Stellar structure, magnetism and the variational principle

TL;DR

This paper develops a variational model for stellar structure that incorporates electromagnetic effects and angular momentum, providing new insights into the balance of forces in astrophysical objects.

Contribution

It reformulates the polytropic stellar model to include electromagnetic interactions and rotation within a variational framework, extending traditional models.

Findings

Electromagnetic effects can be integrated into stellar models via a surface integral approach.

Exact solutions are obtainable under simplifying assumptions.

The phase diagram reveals patterns indicating the complex interplay of matter, gravity, and electromagnetism.

Abstract

Matter interacts through two long range forces: gravity and electromagnetism. While all matter contributes to the gravitational potential, electromagnetic effects were traditionally expected to cancel in large systems because positive and negative charges balance. Yet astrophysical objects clearly show long range electromagnetic behavior, so the cancellation cannot be perfect. This paper develops a model for stationary aggregation of matter into a star that consistently includes angular momentum and electromagnetic effects. We reformulate the standard polytropic stellar model as a variational problem and extend it to include the kinetic energy of rigid rotation and the electromagnetic interaction energy between oppositely charged baryonic matter. The electromagnetic contribution to the action is taken to be the minimal energy required to generate the stellar magnetic dipole moment. This energy has two parts: the pure electromagnetic contribution, expressible as a surface integral, and the free energy difference between magnetized and unmagnetized matter, obtained by analyzing a degenerate electron gas in a background of cold ions. Differential forms provide a convenient mathematical framework. The resulting model incorporates electromagnetic effects into stellar structure in a way consistent with linearized general relativity. Although the full system forms a complex open boundary problem, exact solutions exist under simplifying assumptions. The phase diagram predicted by the simplified model shows patterns that may motivate further study of the balance between matter, gravitation, and electromagnetism