Dynamical Tides in Compact White Dwarf Binaries: Tidal Synchronization and Dissipation

TL;DR

This paper investigates how dynamical tides involving gravity waves affect the evolution, synchronization, and observable signals of compact white dwarf binaries, highlighting their importance in gravitational wave detection and stellar heating.

Contribution

It provides detailed calculations of gravity wave excitation and dissipation in white dwarfs, revealing erratic tidal torque behavior and implications for binary evolution and gravitational wave signals.

Findings

Tidal energy transfer scales as iveive with orbital frequency.

Dynamical tides drive white dwarf spin toward synchronization above a critical frequency.

Tidal dissipation can cause observable heating and phase errors in gravitational waveforms.

Abstract

In compact white dwarf (WD) binary systems (with periods ranging from minutes to hours), dynamical tides involving the excitation and dissipation of gravity waves play a dominant role in determining the physical conditions of the WDs prior to mass transfer or binary merger. We calculate the amplitude of the tidally excited gravity waves as a function of the tidal forcing frequency \omega=2(\Omega-\Omega_s) (where \Omega is the orbital frequency and \Omega_s is the spin frequency) for several realistic carbon-oxygen WD models, assuming that the waves are efficiently dissipated in the outer layer of the star by nonlinear effects or radiative damping. The mechanism of wave excitation in WDs is complex due to the sharp features associated with composition changes inside the WD, and in our WD models gravity waves are launched just below the helium-carbon boundary. We find that the tidal torque on the WD and the related tidal energy transfer rate, \dot E_{\rm tide}, depend on \omega in an erratic way. On average, \dot E_{\rm tide} scales approximately as \Omega^5\omega^5 for a large range of tidal frequencies. We also study the effects of dynamical tides on the long-term evolution of WD binaries. Above a critical orbital frequency \Omega_c, corresponding to an orbital period of order one hour (depending on WD models), dynamical tides efficiently drive \Omega_s toward \Omega, although a small, almost constant degree of asynchronization (\Omega-\Omega_s\sim {\rm constant}) is maintained even at the smallest binary periods. While the orbital decay is always dominated by gravitational radiation, the tidal energy transfer can induce significant phase error in the low-frequency gravitational waveforms, detectable by the planned LISA project. Tidal dissipation may also lead to significant heating of the WD envelope and brightening of the system long before binary merger.