Dynamical Tides in Compact White Dwarf Binaries: Helium Core White Dwarfs, Tidal Heating, and Observational Signatures

Abstract

Tidal dissipation in compact white dwarf (WD) binary systems significantly influences the physical conditions (such as surface temperature and rotation rate) of the WDs prior to mass transfer or merger. In these systems, the dominant tidal effects involve the excitation of gravity waves and their dissipation in the outer envelope of the star. We calculate the amplitude of tidally excited gravity waves in low-mass (0.3M_\odot) helium-core (He) WDs as a function of the tidal forcing frequency ω. Like carbon-oxygen (CO) WDs studied in our previous paper, we find that the dimensionless tidal torque F(ω) (inversely proportional to the effective tidal quality factor) has an erratic dependence on ω. On average, F(ω) scales approximately as ω^6, and is several orders of magnitude smaller for He WDs than for CO WDs. We find that tidal torques can begin to synchronize the WD rotation when the orbital period is less than about a hour, although a nearly constant asynchronization is maintained even at small periods. We examine where the tidally excited gravity waves experience non-linear breaking or resonant absorption at a critical layer, allowing us to estimate the location and magnitude of tidal heating in the WD envelope. We then incorporate tidal heating in the MESA stellar evolution code, calculating the physical conditions of the WD as a function of orbital period for different WD models. We find that tidal heating makes a significant contribution to the WD luminosity for short-period (~10 min) systems such as SDSS J0651+2844. We also find that for WDs containing a hydrogen envelope, tidal heating can trigger runaway hydrogen shell burning, leading to a nova-like event before the onset of mass transfer.