Survivability of radio-loud planetary cores orbiting white dwarfs

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 focused 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 ⁻¹ ) 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.