78: 15.64 15.42
2547 547.560 15.91: 15.75: 15.76 15.60 15.45
2548 547.568 15.65: 15.87: 15.86: 15.60 15.45
2557 568.501 15.76 - - 15.75 15.49
2558 568.510 — 15.58 - 15.68 15.50
2559 568.517 — - 15.99: 15.67 15.47
2554 568.582 15.66 15.72: — 15.56 15.42
2555 568.599 - — 16.04: 15.56 15.41
2556 568.615 - - — 15.50 15.41
2560 569.578 15.57 — 15.44: 15.72 15.50
2562 569.594 - — 15.66: 15.71 15.53
2570 570.507 15.39 15.51: 15.50: 15.70 15.51
2571 570.514 15.41: 15.57 15.60: 15.67 15.51
2575 570.568 15.70 15.68: 15.69: 15.67 15.45
2576 570.576 15.81: — — 15.59 15.43
2577 570.591 - 15.66: - 15.53 15.44
2582 574.536 15.64: - — 15.67 15.55
2583 574.544 15.80: 15.86: 15.43 15.66 15.55
2584 574.552 15.63: 15.95: 15.38: - 15.53
3508 802.823 — 15.46: 15.54: 15.65 15.42
3509 802.831 15.91: 15.41 15.42 15.65 15.45
3510 802.839 — 15.35 — 15.67 15.38
3517 831.803 15.38 15.61 16.06: 15.50 15.45
3518 831.810 15.47 15.51 - 15.51 15.45
3519 831.819 15.59 15.49: - 15.53 15.47
3523 831.854 15.53 15.28: — 15.59 15.51
3524 831.862 15.57: 15.30 — 15.60 15.50
3525 831.869 15.61: 15.26: - 15.61 15.52
3530 835.749 15.71 15.48: 15.79: 15.75 15.37
3531 835.758 15.74 15.52: 15.93: 15.69 15.38
3532 835.766 15.80: 15.50 15.75: 15.72 15.37
3548 836.743 15.70: 15.87 - 15.66 15.49
3549 836.751 15.83: 15.92: 15.98: 15.63 15.50
3550 836.758 15.74: 15.83: 15.88: 15.63 15.53
3557 839.769 — 15.69: 15.80: 15.62 15.41
3558 839.777 16.04: 15.67: 15.68 15.69 15.39
3559 839.785 16.00: 15.74: 15.69: 15.65 15.40
3565 840.713 15.59 15.31 - 15.74 15.42
3566 840.721 15.51 15.28 - 15.74 15.44
3567 840.729 15.53 15.30 — 15.73 15.43
4554 869.589 15.80: - 15.36: 15.49 15.48
4555 869.606 15.96: 15.76 - 15.52 15.52
4556 869.613 - 15.88 15.43: 15.54 15.52
4557 869.640 — 15.86 15.55: 15.59 15.53
4558 869.648 16.00: 15.83 15.53: 15.61 15.52

 

204

Table A.2 (cont’d).

 

 

11.1 D
frame 2448000+ v67 v74 v97 V99 v113
4559 869.656 — — 15.42: 15.62 15.55
4573 889.569 — 15.30 - 15.72 15.53
4574 889.585 — 15.37: — 15.71 15.55
4575 889.593 15.61 15.44 - 15.69 15.54
4576 889.601 15.69 15.38: - 15.70 15.55
4577 889.609 15.81: 15.40: 15.88: 15.70 15.52
4578 889.617 15.50 15.41 — 15.65 15.52
4579 889.625 15.64 15.48 — 15.65 15.52
4580 889.633 15.68 15.43 - 15.64 15.56
4581 889.641 15.73: 15.50 - 15.63 15.49
4582 889.649 15.76 15.53 - 15.61 15.45
4583 889.657 15.68 15.54 16.20: 15.61 15.47
4584 889.666 15.64 15.51 - 15.60 15.47
4585 889.682 15.67: 15.64: 16.09: 15.61 15.45
4586 889.689 15.75: — - 15.59 15.45
4587 889.697 15.64 — - 15.58 15.44
4588 889.705 15.74 15.68 15.81: 15.59 15.44
5505 891.560 15.60: — 15.72 15.74 15.55
5506 891.568 — 15.84: 15.80: 15.72 15.53
5507 891.577 - 15.73 15.71: 15.74 15.56
5508 891.593 — 15.75: — 15.74 15.57
5509 891.601 — 15.66 - 15.71 15.55
5525 897.539 — 15.56 15.37: 15.59 15.43
5526 897.546 - 15.47 15.32: 15.62 15.45
5527 897.562 — 15.52 15.43: 15.62 15.44
5528 897.571 — 15.41 15.41: 15.62 15.43
5529 897.578 15.83: 15.41: 15.44: 15.64 15.49
5530 897.594 — 15.54 15.54 15.72 15.48
5531 897.602 15.86: 15.60: 15.52 15.67 15.48
5532 897.610 16.07: 15.57 15.51 15.72 15.48
5533 897.618 15.89 15.54: 15.53: 15.74 15.49
5534 897.626 15.89 15.60 15.62 15.69 15.47
5535 897.634 16.02: 15.64: 15.59 15.69 15.52
5536 897.642 - 15.63: 15.74: 15.74 15.50
5537 897.650 15.84 15.63: 15.75: 15.71 15.51
5538 897.658 15.89 15.65: 15.82 15.69 15.52
5539 897.666 15.95: 15.67: 15.71 15.70 15.54
5540 897.674 15.86: 15.67: 15.76: 15.67 15.55
5541 897.682 15.85: 15.74: 15.86: 15.71 15.52

 

 

205

Table A3. WIRO B Photometry of M15 Variables

 

 

 

 

 

 

