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The Effects of Metallicity on the Brightness of Type la
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THE EFFECTS OF METALLICITY ON THE BRIGHTNESS OF TYPE IA
SUPERNOVAE

By

Kimberly L. Dupczak

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
Astrophysics and Astronomy
2008

ABSTRACT

THE EFFECTS OF METALLICITY ON THE BRIGHTNESS OF TYPE IA
SUPERNOVAE

By
Kimberly L. Dupczak

One of the primary uses of Type Ia supernovae (SNe la) is as standard candles
(objects of known brightness) to calculate the distance to galaxies. SNe Ia are
used as standard candles because they have a peak brightness and lightcurve shape
relationship, where the brighter supernovae have broader lightcurves. While this
relationship, known as the Phillips’ relation, is useful in estimating the peak bright-
ness of SNe la, the cause for this relationship is not completely understood. One
theory for the observed differences is that the amount of 56Ni present determines the
brightness: the more 56Ni, the brighter the supernova. This is not the only difference
observed among SNe Ia. A dichotomy in where these supernovae occur also exists:
the brightest supernovae only occur in galaxies with on-going star formation, while
the dimmest ones tend to occur in galaxies with little to no star formation. Several
theories exist which attempt to explain these observed relationships, including the
possibility of a relationship with the metallicity of the galaxy to the delay time from
progenitor formation. In this thesis, I investigate the effects of the galaxies’ metal-
licities on the brightness of the SN e Ia using samples of supernovae and searching for
correlations between their change in magnitude over fifteen days vs the metallicity
of the host galaxy. The metallicity of the galaxy does not seem to have a strong

effect on the brightness of the SNe Ia.

TABLE OF CONTENTS

List of Figures .................................. iv
1 Introduction: Use of Type Ia Supernovae 1
1.1 Basics of Type Ia Supernovae ...................... 1
1.2 Type Ia Supernovae as Standard Candles ................ 2
1.3 Cosmological Uses for Type Ia Supernovae ............... 3
2 The Physics of Type Ia Supernovae 5
2.1 What Defines a Type Ia Supernova? ................... 5
2.1.1 Differences among SNe Ia .................... 7
2.1.2 Relationship between Peak Brightness and 56N i ........ 8
2.1.3 Relationships between Color, Lightcurves, and MN, ...... 11
2.2 Why Carbon-Oxygen White Dwarfs as the Progenitors? ........ 13
2.2.1 White Dwarfs as the Progenitor ................. 13
2.2.2 Carbon-Oxygen White Dwarfs as the Progenitor ........ 14

2.3 The Single and Double Degenerate Models of Type Ia Supernovae
Progenitors ................................ 16
2.3.1 Single-Degenerate System .................... 16
2.3.2 Double-Degenerate System .................... 17
3 Testing for Correlations 19
3.1 Background ................................ 19
3.2 Data Analysis ............................... 20
3.2.1 The Sample ............................ 20
3.2.2 Test Used ............................. 21
3.23 Am15 VS M3( ........................... 22
3.2.4 Amls vs logoQ )+ 12 ....................... 22
3.2.5 MN, vs log(— + 12 ........................ 25
4 Contemporary Studies 27
4.1 Metallicity Effects ............................. 27
4.2 Two—Component Model .......................... 28
4.2.1 Evidence for the Two-Component Model ............ 28
4.2.2 Evidence against the Two-Component Model .......... 31
4.2.3 Differences between the SN LS and GOODS Surveys ...... 32
4.3 Future Studies ............................... 33

BIBLIOGRAPHY 35

iii

LIST OF FIGURES

3.1 Change in Magnitude of Supernova vs. Magnitude of Host Galaxy . . 23
3.2 Change in Magnitude of Supernova vs. Metallicity of Host Galaxy . . 24
3.3 Mass of Nickel of Progenitor vs. Metallicity of Host Galaxy ...... 26

iv

Chapter 1

Introduction: Use of Type Ia

Supernovae

1.1 Basics of Type Ia Supernovae

Spectroscopically, two types of supernovae exist: Type I supernovae that do not
contain hydrogen in their spectra, and Type II supernovae that do contain hydrogen
in their spectra. These two types are then further broken down into sub-classes based
on the features in their spectra. Type Ia supernovae (SNe Ia) lack Balmer hydrogen
lines and has strong SiII absorption lines in their spectra. SNe Ia are thought to be
the explosion of GO white dwarfs whose masses are near the Chandrasekhar mass
limit, which is the maximum mass that can be supported by electron degeneracy
pressure. White dwarfs are essentially the core of a star that has blown off its outer
layers. While thermonuclear fusion generally does not occur in the white dwarf, it
can be reignited if the white dwarf accretes enough matter on the outside layers to
increase the pressure, and thus the temperature, inside the core. This ignition occurs

as the star approaches the Chandrasekhar mass limit of 1.4 MG (Iben & Tutukov,

1984; Woosley et al., 1986; Phillips, 1993).

1.2 Type Ia Supernovae as Standard Candles

Since SNe Ia are thought to be the result of the same physical process, all of the
supernovae should have approximately the same peak brightness. When the abso-
lute brightness of an object is known, it is possible to find the distance to it after
measuring the apparent brightness. While the peak brightnesses of the supernovae
is not exactly the same for every event, the spread in their intrinisic brightness is
relativley small. Locally, the dispersion is peak magnitude is ~ 0.5 mag in B and
V. When including more distant SNe la in the sample, subluminous events broaden

this dispersion to ~ 1 mag in B and V (Sullivan et al., 2006).

