The Maclaurin spheroid in disguise. New figures of equilibrium with external magnetic support

TL;DR

This paper demonstrates that magnetic fields can support rotating homogeneous ellipsoids, allowing prolate shapes and modifying rotation rates, with implications for interstellar cloud structures.

Contribution

It extends Maclaurin's classical formula to include magnetic support, revealing new equilibrium figures and critical states for magnetic, rotating ellipsoids.

Findings

Magnetic fields enable prolate equilibrium shapes.

Rotation rates are altered by magnetic support.

Prolate states persist under gas compressibility.

Abstract

We show that a rigidly rotating, homogeneous ellipsoid of revolution threaded by a uniform, coaxial magnetic field is a possible figure of equilibrium. While the spheroidal shape is fully preserved, the rotation rate is modified. Accordingly, we extend the fundamental formula by Maclaurin. In contrast with the non-magnetic case, prolate shapes are permitted, but there are critical states in the form of maximum elongations, depending on ionisation fraction, ion/electron drift, magnetic field and mass-density. As checked from numerical simulations based on the Self-Consistent-Field method, prolate states survive to gas compressibility. The relevance to interstellar clouds is outlined.