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Astron. Astrophys. 320, 181-184 (1997)

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2. Source grid of theoretical spectra

In this paper we analyse the set of model atmospheres of hot neutron stars, which was described and published in Madej (1991), hereafter Paper I. All the models were computed assuming plane-parallel geometry, hydrostatic and radiative equilibrium, and an equation of state for an ideal gas consisting of perfectly ionized hydrogen and helium of the solar number abundance, [FORMULA]. No heavier elements were included in computations. A total of 20 model atmospheres were computed, and their parameters ([FORMULA] and surface [FORMULA]) are listed in Table 1 (cgs units).


Table 1. Listing of source model atmospheres

Table 1 lists also logarithms of the critical gravities, at which radiation pressure gradient precisely compensates the gradient of gas pressure at some level in H/He atmosphere, thus limiting [FORMULA] of hydrostatic models. Values of [FORMULA] were obtained by extrapolation of non-grey hydrostatic models.

The models in Paper I included very careful treatment of Compton scattering, which is the dominant source of opacity in almost all X-ray bursting neutron stars. The presence of very strong scattering terms in the source functions generally causes deviations from the Planckian shape and introduces non-local coupling in the atmosphere, typical to NLTE models (Mihalas 1978). Both the equation of transfer and the equation of radiative equilibrium included Compton scattering frequency redistribution profiles (Pomraning 1973), which allow us to trace in detail the transfer of photons in frequency space also in cases that the photon energy is not much less than the electron rest mass, [FORMULA] keV. In fact, the hottest models in Table 1 ([FORMULA]) were computed with the mesh of discrete photon energies exceeding 140 keV. Such computations cannot be accurately done with a simplified Kompaneets equation, which is valid in the range [FORMULA] (Rybicki & Lightman 1979). Moreover, the Kompaneets equation ignores the finite width of the Compton scattering profile and its asymmetry.

Figs. 1 and 2 display some of the X-ray spectra presented in Paper I, computed for extreme values of [FORMULA], together with the Planck function corresponding to that [FORMULA]. It is evident, that all theoretical spectra are significantly harder, than the blackbody curve. Moreover, the theoretical X-ray spectra clearly exhibit a dependence on the surface gravity [FORMULA] of a neutron star. In case of the coolest models at [FORMULA] K (Fig. 1), a decrease of the surface gravity [FORMULA] from 15.0 down to 12.5 (cgs units) causes distinct rise of the low-energy branch of X-ray spectra and a slight decrease around flux maximum (both effects were also discussed by Lewin et al. 1993). For the hottest models ([FORMULA] K) the most significant changes occur in a wide region around the peak in the flux distribution, with a [FORMULA] dependence that is of opposite sign compared to the [FORMULA] K models. The models in Paper I are quite accurate numerically, therefore it is worthwhile to seek for a simplified analytical representation of both gravity effects, for the subsequent fitting of observed spectra of X-ray burst sources.

[FIGURE] Fig. 1. X-ray spectra of hydrogen/helium models with [FORMULA] K [FORMULA] keV and various surface gravities. Solid curve (BB) denotes blackbody spectrum of the [FORMULA]. Spectra of model atmospheres evolve with changing [FORMULA], which is mostly pronounced in low energy tail. Decrease of gravity causes increase of soft X-ray flux, and slight flattening around the peak flux
[FIGURE] Fig. 2. Same for models with [FORMULA] K [FORMULA] keV. Here the evolution of spectra with [FORMULA] is qualitatively different than in Fig. 1
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© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998