We have entered an era of studying the atmospheres of exoplanets in unprecedented detail,particularly through transmission spectroscopy of transiting planets using the James Webb Space Telescope (JWST). However, most of the 4300+ confirmed transiting planets are not currently accessible to JWST during its mission lifetime. This widespread problem is due mostly to ephemeris degradation: while the transit time and period of the planet may be known to a precision of minutes at discovery, the uncertainties compound with each successive transit, which can culminate in the projected time of future transits being off by hours to days when follow-up observations are being made years later. This costly problem can be alleviated by reobserving transits to greatly narrow down the future transit window before scheduling observations for characterization. Fortunately, NASA’s Transiting Exoplanet Survey Satellite (TESS) mission is observing most of the sky for transit signals, providing an efficient and timely avenue for refreshing the ephemerides of hundreds of planets. With this in mind, the K2 & TESS Synergy is a large scale effort to reanalyze planets originally discovered by NASA’s K2 mission with new observations from the ongoing TESS mission.We combine light curves obtained by both NASA missions along with archival radial velocities,Gaia parallaxes, and spectral energy distributions in global fits using EXOFASTv2, which not only allows us to update the ephemerides, but also build a self-consistent catalog of parameters for the planets and host stars. We present a reanalysis of 26 single-planet systems reobserved by TESS during its prime mission. For half of the planets, we improve the average 3? uncertainties by 2030 from the order of tens of hours down to under one hour. As a result of the faintness of some systems, 13 planets do not have transits detectable by TESS. In those cases, we exclude the TESS photometry from the global fits, resulting in a corresponding ephemeris improvement of 43.2 to 35.6 hours.This systematic approach also provides opportunity to amend ephemerides that were originallyincorrect due to problems such as false positive transits in additional photometry used at discovery. We address one such case, that of K2’s first planet discovery, K2-2 b, where the period was 28.8 minutes (∼40?) away from the true value at the time of discovery. In addition to the K2 and TESS light curves, we use a variety of other space- and ground-based photometry to hunt for the transit of K2-2 b. We successfully caught multiple transits of K2-2 b, allowing us to correct and refine the ephemeris such that the transit time uncertainty will be known to within <13 minutes by 2030. We continue the broader reanalysis to the top 50 planets for atmospheric characterization in the K2 catalog to ensure that JWST can be used to obtain transmission spectra for these planets. Seven of the planets in this sample have been part of the previous K2 & TESS Synergy analyses. Most planets in this sample are equally suitable for atmospheric characterization using JWST as other current targets. There are also many targets that would be useful for understanding the formation and evolution processes of sub-Neptunes and giant planets. We have completed analysis for 34 of these planets, with their average ephemeris uncertainties by 2030 improved from 17.4 hours to 16 minutes, enabling future targeted observations be scheduled.The culmination of the work in this thesis is updated global parameters for 54 planets and theirhosts. Efforts like the K2 and TESS Synergy will ensure the accessibility of transiting planets for future characterization while leading to a self-consistent catalog of stellar and planetary parameters for future population efforts.
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