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.

Abstract. We present results of an analysis of broadband X-ray spectra of 14 intermediate polars obtained with the RXTE observatory (PCA and HEXTE spectrometers, 3-100 keV). For this we have calculated theoretical models of the structure and the emergent spectrum of the post-shock region of intermediate polars. By fitting theoretical model spectra to the observed spectra we derive estimates for the masses of the white dwarfs. We compare the resulting masses with masses obtained by other authors and other methods. The masses obtained by us are smaller than the masses obtained by using PCA and GINGA data, and they are in good agreement with the masses derived from radial velocity studies.

The accretion flow around X-ray pulsars with a strong magnetic field is funnelled by the field to relatively small regions close to the magnetic poles of the neutron star (NS), the hotspots. During strong outbursts regularly observed from some X-ray pulsars, the X-ray luminosity can be so high, that the emerging radiation is able to stop the accreting matter above the surface via radiation-dominated shock, and the accretion column begins to rise. This border luminosity is usually called the "critical luminosity". Here we calculate the critical luminosity as a function of the NS magnetic field strength B using exact Compton scattering cross section in strong magnetic field. Influence of the resonant scattering and photon polarization is taken into account for the first time. We show that the critical luminosity is not a monotonic function of the B-field. It reaches a minimum of a few 10 36 erg s −1 when the cyclotron energy is about 10 keV and a considerable amount of photons from a hotspot have energy close to the cyclotron resonance. For small B, this luminosity is about 10 37 erg s −1 , nearly independent of the parameters. It grows for the B-field in excess of 10 12 G because of the drop in the effective cross-section of interaction below the cyclotron energy. We investigate how different types of the accretion flow and geometries of the accretion channel affect the results and demonstrate that the general behaviour of the critical luminosity on B-field is very robust. The obtained results are shown to be in a good agreement with the available observational data and provide a necessary ground for the interpretation of upcoming high quality data from the currently operating and planned X-ray telescopes.

Spectral measurements of thermonuclear (type-I) X-ray bursts from low mass X-ray binaries have been used to measure neutron star (NS) masses and radii. A number of systematic issues affect such measurements and have raised concerns as to the robustness of the methods. We present analysis of the X-ray emission from bursts observed from 4U 1608-52 at various persistent fluxes. We find a strong dependence of the burst properties on the flux and spectral hardness of the persistent emission before burst. Bursts occurring during the low-accretion rate (hard) state exhibit evolution of the black body normalisation consistent with the theoretical predictions of NS atmosphere models. However, bursts occurring during the high-accretion rate (soft) state show roughly constant normalisation, which is inconsistent with the NS atmosphere models and therefore these bursts cannot be easily used to determine NS parameters. We analyse the hard-state burst to put the lower limit on the neutron star radius in 4U 1608-52 of 13 km (for masses 1.2-2.4 M ⊙ ). The best agreement with the theoretical NS mass-radius relations is achieved for source distances in the range 3.1-3.7 kpc. We expect that the radius limit will be 10 per cent lower if spectral models including rapid rotation are used instead.

The cooling phase of thermonuclear (type-I) X-ray bursts can be used to constrain the neutron star (NS) compactness by comparing the observed cooling tracks of bursts to accurate theoretical atmosphere model calculations. By applying the so-called cooling tail method, where the information from the whole cooling track is used, we constrain the mass, radius, and distance for three different NSs in low-mass X-ray binaries 4U 1702−429, 4U 1724−307, and SAX J1810.8−260. Care is taken to only use the hard state bursts where it is thought that only the NS surface alone is emitting. We then utilize a Markov chain Monte Carlo algorithm within a Bayesian framework to obtain a parameterized equation of state (EoS) of cold dense matter from our initial mass and radius constraints. This allows us to set limits on various nuclear parameters and to constrain an empirical pressure-density relation for the dense matter. Our predicted EoS results in NS radius between 10.5 − 12.8 km (95% confidence limits) for a mass of 1.4 M depending slightly on the assumed composition. Due to systematic errors and uncertainty in the composition these results should be interpreted as lower limits for the radius.