111 D
frame 2448000+ v3 v4 v5 v11 v12 v13 v14 v15 v35
50 1183.890 16.05 16.21 16.02 15.84 - 15.86 16.47 16.74 16.47
58 1183.918 15.89 16.33 16.17 15.77 15.70 15.46 16.24 16.72 16.49
66 1183.940 15.85 16.40 16.25 15.83 15.66 15.51 16.11 16.62 16.58
123 1184.848 16.22 16.29 16.45 16.47 - 16.65 16.18 16.52 16.07
143 1184.893 16.38 16.47 16.12 15.97 16.55 16.61 16.41 16.65 15.97
151 1184.914 16.44 16.55 15.97 15.82 16.50 16.60 16.48 16.71 15.99
197 1185.824 16.09 16.42 16.08 16.55 16.08 16.27 16.26 15.48 16.51
205 1185.846 15.97 16.50 16.14 16.52 16.11 16.34 16.09 15.63 16.55
221 1185.889 15.91 16.58 16.32 16.41 16.32 16.45 15.87 15.91 16.56
229 1185.915 15.92 16.44 16.40 16.09 16.22 16.52 15.94 16.09 16.57
237 1185.936 15.99 16.22 16.47 15.81 16.32 16.59 16.02 16.23 16.58
301 1186.847 16.40 16.48 15.89 16.49 — 15.74 16.54 16.69 16.03
309 1186.868 16.47 16.32 15.79 16.54 — 15.86 16.56 16.58 16.09
317 1186.890 16.47 16.00 15.81 16.53 - 15.97 16.56 16.39 16.16
325 1186.911 16.55 15.80 - 16.49 15.61 16.09 16.59 16.01 16.22
HJ D
frame 2448000+ v38 v39 v40 v42 v52 v53 v66 v74 v113
50 1183.890 16.38 16.21 16.39 16.17 16.53 16.33 16.03 16.17 16.15
58 1183.918 16.37 16.31 16.50 16.28 16.64 16.00 16.10 16.36 16.18
66 1183.940 16.16 16.38 16.50 16.41 16.64 15.87 16.13 16.41 16.18
123 1184848 16.07 16.08 15.89 15.91 15.70 16.08 16.55 16.49 16.06
143 1184.893 16.31 15.76 15.91 15.86 15.99 16.09 16.43 16.57 16.01
151 1184.914 16.42 15.77 15.96 15.91 16.08 16.12 16.26 16.59 16.00
197 1185.824 16.09 16.32 16.51 16.56 16.68 16.34 16.10 16.43 15.99
205 1185.846 15.95 16.34 16.50 16.51 16.62 16.42 16.21 16.22 16.03
221 1185.889 - 16.40 16.57 16.32 16.76 16.46 16.34 15.84 16.10
229 1185.915 15.88 16.44 16.38 15.98 16.62 16.49 16.46 15.82 16.11
237 1185.936 15.96 16.47 16.14 15.86 15.90 16.49 16.54 16.00 16.15
301 1186.847 16.50 16.11 16.12 16.48 16.74 15.89 16.06 16.19 16.12
309 1186.868 16.49 16.04 16.19 16.55 16.78 15.92 15.97 16.37 16.05
317 1186.890 16.49 16.02 16.32 16.57 16.79 15.96 15.96 16.38 16.03
325 1186.911 16.37 15.95 16.43 16.48 16.84 15.94 15.98 16.40 16.01

 

 

206

Table A4. WIRO V Photometry of M15 Variables

 

 

111 D
frame 2448000+ V3 V4 V5 v11 v12 v13 v14 v15 v35

 

51 1183.892 15.67 15.92 15.71 15.55 — 15.49 16.05 16.23 16.04
59 1183.920 15.56 15.99 15.79 15.53 15.37 15.21 15.84 16.17 16.11
67 1183.942 15.52 16.07 15.86 15.56 15.32 15.29 15.74 16.10 16.13

124 1184.850 15.80 15.95 16.00 16.06 -- 16.12 15.84 16.03 15.73
144 1184.895 15.93 16.11 15.74 15.67 -- 16.11 16.00 16.13 15.66
152 1184.916 15.98 16.16 15.62 15.55 - — 16.05 16.18 15.71

198 1185.827 15.72 16.06 15.72 16.12 15.62 15.84 15.85 15.28 16.07
206 1185.848 15.61 16.15 15.78 16.11 15.67 15.88 15.73 15.39 16.11
214 1185.868 15.51 16.18 15.87 16.10 15.71 15.93 15.68 15.54 16.14

222 1185.891 15.57 16.14 15.92 16.01 - 15.96 15.63 15.63 16.15
230 1185.918 15.61 16.06 15.99 15.74 15.79 16.04 15.65 15.72 16.13
238 1185.938 15.63 15.96 16.12 15.51 - 16.01 15.76 15.87 16.20

 

302 1186.849 15.97 16.09 15.55 16.11 15.58 15.46 16.10 16.16 15.74
310 1186.870 16.01 16.00 15.52 16.13 15.42 15.56 16.11 16.07 15.77
318 1186.891 16.03 15.71 15.55 16.10 - 15.61 16.13 15.91 15.83
326 1186.912 16.03 15.60 15.60 16.07 15.33 15.67 16.13 15.63 15.89

 

 

HJD
frame 2448000+ v38 v39 v40 v42 v52 v53, v66 v74 v113

 

51 1183.892 — 15.84 16.01 - 16.04 15.86 15.70 — 15.78
59 1183.920 15.96 15.90 16.04 15.90 16.08 15.65 15.75 16.03 15.80
67 1183.942 15.84 15.97 16.09 - 16.11 15.53 15.80 — 15.81
124 1184.850 15.76 15.72 15.61 15.58 15.45 15.72 16.11 16.22 15.72
144 1184.895 15.91 15.50 15.63 15.57 15.64 15.72 16.01 — 15.68
152 1184.916 15.99 15.50 15.66 15.62 15.71 15.74 15.87 16.23 15.67
198 1185.827 15.71 15.89 16.07 16.12 16.17 15.94 15.77 16.11 15.66
206 1185.848 15.64 15.95 16.10 16.09 16.11 15.96 15.84 15.87 15.70
214 1185.868 15.58 15.94 16.10 16.01 16.16 16.01 15.91 15.77 15.74
222 1185.891 15.52 15.98 16.06 15.88 16.26 16.02 15.98 15.60 15.74
230 1185.918 15.57 16.00 15.96 15.64 16.06 16.04 16.04 15.70 15.77
238 1185.938 15.74 16.06 15.79 15.53 15.48 16.04 16.13 15.81 -

302 1186.849 16.04 15.75 15.77 16.04 16.20 15.59 15.73 15.98 15.75
310 1186.870 16.07 15.70 15.86 16.09 16.23 15.60 15.66 16.07 15.72
318 1186.891 16.06 15.66 15.93 16.10 16.25 15.61 15.66 16.11 15.70
326 1186.912 16.02 15.66 16.03 16.10 16.22 15.62 15.68 16.12 15.68

 

 

207

Table A5. WIRO R Photometry of M15 Variables

 

 

 

 

 

 

 

HJD

frame 2448000+ v3 v4 v5 v11 v12 V13 v14 v15 v35
52 1183.894 - — 15.49 - — 15.22 - 15.87 15.74
60 1183.922 15.37 15.77 15.54 - 15.13 15.08 - - 15.81
68 1183.944 15.35 15.82 15.59 15.40 15.09 15.11 15.52 15.77 15.82
125 1184.852 15.56 15.73 15.70 15.80 - 15.73 15.60 15.71 15.52
145 1184.897 15.66 15.88 15.48 15.46 — 15.76 15.71 15.79 15.48
153 1184.918 15.69 15.91 15.41 15.38 -— , — 15.77 15.83 15.50
199 1185.825 15.49 15.82 15.47 15.85 15.31 15.52 15.59 15.12 15.77
207 1185.850 15.40 15.87 15.54 15.84 15.37 15.55 15.51 15.23 15.81
215 1185.870 15.35 15.92 15.59 15.82 — 15.59 15.45 15.32 15.83
223 1185.893 15.39 15.88 15.62 15.75 15.37 15.60 15.41 15.40 15.82
231 1185.920 15.40 15.82 15.70 15.52 — 15.67 15.44 15.47 15.84
239 1185.941 15.41 15.70 15.79 15.37 - 15.65 15.55 15.58 15.87
303 1186.852 15.68 15.87 15.35 - 15.24 15.27 15.78 15.83 15.51
311 1186.873 15.72 15.76 15.33 15.86 - 15.32 15.82 15.76 15.53
319 1186.894 15.74 15.53 15.35 15.85 — 15.36 15.84 15.62 15.58
327 1186.914 15.73 15.47 15.40 15.84 — 15.39 15.84 15.38 15.63

