# Constraining the magnetic field on white dwarf surfaces; Zeeman effects and fine structure constant variation

## TL;DR

This study models atomic absorption lines in white dwarf atmospheres to constrain magnetic fields and assess their impact on measurements of the fine structure constant, finding the magnetic field in G191-B2B is below 2300 Gauss.

## Contribution

The paper introduces a method to model Zeeman effects in white dwarf spectra, enabling precise magnetic field constraints and evaluating their influence on fundamental constant measurements.

## Key findings

- Magnetic field in G191-B2B is less than 2300 Gauss at 3σ.
- Quadratic Zeeman shifts are negligible compared to wavelength uncertainties.
- The method improves magnetic field estimation in white dwarf atmospheres.

## Abstract

White dwarf atmospheres are subjected to gravitational potentials around $10^5$ times larger than occur on Earth. They provide a unique environment in which to search for any possible variation in fundamental physics in the presence of strong gravitational fields. However, a sufficiently strong magnetic field will alter absorption line profiles and introduce additional uncertainties in measurements of the fine structure constant. Estimating the magnetic field strength is thus essential in this context. Here we model the absorption profiles of a large number of atomic transitions in the white dwarf photosphere, including first-order Zeeman effects in the line profiles, varying the magnetic field as a free parameter. We apply the method to a high signal-to-noise, high-resolution, far-ultraviolet HST/STIS spectrum of the white dwarf G191-B2B. The method yields a sensitive upper limit on its magnetic field of $B < 2300$ Gauss at the $3\sigma$ level. Using this upper limit we find that the potential impact of quadratic Zeeman shifts on measurements of the fine structure constant in G191-B2B is 4 orders of magnitude below laboratory wavelength uncertainties.