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Register a new userPhotoionization of hydrogen in atmospheres of magnetic neutron stars
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The strong magnetic fields (B ~ 10^{12} - 10^{13} G) characteristic of neutron stars make all the properties of an atom strongly dependent on the transverse component K_perp of its generalized momentum. In particular, the photoionization process is modified substantially: (i) threshold energies are decreased as compared with those for an atom at rest, (ii) cross section values are changed significantly, and (iii) selection rules valid for atoms at rest are violated by the motion so that new photoionization channels become allowed. To calculate the photoionization cross sections, we, for the first time, employ exact numerical treatment of both initial and final atomic states. This enables us to take into account the quasi-bound (autoionizing) atomic states as well as coupling of different ionization channels. We extend the previous consideration, restricted to the so-called centered states corresponding to relatively small values of K_perp, to arbitrary states of atomic motion. We fold the cross sections with the thermal distribution of atoms over K. For typical temperatures of neutron star atmospheres, the averaged cross sections differ substantially from those of atoms at rest. In particular, the photoionization edges are strongly broadened by the thermal motion of atoms; this magnetic broadening exceeds the usual Doppler broadening by orders of magnitude. The decentered states of the atoms give rise to the low-energy component of the photoionization cross section. This new component grows significantly with increasing temperature above 10^{5.5} K and decreasing density below 1 g/cm^3, i.e., for the conditions expected in atmospheres of middle-aged neutron stars.
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We construct partially ionized hydrogen atmosphere models for magnetized neutron stars in radiative equilibrium with fixed surface fields between B=10^12 and 2x10^13 G and effective temperatures logT_eff=5.5-6.8, as well as with surface B and T_eff distributions around these values. The models are based on the latest equation of state and opacity results for magnetized, partially ionized hydrogen plasmas. The atmospheres directly determine the characteristics of thermal emission from the surface of neutron stars. We also incorporate these model spectra into XSPEC, under the model name NSMAX, thus allowing them to be used by the community to fit X-ray observations of neutron stars.
We present a detailed investigation of atmospheres around accreting neutron stars with high magnetic field ($Bgtrsim 10^{12}$ G) and low luminosity ($Llesssim 10^{33}$ erg/s). We compute the atmospheric structure, intensity and emergent spectrum for a plane-parallel, pure hydrogen medium by solving the transfer equations for the normal modes coupled to the hydrostatic and energy balance equations. The hard tail found in previous investigations for accreting, non-magnetic neutron stars with comparable luminosity is suppressed and the X-ray spectrum, although still harder than a blackbody at the star effective temperature, is nearly planckian in shape. Spectra from accreting atmospheres, both with high and low fields, are found to exhibit a significant excess at optical wavelengths above the Rayleigh-Jeans tail of the X-ray continuum.
We assess the partition function and ionization degree of magnetized hydrogen atoms at thermodynamic equilibrium for a wide range of field intensities, $Bapprox 10^5$-$10^{12}$~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 $Tapprox 5000$-$80000$~K and densities $rhoapprox 10^{-12}$-$10^{-3}$~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.
Some thermonuclear (type I) X-ray bursts at the neutron star surfaces in low-mass X-ray binaries take place during hard persistent states of the systems. Spectral evolution of these bursts is well described by the atmosphere model of a passively cooling neutron star when the burst luminosity is high enough. The observed spectral evolution deviates from the model predictions when the burst luminosity drops below a critical value of 20-70% of the maximum luminosity. We suggest that these deviations are induced by the additional heating of the accreted particles. We present a method for computation of the neutron star atmosphere models heated by accreted particles assuming that their energy is released via Coulomb interactions with electrons. We compute the temperature structures and the emergent spectra of the atmospheres of various chemical compositions and investigate the dependence of the results on the other model parameters. We show that the heated atmosphere develops the hot (20--100 keV) corona-like surface layer cooled by Compton scattering, and the deeper, almost isothermal optically thick region with a temperature of a few keV. The emergent spectra deviate strongly from those of undisturbed neutron star atmospheres, with the main differences being the presence of a high-energy tail and a strong excess in the low-energy part of the spectrum. They also lack the iron absorption edge, which is visible in the spectra of undisturbed low-luminosity atmospheres with solar chemical composition. Using the computed spectra, we obtained the dependences of the dilution and color-correction factors as functions of relative luminosities for pure helium and solar abundance atmospheres. We show that the helium model atmosphere heated by accretion corresponding to 5% of the Eddington luminosity describes well the late stages of the X-ray bursts in 4U 1820-30.
The S-matrix theory formulation of closed-orbit theory recently proposed by Granger and Greene is extended to atoms in crossed electric and magnetic fields. We then present a semiclassical quantization of the hydrogen atom in crossed fields, which succeeds in resolving individual lines in the spectrum, but is restricted to the strongest lines of each n-manifold. By means of a detailed semiclassical analysis of the quantum spectrum, we demonstrate that it is the abundance of bifurcations of closed orbits that precludes the resolution of finer details. They necessitate the inclusion of uniform semiclassical approximations into the quantization process. Uniform approximations for the generic types of closed-orbit bifurcation are derived, and a general method for including them in a high-resolution semiclassical quantization is devised.
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