HJD .

frame 2448000+ V38 v39 v40 V42 v52 v53 v66 v74 v113
52 1183.894 - — 15.72 15.61 15.69 15.58 15.49 - 15.55
60 1183.922 15.69 15.59 15.76 15.66 - - — - -
68 1183.944 - 15.65 15.80 15.70 15.75 15.31 15.57 15.93 15.57
125 1184.852 15.52 15.45 15.39 15.38 15.26 15.48 15.80 15.93 15.50
145 1184.897 15.65 15.28 15.43 15.37 15.40 15.47 15.71 - 15.46
153 1184.918 - 15.31 15.46 15.42 15.46 15.49 15.61 16.00 15.45

199 1185.825 15.49 15.60 15.77 15.82 15.84 15.63 15.55 15.86 15.44
207 1185.850 15.40 15.65 15.79 15.80 15.80 15.65 15.58 15.67 15.47
215 1185.870 15.41 15.64 15.78 15.76 15.84 15.70 15.62 15.57 15.51
223 1185.893 15.35 15.68 15.74 15.61 15.91 15.71 15.68 15.48 15.51
231 1185.920 15.39 15.70 15.67 15.45 15.71 15.71 15.75 15.70 15.53
239 1185.941 15.50 15.74 15.53 15.37 15.28 15.71 15.81 15.61 -

303 1186.852 15.75 15.49 15.49 15.75 15.82 15.36 15.49 15.81 15.53
311 1186.873 15.79 15.45 15.56 15.80 15.85 15.37 15.45 15.86 15.50
319 1186.894 15.77 15.43 15.63 15.81 15.86 15.38 15.45 - 15.48
327 1186.914 - 15.43 15.69 15.80 15.87 15.40 15.47 - 15.47

 

 

208

Table A6. WIRO I Photometry of M15 Variables

 

 

 

 

 

 

111 D
frame 2448000+ V3 V4 V5 V11 v12 v13 v14 v15 v35
53 1183.897 15.22 15.51 15.25 — — — 15.52 15.60 15.50
61 1183.924 15.16 15.55 15.30 15.16 — 14.89 15.37 15.53 15.53
69 1183.945 15.14 15.60 15.35 15.23 -— 14.94 15.31 15.48 15.52
126 1184.854 15.30 15.53 15.44 15.48 15.23 15.41 15.36 15.40 15.29
146 1184.899 15.39 15.61 15.26 15.26 - 15.40 15.46 15.44 15.27
154 1184.920 15.40 15.66 15.18 15.18 - — 15.51 15.49 15.26
200 1185.832 15.25 15.58 15.23 15.59 15.01 15.18 15.35 14.98 15.48
208 1185.852 15.18 15.63 15.29 15.58 15.05 15.22 15.30 15.04 15.53
216 1185.873 15.14 15.67 15.32 15.54 — 15.25 15.25 15.12 15.54
224 1185.895 15.17 15.60 15.35 15.45 — 15.26 15.23 15.16 15.53
232 1185.923 15.19 15.58 15.43 15.29 — 15.33 15.27 15.24 15.56
240 1185.943 15.18 15.45 15.44 15.24 — 15.34 15.29 15.30 15.50
304 1186.854 15.40 15.61 15.13 — — 15.02 15.51 15.50 15.26
312 1186.875 15.42 15.52 15.13 15.58 — 15.05 15.55 15.46 15.35
320 1186.896 15.44 15.35 15.14 15.60 - 15.09 15.58 15.33 15.35
328 1186.917 15.44 15.33 15.20 15.51 - 15.10 15.57 15.14 15.38
HJ D
frame 2448000+ V38 V39 v40 v42 V52 V53 V66 v74 V113
53 1183.897 - - 15.48 15.34 15.37 15.33 15.30 — 15.35
61 1183.924 15.44 15.33 15.52 15.39 15.41 15.19 15.31 — 15.35
69 1183.945 - 15.36 15.48 15.44 15.38 15.15 15.32 - 15.34
126 1184.854 15.31 15.23 15.25 15.20 15.09 15.24 15.54 -— 15.29
146 1184.899 15.38 15.11 15.25 15.19 15.19 15.23 15.50 15.82 15.26
154 1184.920 15.43 15.13 15.28 15.22 15.22 15.26 15.37 - ' 15.26
200 1185.832 15.26 15.36 15.47 15.52 15.54 15.36 15.30 15.54 15.25
208 1185.852 15.24 15.38 15.49 15.51 15.52 15.41 15.35 15.59 15.27
216 1185.873 15.21 15.42 15.52 15.46 15.57 15.40 15.37 15.43 15.30
224 1185.895 15.17 15.41 15.47 15.32 15.64 15.45 15.42 15.17 15.29
232 1185.923 15.17 15.42 15.36 15.22 15.36 15.41 15.50 15.44 15.32
240 1185.943 — 15.42 15.30 15.18 15.08 15.38 15.47 15.43 15.33
304 1186.854 15.48 15.26 15.24 15.49 15.52 15.17 15.29 15.41 15.31
312 1186.875 15.52 15.23 15.33 15.49 15.54 15.17 15.26 15.54 15.29
320 1186.896 15.49 15.22 15.37 15.51 15.55 15.19 15.25 15.55 15.28
328 1186.917 15.47 15.24 15.43 15.50 - 15.18 15.25 15.67 15.27

 

 

209

Table A7. WIRO B Photometry of M15 Variables - Northwest Field

 

 

 

 

 

 

 

HJD
frame 2448000+ V1 v2 v24 V30 v31 v32 v67 v97

54 1183.901 15.20 16.26 15.92 16.32 16.33 - — —
62 1183.928 - 16.28 — - 16.02 15.50 16.30 16.51
127 1184.858 14.98 16.28 16.53 15.75 16.18 - - 16.79
147 1184.903 14.79 15.99 16.25 15.70 16.18 16.50 16.17 16.91
155 1184.923 14.75 15.86 16.11 15.78 16.22 16.44 15.97 16.78
201 1185.835 15.89 16.06 16.17 16.08 16.48 15.69 16.27 16.16
209 1185.856 15.94 16.14 16.27 16.10 16.50 15.73 16.17 16.26
217 1185.876 15.90 16.15 — 16.13 16.53 15.83 16.19 16.33
225 1185.899 15.89 16.17 16.35 16.20 16.58 15.93 16.37 16.75
233 1185.926 15.93 16.21 16.43 16.24 16.54 15.98 16.30 16.42
305 1186.857 15.52 16.31 15.91 16.28 16.05 16.32 16.71 16.76
313 1186.878 15.56 — 15.93 16.12 16.10 16.38 16.69 16.71
321 1186.900 15.56 - 16.01 15.99 16.14 16.43 16.71 16.75
329 1186.919 15.63 — 16.12 15.85 16.12 16.47 - -

