Hydrogen photoionization in a magnetized medium: the rigid-wavefunction approach revisited

TL;DR

This paper revisits the rigid-wavefunction approach for modeling hydrogen photoionization in magnetized environments, providing explicit formulas and analyzing magnetic field effects on absorption features.

Contribution

It offers a comprehensive, explicit treatment of degeneracy-level breaking and bound state occupation in magnetized gases, improving opacity calculations for white dwarf spectra.

Findings

Significant modifications of absorption occur even below 10 MG magnetic fields.

Pronounced dichroic features emerge in hydrogen continuum absorption across various magnetic field strengths.

The approach enables more accurate modeling where rigorous quantum calculations are computationally demanding.

Abstract

Realistic modeling of stellar spectra requires accurate radiative opacity coefficients. Owing to the fragmentary nature of existing data from rigorous quantum-mechanical calculations, photoionization coefficients based on the rigid-wavefunction approximation remain the only practical option for studies of magnetic white dwarfs. Although variants of this approach have been widely used in spectral analyses for decades, a complete and explicit treatment of degeneracy-level breaking has not previously been presented. In this work, we provide a comprehensive description of this procedure, including explicit expressions for the photoionization probability of individual bound-free transitions as functions of magnetic field strength and radiation polarization. We also evaluate the occupation numbers of bound states in a magnetized gas under ionization equilibrium, enabling the calculation of absolute photoionization opacities. Because high-lying atomic states are strongly perturbed by the magnetic field and ultimately dissolved, substantial modifications of the monochromatic absorption are found even for fields below 10 MG--a regime where fully rigorous quantum calculations are numerically demanding and have not yet been applied. Over a wide range of magnetic field strengths, pronounced dichroic features appear in the hydrogen continuum absorption.