Magnetic fields in late-stage proto-neutron stars

TL;DR

This paper models the thermal and magnetic structures of late-stage proto-neutron stars, revealing how magnetic fields and rotation influence their shape, stability, and maximum rotation rates, with implications for understanding neutron star evolution.

Contribution

It introduces a simplified equation of state for hot neutron stars and explores the effects of magnetic fields and rotation on their equilibrium configurations, including the impact of magnetic multipole truncation.

Findings

Magnetic fields >10^{14} G lead to similar equilibrium states in hot and cold stars.

Hotter stars have lower Keplerian rotation velocities, suggesting a maximum rotation rate.

Truncating magnetic solutions at low multipoles causes significant inaccuracies.

Abstract

We explore the thermal and magnetic-field structure of a late-stage proto-neutron star. We find the dominant contribution to the entropy in different regions of the star, from which we build a simplified equation of state for the hot neutron star. With this, we numerically solve the stellar equilibrium equations to find a range of models, including magnetic fields and rotation up to Keplerian velocity. We approximate the equation of state as a barotrope, and discuss the validity of this assumption. For fixed magnetic-field strength, the induced ellipticity increases with temperature; we give quantitative formulae for this. The Keplerian velocity is considerably lower for hotter stars, which may set a de-facto maximum rotation rate for non-recycled NSs well below 1 kHz. Magnetic fields stronger than around $10^{14}$ G have qualitatively similar equilibrium states in both hot and cold neutron stars, with large-scale simple structure and the poloidal field component dominating over the toroidal one; we argue this result may be universal. We show that truncating magnetic-field solutions at low multipoles leads to serious inaccuracies, especially for models with rapid rotation or a strong toroidal-field component.