Table A8. WIRO V Photometry of M15 Variables - Northwest Field

HJD

frame 2448000+ V1 V2 v24 v30 V31 v32 v67 v97

55 1183.905 14.77 - - - 15.90 15.59 - 15.92
63 1183.931 - 15.66 15.59 15.90 15.65 15.17 16.03 15.92
128 1184.861 14.65 - - 15.43 15.80 - - -
148 1184.906 14.50 — 15.84 15.42 15.80 15.93 15.71 16.25
156 1184.926 14.46 - 15.66 15.47 15.82 15.92 15.58 16.19
202 1185.838 15.31 15.57 15.74 15.68 16.03 15.33 15.87 15.69
210 1185.858 15.30 15.59 15.77 15.71 16.05 15.39 15.86 15.71
218 1185.880 15.31 15.57 15.86 15.74 16.08 15.48 15.90 15.80
226 1185.905 15.35 - - 15.78 16.06 15.53 15.89 15.86
234 1185.928 15.35 15.62 15.94 15.81 16.07 15.60 15.91 15.88
306 1186.860 14.97 - 15.54 15.82 15.71 15.90 16.11 16.04
314 1186.881 15.00 - 15.58 15.71 15.72 15.95 16.38 16.07
322 1186.902 15.03 - 15.66 15.57 15.75 - 16.24 —
330 1186.922 15.05 - 15.70 15.51 15.76 15.85 16.13 -

 

 

210

Table A9. WIRO R Photometry of M15 Variables - Northwest Field

 

 

 

 

 

 

 

HJD
frame 2448000+ v1 v2 v24 v30 v31 v32 v67 v97

56 1183.908 14.52 - 15.35 - 15.63 15.26 15.60 —
64 1183.933 14.59 — — — 15.42 - — —
129 1184.863 14.45 - - - 15.54 - 15.89 -
149 1184.908 14.31 - — 15.23 15.56 15.59 15.52 —
157 1184.928 14.28 - 15.42 15.27 15.56 15.57 15.42 15.85
203 1185.840 14.94 15.21 - 15.43 15.70 15.13 15.63 —
211 1185.860 14.94 15.19 — 15.46 15.73 15.18 15.63 15.45
219 1185.883 14.96 - — 15.48 15.77 15.24 15.63 15.52
227 1185.907 14.98 — 15.66 - 15.78 — 15.65 -
235 1185.930 14.98 - - 15.53 15.75 15.30 15.64 15.58
307 1186.863 14.68 — 15.34 15.57 15.46 — - -
315 1186.882 14.73 — — — 15.50 15.61 15.96 -
323 1186.905 14.71 — - - 15.51 — 16.03 -
331 1186.924 14.72 - - 15.30 15.52 15.51 15.87 -

Table A10. WIRO I Photometry of M15 Variables - Northwest Field

HJD

frame 2448000+ V1 v2 V24 v30 V31 v32 v67 v97

57 1183.911 14.25 14.92 — 15.29 15.31 14.94 15.33 -—
65 1183.935 14.32 - - - 15.18 — 15.31 -
130 1184.865 14.23 - - 15.03 15.30 — 15.40 -
150 1184.910 14.13 — — 15.03 15.30 - 15.23 -
158 1184.930 14.11 - 15.15 15.07 15.28 - 15.12 -
204 1185.843 14.59 - 15.18 15.18 15.43 — 15.30 15.25
212 1185.862 — — - 15.19 15.42 14.89 15.24 —
220 1185.885 14.65 14.88 15.31 15.23 15.44 14.92 15.33 -
228 1185.909 14.64 14.92 15.26 15.22 15.46 14.93 15.30 -
236 1185.933 14.64 — 15.26 15.29 15.49 14.94 15.28 -
308 1186.865 14.35 - - 15.29 15.22 15.20 - —
316 1186.884 14.36 - 15.14 15.21 15.24 - 15.55 -
324 1186.907 14.38 - - 15.12 — — — —
332 1186.927 14.41 14.99 - 15.09 15.28 - - —

 

 

211

Table A.11. Photometry for HB Non-variable Stars

 

 

 

fin <V> <V-R>

1 15.516 0.402
2 15.578 0.247
3 15.581 0.377
4 15.612 0.450
5 15.614 0.425
6 15.697 0.388
7 15.718 0.431
8 15.722 0.426
9 15.723 0.340
10 15.736 0.209
11 15.739 0.167
12 15.752 0.333
13 15.787 0.182
14 15.860 0.120
15 15.869 0.448
16 15.893 0.397
17 15.897 0.158
18 15.910 0.109
19 15.916 0.099
20 15.920 0.111
21 15.922 0.140
22 15.928 0.130
23 15.937 0.170
24 15.942 0.134
25 15.958 0.157
26 15.961 0.088
27 15.961 0.107
28 15.981 0.137
29 16.001 0.077
30 16.003 0.084
31 16.007 0.139
32 16.025 0.193
33 16.029 0.066
34 16.032 0.061
35 16.078 0.066
36 16.106 0.480

 

 

 

APPENDIX B

This appendix contains Phase of Maxima tables for the RR Lyrae variable stars

in M15. The tables begin on the next page

212

 

Table B.1.

213

Dates and Phases of Maxima

 

HJD

V2

V3

V4

V5

 

14000
20950
21650
24400
26950
27350
29140
33875

35400
36488
37500
37950
39750
43360
44133
44156
44180
44820
48660

0.451
0.480
0.569
0.167

0.537
0.600
0.558
0.869
0.149
0.231
0.460
0.091
0.391
0.669
0.303

0.663
0.131

41".“

0.22 :1: 0.05
0.25 :1: 0.05
0.26 :h 0.04
0.27 :1: 0.03

0.30 :1: 0.05
0.17 :1: 0.03
0.20 :1: 0.02
0.22 :1: 0.06
0.20 :1: 0.02
0.25 :1: 0.06
0.22 :1: 0.06
0.22 :1: 0.05
0.35 :1: 0.04
0.43 :1: 0.06
0.51 :1: 0.05

0.41 :1: 0.06
0.45 :1: 0.03

0.044
0.323
0.049
0.000
0.162
0.175
0.345
0.214
0.235
0.238
0.319
0.250
0.019
0.269
0.166
0.762
0.310

0.657
0.293

¢moz

0.84 :1: 0.16
0.80 :1: 0.04
0.78 :1: 0.04
0.78 :1: 0.05
0.84 :1: 0.04
0.84 :1: 0.08
0.88 :1: 0.06
0.90 :1: 0.08
0.91 :1: 0.03
0.89 :1: 0.03
0.87 :1: 0.03
0.98 :1: 0.07
0.97 :1: 0.03
0.95 :1: 0.06
1.07 i 0.06
1.08 :1: 0.05
1.08 :1: 0.04

1.05 :1: 0.05
1.17 :1: 0.03

d
0.245
0.022
0.240
0.283
0.275
0.094
0.257
0.276
0.085
0.201
0.027
0.256
0.227
0.177
0.047
0.618
0.187

