Linking the Interiors and Surfaces of Magnetic Stars

TL;DR

This paper models the internal magnetic and thermal structure of magnetic stars, revealing that magnetic flux perturbations are too small to explain observed brightness variations, implying other mechanisms are responsible.

Contribution

It provides semi-analytical models of magnetically perturbed stellar structures with stable fossil fields, linking internal magnetic configurations to surface flux perturbations.

Findings

Magnetic flux perturbations are much smaller than surface magnetic pressure.

Surface flux variations are too small to account for observed brightness modulations.

Magnetic poles can be hotter or cooler depending on field configuration.

Abstract

Strong magnetic fields are observed in a substantial fraction of upper main sequence stars and white dwarfs. Many such stars are observed to exhibit photometric modulations as the magnetic poles rotate in and out of view, which could be a consequence of magnetic perturbations to the star's thermal structure. The magnetic pressure is typically larger than the gas pressure at the star's photosphere, but much smaller than the gas pressure in the star's interior, so the expected surface flux perturbations are not clear. We compute magnetically perturbed stellar structures of young $3 \, M_\odot$ stars that are in both hydrostatic and thermal equilibrium, and which contain both poloidal and toroidal components of a dipolar magnetic field as expected for stable fossil fields. This provides semi-analytical models of such fields in baroclinic stably stratified regions. The star's internal pressure, temperature, and flux perturbations can have a range of magnitudes, though we argue the most likely configurations exhibit flux perturbations much smaller than the ratio of surface magnetic pressure to surface gas pressure, but much larger than the ratio of surface magnetic pressure to central gas pressure. The magnetic pole is hotter than the equator in our models, but a cooler magnetic pole is possible depending on the magnetic field configuration. The expected flux variations for observed field strengths are $\delta L/L \! \lesssim \! 10^{-6}$, much smaller than those observed in magnetic stars, suggesting that observed perturbations stem from changes to the emergent spectrum rather than changes to the bolometric flux.