# Survivability of radio-loud planetary cores orbiting white dwarfs

## TL;DR

This study models the survivability of metallic planetary cores orbiting white dwarfs by coupling gravitational tides and Lorentz drift effects, identifying conditions under which cores can survive over a billion years for potential radio detection.

## Contribution

It introduces a coupled model of gravitational and electromagnetic forces affecting planetary core survivability, expanding previous models by including a Maxwell rheological framework.

## Key findings

- High viscosity cores (>~10^{24} Pa*s) are more likely to survive.
- Survivability is maximized in white dwarfs with magnetic fields in the kG range.
- Cores can persist over Gyr timescales under certain physical conditions.

## Abstract

The discovery of the intact metallic planetary core fragment orbiting the white dwarf SDSS J1228+1040 within one Solar radius highlights the possibility of detecting larger, unfragmented conducting cores around magnetic white dwarfs through radio emission. Previous models of this decades-old idea focussed on determining survivability of the cores based on their inward Lorentz drift towards the star. However, gravitational tides may represent an equal or dominant force. Here, we couple both effects by assuming a Maxwell rheological model and performing simulations over the entire range of observable white dwarf magnetic field strengths (10^3 -- 10^9 G) and their potential atmospheric electrical conductivities (10^{-1} -- 10^4 S/m) in order to more accurately constrain survivability lifetimes. This force coupling allows us to better pinpoint the physical and orbital parameters which allow planetary cores to survive for over a Gyr, maximizing the possibility that they can be detected. The most robust survivors showcase high dynamic viscosities (>~ 10^{24} Pa*s) and orbit within kG-level magnetic fields.