# The Equilibrium Structure of Prolate Magnetized Molecular Cores

## TL;DR

This paper investigates the equilibrium shapes of magnetized molecular cloud cores, revealing conditions under which prolate spheroidal configurations can exist alongside oblate ones, with implications for magnetic field structures.

## Contribution

It introduces new solutions for prolate spheroidal cloud cores supported by magnetic fields, expanding the understanding beyond previously known oblate configurations.

## Key findings

- Prolate cores can exist at lower masses than oblate ones.
- Prolate cores have a maximum radius dependent on sound speed and external pressure.
- Prolate solutions do not require toroidal magnetic fields.

## Abstract

The structure of molecular cloud cores supported by thermal pressure and a poloidal magnetic field is reinvestigated in the magnetohydrostatic and axisymmetric approximation. In addition to oblate configurations found in earlier work, solutions yielding prolate spheroidal shapes have also been obtained for a reference state described by a uniform sphere threaded by a uniform background magnetic field. The solutions for prolate configurations are found to be relevant for lower masses than for their oblate counterparts. Of particular importance is the result that the prolate cloud cores have radii less than a maximum given by $0.25 pc (a/0.2km/s)^2 (P_{\rm ext}/10^{-12} dyne/cm^2)^{-1/2}$, where $a$ is the sound speed and $P_{\rm ext}$ is the external pressure of the background medium. The existence of such solutions obviates the presence of toroidal fields in such modeled structures.