Internal-current Lorentz-force Heating of Astrophysical Objects

Abstract

Two forms of ohmic heating of astrophysical secondaries have received particular attention: unipolar-generator heating with currents running between the primary and secondary, and magnetic induction heating due to the primary’s time-varying field. Neither appears to cause significant dissipation in the contemporary solar system. But these discussions have overlooked heating derived from the spatial variation of the primary’s field across the interior of the secondary. This leads to Lorentz-force-driven currents around paths entirely internal to the secondary, with resulting ohmic heating. We examine three ways to drive such currents, by the cross product of (1) the secondary’s azimuthal orbital velocity with the nonaxially symmetric field of the primary, (2) the radial velocity (due to nonzero eccentricity) of the secondary with the primary’s field, or (3) the out-of-plane velocity (due to nonzero inclination) with the primary’s field. The first of these operates even for a spin-locked secondary whose orbit has zero eccentricity, in strong contrast to tidal dissipation. We show that Jupiter’s moon Io today could dissipate about 600 GW (more than likely current radiogenic heating) in the outer 100 m of its metallic core by this mechanism. Had Io ever been at 3 Jovian radii instead of its current 5.9, it could have been dissipating 15,000 GW. Ohmic dissipation provides a mechanism that could operate in any solar system to drive inward migration of secondaries that then necessarily comes to a halt upon reaching a sufficiently close distance to the primary.

Magnetic Interactions in Orbital Dynamics

“…A body with a permanent or induced magnetic moment can respond to the local magnetic field tied to a magnetic host star. While these interactions are weak compared to gravity, cumulative effects of magnetic interactions can change the orbital energy of asteroids (Bromley & Kenyon 2019), rocky planets (Kislyakova et al 2017(Kislyakova et al , 2018Kislyakova & Noack 2020;Noack et al 2021), and gas giants (Laine et al 2008;Chang et al 2012;Laine & Lin 2012;Strugarek et al 2017;Chyba & Hand 2021). Even stellar partners can influence each other magnetically (Joss et al 1979;Campbell 1983;Katz 1989Katz , 2017Mikóczi 2021;Bourgoin et al 2022).…”