Orbital relaxation and excitation of planets tidally interacting with white dwarfs. (arXiv:1904.03195v1 [astro-ph.EP])
<a href="http://arxiv.org/find/astro-ph/1/au:+Veras_D/0/1/0/all/0/1">Dimitri Veras</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Efroimsky_M/0/1/0/all/0/1">Michael Efroimsky</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Makarov_V/0/1/0/all/0/1">Valeri V. Makarov</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Boue_G/0/1/0/all/0/1">Gwenaël Boué</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Wolthoff_V/0/1/0/all/0/1">Vera Wolthoff</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Reffert_S/0/1/0/all/0/1">Sabine Reffert</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Quirrenbach_A/0/1/0/all/0/1">Andreas Quirrenbach</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Tremblay_P/0/1/0/all/0/1">Pier-Emmanuel Tremblay</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Gansicke_B/0/1/0/all/0/1">Boris T. Gänsicke</a>
Observational evidence of white dwarf planetary systems is dominated by the
remains of exo-asteroids through accreted metals, debris discs, and orbiting
planetesimals. However, exo-planets in these systems play crucial roles as
perturbing agents, and can themselves be perturbed close to the white dwarf
Roche radius. Here, we illustrate a procedure for computing the tidal
interaction between a white dwarf and a near-spherical solid planet. This
method determines the planet’s inward and/or outward drift, and whether the
planet will reach the Roche radius and be destroyed. We avoid constant tidal
lag formulations and instead employ the self-consistent secular Darwin-Kaula
expansions from Bou'{e} & Efroimsky (2019), which feature an arbitrary
frequency dependence on the quality functions. We adopt wide ranges of dynamic
viscosities and spin rates for the planet in order to straddle many possible
outcomes, and provide a foundation for the future study of individual systems
with known or assumed rheologies. We find that: (i) massive Super-Earths are
destroyed more readily than minor planets (such as the ones orbiting WD
1145+017 and SDSS J1228+1040), (ii) low-viscosity planets are destroyed more
easily than high-viscosity planets, and (iii) the boundary between survival and
destruction is likely to be fractal and chaotic.
Observational evidence of white dwarf planetary systems is dominated by the
remains of exo-asteroids through accreted metals, debris discs, and orbiting
planetesimals. However, exo-planets in these systems play crucial roles as
perturbing agents, and can themselves be perturbed close to the white dwarf
Roche radius. Here, we illustrate a procedure for computing the tidal
interaction between a white dwarf and a near-spherical solid planet. This
method determines the planet’s inward and/or outward drift, and whether the
planet will reach the Roche radius and be destroyed. We avoid constant tidal
lag formulations and instead employ the self-consistent secular Darwin-Kaula
expansions from Bou'{e} & Efroimsky (2019), which feature an arbitrary
frequency dependence on the quality functions. We adopt wide ranges of dynamic
viscosities and spin rates for the planet in order to straddle many possible
outcomes, and provide a foundation for the future study of individual systems
with known or assumed rheologies. We find that: (i) massive Super-Earths are
destroyed more readily than minor planets (such as the ones orbiting WD
1145+017 and SDSS J1228+1040), (ii) low-viscosity planets are destroyed more
easily than high-viscosity planets, and (iii) the boundary between survival and
destruction is likely to be fractal and chaotic.
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