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 (such as rotation rate and temperature) 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 ω= 2(Ω−Ωs) (where Ω is the orbital frequency and Ωs is the spin frequency) for several realistic carbon–oxygen WD models, under the assumption that the outgoing propagating waves are efficiently dissipated in the outer layer of the star by non-linear effects or radiative damping. Unlike main-sequence stars with distinct radiative and convection zones, the mechanism of wave excitation in WDs is more complex due to the sharp features associated with composition changes inside the WD. In our WD models, the gravity waves are launched just below the helium–carbon boundary and propagate outwards. We find that the tidal torque on the WD and the related tidal energy transfer rate, ⁠, depend on ω in an erratic way, with varying by orders of magnitude over small frequency ranges. On average, scales approximately as Ω5ω5 for a large range of tidal frequencies. We also study the effects of dynamical tides on the long-term evolution of WD binaries prior to mass transfer or merger. Above a critical orbital frequency Ωc, corresponding to an orbital period of the order of 1h (depending on WD models), dynamical tides efficiently drive Ωs towards Ω, although a small, almost constant degree of synchronization (Ω−Ωs∼ 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 a significant phase error in the low-frequency gravitational waveforms, detectable by the planned Laser Interferometer Space Antenna project. Tidal dissipation may also lead to significant heating of the WD envelope and brightening of the system long before binary merger.

Highlights

  • Compact white dwarf (WD) binary systems harbour many interesting and unanswered astrophysical questions

  • We have studied the tidal excitation of gravity waves in binary WDs and computed the energy and angular momentum transfer rates as a function of the orbital frequency for several WD models

  • Our calculations are based on the outgoing wave boundary condition, which implicitly assumes that the tidally excited gravity waves are damped by nonlinear effects or radiative diffusion as they propagate towards the WD surface

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Summary

INTRODUCTION

Compact white dwarf (WD) binary systems (with orbital periods in the range of minutes to hours) harbour many interesting and unanswered astrophysical questions. Iben et al (1998) estimated the effect of tidal heating in the WD based on the assumption that the (spherically averaged) local heating rate is equal to the rate of rotational energy deposition required to maintain synchronization They suggested that the binary WDs may brighten by several magnitudes before merger. We calculate the tidal excitation of gravity waves in binary WDs assuming that the waves are efficiently damped in the WD envelope To this end, we implement an outgoing wave boundary condition near the WD surface.

BASIC EQUATIONS
BOUNDARY CONDITIONS
ANGULAR MOMENTUM AND ENERGY FLUX
WHITE DWA RFMODELS
Numerical method and importance of a self-consistent stellar model
Calculation with toy white dwarf model
Calculation with realistic white dwarf model
Relation to tidal overlap integral
Justification of the outer boundary condition
SIMPLEMODELFORGR AV I T Y WAV E EXCITATION
SPIN–ORBIT EVOLUTION
Synchronization
Tidal effect on the orbital decay rate and phase of gravitational waves
Tidal heating
DISCUSSION

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