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

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.

Figures (5)

• Figure 1: Cumulative distribution (in percentage) of known MWDs with mean field strengths greater than $B$ (thick blue line). Field strength ranges analized in photoionization studies are indicated. The insert figure shows a cross-section evaluated by a fully quantum-mechanic method zhao2007 and the results obtained by the RWA approach (see text). The dark line represents a Gaussian convolution of the Zhao & Stancil evaluation with a FWHM of 3.5 nm ($\approx 10^{-3}$ Ry).
• Figure 2: Branching fractions in the form $(2l+1)n^{-2}Q_{nl,kl'}/P_{n,k}$ as a function of the light wavelength, for continua from Balmer ($n=2$) to Hansen-Strong ($n=7$) in zero magnetic field. Vertical dashed line denotes the limit wavelength of photoionization. The strongest transitions are labeled.
• Figure 3: Extinction coefficient due to photoionizations from atomic hydrogen at $T=20000$ K and $\log \rho=10^{-8}$ g/cm$^3$, calculated for various photon polarizations ($q=0,\pm1$) and different magnetic field strengths.
• Figure 4: Total photoionization absorption $\chi^q$ (gray thick line) and partial contributions ($\sigma^q_\xi n_\xi$) from spin-down sublevels at $n=2$ and $n=8$ manifolds calculated for $B\approx47$ MG ($\log\beta=-2$) and photon polarizations $q=0,\pm1$. The colors distinguish the contributions of states with different values of $m$: green for $m=0$, light blue for $m<0$ (blue for $m=-l$), light red for $m>0$ (red for $m=l$).
• Figure 5: Abundances and binding energies $\mathcal{E}_{-|m|}$ of spin-down atoms at sublevels associated to the $n=8$ manifold, ordered by the quantum number $l$. The colors distinguish the value of $m$: green for $m=0$, light blue for $m<0$ (blue for $m=-l$), light red for $m>0$ (red for $m=l$). Gray lines show the corresponding value at zero-field (the same value for all sublevels associated to the field-free level $n=8$).