Internal structure of white dwarfs from gravitational waves. (arXiv:1901.09045v1 [astro-ph.HE])
<a href="http://arxiv.org/find/astro-ph/1/au:+McNeill_L/0/1/0/all/0/1">L. O. McNeill</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Mardling_R/0/1/0/all/0/1">Rosemary A. Mardling</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Muller_B/0/1/0/all/0/1">B. Müller</a>
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.
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.
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