0.680
0.108

¢mu

0.20 :l: 0.07
0.24 :1: 0.05
0.26 :1: 0.05
0.23 :1: 0.04
0.23 :1: 0.05
0.27 :1: 0.05
0.15 :1: 0.06
0.26 :1: 0.05
0.31 :1: 0.04
0.29 :1: 0.06
0.40 :1: 0.03
0.43 :1: 0.07
0.40 :1: 0.03
0.50 :1: 0.03
0.48 :1: 0.05
0.42 :1: 0.05
0.39 :1: 0.03

0.48 :1: 0.05
0.53 :1: 0.03

d
0.096
0.123
0.161
0.374
0.377
0.371
0.034
0.094
0.102
0.057
0.165

0.102
0.142
0.233
0.657
0.325

0.642
0.120

¢mas

0.26 :1: 0.09
0.20 :1: 0.04
0.20 :h 0.06
0.22 :1: 0.08
0.15 :1: 0.06
0.22 :1: 0.07
0.24 :l: 0.08
0.25 :1: 0.04
0.29 :1: 0.03
0.26 :1: 0.06
0.33 :1: 0.03

0.30 :1: 0.05
0.29 :1: 0.04
0.38 :1: 0.06
0.38 :1: 0.05
0.38 :1: 0.06

0.41 :1: 0.05
0.48 :1: 0.03

 

 

HJD

V6

V7

V8

V9

 

14000
20950
21650
24400
26950
27350
29140
33875
35000
35400
36488
37500
37950
39750
43360
44133
44156
44180
44820
48660

0.642
0.022
0.584
0.425

0.656
0.096
0.122
0.625
0.221
0.385

0.461

0.313

0.253

¢mu

0.90 :1: 0.12
0.86 :1: 0.04
0.80 :1: 0.06
0.87 :1; 0.03

0.84 :1: 0.05
0.80 :1: 0.04
0.76 :t 0.05
0.78 :1: 0.03
0.80 :1: 0.07
0.75 :1: 0.03

0.63 :1: 0.04

0.66 :1: 0.04

0.62 :1: 0.04

0.330
0.163
0.261
0.010
0.288
0.369
0.277
0.085
0.344
0.325

0.003

0.194

0.342

¢mu

0.24 :1: 0.05
0.23 d: 0.07
0.25 :1: 0.05
0.19 :1: 0.04
0.20 i 0.04
0.36 :1: 0.10
0.33 i 0.05
0.52 :t 0.03
0.48 :l: 0.07
0.48 :1: 0.03

0.82 :1: 0.06

0.97 :1: 0.05

1.13 i 0.06

0.265
0.643
0.527
0.273
0.366

0.487
0.515
0.644
0.040
0.270
0.121
0.434
0.620

0.323
0.287

¢mas

1.02 :1: 0.04
1.04 :1: 0.03
1.04 :1: 0.04
1.00 d: 0.03
1.02 :1: 0.03

1.01 :1: 0.06
1.00 :h 0.04
1.02 :1: 0.02
1.05 :l: 0.04
0.98 :1: 0.03
1.05 :1: 0.02
0.97 i 0.03
0.99 :h 0.05

1.00 :1: 0.04
0.96 :l: 0.02

0.659
0.310
0.558
0.119
0.109
0.653
0.269
0.457
0.603
0.493
0.392

0.450
0.155
0.365
0.255

0.760
0.437

4m

0.60 :1: 0.18
0.55 :l: 0.04
0.53 :1: 0.05
0.55 :1: 0.03
0.56 :1: 0.02
0.54 :1: 0.02
0.51 :1; 0.03
0.53 :1: 0.02
0.54 :1: 0.02
0.53 :1: 0.03
0.54 :l: 0.02

0.57 :t 0.04
0.60 :1: 0.03
0.58 :1: 0.04
0.58 :1: 0.04

0.60 :1: 0.04
0.65 :1: 0.03

 

 

 

214

Table B.1. Cont’d

 

 

111 D

V10

V11

V12

V13

 

14000
20950
21650
24400
26950
27350
29140
33875
35000
35400
36488
37500
37950
39750
43360
44133
44156
44180
44820
48660

d
0.095
0.232
0.357
0.375
0.154
0.098
0.202
0.396
0.226
0.141
0.232

0.312
0.188
0.324
0.169

0.712
0.293

mm

-0.02 :1: 0.12
0.29 :1: 0.04
0.25 :1: 0.05
0.44 :1: 0.05
0.40 :1: 0.04
0.48 :1: 0.07
0.36 :1: 0.05
0.29 :t 0.04
0.40 :1: 0.03
0.41 :1: 0.03
0.44 :t 0.02

0.39 :1: 0.04
0.42 :1: 0.02
0.34 :1: 0.05
0.46 :1: 0.06

0.33 :1: 0.05
0.37 :t 0.04

d
0.019
0.178
0.077
0.063
0.084
0.316
0.108
0.052
0.243
0.123
0.251
0.813
0.831
0.793
0.227
0.126
0.466

0.632
0.085

¢mu

-1.66 :1: 0.10
-0.72 :t 0.04
-0.70 :l: 0.05
-0.15 :l: 0.04
—0.16 :1: 0.04
-0.16 :1: 0.05
0.06 :1: 0.06
0.41 :1: 0.03
0.42 :1: 0.04
0.39 :1: 0.08
0.44 :1: 0.03
0.43 :1: 0.07
0.48 :1: 0.04
0.31 :1: 0.03
-0.37 :1: 0.06
-0.68 :1: 0.05
-0.69 :1: 0.04
-0.77 :t 0.05
-1.27 :h 0.04

d
0.028
0.235

0.302
0.129
0.307
0.066
0.049
0.376
0.579
0.438
0.547
0.489
0.423

0.404
0.522

0.536

¢mat

1.87 i 0.22
1.29 :1: 0.05

0.77 :1: 0.04
0.75 :1: 0.05
0.76 :1: 0.14
0.68 :t 0.04
0.52 :1: 0.03
0.69 :h 0.03
0.74 :1: 0.06
0.71 :t 0.03
0.91 :1: 0.04
0.86 :1: 0.03
0.94 :t 0.04

1.03 :1: 0.05
1.03 :1: 0.04

1.07 :1: 0.05

d
0.164
0.450
0.755
0.211
0.142
0.338
0.114
0.351
0.526
0.090
0.439
0.326
0.503
0.033
0.008
0.277
0.285

0.890
0.169

¢mu

0.76 :1: 0.10
1.04 :1: 0.04
0.97 :1: 0.04
1.03 :1: 0.03
0.99 :1: 0.03
1.04 i: 0.07
0.90 :1: 0.03
0.65 :1: 0.02
0.61 :t 0.02
0.55 :1: 0.04
0.49 :1: 0.03
0.38 :1: 0.04
0.36 :1: 0.03
0.18 :1: 0.03
-0.18 :L- 0.05
~0.27 :1: 0.04
-0.25 :t 0.04

-0.34 :1: 0.04
-0.88 i 0.03

 

 

11.1 D

V14

V15

V17

V18

 

14000
20950
21650
24400
26950
27350
29140
33875
35000
35400
36488
37500
37950
39750
43360
44133
44156
44180
44820
48660

