Tidal dissipation and evolution of white dwarfs around massive black holes: an eccentric path to tidal disruption

A white dwarf (WD) captured into a high-eccentricity orbit around a massive black hole (MBH) may undergo many pericentre passages before tidal disruption. During these passages, the tidal potential of the MBH excites internal oscillations or waves in the WD, and the dissipation of these oscillations can significantly influence the physical properties of the WD prior to its disruption. We calculate the amplitude of the tidally excited gravity (buoyancy) waves in the WD as a function of the pericentre distance and eccentricity for realistic WD models, under the assumption that these outgoing gravity waves are efficiently dissipated in the outer layers of the WD by non-linear effects or radiative damping. We obtain fitting formulae for the tidal energy and angular momentum transfer rates as well as the tidal heating rate. We find that these dynamical tides are much weaker than gravitational radiation in driving the orbital decay of the WD–MBH binary, and they are also inefficient in changing the WD spin during the orbital evolution. Incorporating our computed tidal dissipation rate into a MESA-based WD evolution code, we find that tidal heating can lead to appreciable brightening of the WD and may induce runaway fusion in the hydrogen envelope well before the WD undergoes tidal disruption.