The dynamical tides in highly eccentric white dwarf-massive black hole binaries

Tight, highly eccentric white dwarf-massive black hole binary systems are one of the target gravitational wave sources of the upcoming space-based detector LISA, and can be a high-energy electromagnetic transient source at the galactic centers. The orbital motion of these systems is influenced by the dynamical tide in the white dwarf. With close periastron passages of about twice the tidal radius, the tide can cause the orbit to evolve chaotically and the tidal energy can build up for several orders of magnitude. For larger separations, the orbit evolves periodically and provides a source of gravitational wave signals that can potentially be measured by LISA. In this talk, I will discuss the influence of dynamical tide on these systems. We employ an efficient iterative method modified from previous studies in Newtonian context to quantify the effects of dynamical tide over multiple orbits, which includes the post-Newtonian periastron precession and the redshift in the frequencies of the pulsation modes excited by the tide, as well as the effect of non-linear hydrodynamic response. We study the chaotic regime, where the dynamical tide leads to drastic deformations of the white dwarf that can drive a transfer of mass toward the black hole, potentially explaining the recently discovered quasi-periodic X-ray bursts observed at galactic centers. We also consider the periodic regime where the gravitational waveform is modified by the dynamical tide.