0.014
0.164
0.353
0.367
0.226
0.201
0.212
0.208
0.201
0.137
0.084

0.432
0.412
0.302
0.456
0.392

0.678
0.228

¢mu

0.16 :h 0.10
0.22 :1: 0.05
0.17 :1: 0.08
0.14 :1: 0.05
0.15 :h 0.05
0.20 :h 0.08
0.08 :1: 0.10
0.32 :1: 0.06
0.32 :h 0.02
0.27 :1: 0.05
0.29 :1: 0.03

0.42 :1: 0.06
0.40 :1: 0.05
0.35 :1: 0.05
0.30 :1: 0.06
0.35 :1: 0.06

0.31 :1: 0.06
0.45 :h 0.04

d
0.024
0.218
0.470
0.521
0.399
0.183
0.141
0.235
0.330
0.049
0.365
0.229
0.148
0.262
0.440
0.580
0.349

0.357
0.101

¢mu

0.36 :1: 0.08
0.17 :h 0.04
0.22 :1: 0.08
0.08 :1: 0.05
-0.10 i 0.04
0.03 :1: 0.05
-0.45 :1: 0.02
0.25 :1: 0.03
0.37 :1: 0.03
0.39 :1: 0.04
0.47 :t 0.03
0.54 :1: 0.06
0.58 :1: 0.04
0.51 :1: 0.05
0.40 :l: 0.05
0.36 :1: 0.05
0.38 :1: 0.08

0.32 :1: 0.05
0.63 :1: 0.03

0.023
0.142

0.287

0.118
0.389
0.335
0.327
0.082
0.215
0.370
0.235

0.400
0.278
0.407

0.777
0.302

¢maz

0.94 :1: 0.15
0.59 :1: 0.05

0.82 :1: 0.05

0.54 :1: 0.06
0.67 :1: 0.10
0.50 :1: 0.10
0.49 :t 0.05
0.54 :1: 0.04
0.59 d: 0.04
0.50 :1: 0.06
0.39 :1: 0.05

0.53 :1: 0.08
0.55 :1: 0.10
0.47 :1: 0.12

0.49 :1: 0.10
0.59 :1: 0.10

0.530
0.649

0.645
0.055
0.040
0.702
0.794
0.183
0.598
0.687
0.765
0.141
0.146
0.323

0.815
0.051

¢mas

0.32 :1: 0.04
0.32 :1: 0.06

0.32 :1: 0.06
0.30 :1: 0.07
0.27 :1: 0.03
0.32 :1: 0.03
0.30 :1: 0.05
0.27 :1: 0.03
0.35 :1: 0.10
0.29 :1: 0.04
0.29 :1: 0.05
0.35 :1: 0.06
0.41 :1: 0.05
0.43 :1: 0.04

0.40 :h 0.05
0.55 :1: 0.04

 

 

215

Table B.1. Cont’d

 

 

11.1 D

V19

V20

V22

V23

 

14000
20950
21650
24400
26950
27350
29140
33875
35000
35400
36488
37500
37950
39750
43360
44133
44156
44180
44820
48660

0.074
0.536

0.377

0.604
0.209
0.461
0.609
0.646
0.059
0.422
0.309
0.237
0.337
0.534
0.428

0.867
0.514

¢m¢s

0.71 :h 0.10
0.44 :1: 0.04

0.44 :1: 0.04

0.45 :t 0.03
0.48 :1: 0.03
0.51 :1: 0.02
0.51 :1: 0.02
0.50 :1: 0.03
0.57 :1: 0.03
0.50 :1: 0.03
0.60 :1: 0.03
0.66 :1: 0.03
0.69 :1: 0.04
0.72 :1: 0.04
0.72 :1: 0.04

0.71 :1: 0.04
0.84 :1: 0.02

¢mas

0.63 :1: 0.05

0.77 :1: 0.10
0.69 :1: 0.02

0.58 :1: 0.03

0.58 :1: 0.05

0.45 :1: 0.03

0.650
0.852

0.381

0.784
0.319
0.298
0.911
0.628
0.094
0.639
0.738
0.527
0.018
0.457
0.503

0.484
0.467

¢mas

0.40 :1: 0.10
0.50 i 0.03

0.54 :1: 0.02

0.49 :1: 0.08
0.45 :1: 0.04
0.47 :1: 0.03
0.51 :1: 0.01
0.56 :1: 0.02
0.62 :1: 0.02
0.65 :1: 0.04
0.66 :1: 0.03
0.86 :1: 0.03
1.02 :1: 0.03
1.02 :t 0.06
1.25 :h 0.10

1.03 :1: 0.06
1.27 :h 0.03

d
0.638
0.771

0.839

0.417
0.372
0.468
0.418
0.290
0.545

0.679
0.729
0.255
0.385
0.183

0.463
0.170

¢mac

0.40 :1: 0.10
0.28 :1: 0.03

0.21 :1: 0.04

0.10 :1: 0.08
0.17 :1: 0.04
0.12 :1: 0.03
0.14 :1: 0.02
0.15 :1: 0.02
0.16 :1: 0.02

0.11 :1: 0.03
0.14 :l: 0.02
0.09 :1: 0.04
0.05 :1: 0.04
0.08 :t 0.05

-0.01 :1: 0.04
-0.24 :1: 0.02

 

 

HJD

V24

V25

V26

V28

 

14000
20950
21650
24400
26950
27350
29140
33875
35000
35400
36488
37500
37950
39750
43360
44133
44156
44180
44820
48660

¢mu

0.35 :t 0.12

0.17 :1: 0.20

0.41 :1: 0.07
0.04 :1; 0.05
0.11 :1: 0.06

0.24 :1: 0.05

0.22 :k 0.13
0.09 :t 0.12

0.13 :1: 0.04

0.217
0.216

0.632

0.707
0.407
0.551
0.626

0.299
0.965
0.700
0.415
0.478
0.573
0.210

0.871
0.496

¢mu

0.55 :1: 0.08
0.51 :1: 0.02

0.54 :1: 0.06

0.54 :1: 0.06
0.49 :1: 0.02
0.49 :h 0.03
0.49 :t 0.02

0.49 :t 0.02
0.54 :1: 0.12
0.50 :1: 0.02
0.50 :1: 0.01
0.48 :1: 0.02
0.46 :1: 0.04
0.48 :1: 0.05

0.48 :1: 0.04
0.50 :1: 0.03

0.136
0.371

0.072
0.142
0.670
0.566
0.290

0.584
0.331
0.322
0.072
0.405

0.524
0.211

¢m 68

0.83 :1: 0.05
0.37 :t 0.05

0.09 :1: 0.10
-0.04 :1: 0.10
-0.10 :1: 0.05
0.00 :1: 0.06
-0.03 :1: 0.03

0.07 :1: 0.06
0.05 :1: 0.06
0.10 :1: 0.06
0.07 :l: 0.07
0.08 :1: 0.06

0.01 :1: 0.07
0.06 :h 0.06

0.227
0.753

0.022
0.483
0.822
0.523

0.330
0.341
0.447
0.046
0.527
0.669
0.460

¢mas

0.67 :h 0.25
0.57 :1: 0.04

0.55 :1: 0.05
0.57 :1: 0.02
0.56 :1: 0.02
0.55 :1: 0.02

0.55 :1: 0.02
0.54 :1: 0.02
0.55 i 0.03
0.57 :1: 0.04
0.58 :1: 0.06
0.58 :1: 0.03
0.57 :1: 0.04

