Relativistic effects in the tidal interaction between a white dwarf and a massive black hole in Fermi normal coordinates

TL;DR

This paper models relativistic tidal interactions between white dwarfs and black holes using Fermi normal coordinates, revealing effects on mass loss, energy transfer, and orbital dynamics, with implications for tidal disruption events.

Contribution

It introduces a novel numerical approach combining hydrodynamics and relativistic coordinates to analyze tidal encounters, including higher multipole moments and relativistic corrections.

Findings

Relativistic suppression of tidal energy transfer observed.

Quantitative estimates of mass loss and heating effects.

First calculation of center of mass deflection due to octupole tides.

Abstract

We consider tidal encounters between a white dwarf and an intermediate mass black hole. Both weak encounters and those at the threshold of disruption are modeled. The numerical code combines mesh-based hydrodynamics, a spectral method solution of the self-gravity, and a general relativistic Fermi normal coordinate system that follows the star and debris. Fermi normal coordinates provide an expansion of the black hole tidal field that includes quadrupole and higher multipole moments and relativistic corrections. We compute the mass loss from the white dwarf that occurs in weak tidal encounters. Secondly, we compute carefully the energy deposition onto the star, examining the effects of nonradial and radial mode excitation, surface layer heating, mass loss, and relativistic orbital motion. We find evidence of a slight relativistic suppression in tidal energy transfer. Tidal energy deposition is compared to orbital energy loss due to gravitational bremsstrahlung and the combined losses are used to estimate tidal capture orbits. Heating and partial mass stripping will lead to an expansion of the white dwarf, making it easier for the star to be tidally disrupted on the next passage. Finally, we examine angular momentum deposition. By including the octupole tide, we are able for the first time to calculate deflection of the center of mass of the star and debris. With this observed deflection, and taking into account orbital relativistic effects, we compute directly the change in orbital angular momentum and show its balance with computed spin angular momentum deposition.