Other advantages SNe Ia have as distance indicators include where they occur
and their lightcurve shape. SNe Ia occur in both spiral and elliptical galaxies, thus
one is not limited by galaxy type when determining the distance to the galaxy
(Colgate, 1979). The homogeneity of the lightcurve shape also puts SNe Ia at an
advantage as a standard candle. The lightcurve of an SNe la is distinguishable from
other types of supernovae. Thus, one can identify a SNe Ia even if it not observed
until sometime after peak brightness. The observed lightcurve can also be fitted to
templates so that the peak brightness of the SNe Ia can be determined (Riess et al.,
1995)

1.3 Cosmological Uses for Type Ia Supernovae

SNe Ia can also be used to determine the Hubble constant Ho and the cosmological
constants OM and QA. Ho relates the recessional velocity of an object to its distance
from us, 22 = Hod. Thus, the further an object is from us in space, the faster it
is moving away from us. OM is defined as the average density of matter over the
whole universe divided by the critical density, where the critical density is the energy
needed to counteract Ho. 52A is defined as the average vacuum energy density over
the whole universe divided by the critical density. Colgate (1979) suggested using
SNe Ia as a way to measure Ho with greater accuracy than other standard candles
The measured luminosity is dependent on the redshift and Ho. Thus, if the rest
frame luminosity is known, one can constrain Ho based on the measured luminosity
and redshift. Goobar & Perlmutter (1995) also advocated the use of standard candles
as a way to measure OM and DA. If (2A is not zero, then the magnitude-redshift
measurement is sensitive to OM and QA through the luminosity distance DL. The

magnitude-redshift distance is defined as
m = M + 5 log[DL(z; QM,QA)] + K + 25, (1.1)

where K is the K—correction applied to the object. The K-correction is a correction
of an object’s magnitude through a filter so that the measurements can be compared

to the object’s magnitude in the rest frame. The luminosity distance DL is defined

 

as
DL(Z;QM,QA)=I1I0+\/ZE S (fl/ [(1 + zl)2(1+ QMZ’) _ z’(2 + 2’)QA]-l/2dZI),
0
(1.2)
where

o if QM + 0A < 1, 8(3) = sin(x), K =1— QM — 0A, and the universe is defined

as closed

0 if QM +QA > 1, S(:r) = sinh(:r), it = 1— QM - 52A, and the universe is defined

as open

0 if QM + (2A = 1, S(a:) = 2:, rs = 1, and the universe is defined as flat.

Using these two equations, one can predict the apparant magnitude of a standard
candle at a given redshift 2 based on the pair of OM and {2A. When actual apparent
magnitude measurements of a standard candle are made at a specific 2, one can
narrow the ranges of OM and 52A. Two such measurements at different redshifts can
define two ranges of possible OM and 9A that cross in a more narrowly constrained
region. In the special case of a flat universe, which is the universe predicted by
inflationary theories, the apparent magnitude as a function of z is extremely sensitive
to 9A. A measurement of .a standard candle at z = 1 would strongly constrain DA

and test inflationary theories.

Perlmutter et al. (1999) studied 42 SNe Ia at z = 0.18 — 0.83 and found that
a flat universe with QA=0 is strongly inconsistent with the data. Instead, if the
simplest inflationary models were correct and the universe was flat, then there was
a significant, positive (2A. Therefore, the universe could be flat or there was a small
or no DA. Perlmutter et al. found that if the universe was flat, then QM = 0.28:3;82,
which indicated that 9,, z 0.72. This value of 0A further indicated that the cos-
mological constant A, which is related to (M by (2,, E A/3H02, was a significant
constituent of the energy density of the universe. Results from the Wilkinson Mi-
crowave Anisotropy Probe (WMAP) confirm these values for OM and {2A (Tegmark

et al., 2004).

Chapter 2

The Physics of Type Ia

Supernovae

2.1 What Defines a Type Ia Supernova?

Historically, supernovae were divided into two classes, Type I and Type II. Super-
novae classified as Type I do not contain Balmer hydrogen lines in their optical
spectra, while the supernovae classified as Type II do (Doggett & Branch, 1985). If
the spectrum of the supernova was unavailable, then the supernova could be classi-
fied by the shape of its lightcurve. The lightcurve of a Type I supernova generally
has the following characteristics: a sharp change in the rate of decline occurs about
30 days after maximum brightness with the fast, early decline ending and a slower,
final decline beginning; at this point, the change in magnitude is about 2.7 (Barbon
et al., 1973).

Some spectra and lightcurves of supernova classified as Type I did not have all

of these characteristics. In the mid-80$, astronomers divided Type I supernovae into

two classes: Type Ia have the above mentioned characteristics in their spectra and
lightcurves, and Type Ib do not. The spectra of Type Ia and Type Ib are initially
very different. In a Type la, the optical spectrum at maximum light contains a strong
absorption feature of SiII A6355 and features which are interpreted as overlapping
P-Cygni profiles of neutral and singly ionized intermediate-mass elements, such as
oxygen, silicon, and calcium. (A P-Cygni profile arises when a star has a hot, stellar
wind. The spectrum from such a star contains blue-shifted absorption features,
which arises from material directly along the line of sight moving through the wind,
and red-shifted emission features, which arises from radiation scattering off of the
wind on the back and sides.) The outer layers of the ejecta are mainly composed
of these intermediate mass elements. Permitted FeII lines begin to dominate the
spectra ~ 2 weeks after maximum light. Finally, about one month after maximum
light, features from the intermediate-mass elements disappear and forbidden FeII,
FeIII, and CoIII features become dominant (Branch, 1986; Hillebrandt & Niemeyer,
2000). On the other hand, the optical spectrum of a Type Ib supernova lacks the
intermediate-mass features and the SiII A6355 absorption feature at maximum light.

Instead, the spectrum is dominated by the FeII blends (Branch, 1986).

The lightcurves of Type Ia and Ib supernovae can also be used to distinguish
between the two, especially in the infrared. The infrared lightcurve of a Type Ia
supernova displays an absorption dip ~ 20 days after maximum light and a secondary
peak ~ 30 days after maximum light. On the other hand, a Type Ib light curve
does not contain these features. Instead, the lightcurve falls monotonically after

maximum light (Gaskell et al., 1986).

2.1.1 Differences among SNe Ia

SNe Ia are thought to be the explosion of CO white dwarfs that are approaching
the Chandrasekhar mass limit of 1.4MO. Since the SNe Ia are caused by the same
process, they should all achieve the same peak brightness (Iben & Tutukov, 1984;
Woosley et al., 1986; Phillips, 1993). Observations of several supernovae, however,
questioned the apparent homogeneous nature of SNe Ia. Leibundgut et al. (1993)
reported that SN 1991bg was an unusually dim SNe Ia. Branch & Miller (1993)
confirmed that this was an intrinsically dim supernova, noting that its lightcurve

was fast-declining.

The observation of the dim supernovae having a faster declining lightcurve sup-
ported the peak brightness — initial decline rate correlation claimed by Pskovskii
(1977, 1984). To measure the initial decline rate of the lightcurve, Pskovskii (1984)
defined a slope parameter 6 as the mean rate of decline of the B-band light curve
between the peak brightness and the bend in the light curve, which usually occurs
25-30 days later. Phillips (1993) employed a much simpler method. Instead of mea-
suring the rate of decline, Phillips measured the total amount in magnitudes that
the light curve decayed from peak brightness during some specified period following
peak brightness. A time interval of 15 days showed the greatest discrimination, be-
coming known as the Am15 parameter. SNe Ia with low Am15 values are brighter,

while SNe Ia with high Am”, are dimmer.