 

216

Table B.1. Cont’d

 

 

111 D

V29

V30

V31

V32

 

14000
20950
21650
24400
26950
27350
29140
33875
35000
35400
36488
37500
37950
39750
43360
44133
44156
44180
44820
48660

0.354
0.513

0.314

0.037
0.524
0.539
0.148
0.348
0.190

0.345
0.300
0.624
0.065

0.774
0.457

¢m¢s

0.50 :1: 0.12
0.26 i 0.05

0.22 :h 0.07

0.35 :1: 0.04
0.37 :1: 0.07
0.54 :1: 0.03
0.47 :1: 0.03
0.50 :1: 0.05
0.48 :1: 0.03

0.47 :1: 0.05
0.50 :l: 0.04
0.46 :1: 0.05
0.49 :1: 0.05

0.56 :t 0.05
0.56 :1: 0.04

d
0.200
0.168

0.230

0.146
0.050
0.315
0.327
0.230
0.262
0.336
0.227

0.246
0.241
0.400

0.639
0.354

¢maz

0.95 :1: 0.11
0.94 :1: 0.05

1.05 :1: 0.05

1.21 :t 0.07
1.06 :1: 0.10
0.85 :1: 0.08
0.95 :1: 0.03
0.98 :1: 0.05
0.99 :1: 0.03
0.91 :1: 0.07
1.07 :1: 0.05

0.90 :1: 0.06
0.92 :1: 0.07
0.96 :1: 0.08

1.10 :1: 0.07
1.00 :1: 0.06

d
0.313
0.316

0.241

0.124
0.023
0.292
0.214
0.323
0.031

0.113
0.195
0.135
0.212
0.128

0.620
0.319

¢mu

0.53 :1: 0.08
0.42 :1: 0.04

0.43 :1: 0.04

0.38 :1: 0.08
0.48 :1: 0.06
0.47 :t 0.03
0.43 :1: 0.03
0.66 :1: 0.08
0.45 :1: 0.03

0.42 :1: 0.04
0.46 :1: 0.04
0.49 :1: 0.06
0.47 :1: 0.07
0.61 :1: 0.15

0.55 :1: 0.07
0.48 :1: 0.06

d
0.450
0.351

0.508
0.011
0.154
0.611
0.468

0.020
0.533

0.523

0.624

0.205

¢maz

0.95 :1: 0.15
0.80 :1: 0.03

0.77 :1: 0.03

0.76 :1: 0.06
0.72 :1: 0.04
0.75 :1: 0.02
0.79 :1: 0.03
0.77 :1: 0.04
0.78 :1: 0.02

0.93 :1: 0.03

0.93 :1: 0.05

0.95 :1: 0.04

 

 

H.) D

V35

V36

V38

V39

 

'14000
20950
21650
24400
26950
27350
29140
33875
35000
35400
36488
37500
37950
39750
43360
44133
44156
44180
44820
48660

0.219
0.161

0.345

0.993
0.425
0.178
0.695
0.437
0.309

0.173
0.369
0.002
0.385
0.430

0.746
0.326

¢maz

0.19 :1: 0.10
0.14 :1: 0.06

0.06 :t 0.04

0.10 :1: 0.04
0.12 :1: 0.04
0.30 :1: 0.06
0.35 :1: 0.03
0.36 :1; 0.08
0.38 :1: 0.03

0.35 :1: 0.05
0.39 :1: 0.03
0.55 :1: 0.05
0.59 :1: 0.05
0.60 :1: 0.05

0.60 i 0.05
0.59 :1: 0.03

¢m08

0.22 :1: 0.04

0.21 :1: 0.03

0.39 :1.- 0.03

0.21 :1: 0.04

0.16 :t 0.04

0.194
0.663

0.551

0.605
0.327
0.207
0.679
0.714
0.246
0.742
0.683
0.542
0.244
0.289
0.219

0.772
0.140

$0302

0.59 :1: 0.10
0.64 :1: 0.06

0.63 :t 0.05

0.69 :1: 0.05
0.80 :1: 0.03
0.93 :1: 0.03
0.99 :1: 0.04
0.98 :1: 0.05
0.95 :1: 0.03
0.96 :1: 0.08
0.94 :1: 0.05
1.05 :1: 0.04
0.89 :1: 0.06
0.84 :l: 0.04
0.94 :1: 0.05

0.79 :1: 0.04
0.63 :r 0.03

0.082
0.363

0.053

0.262
0.349
0.190
0.240
0.332
0.032
0.178
0.100
0.325
0.045
0.306
0.335

0.880
0.192

¢mu

1.08 :1: 0.20
0.89 :1: 0.04

0.97 :l: 0.05

0.92 :1: 0.10
0.93 :1: 0.12
0.89 :1: 0.10
0.80 :1: 0.03
0.81 :1: 0.04
0.84 :1: 0.03
0.94 :t 0.07
0.86 :1: 0.04
0.89 :1: 0.06
0.75 :1: 0.05
0.65 :1: 0.07
0.76 :1: 0.08

0.59 :1: 0.07
0.80 :1: 0.07

 

217

Table B. 1. Cont’d

 

 

 

 

 

 

HJD V40 V41 V42 V43
d ¢mas d ¢mu d ¢mu d ¢mu
14000 0.141 0.17 :1: 0.08 - - 0.061 0.21 :t 0.05 0.391 0.15 :1: 0.10
20950 0.472 -0.06 :1: 0.04 0.056 0.22 :1: 0.05 0.185 -0.25 :1: 0.05 0.153 0.36 :1: 0.06
21650 -— — - - — — - -
24400 0.043 0.00 :1: 0.03 - - 0.283 -0.29 :t 0.06 0.372 0.19 :t 0.06
26950 - - — — — - — -
27350 0.029 0.05 i 0.05 — — 0.448 ~0.36 :h 0.05 0.222 0.44 :1: 0.08
29140 0.094 0.08 :1: 0.05 — - 0.198 -0.25 :1: 0.04 0.176 0.60 :1: 0.06
33875 0.208 0.08 :1: 0.05 — - 0.085 -0.16 :1: 0.04 0.460 0.60 :1: 0.04
35000 0.051 0.14 :1: 0.05 — - 0.674 0.02 :t 0.03 0.384 0.37 :1: 0.04
35400 0.013 0.12 :1: 0.05 -- - 0.468 -0.04 :1: 0.04 0.333 0.36 :h 0.07
36488 0.214 0.07 :t 0.03 - - 0.235 0.07 :1: 0.03 0.147 0.41 :1: 0.03
37500 - - - - 0.666 0.02 :t 0.07 0.307 0.42 :1: 0.07
37950 0.003 0.10 :1: 0.06 — - 0.543 0.07 :1: 0.05 0.115 0.32 :1: 0.05
39750 0.238 0.08 :1: 0.03 — - 0.370 0.17 :1: 0.05 0.315 0.36 :1: 0.06
43360 0.248 0.33 :1: 0.05 0.089 0.17 :1: 0.03 0.063 0.23 :1: 0.04 0.389 0.87 :1: 0.08
44133 0.403 0.35 :t 0.05 - - 0.352 0.22 :1: 0.04 0.364 0.86 :1: 0.06
44156 0.417 0.34 :1: 0.04 0.160 0.95 :1: 0.07 0.408 0.23 :t 0.02 0.353 0.97 :1: 0.06
44180 - - — -— - - 0.109 0.90 :l: 0.05
44820 0.539 0.40 :1: 0.05 — — 0.573 0.24 :1: 0.04 0.845 0.95 :l: 0.06
48660 0.362 0.70 :1: 0.04 - — 0.112 0.45 :1: 0.04 — -
HJD V44 V49 V50 V51
d ¢mas d ¢mae d ¢mar d ¢m¢z

