Hydrogen ionization equilibrium in magnetic fields

Abstract

We assess the partition function and ionization degree of magnetized hydrogen atoms at thermodynamic equilibrium for a wide range of field intensities, $B\approx 10^5$-$10^{12}$~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 stars (MWDs), with temperatures $T\approx 5000$-$80000$~K and densities $\rho \approx 10^{-12}$-$10^{-3}$~g~cm${}^3$. 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.

15 pages, 10 figures. Accepted for publication in Astronomy & Astrophysics

References in corpus (6)

• Physics of Strongly Magnetized Neutron Stars
• Magnetic White Dwarfs
• New white dwarf stars in the Sloan Digital Sky Survey Data Release 10
• Magnetic Fields of Neutron Stars
• Zeeman tomography of magnetic white dwarfs, I. Reconstruction of the field geometry from synthetic spectra
• Opacities and spectra of hydrogen atmospheres of moderately magnetized neutron stars

Cited by in corpus (5)

• Current challenges in the physics of white dwarf stars
• A Practical Guide to the Partition Function of Atoms and Ions
• A numerical code for the analysis of magnetic white dwarf spectra that includes field effects on the chemical equilibrium
• Strong signature of right-handed circularly polarized photoionization close to the cyclotron line in the atmosphere of magnetic white dwarfs
• Hydrogen photoionization in a magnetized medium: the rigid-wavefunction approach revisited