Internal-Current Lorentz-Force Heating of Astrophysical Objects

TL;DR

This paper explores a new internal-current Lorentz-force heating mechanism in astrophysical objects, showing it can cause significant internal heating and influence orbital migration, especially in moons like Io.

Contribution

It introduces a novel internal-current Lorentz-force heating process driven by spatial magnetic field variations, distinct from prior unipolar and induction heating models.

Findings

Io could dissipate about 600 GW today due to this mechanism.

At 3 jovian radii, Io could dissipate up to 15,000 GW.

The mechanism can cause inward orbital migration of secondaries.

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 non-axially symmetric field of the primary; (2) the radial velocity (due to non-zero eccentricity) of the secondary with the primary's field; or (3) the out-of-plane velocity (due to non-zero 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 hundred meters 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.