# Orbital relaxation and excitation of planets tidally interacting with white dwarfs

## TL;DR

This paper presents a new method to analyze how planets near white dwarfs are tidally affected, determining their potential inward or outward drift and destruction, with implications for understanding white dwarf planetary systems.

## Contribution

It introduces a self-consistent secular approach to model tidal interactions without constant lag assumptions, considering diverse planetary rheologies and spin states.

## Key findings

- Massive Super-Earths are more prone to destruction than minor planets.
- Low-viscosity planets are destroyed more easily than high-viscosity ones.
- The boundary between planetary survival and destruction is fractal and chaotic.

## 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 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.