Hydrogen ionization equilibrium in magnetic fields

Instituto de Ciencias Astronómicas, de la Tierra y del Espacio (CONICET), Av. España 1512 (sur), 5400 San Juan, Argentina
e-mail: rene.rohrmann@conicet.gov.ar

Received: 24 December 2019
Accepted: 10 February 2020

Abstract

We assess the partition function and ionization degree of magnetized hydrogen atoms at thermodynamic equilibrium for a wide range of field intensities, B ≈ 10⁵–10¹² G. Evaluations include fitting formulae for an arbitrary number of binding energies, the coupling between the internal atomic structure and the center-of-mass motion across the magnetic field, and the formation of the so-called decentered states (bound states with the electron shifted from the Coulomb well). Non-ideal gas effects are treated within the occupational probability method. We also present general mathematical expressions for the bound state correspondence between the limits of zero-field and high-field. This let us evaluate the atomic partition function in a continuous way from the Zeeman perturbative regime to very strong fields. Results are shown for conditions found in atmospheres of magnetic white dwarf (MWD) stars, with temperatures T ≈ 5000–80 000 K and densities ρ ≈ 10⁻¹²–10⁻³ g cm³. Our evaluations show a marked reduction of the gas ionization due to the magnetic field in the atmospheres of strong MWDs. We also found that decentered states could be present in the atmospheres of currently known hot MWDs, giving a significant contribution to the partition function in the strongest magnetized atmospheres.