Tidal Excitation of Oscillation Modes in Compact White Dwarf Binaries: I. Linear Theory

TL;DR

This paper investigates how tidal forces in compact white dwarf binaries excite gravity modes, leading to significant stellar heating and potential nonlinear effects as the orbit evolves through resonances.

Contribution

It provides a detailed linear theory calculation of mode excitation, including eigenfrequencies, coupling coefficients, and resonance effects, with analytical estimates matching numerical results.

Findings

g-modes can reach amplitude up to 0.1

Mode energy can be about 10^{-3} of the star's binding energy

White dwarfs may be significantly heated by tidal interactions before merger

Abstract

We study the tidal excitation of gravity modes (g-modes) in compact white dwarf binary systems with periods ranging from minutes to hours. As the orbit of the system decays via gravitational radiation, the orbital frequency increases and sweeps through a series of resonances with the g-modes of the white dwarf. At each resonance, the tidal force excites the g-mode to a relatively large amplitude, transferring the orbital energy to the stellar oscillation. We calculate the eigenfrequencies of g-modes and their coupling coefficients with the tidal field for realistic non-rotating white dwarf models. Using these mode properties, we numerically compute the excited mode amplitude in the linear approximation as the orbit passes though the resonance, including the backreaction of the mode on the orbit. We also derive analytical estimates for the mode amplitude and the duration of the resonance, which accurately reproduce our numerical results for most binary parameters. We find that the g-modes can be excited to a dimensionless (mass-weighted) amplitude up to 0.1, with the mode energy approaching $10^{-3}$ of the gravitational binding energy of the star. This suggests that thousands of years prior to the binary merger, the white dwarf may be heated up significantly by tidal interactions. However, more study is needed since the physical amplitudes of the excited oscillation modes become highly nonlinear in the outer layer of the star, which can reduce the mode amplitude attained by tidal excitation.