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

Abstract

A white dwarf (WD) captured into a high-eccentricity orbit around a massive black hole (MBH) may undergo many pericenter 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 pericenter distance and eccentricity for realistic WD models, under the assumption that these outgoing gravity waves are efficiently dissipated in outer layers of the WD by nonlinear 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.

Tidal circularization of gaseous planets orbiting white dwarfs

“…Solid body tidal mechanisms cannot be applied to gas giant planets, which require a completely different treatment. Because white dwarfs are negligibly tidally distorted by planetary companions, tidal interaction mechanisms between a white dwarf and other stars (Fuller & Lai 2011Valsecchi et al 2012;Sravan et al 2014;Vick et al 2017;McNeill et al 2019) are also not necessarily suitable. However, other stars, through their fluid-like nature, do have stronger links to giant planets.…”

Tidal effects in eccentric coalescing neutron star binaries

“…1) as a sum of multiple forcing frequencies, nΩ orb , with positive integer n. We neglect PN effects (other than gravitational radiation) in this analysis. The time evolution of the mode amplitude c α satisfies [e.g 51,63]. c α +iω α c α = iM 2 W lm Q α 2ω α a l+1 n mn exp −it dt nΩ orb (t) , (A.2) where a is the Newtonian semi-major axis, and F mn = 1 π π 0 cos[n(E − e sin E) − mΦ(t)] (1 − e cos E) 2 dE, (A.3) with E the eccentric anomaly and cos Φ(t) = cos E − e 1 − e cos E .…”

Orbital relaxation and excitation of planets tidally interacting with white dwarfs

“…Despite these numerous motivations, tidal investigations of white dwarfs have been limited to star-star interactions (Fuller & Lai 2011, 2012Valsecchi et al 2012;Sravan et al 2014;Vick et al 2017;McNeill et al 2019). In contrast, abundant studies of the main-sequence and giantbranch phases of evolution have analysed the star-planet interaction, and have adopted a variety of approaches with both equilibrium and dynamical tides.…”