Aims. X-ray bursting neutron stars in low-mass X-ray binaries constitute an appropriate source class for constraining the masses and radii of neutron stars, but a sufficiently extended set of corresponding model atmospheres is necessary for these investigations. Methods. We computed such a set of model atmospheres and emergent spectra in a plane-parallel, hydrostatic, and LTE approximation with Compton scattering taken into account.Results. The models were calculated for six different chemical compositions: pure hydrogen, pure helium, and a solar mix of hydrogen and helium with various heavy element abundances Z = 1, 0.3, 0.1, and 0.01 Z . For each chemical composition the models are computed for three values of surface gravity, log g =14.0, 14.3, and 14.6, and for 20 values of the luminosity in units of the Eddington luminosity, L/L Edd , in the range 0.001-0.98. The emergent spectra of all models are redshifted and fitted by a diluted blackbody in the RXTE/PCA 3-20 keV energy band, and corresponding values of the color correction (hardness factors) f c are presented. Conclusions. Theoretical dependences f c -L/L Edd can be fitted to the observed dependence K −1/4 -F of the blackbody normalization K on flux during cooling stages of X-ray bursts to determine the Eddington flux and the ratio of the apparent neutron star radius to the source distance. If the distance is known, these parameters can be transformed to the constraints on neutron star mass and radius. Theoretical atmosphere spectra can also be used for direct comparison with the observed X-ray burst spectra.

Thermal emission during X-ray bursts is a powerful tool to determine neutron star masses and radii, if the Eddington flux and the apparent radius in the cooling tail can be measured accurately, and distances to the sources are known. We propose here an improved method of determining the basic stellar parameters using the data from the cooling phase of photospheric radius expansion bursts covering a large range of luminosities. Because at that phase the blackbody apparent radius depends only on the spectral hardening factor (colorcorrection), we suggest to fit the theoretical dependences of the color-correction versus flux in Eddington units to the observed variations of the inverse square root of the apparent blackbody radius with the flux. For that we use a large set of atmosphere models for burst luminosities varying by three orders of magnitude and for various chemical compositions and surface gravities. We show that spectral variations observed during a long photospheric radius expansion burst from 4U 1724-307 are entirely consistent with the theoretical expectations for the passively cooling neutron star atmospheres. Our method allows us to determine both the Eddington flux (which is found to be smaller than the touchdown flux by 15%) and the ratio of the stellar apparent radius to the distance much more reliably. We then find a lower limit on the neutron star radius of 14 km for masses below 2.2M ⊙ , independently of the chemical composition. These results suggest that the matter inside neutron stars is characterized by a stiff equation of state. We also find evidences in favour of hydrogen rich accreting matter and obtain an upper limit to the distance of 7 kpc. We finally show that the apparent blackbody emitting area in the cooling tails of the short bursts from 4U 1724-307 is two times smaller than that for the long burst and their evolution does not follow the theory. This makes their usage for determination of the neutron star parameters questionable and casts serious doubts on the results of previous works that used for the analysis similar bursts from other sources.

Context. Theoretical spectra of X-ray bursting neutron star (NS) model atmospheres are widely used to determine the basic NS parameters such as their masses and radii. Compton scattering, which plays an important role in spectra formation at high luminosities, is often accounted for using the differential Kompaneets operator, while in other models a more general, integral operator for the Compton scattering kernel is used. Aims. We construct accurate NS atmosphere models using for the first time an exact treatment of Compton scattering via the integral relativistic kinetic equation. We also test various approximations to the Compton scattering redistribution function and compare the results with the previous calculations based on the Kompaneets operator. Methods. We solve the radiation transfer equation together with the hydrostatic equilibrium equation accounting exactly for the radiation pressure by electron scattering. We use the exact relativistic angle-dependent redistribution function as well as its simple approximate representations. Results. We thus construct a new set of plane-parallel atmosphere models in local thermodynamic equilibrium (LTE) for hot NSs. The models were computed for six chemical compositions (pure H, pure He, solar H/He mix with various heavy elements abundances Z = 1, 0.3, 0.1, and 0.01 Z , and three surface gravities log g = 14.0, 14.3, and 14.6. For each chemical composition and surface gravity, we compute more than 26 model atmospheres with various luminosities relative to the Eddington luminosity L Edd computed for the Thomson cross-section. The maximum relative luminosities L/L Edd reach values of up to 1.1 for high gravity models. The emergent spectra of all models are redshifted and fitted by diluted blackbody spectra in the 3−20 keV energy range appropriate for the RXTE/PCA. We also compute the color correction factors f c . Conclusions. The radiative acceleration g rad in our luminous, hot-atmosphere models is significantly smaller than in corresponding models based on the Kompaneets operator, because of the Klein-Nishina reduction of the electron scattering cross-section, and therefore formally "super-Eddington" model atmospheres do exist. The differences between the new and old model atmospheres are small for L/L Edd < 0.8. For the same g rad /g, the new f c are slightly larger (by approximately 1%) than the old values. We also find that the model atmospheres, the emergent spectra, and the color correction factor computed using angle-averaged and approximate Compton scattering kernels differ from the exact solutions by less than 2%.

We study properties of luminous X-ray pulsars using a simplified model of the accretion column. The maximal possible luminosity is calculated as a function of the neutron star (NS) magnetic field and spin period. It is shown that the luminosity can reach values of the order of 10 40 erg s −1 for the magnetar-like magnetic field (B ∼ > 10 14 G) and long spin periods (P ∼ > 1.5 s). The relative narrowness of an area of feasible NS parameters which are able to provide higher luminosities leads to the conclusion that L ≃ 10 40 erg s −1 is a good estimate for the limiting accretion luminosity of a NS. Because this luminosity coincides with the cut-off observed in the high mass Xray binaries luminosity function which otherwise does not show any features at lower luminosities, we can conclude that a substantial part of ultra-luminous X-ray sources are accreting neutron stars in binary systems.