Related to the Am15 parameter is the stretch factor of the supernova lightcurve
(Perlmutter et al., 1997). The lightcurves of SNe Ia have the same general shape -
the rate of decline affects how wide the lightcurve is. When working with the stretch
of the lightcurve, the time axis of a template curve is multiplied by a scale factor

to fit the observed data. This allows for an estimation of the peak brightness of the

supernova.

2.1.2 Relationship between Peak Brightness and 56Ni

Colgate & McKee (1969) found that a large mass fraction of 56Ni was critical to
explain the observed lightcurves. The rate of the radioactive heating within the

supernova is determined by the following equation:

dN Ni dNCo

S = film—.00? + QCerT, (2-1)

where q is the energy factor for the reaction. The change in abundance of 56Ni and

56Co are denoted by:
(“V Ni

dt = AfotB—VI’I’TCO (2.2)

 

and
dN o N _ . _

 

where 'y is the inverse of the half-life of the element, and No is the original amount
of 56Ni. After substituting 700 = (111 d)'1, 7N, = (8.7 d)‘1, qu = 3426.1 keV, and
W = 4566.0 keV, we get

S(t) = [7.79 x 1043e—‘/8'7 + 1.41 x 1043 (e‘t/111 — e“/8'7)] ergs s‘lMcg1 (2.4)

for t in days. The decay process 56Ni —-> 56C0 supplies the radiant energy leading
up to the maximum brightness, while the decay process 56Co -+ 56Fe contributes to

the exponential light-decay after peak brightness.

Arnett (1982) expanded on this model. Based on Arnett’s models, the peak

brightness is a function of 56Ni mass: the more 56Ni synthesized, the brighter the

supernova, 01'

L80]
AI i = —, 2.5
N 780,.) ( ’

where L301 is the bolometric luminosity, '7 is a scaling factor, and S (t R) is the rate of
radioactive heating given in 2.4 evaluated at the risetime (time to reach maximum
brightness) in days. Substituting in L301 = L0100'4(4'75‘MB°'), the bolometric mag-
nitude M301 = —19.31 + 0.18 —1.52(s — 1), and 7 = 1.2 (Nugent et al., 1995; Howell
et al., 2006) into the above equation, and evaluating it at t R = 19.5 x s (Astier et al.,

2006), we get
1.1561'4("1)

M , = ,
N 7198—2233 + 1.41 (e-O.1768 _ 6—2.233)

(2.6)

 

where s is the stretch factor for the timescale, and t3 = 19.5 is the risetime in
days for the standard model. Evaluating at s = 1, which is the stretch factor for
the standard template, yields MN, = 0.615 Mg. While the rise to peak brightness
is driven by the decay of 56Ni, the energy released from the decay of 56Co to 56Fe
exceeds that of 56N i at approximately the time of maximum brightness. This is due
to the fact that it takes time for this energy to diffuse out of the star. Thus the
contribution of the 56Co energy to the shape of the lightcurve is seen after the peak

brightness.

Further models by Arnett (1999) demonstrated under what conditions one would
then have the observed Phillips relation. Arnett defined the bolometric luminosity

of the supernova as

LBol = 6NiMNiA(a:l 3!) (2‘7)

Here, cm is the energy of radioactive decay of 56Ni per unit mass, divided by the

mean lifetime of 56Ni rm, and A(:r, y) is the dimensionless function

Amy) = 6-32 / e‘2zy+222zdz. (2.8)
0

Here, a: = t / rm and y = W/ (27m), where Tm is the effective escape time, T). is the
expansion time, and To is the diffusion time. To get the observed Phillips’ relation,
Arnett determined how M (Ni) changed with y. Assuming that To = Rzpn/c, where
R is the radius, p is the average density, K. is a constant opacity, and c is the speed
of light, then

(2'I';,7'0)1/2

27' Ni

or (ThTo)l/2
R2 1/2
°< (a 5")

After substituting in p or M / R3, where M is the total mass, and 77, = 12/1)“, where

 

vac is a characteristic velocity scale, we find

M3 1/2
vac

The total energy of the supernova ESN is

 

ESN = %M<Ufc> .

Thus

cc — . 2.9
y (ESN ( )

Using the above proportion we get

L = 6NiMNiAmax
O< MNiAmax

OC MNi/y

10

where Am“ oc 1/y and E > 0.7 x 1051 ergs (Arnett, 1982, 1999). This equation

gives the Phillips’ relation of brighter SNe Ia have broader lightcurves.

However, if the 56Ni is distributed as a central sphere of pure 56Ni, then the
average distance of the 56Ni to the surface increases with MM, and so does the
probability of energy leakage from gamma and x-ray emission. This leakage changes
the lightcurve shape, and thus the Phillips relation may be destroyed. Alternatively,
if the 56Ni distribution is not a strong function of the MN, at a time several days
after explosion, then the Phillips’ relation is observed (Arnett, 1999, and references

therein) .

2.1.3 Relationships between Color, Lightcurves, and MN,

Color and MN,

Since there is a correlation with the lightcurve shape, and thus Amls, and Mm,
one can estimate the amount of 56Ni in the progenitor. Kasen & Woosley (2007)
created models which estimated the amount of 56Ni based on the Amls. Within
these models, Kasen and Woosley discovered that MN, had a greater effect on the
color and spectroscopic evolutions of the models. The faster-declining (dimmer) SN e
la were redder 15 days later. This color evolution was due to the impact of iron group
lines on post-maximum spectra: dimmer SNe Ia have a more rapid development of
Fe II/Co II lines. Thus, for a given Mm, enhancing the iron group abundance in
the outer layers of the ejecta increased the B-band decline rate, producing dimmer

supernovae.

11

Lightcurve and MN,

How well the MN, is mixed within the progenitor has an effect on the shape of the
observed lightcurve, specifically in the infrared. Near-infrared observations, such as
those with the I- through K-bands, show that the supernovae have a secondary max-
imum roughly 20-30 days after the primary maximum. Kasen (2006) demonstrated
that these double maxima in SNe Ia are directly related to the ionization evolution
of the iron group elements, such as 56Ni, in the supernovae ejecta. Specifically, the
N IR emissivity of iron /cobalt increases sharply at a temperature T w 7000K. The
cooling of the iron rich layers of ejecta to this temperature is accompianied by a

sudden increase in emission at NIR wavelengths.

