# Gravitational waves from dynamical tides in white dwarf binaries

## TL;DR

This paper investigates how dynamical tides in white dwarf binaries influence gravitational wave signals, revealing new harmonic features and potential insights into stellar internal structures through gravitational wave observations.

## Contribution

It introduces a novel analysis of tidal effects on gravitational waves from non-equilibrium white dwarf binaries, highlighting the excitation of harmonics not present in equilibrium models.

## Key findings

- Tidal forcing induces additional gravitational wave harmonics.
- Strain amplitudes depend on stellar density profiles.
- Analytic expressions relate eccentricity and harmonics to stellar parameters.

## Abstract

We study the effect of tidal forcing on gravitational wave signals from tidally relaxed white dwarf pairs in the LISA, DECIGO and BBO frequency band ($0.1-100\,{\rm mHz}$). We show that for stars not in hydrostatic equilibrium (in their own rotating frames), tidal forcing will result in energy and angular momentum exchange between the orbit and the stars, thereby deforming the orbit and producing gravitational wave power in harmonics not excited in perfectly circular synchronous binaries. This effect is not present in the usual orbit-averaged treatment of the equilibrium tide, and is analogous to transit timing variations in multiplanet systems. It should be present for all LISA white dwarf pairs since gravitational waves carry away angular momentum faster than tidal torques can act to synchronize the spins, and when mass transfer occurs as it does for at least eight LISA verification binaries. With the strain amplitudes of the excited harmonics depending directly on the density profiles of the stars, gravitational wave astronomy offers the possibility of studying the internal structure of white dwarfs, complimenting information obtained from asteroseismology of pulsating white dwarfs. Since the vast majority of white-dwarf pairs in this frequency band are expected to be in the quasi-circular state, we focus here on these binaries, providing general analytic expressions for the dependence of the induced eccentricity and strain amplitudes on the stellar apsidal motion constants and their radius and mass ratios. Tidal dissipation and gravitation wave damping will affect the results presented here and will be considered elsewhere.