14000 0.052 0.60 :1: 0.15 — — — - 0.089 0.75 :1: 0.10
20950 0.254 0.74 :1: 0.04 0.193 0.00 :t 0.03 0.026 0.35 :1: 0.05 0.052 0.96 :1: 0.05
21650 - — - -— — — - —
24400 0.336 0.80 :t 0.04 - — - - 0.000 1.00 :1: 0.05
26950 - - — - — — — —
27350 - - - - - — - -
29140 0.247 0.62 :1: 0.03 0.175 0.17 :l: 0.05 0.049 0.37 :1: 0.05 0.464 1.09 :1: 0.04
33875 0.529 0.67 :1: 0.02 0.713 0.78 :1: 0.03 0.018 0.44 :1: 0.04 0.312 1.02 :1: 0.05
35000 0.565 0.73 i: 0.03 - - - — 0.280 1.02 :1: 0.05
35400 0.164 0.70 :1: 0.05 — - — — 0.019 1.04 :1: 0.06
36488 0.234 0.69 :1: 0.03 - - — — 0.062 1.01 :1: 0.03
37500 - - - — - - - —
37950 0.333 0.71 :1: 0.04 — - — - — -
39750 - — — - - — — —
43360 0.502 0.97 :1: 0.05 0.179 0.99 :1: 0.05 0.160 0.43 :1: 0.06 0.231 1.24 :h 0.05
44133 0.525 0.95 :1: 0.04 - - — — - -
44156 0.210 1.05 :1: 0.05 0.243 0.98 :1: 0.04 0.265 0.40 :1: 0.04 0.119 1.23 :1: 0.06
44180 - - — - - — - -
44820 0.779 0.93 :h 0.04 - — - - -— -
48660 0.141 1.18 :1: 0.03 0.638 0.76 :1: 0.04 0.266 0.55 :1: 0.04 0.353 1.20 :1: 0.05

 

 

218

Table B. 1. Cont’d

 

 

 

 

 

 

HJD V52 V53 V54 V57
d ¢mas d ¢mac d ¢mas d ¢mu
14000 — — 0.075 0.40 :1: 0.15 0.134 0.15 :h 0.15 - —
20950 0.440 1.05 :1: 0.03 0.066 0.75 m 0.04 0.209 0.114 0.05 0.331 0.25 4 0.15
21650 - — - — - - - -
24400 0.057 0.88 a 0.04 0.137 0.74 a 0.05 0.078 0.10 :1: 0.10 — -
26950 — -— -- - — — — —
27350 0.091 0.81 :1: 0.04 0.327 0.65 a; 0.07 0.058 0.02 4; 0.07 - -
29140 0.246 0.75 a 0.02 0.249 0.83 :1; 0.06 0.134 0.04 a 0.15 0.186 0.81 :h 0.03
33875 0.297 0.69 a 0.02 0.265 0.61 :t 0.10 0.367 -0.08 :1; 0.03 0.137 0.40 :1: 0.04
35000 0.075 0.71 :1: 0.03 0.081 0.74 a 0.05 0.137 -012 :1; 0.05 - -
35400 0.139 0.72 m 0.04 0.146 0.79 :1: 0.05 0.137 -004 a; 0.06 - —
36488 0.055 0.70 :1 0.03 0.067 0.82 a 0.05 0.157 -005 :t 0.04 - -
37500 0.016 0.72 :1: 0.05 — - — — - —
37950 0.171 0.75 a 0.03 0.301 0.72 a 0.05 — - - -
39750 - — - — — - - —
43360 0.509 0.83 :1: 0.04 0.066 0.84 :1: 0.06 0.383 0.07 :1 0.06 0.710 0.44 :1: 0.06
44133 0.585 0.86 a 0.04 0.289 0.97 a 0.06 - - - -
44156 0.005 0.80 a 0.06 0.487 0.99 a 0.07 0.342 0.12 :1: 0.12 0.199 0.83 :1: 0.05
44180 - - - — — - — -
44820 0.313 0.87 a 0.04 0.728 0.95 a 0.06 - — — —
48660 0.403 1.05 a 0.03 0.130 1.07 a 0.05 0.223 -001 a: 0.04 — -
HJD V65 V66 V67 V74
d ¢mas d ¢mas d ¢mas d ¢mu

14000 - - — — — _ .. -
20950 0.809 0.22 :1 0.03 0.133 0.69 a: 0.05 — - — -
21650 - — — — — - _ _
24400 - — 0.316 0.72 a 0.05 — — — —
26950 — — — — — .. _ _
27350 - - 0.107 0.67 :1: 0.07 - — — —
29140 — - 0.254 0.68 a 0.08 - — 0.048 0.55 :1: 0.09
33875 — - 0.286 0.713: 0.07 0.115 1.26 :1: 0.08 0.020 0.50 :1: 0.04
35000 - — 0.050 0.70 :1: 0.03 - - — -
35400 — — 0.270 0.72 :t 0.06 — - - —
36488 — - 0.227 0.69 :1: 0.03 - — — —
37500 — — — - ._ _ _ _
37950 — - 0.254 0.74 :1; 0.04 — — - _
39750 — - _ .. _ _ _ _
43360 0.254 0.98 a 0.04 0.079 0.59 :1; 0.06 0.263 0.78 :1: 0.04 0.100 0.69 :1: 0.07
44133 - - 0.176 0.55 a 0.05 - — -— —
44156 0.022 0.75 a 0.04 0.322 0.57 :1: 0.06 0.153 0.82 a: 0.12 0.377 0.17 a 0.03
44180 — — — - _ - _ _
44820 - - 0.555 0.55 :1: 0.05 — — - -
48660 0.525 0.38 a 0.03 0.346 0.63 :1: 0.03 0.230 0.64 a 0.07 0.164 0.03 :1: 0.04

 

 

 

 

219

Table B. 1. Cont’d

 

 

HJD

V97

 

14000
20950
21650
24400
26950
27350
29140
33875
35000
35400
36488
37500
37950
39750
43360
44133
44156
44180
44820
48660

0.42 :1: 0.03
0.37 :1: 0.03

0.37 :1: 0.02

0.37 a 0.04

0.37 :1: 0.03

 

 

 

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