Kasen (2006) also demonstrated the dependence of the secondary maximum on
the mixing of the MN, in the progenitor. If the progenitor has a thoroughly mixed
composition, then the first and second maxima are indistinguishable in every band.
If the composition is more stratified, then the two maxima are more distinguishable
from each other. Thus, the appearance of the maxima is useful in constraining
the exact degree of mixing within the progenitor. The MN, also has an effect on the
appearance of the second maximum. In the visible bands, the more Mm, the brighter
the supernova (Arnett, 1982, 1999), thus the more pronounced the first maximum.

This effect can also be seen in the second maximum in the NIR bands.

12

2.2 Why Carbon-Oxygen White Dwarfs as the

Progenitors?

2.2.1 White Dwarfs as the Progenitor

The features observed in the spectra and lightcurves of Type Ia supernovae indi-
cate that a compact object is the progenitor of these phenomena. The change in
the spectrum from being dominated by intermediate-mass elements to FeII approxi-
mately two weeks after maximum light indicates that the supernovae are caused by
the thermonuclear explosions of compact objects, such as the cores of main-sequence
stars with masses 6-8 M9 or white dwarfs. The presence of some UV flux, the width
of the peak of the early lightcurve, and the fact that models of the radioactive decay
of 56Ni -+ 56Co —> 56Fe fit the observed emi$ion well, support the idea that the
progenitor is a star with a radius of less than 10,000 km (Hillebrandt 85 N iemeyer,
2000). The observation of 56Fe and the radioactive decay products of 56Ni and 56Co
in the spectrum of the supernova supports this hypothesis. The velocities inferred
from spectral measurements and the total energy emitted from the supernovae agree
with the calculations one would obtain by converting a fraction of the mass of a white
dwarf to 56Fe or 56N i. The degenerative nature of white dwarfs guarantees that a
nuclear runaway reaction will convert a substantial fraction of the mass of a white
dwarf on a short timescale, with the resulting lightcurve being generated by the

decay of the radioactive species in the reaction (Woosley et al., 1986).

Other evidence for white dwarfs being the progenitors include the location of the
supernovae. Unlike core-collapse supernovae, SNe Ia occur in all types of galaxies.
This implies that the progenitor is an evolved star, such as a white dwarf. SNe Ia

are not associated with HII regions in spiral galaxies, which are areas of active star

13

formation (van Dyk, 1992), and they also occur in elliptical galaxies, which has little
to no active star formation (Turatto et al., 1994). Both observations imply that the
supernovae do not result from the core collapse of stars with masses greater than 8

M0 (Branch et al., 1995).

2.2.2 Carbon-Oxygen White Dwarfs as the Progenitor

Astronomers further suspect that white dwarfs composed of carbon and oxygen, as
opposed to helium or oxygen, neon, and magnesium, are the progenitors of SNe
Ia. While He white dwarfs can be formed from stars in a binary system and can
explode, the ejected matter does not match the observations of the spectra of SNe
Ia. Woosley et al. (1986) have shown that the spectrum of He white dwarf explosion
severely disagrees with the observed spectrum of SN e la at early and late times. For
example, the helium white dwarf models do not contain any appreciable abundance
of silicon or sulfur, two elements which have high abundances in the spectra of SNe
Ia. Also, the high velocities associated with the explosion would cause broader and
more highly shifted emission lines. The models in Woosley et al. (1986) indicate
that the higher velocities would cause broader emission lines of iron than what is
observed. Other consequences of the higher velocities include very high ionization

stages of iron at later times, which is in disagreement with observations.

O-Ne-Mg white dwarfs are also possible progenitors for SNe Ia. However, if the
O—Ne—Mg white dwarf does approach its Chandrasekhar mass limit, it is expected to
collapse and form a neutron star, not explode into a supernova. Miyaji et al. (1980)
have shown that as the O—Ne—Mg white dwarf accretes matter from a companion
star, electrons capture onto 24Mg and 24Na first, then onto 20N e and 20F later. This

3

causes 20Ne and 16O to explosively ignite at a central density of ,0c > 2 x 1010 g cm’ .

At this high of a density, the fast electron captures onto the nuclear statistical

14

equilibrium material quickly reduces the Chandrasekhar mass limit to less than
that of the actual mass of the core, inducing gravitational collapse. Gutierrez et al.
(1996) demonstrated that if convective mixing occurs, then the range of densities for
explosive ignition is (9.74 — 21.2) x 109 g cm‘3. These values lie above the minimum
ignition density for gravitational collapse: 9 x 109 gcm‘3. Thus, unless the O-Ne-
Mg white dwarf ignites 24Ne before the electron captures onto 24Mg and 24Na, the
core will collapse to nuclear matter densities. In the case of a mass-accreting white

dwarf, the result is a non-explosive collapse to a neutron star.

Models of carbon—oxygen white dwarfs, on the other hand, best reproduce the ob-
served conditions described in the previous section (Woosley et al., 1986; Hillebrandt
& Niemeyer, 2000). The element 56Ni is the dominant product of nucleosynthesis
starting from fuel with equal numbers of protons and neutrons, like 12C and 16O
(Woosley et al., 2007). Also, unlike the O-Ne-Mg white dwarfs which will gravita-
tionally collapse as it approaches its Chandrasekhar mass limit, a CO white dwarf
will undergo carbon deflagration in its core as it approaches its Chandrasekhar mass
limit, as long as the mass accretion rate is high enough so that matter can accu-
mulate on the white dwarf uninterrupted by mass ejection (Taam, 1980). Based
on models, carbon deflagration naturally accounts for the existence of intermediate
mass elements Ca through O in the outer layers of the white dwarf. These models
also show that the ejecta contains substantial amounts of Ca through Si and produce
Si peak elements, which are consistent with observations. Finally, the carbon de-
flagration model predicts complete disruption of the progenitor, which is consistent

with observations (Nomoto et al., 1984).

