Orbital relaxation and excitation of planets tidally interacting with white dwarfs

Abstract

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 Boué & 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.

Survivability of radio-loud planetary cores orbiting white dwarfs

“…where the magnetic field strength is given by B⋆ and the vertically-averaged electrical conductivity in the white dwarf atmosphere is given by γ⋆ . All notations are consistent with those in Veras et al (2019b).…”

“…Surviving planets may alter their orbits in non-obvious ways due to tides alone (Veras et al 2019b), and especially now when coupled with an electromagnetic force. Nevertheless, conveniently we found that the planets do not move outward enough to exceed acrit.…”

“…In order to simulate the planet's evolution, we added equation (1) to Eq. C1 of Veras et al (2019b). However, equation (1) requires us to establish values for two additional and important parameters: B⋆ and γ⋆ .…”

“…The numerical implementation involved coupling equation (1) to Eqs. C1-C10 of Veras et al (2019b). We do not repeat the details of the implementation here, except to say that we used the same generous range of the index q in order to compute the eccentricity functions in their Eq.…”

A Gap in the Mass Distribution for Warm Neptune and Terrestrial Planets

“…Capture into spin-orbit resonances and psuedo-synchronous rotation states cannot be accurately realised with such models (Makarov & Efroimsky 2013;Noyelles et al 2014). Instead, the direction of the net tidally-induced migration is chaotic with respect to the multi-dimensional parameter space (Veras et al 2019), and hence very well might produce gaps like the one seen here.…”