Pulsational oddities at the extremes of the DA white dwarf instability strip
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White dwarf stars are the remnant products of the vast majority of Galactic stellar evolution. They are compact objects that serve as remote laboratories for studying high energy/density physics. The outer regions of hydrogen-atmosphere (DA) white dwarfs become convective and able to drive global, nonradial, gravity-mode pulsations below roughly 12,500 K. The pulsations propagate through and are affected by the interior structures of these stars. The oscillations cause a pulsating star to exhibit brightness variations at its characteristic frequencies as a physical system. These frequencies can be measured through Fourier analysis of time series photometric observations. I have focused my studies on new pulsational phenomena near the cool and low-mass edges of the DA white dwarf instability strip, using extensive space-based data from the Kepler spacecraft and the K2 mission, as well as high-speed ground-based photometry from the 2.1-meter Otto Struve Telescope at McDonald Observatory (where I have personally observed 225 nights). The extensive short-cadence (1-min exposures) light curve of the first DAV (DA variable) identified within the original Kepler field of view provided one of the most complete and sensitive records of white dwarf pulsations ever. The light curve also revealed a new, completely unexpected outburst-like phenomenon. I detected 178 instances of significant brightness enhancement in 20 months of observations of the cool DAV KIC 4552982. Recurring with a quasi-period of 2.7 days, the outbursts last 4–25 hours and increase the stellar flux by up to 17%. I estimate the energy of each outburst to be of-order 10³³ ergs. After the Kepler spacecraft suffered the loss of a second reaction wheel in May 2013, it began the K2 mission, visiting new fields along the ecliptic roughly every 80 days. This allowed us to increase the number of DAVs with extensive space-based photometry, and we quickly discovered a second, more dramatic example of this new outburst behavior in PG 1149+057 (Hermes et al. 2015b). I have led the efforts to characterize the outbursts in DAVs ever since and have detected these events in eight DAVs through K2 Campaign 10. Notably, spectroscopic effective temperature constraints place all known members of this new outbursting class of DAV near the cool (red) edge of the instability strip. With a growing outbursting class of DAV, we begin to study their ensemble outburst properties to inform a theory of their physical mechanism. Much of my work from McDonald Observatory has continued in the recent tradition of discovering and characterizing new pulsating extremely low-mass (ELM) white dwarfs. After identifying candidate ELM variables (ELMVs) from the ELM Survey catalog and parameters from model fits to the Sloan Digital Sky Survey spectroscopic data, I obtained time series photometric observations on the 2.1-meter Otto Struve telescope. I published SDSS J1618+3854 as the sixth member of this new class of variable star. However, most of the variability that I measured for this project was inconsistent with expectations for cooling track ELM white dwarfs. This includes long pulsation periods, high pulsation amplitudes, long eclipse timescales, and an overabundance of photometric variables that are not in confirmed short-period binaries from time series radial velocity measurements. Either the surface gravities of another class of star are being systematically overestimated from model fits to hydrogen line profiles in stellar spectra, or these observations are revealing an unexpectedly large population of recently formed pre-ELM white dwarfs. In total, I have discovered and characterized the variability of nine new pulsating stars in the spectroscopic parameter space of ELM white dwarfs, and I also developed an improved framework for interpreting measurements of tidally induced ellipsoidal variations in photometric binaries. Beyond these main results of my thesis on extreme pulsating white dwarfs, I have also explored the limits of the detectability of stellar pulsations in extreme photometric data sets. I analyze long-cadence (30-minute) K2 observations of two fairly typical DAVs in one such study, where the pulsations are severely undersampled. While accurate frequency determinations are nontrivial in such cases, I am able to recover the super-Nyquist frequencies of some pulsation modes with full K2 precision with the help of a few hours of ground-based observations. The space-based data, in turn, enables me to select the intrinsic frequency from the complex alias structure of multi-night ground-based data, providing a practical demonstration of the importance of carefully considering the spectral window. I apply what I have learned about undersampled data to anticipate upcoming pulsating star science in the next generation of synoptic time domain photometric surveys such as the Zwicky Transient Facility and the Large Synoptic Survey Telescope.