15

2.3 The Single and Double Degenerate Models of

Type Ia Supernovae Progenitors

Most astronomers agree that while a CO white dwarf is the progenitor of a SNe
Ia, the white dwarf must be in a binary system in order to accrete enough matter
to approach the Chandrasekhar mass limit in order to explode. The white dwarfs
accrete mass from the companions until they explode (Branch et al., 1995, and
references therein). Two of the most common models are the single degenerate (SD)
system, where a non-degenerate companion, eg, a red giant, orbits the white dwarf,
and a double-degenerate (DD) system, where two white dwarfs orbit each other
(Nomoto, 1982; Iben & Tutukov, 1984).

2.3.1 Single-Degenerate System

In the SD system, a non-degenerate companion star begins to expand over its Roche
lobe (limit where orbiting material is gravitationally bound to the star) and accretes
matter onto the white dwarf. When enough hydrogen-rich material is accreted onto
the surface of the white dwarf, hydrogen-shell burning begins. If the rate of accretion
is rapid, then burning is stable and the resultant helium settles onto the surface of
the white dwarf. Eventually, if enough mass accretes rapidly enough, the pressure
increases enough for carbon fusion to occur in the core. While the pressure in the
core increases slowly, the temperature continues to rise, which increases the fusion
rate. This in turn leads to a runaway reaction, and the white dwarf explodes due
to the carbon deflagration (Nomoto, 1982). This central carbon-deflagration of the
white dwarf would produce iron and traces of elements from carbon to silicon, which

matches observations (Matteucci et al., 2006). The observed diverisity in SNe Ia

16

would be caused by differences in the ejected MN, (Branch, 2001).

However, there is a narrow range of permitted values for steady mass accretion
rate onto the white dwarf. If the accretion rate is not steady, then the white dwarf
could undergo a nova explosion, where it expels its outer layers but does not de-
stroy itself, and mass loss. Because of this, the white dwarf would never reach the
Chandrasekhar mass limit (Matteucci et al., 2006). Also, simulations of this sce-
nario imply the presence of low-velocity Ha—emission in the late-time spectra of the
supernovae since a portion of the companion’s envelope gets mixed with the ejecta.
While the Ha-emission has not been detected, it rarely has been sought (Leonard,

2007)

2.3.2 Double-Degenerate System

In the DD system, two CO white dwarfs coalesce until their combined mass exceeds
the Chandrasekhar mass limit. For degenerate white dwarfs, the larger the mass, the
smaller the radius of the star. Thus, the lower mass white dwarf will fill its Roche
lobe first. This matter is accreted onto the higher mass white dwarf. However,
the matter does not settle onto the accreting white dwarf immediately. Instead,
matter first forms a disk around the accreting white dwarf. The disk formation
may be a response to conserve angular momentum. This disk will then cause the
accreting white dwarf to expand its radius until it is at least as large as that given
by the Eddington luminosity, or the maximum luminosity a star can have before the
radiation pressure exceeds the gravitational force. Eventually, the accreting white
dwarf will be able to accept the matter from the disk surrounding it. When enough
matter builds up, then like the SD system, the white dwarf will explode due to
carbon deflagration (Iben & Tutukov, 1984).

17

While the DD scenario would explain the lack of hydrogen observed in the spec-
tra, there are several problems with it observationally and theoretically. Observa-
tionally, of the ~ 120 DD systems known, none of them are in excess of Chan-
drasekhar mass limit. Theoretically, the largest mergers would most likely lead to a
collapse to a neutron star rather than a thermonuclear explosion (Leonard, 2007).
However, Piersanti et al. (2003) found that if the mass accretion rate M and initial
angular momentum coo of the accreting white dwarf is low enough, then the star
can accrete enough matter to approach 1.4M0. Otherwise, if M and wo are too

high, then the accreting star becomes gravitationally unbound and no matter can

be added to it.

18

 

Chapter 3

Testing for Correlations

3. 1 Background

Observations have shown that a disparity exists between the locations of dim and
bright supernovae. Dimmer supernovae tended to occur in galaxies with zero-to—low
star formation (“passive”); brighter supernovae in galaxies with high star formation
(“active”)(Hamuy et al., 2000; Hachinger et al., 2006). The passive galaxies tend
to be older elliptical galaxies with higher metallicity. No bright supernovae have
been observed in these types of galaxies. The active galaxies tend to be young spiral
galaxies with lower metallicity. Unlike the passive galaxies, active galaxies could
host dimmer supernovae (Hamuy et al., 2000; Gallagher et al., 2005; Hachinger
et al., 2006).

Two galactic properties that could affect the peak brightness of the supernovae
within the galaxy are the metallicity of the galaxy and the age of the galaxy. Hamuy
et al. (2000) pointed out that the brightest supernovae occurred in the least lumi-

nous galaxies. These galaxies also tend to be bluer in color. The galaxies are less

19

luminous because they are less massive, and therefore not able to retain the metals
as efficiently. If there are less metals in the progenitor, the energy will be able to
radiate outwards more efliciently, thereby reducing diffusion time and leading to a
brighter supernova. Thus, metallicity of the galaxy could be a factor of variations
in peak brightness. On the other hand, since these galaxies are bluer, they are
younger. Thus, age could be a factor. However, one characteristic could mask the
other’s importance in determining the brightness of the supernova. For example,
younger galaxies tend not to have a very high metallicity because the stars within
the galaxy have not had the time to produce the metals. Thus, it is important to

separate the effects of one factor over the other.

Since this difference in location of the supernovae does exist, we wanted to see
if the metallicity of the progenitor was a factor in the brightness of the supernova.
Timmes et al. (2003) showed that the metallicity of the progenitor would affect the
amount of 56N i: the higher the metallicity, the lower the amount of 56N i. When
testing for a correlation between the metallicity of the progenitor and the brightness
of the supernova, we had to assume that the metallicity of the progenitor was similar
to the average metallicity of the galaxy. It is impossible to measure the individual
metallicity of the progenitor. With a large enough sample, a trend in the metallicity

ought to be discernable.

3.2 Data Analysis

3.2.1 The Sample

The sample of the supernovae came from Hachinger et al. (2006) and Gallagher

et al. (2005) papers. From these papers I gathered the supernova names, Amls

20

parameter and corresponding error, and host galaxy name. The Amls parameter
and corresponding error were important because this indicates the brightness of the
supernova: brighter supernovae have smaller Am”, values. However, information
about the properties of the host galaxy, such as absolute brightness and metallic-
ity, was usually found from other sources or calculated, which is described below.
Following the criteria listed in Reindl et al. (2005), I removed any supernovae that
were considered “non-standard.” The non-standard criteria included those super—
novae that were very overluminous and very underluminous. The overluminous ones
had peculiar spectra, while the underluminous ones were very red and had very fast

decline rates, Amlsz 1.9.

