http://arxiv.org/abs/1901.09045
We study the effect of tidal forcing on gravitational wave signals from tidally relaxed white dwarf pairs in the Laser Interferometer Space Antenna (LISA), DECi-hertz Interferometer Gravitational wave Observatory (DECIGO) and Big Bang Observer (BBO) frequency band ($0.1-100\,{\rm mHz}$). In particular, we show that as a result of the non-Keplerian potential associated with tidal distortion, the end state of tidal circularization is quasi-circular, with the relaxed dynamical tide cyclically forcing the eccentricity at the orbital frequency, while in turn, a non-circular orbit forces the dynamical tide. This effect is not present in the usual orbit-averaged treatment of the equilibrium tide.
The tide-orbit coupling produces gravitational wave power in harmonics not excited in perfectly circular binaries, with the corresponding strain amplitudes depending directly on the density profiles of the stars. Gravitational wave astronomy therefore offers a new window on white dwarf internal structure, complimenting information obtained from asteroseismology of pulsating white dwarfs. Since the vast majority of white-dwarf pairs with orbital periods in this frequency band are expected to be tidally relaxed and hence 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 apsidal motion constants of the stars, the ratio of their radii to the binary separation, and the mass ratio. We show that the f-mode produces a measurable effect in LISA and DECIGO/BBO for at least one LISA verification binary at 3mHz, even though the associated mode frequency is far from orbital resonance.
L. McNeill, R. Mardling and B. Müller
Tue, 29 Jan 19
8/62
Comments: 11 pages, 6 figures. Submitted to MNRAS
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