Analytic approximations to photoabsorption cross sections of once-ionized helium in magnetar atmospheres

Magnetar atmospheres can contain a substantial fraction of once-ionized helium. At the magnetic fields about 10¹⁴ - 10¹⁵ G, typical of magnetars, Landau quantization is important not only for the electrons, but also for the centre-of-mass (CM) motion of the He⁺ ion. The CM and internal motions are mutually dependent, which complicates theoretical studies of the He⁺ characteristics. We present asymptotic analytic expressions for the binding energies, oscillator strengths, and photoionization cross sections of the moving hydrogenlike ions in an ultra-strong magnetic field, which can be used to construct approximate models of magnetar atmospheres.