3.2.2 Test Used

To determine any correlations among the variable, we used the Spearman correla-
tion test, which assesses how well an arbitrary monotonic function could describe
the relationship between two variables, without making any assumptions about the
frequency distribution of the variables. In order to do this, the two variable arrays
are ranked from lowest to highest. The test then compares the ranks of the two
corresponding variables and returns a value p between -1 and 1. The value p is

determined by
iii (3,1)

:1.—
p n(n2-1)

where d is the difference between the two corresponding variables and n is the number
of pairs of values. The closer the number is to -1 or 1, the stronger the correlation

between the two variables.

21

3.2.3 Am15 vs MB

In the beginning, as a proxy for the metallicity of the galaxy, we used the absolute
brightness MB of the galaxy, which is generally more readily available than the
metallicity. Since there is a tighter correlation between M B and metallicity of a
spiral galaxy (Henry & Worthey, 1999; Pilyugin et al., 2004), I only looked at the
supernovae that occurred in spiral galaxies. The values for Am15 and M 3 came from
the above papers. If the host galaxy did not have an M 3 listed in the paper, then
the value came from the NASA/IPAC Extragalactic Database. After plotting the
Am15 of the supernvovae vs. the M B of the galaxy, I ran the Spearman correlation
test. With p = —0.36, the test did not reveal a significant correlation between Amls
and M B at the 95% confidence level.

3.2.4 Am15 vs log (3) + 12

Later, I followed a procedure outlined in Tremonti et al. (2004) to calculate the
metallicity of the galaxy using its M 3. Based on the spectra of 53,000 star-forming
galaxies within the Sloan Digital Sky Survey (SDSS), the procedure calculates the
metallicity of the galaxy using strong optical nebular lines, which is an improvement
over methods that rely on single line ratios. The advantages are: the S / N in emis-
sion lines can greatly exceed the S / N in the continuum; the calculations are free of
uncertainties due to age and a-enhancement; easier to interpret the results because
they reflect present-day metal abundance rather than the luminosity-weighted aver-
age of previous stellar generations. The disadvantage is that this method is limited

to galaxies with on-going star formation.

Tremonti et al. (2004) calculated the metallicity as log (g) + 12, where g is the

ratio of the oxygen abundance to the hydrogen abundance in the galaxy. To esti-

22

 

 

20IIIllIFTIITIIITITIHIIIIITIIII]ITTHIIIIIIFIIIIITIT

h— d

_ l T

“57. r a

_ i --
"O, a f % ' ,l -

dm,5

i -

 

05 u... —

 

 

0.0 l l l 1 l l 1 l 1 L 1 L 1 1 L 1 l l L Li 1 L L I l l 1 I I l I L l l 1 LLI I 1 LA 1 I l l L 1
-22 —21 —2O —l9 —18 —17
Absolute M,3

 

Figure 3.1: The change in magnitude of the supernova over 15 days (AmIS) vs. the
absolute magnitude of the host galaxy (M B). A Spearman correlation test on the
data indicated that there is a very weak correlation between M B of the host galaxy
and Amls of the supernova.

23

 

20 r r r l r r T l r I Y T r I l I F

drn,5
23
I I T l
we
7WD BK—l .
l—filf-‘l
#2334.
Has—i
i—x—HH i—x—i
He i—sK—i
r—aK—i
9'“ HE’S H“
rare
Haiti
I l I l

 

 

 

 

0.5 — —-
0.0 I 4; 1 4L 1 l 41 I l 1 l l L I l I L I J
8.4 8.6 8.8 9.0 9.2 9.4

Log (O/H) + 12

Figure 3.2: The change in magnitude over 15 days of the supernova (Am15) vs the
metallicity of the host galaxy (log (g) + 12). A Spearman correlation test indicated
that there was no significant relationship between the metallicity of the host galaxy
and the brightness of the supernova.

mate the metallicities of the galaxies in their sample, they simultaneously fitted the
most prominent emission lines ([011], H8, [0111], Ha, [NH], and [811]) with a model
designed for the interpretation of integrated galaxy spectra. Based on the metallic-
ities and MB of the galaxies, they found that log (g) + 12 = —0.185(i0.001)MB +
5.238(:l:0.0018). I converted M3 of the host galaxies to log (3) + 12 so that I could
directly compare Amls to the metallicity of the galaxy. After obtaining the metal-
licity of the galaxies from our sample using this equation, I plotted Am15 vs. the
results. I also performed the Spearman correlation test on the results as a check.
Since M3 and log (g) + 12 are linearly related, the magnitude of the Spearman

correlation coefficient should be the same, and it was at p = 0.36.

24

3.2.5 MN, vs log (g) + 12

As a final test, I calculated the MN, of the progenitor following the procedure outlined
in Kasen & Woosley (2007). This procedure calculates the MN, based on the Am15 of
the supernova. Astronomers believe that the brightness of the supernova is driven
by the amount of 56Ni decayed. Thus, the more 56Ni decayed, the brighter the
supernovae. The models used in Kasen & Woosley (2007) demonstrated how the
peak brightness and the Amls of the supernova changed with Mm. These models
were also designed to follow the Phillips’ relation. Using the values of MN, and
Am15 listed in Kasen & Woosley (2007), I interpolated the MN, the supernovae in
my sample would have had based on the Amls values. After I did that, I plotted the
MN, vs. 10g (g) +12 and ran the Spearman correlation test. With p = —0.36, the test
indicated that there is no significant correlation between the MN, and log (3) + 12

at the 95% confidence level.

The lack of significant relationships within the above tests indicate that the
metallicity of the galaxy, and by extension, the progenitor, is not a strong parameter

in the peak brightness of the supernova.

25

 

0.23—— 3} H l % l% i
. :l i €

l l ;

 

MNI
I I
I—l-)K—‘

 

 

 

0.2 — _
0.0 . . . 1 . . r l . 1 t l . i . l . . .
8.4 8.6 8.8 9.0 9.2 9.4

Log (O/H) + 12

Figure 3.3: The mass of nickel in the progenitor (Mm) vs. the metallicity of the
host galaxy (log (g) + 12). A Spearman correlation test indicated that there is no
significant correlation between MN, and log (g) + 12.

