Pulsating White Dwarfs and Orbital Decay in Binaries

Three projects related to stellar and binary evolution and waves in stars are investigated.

Motivated by the discovery of a handful of pulsating, extremely low-mass white dwarfs (ELM WDs, mass $M \la 0.18\, M_\odot$) which likely have WD companions, a binary formation model was developed for these systems. ELM WD is formed using angular momentum losses due to magnetic braking by the stellar wind of the primary star. Evolutionary models are constructed using the Modules for Experiments in Stellar Astrophysics (MESA), with ELM WD progenitors in the range $1.0 \la M_{\rm d}/M_{\odot} \la 1.5$ and WD companions in the range $0.4 \la M_{\rm a}/M_{\odot} \la 0.9$. Upon the thinning of the evolved donor's envelope, the donor star shrinks out of contact and mass transfer ceases, revealing the ELM WD. Systems with small helium core masses have previously been suggested as evolving to the short orbital period, hydrogen poor AM CVN accretors. Systems with large helium core masses expand out to orbital periods $P_{\rm orb} \ga 15\, {\rm hr}$, larger than those of the observed pulsators. In between this range, ELM WDs may become pulsators both as pre-WDs and on the WD cooling track. The resulting models for the stellar structure are used to compute expected g and p-mode periods and compare to the observed periods.

WASP-12b is a hot Jupiter with an orbital period of only $P= 1.1$ day, making it one of the shortest-period giant planets known. Recent transit timing observations measure a decreasing orbital period with $P/\dot{P} = -3.2$ Myr. These observations imply that a Gyrs old planet is now about to be destroyed by its star over the next few Myr. One mechanism to produce orbital decay is through tidal friction. The tide raised in the star by the planet may spin up the star, with the orbit contracting to conserve angular momentum. Calculations are presented for the ``dynamical tide" excitation of gravity waves by the time-changing tidal force. The main damping mechanism is nonlinear wave breaking at the center of the star, if the star has a radiative core. I find that the orbital decay rate due to the dynamical tide is insufficient to shrink the orbit if WASP-12 is a main sequence star, since the core is then convective and the low-amplitude gravity wave forms a weakly damped standing wave. However, if WASP-12 is a subgiant star with a radiative core, the dynamical tide breaks nonlinearly at the center of the star. This traveling wave limit may then provide roughly enough friction to account for the observed orbital decay.

In addition to the direct measurement of orbital decay in WASP-12, indirect evidence of orbital decay in binaries containing a post-main sequence star comes from the lack of binaries with close orbital separations, as they have already suffered orbital decay and destruction by the parent star. A broad parameter study of orbital decay is presented for a range of primary and secondary stars as well as orbital separation. The goal is to make predictions for the range of orbital separation at which systems will be missing due to orbital decay and engulfment by the star.