26

Chapter 4

Contemporary Studies

4.1 Metallicity Effects

As can be seen, the metallicity of the host galaxy, and thus the progenitor by ex-
tension, has no correlation with the brightness of the supernova. One explanation is
that the effects from the metallicity are masked by the electron captures from the nu-
clear reactions in the progenitor. Chamulak et al. (2008) and Piro & Bildsten (2008)
show that the electron abundance Ye in the progenitor depends on the amount of
12C consumed during along simmering phase prior to ignition. During this simmer—
ing phase, 12C is consumed via the reactions 12C(12C,a)2°Ne and 12C(lzC,p)23Na.
Electron captures onto 13N and ”Na. via the reactions 12C(p,"y)13N(e‘,14,)13C and
23Na(e‘,1/,,)23Ne, at density p = 3 x 109g cm‘a, reduce Y8. This reduction in Ye
leads to a decrease in the amount of 56N i and increases the amount of 54Fe and
58Ni synthesized during the explosion (Brachwitz et al., 2000; Times et al., 2003).
Thus, since the reduction in Y8 due to electron captures during simmering is greater
than the change due to initial white dwarf composition for metallicity Z S, Z3,

any correlation between host galaxy metallicity and SNe Ia peak luminosity will be

27

weakened (Chamulak et al., 2008; Piro & Bildsten, 2008).

4.2 Two-Component Model

Many astronomers now believe that the differences in the peak brightnesses of SNe
Ia are due to the progenitors having two populations, and not the differences in
the metallicities of the progenitors. Based on lower redshift data, Scannapieco 86
Bildsten (2005) and Mannucci et al. (2005, 2006) proposed that the disparity of
the observed supernovae is caused by two components: one compontent that traces
the star formation rate of the host galaxy, and a component that traces the total
mass of the host galaxy. The component that traces the star-formation rate would
account for the brighter supernovae only seen in active galaxies, while the component
that traces the total mass would account for the dimer supernovae mostly seen
in passive galaxies. Using higher redshift (z < 0.75) data from Supernova Legacy
Survey (SNLS), Sullivan et al. (2006) also found that the two component model
described the observed SNe Ia rate well. However, Dahlen et al. (2004, 2008) and
Strolger et al. (2004), using even higher redshift (z < 1.6) data from the Advanced
Camera for Surveys (ACS) on the Hubble Space Telescope (HST), found that the
two component model does not sufficiently predict the number of SNe Ia discovered

at the higher 2.

4.2.1 Evidence for the Two-Component Model

The basis for the two-component model arises from strong empirical evidence. Man-
nucci et al. (2005) measured the SN rate per unit mass in the local universe. They

found that the rate of SNe Ia very strongly depended on the (B - K) color of the host

28

 

galaxy: blue galaxies (i.e., galaxies with on-going star formation) exhibited a larger
rate of SNe Ia per unit mass than red galaxies (i.e., galaxies with little-to—no on-
going star formation) by a factor of ~ 30. This result indicates that the delay time
(time between progenitor formation and supernova) must have a wide distribution:
in star-forming galaxies, the delay time must be short, while in galaxies without star
formation, the delay time must be much longer. As a result, Mannucci et al. (2005)
proposed that two populations of progenitors exist: one related to the young stellar
population, with the SNe Ia rate proportional to the star formation rate of the host
galaxy, while the other is related to the older stellar population, with the SNe Ia
rate proportional to the total stellar mass. In a later study, Mannucci et al. (2006)
estimated that for the “prompt”-component, which traces the star formation rate
and tends to be brighter, ~ 108 years elapse between progenitor formation and ig-
nition, and for the “tardy”-component, which traces the total mass and tends to be
dimmer, ~ 3 Gyr elapse between progenitor formation and ignition. Furthermore,
based on their models, Mannucci et al. (2006) show that the “prompt”-component
would dominate at z > 1.3 because of an increase in the star-formation rate, while

the “tardy”-component would dominate at z < 1.3.

When adopting their model, Scannapieco & Bildsten (2005) followed Mannucci
et al. (2005) and assumed that the SNe Ia rate is the sum of two components: a
term proportional to the total stellar mass, M..(t) and a term proportional to the

instantaneous star formation rate M..(t),

SNR C(t) _ M..(t) M..(t)
(100 3:1')—1 _ A [’IOIOMQ] + B [IDIOMQ Gyr_1:| (4.1)

where A and B are dimensionless quatities that are fixed with observations. A

is dominant in older stellar populations, while B is dominant in younger stellar

populations. This model is dominated by the prompt component, but allows for

29

significant numbers of SNe Ia to occur at later times. Also, with A = 4.4:};2 x 10‘2
and B = 2.6 :l: 1.1, this model produces the observed cosmic SNe Ia rate to z 5 1,

including observations of galaxies with little-to-no star formation.

This model was also able to predict the Fe and O abundances observed at dif-
ferent redshifts. Since galaxy clusters are dominated by elliptical galaxies, previous
models would combine the observed SNe Ia rate in elliptical galaxies with the total
stellar mass in a cluster when creating models that estimated the amount of iron
(Renzini et al., 1993). However, these models would underestimate the Fe content
by an order of magnitude. On the other hand, Scannapieco & Bildsten (2005) as-
sumed that the dominant source of Fe is from the prompt component, and not the
late-time SNe Ia contribution as expected from elliptical galaxies. This resulted in
[Fe/ H] values that are roughly consistent with observations and are approximately
an order of magnitude higher than previous estimates. This model also predicts
the observed lack of [Fe/ H] evolution with redshift (Tozzi et al., 2003). This lack
of evolution does not appear in models dominated by late-time SNe Ia. Further-
more, Scannapieco 8c Bildsten (2005) looked at the relationship between SNe Ia and
core-collapse SNe at short times and the amount of Fe and O, which is primarily
synthesized in core-collapse SNe, produced. In their model, the overall SNe Ia Fe
contribution as compared to core-collapse SNe is nearly 3 to 1, which means that

the [0/ Fe] should drop by a factor of 3, which is observed.

Sullivan et al. (2006) used SNLS data at 0.2 < z < 0.75 and found that the
supernova rate was fitted well by the two-component model. SNLS uses several
filters when repeatedly imaging the sky. This allows for highly precise lightcurves
of detected supernovae and prompt spectroscopic followup of detected supernovae.
Using these data, Sullivan et al. (2006) found that the SNe Ia rate per unit stellar

mass is a strong function of the host galaxy star formation rate. Galaxies with

30

 

high star formation hosted ~ 10 times as many SNe Ia as galaxies with zero star
formation, which agrees with the findings of Mannucci et a1. (2005). Also, Sullivan
et al. (2006) found that galaxies with a higher star formation rate hosted more SNe
Ia per unit mass than galaxies with a lower star formation rate. Like Scannapieco
& Bildsten (2005), Sullivan et al. (2006) also found that the SNe Ia rate SN R1,, is
well represented by SN Rza(t) = AM (t) + BM (t), where the constants A is SN R1,,
per unit mass and B is the SN R1,, per unit star formation, and M (t) is the total
mass and M (t) is the star formation rate. In addition to calculating the SNe Ia
rate, Sullivan et al. (2006) observed a correlation between lightcurve width and host
galaxy. Like Hamuy et al. (2000) and Mannucci et al. (2005), who observed SNe Ia at
lower 2, Sullivan et al. (2006) observed that SNe Ia with broad lightcurves (brighter
SNe Ia) are found exclusively in galaxies with on-going star formation, while galaxies

with no star formation only host SNe Ia with narrow lightcurves (dimmer SNe Ia).

4.2.2 Evidence against the Two-Component Model

Dahlen et al. (2004) and Strolger et al. (2004) used HS T/ ACS data at 0.2 < z < 1.6.
The data was gathered as a part of the Great Observatories Origins Deep Survey
(GOODS) campaign. During this campaign, two fields of the sky were observed by
HS T/ ACS during five epochs, with each epoch separated by ~ 45 days. Images
were taken of the areas with multiple pointings using several different filters so that
color could be calculated. Based on these data, Dahlen et al. (2004) and Strolger
et al. (2004) found that the two component model overestimated the number of
supernovae that would be seen at 2 ~ 1.4. Instead, what they observed was that
there was a significant increase in the SNe Ia rate from low 2 to 2 ~ 1, and found
that the rate decreased in the redshift range 1 S, 2 S, 1.6. They found that a single

component model with a delay time of r ,2 2 Gyr better fit the data at high redshift.

31

The single-component model also matched the calculated SNe Ia rates from lower

redshift surveys (e.g. see Hardin et al., 2000; Cappellaro et al., 1999).

In a follow up survey, Dahlen et al. (2008) reached similar conclusions. When
looking at higher redshift data (0.2 < z < 1.8), Dahlen et al. (2008) still showed
that the two-component model does not accurately predict the observed SNe Ia
rate. Models such as Scannapieco & Bildsten (2005), where the SNe Ia rate is
dominated by the “prompt” (star formation tracing) component, overpredicted the
SNe Ia rate at z > 1. Instead, Dahlen et al. (2008) observed that the SNe Ia
rate decreased at z > 1. With their new observations, Dahlen et al. (2008) found
that a single component model with a delay time of ~ 3.4 Gyr better matched
their data. Like the previous survey, this model also matched the calculated SNe
Ia rates from lower redshift surveys . However, two-component models where both
components contribute equally to the SNe Ia rate, such as Mannucci et al. (2006)
more closely matched the observations than the two-component models dominated

by the “prompt” component, but not as well as Dahlen et al. (2008).

4.2.3 Differences between the SNLS and GOODS Surveys

Differences between the SNLS and GOODS surveys could affect the observations
and thus the model used to explain the data. One diflerence is how the data is
collected. The SNLS survey is a ground-based “rolling” survey, meaning that the
telescope continually scans sections of the sky on a nightly basis. In this case, the
survey scans four sections of the sky, each about one square degree in size. Obser-
vations are completed every 3-4 nights during dark time (around new moon) with
different filters, allowing for the construction of high-quality multicolor lightcurves
(Sullivan et al., 2006). On the other hand, the GOODS survey is a space-based

“rolling” survey, but the fields are smaller in number and size and the time between

32

observations longer than the SNLS survey. The survey covers two fields within the
Hubble Deep Field - North and the Chandra Deep Field - South with an effective
area of ~ 150 arcminz. The time between observations is ~ 45 days. Like the SNLS

survey, multiple images are taken with multiple filters (Dahlen et al., 2004, 2008).

With a larger effective field of view and shorter time between observations, the
SNLS would be more likely to observe SNe Ia, especially dim ones. Since dim SNe Ia
have lightcurves that decline much more quickly than brighter SNe la, the GOODS
survey may not observe as many dim ones. However, Riess (2007) believes that the
GOODS survey is not missing objects at higher redshift. No apparent bias against
SNe Ia at z > 1.4 exists since GOODS is detecting core-collapse SNe, which are
intrinsically much dimmer than SNe Ia, at higher redshift. When conducting the
survey, the GOODS team took into account the brightness and luminosity function
of SNe Ia. Using this information, the team believes that they are detecting the
majority of the SNe Ia that should exist at higher redshift at 50% and 90% confidence
levels. Based on these observations, the GOODS team is not detecting the “prompt”-
component that, according to Mannucci et al. (2005, 2006) and Scannapieco &
Bildsten (2005) , is supposed to trace star-formation rate, which dominates at higher
redshift (Riess, 2007).

4.3 Future Studies

Further studies are needed to confirm the two-component model. These studies
need to include surveys with large sample sizes that see the entire distribution of
supernovae (ie, from the dimmest to the brightest) and are not biased by galaxy

type. Also, the surveys need to be fast-acting in order to observe dimmer, faster-

33

declining supernovae. The proposed Large Synoptic Survey Telescope (LSST)1 is
an example of such a survey. The LSST is a ground-based telescope that will take
images of the entire sky over a three night period. This will allow for observations
of the the dimer supernovae and no bias in galaxy type. Data from surveys such
as the LSST can help determine the SNe Ia rate at various 2, which in turn can

confirm the two-component model.

Once the type of supernovae is confirmed, then follow—up surveys like the SNLS
would allow for more detailed observations of the supernovae over longer periods of
time. Data from the follow-surveys can help determine progenitor scenario of SNe Ia.
Theoretically, evidence of the companion star would be apparent in late-time spectra
due to the companion’s envelope being mixed with the ejecta of. the supernova.
However, these would be at a lower velocity than the ejecta, thus would appear as
narrower lines (Leonard, 2007). Higher resolution spectra would be necessary to

detect the contributions from the companion star to the spectra of the supernova.

 

lhttp://vvww.lsst.org/lsst_home.shtml

34

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