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.

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.

Magnetized neutron stars power at least some ultra-luminous X-ray sources. The accretion flow in these cases is interrupted at the magnetospheric radius and then reaches the surface of a neutron star following magnetic field lines. Accreting matter moving along magnetic field lines forms the accretion envelope around the central object. We show that, in case of high mass accretion rates 10 19 g s −1 the envelope becomes closed and optically thick, which influences the dynamics of the accretion flow and the observational manifestation of the neutron star hidden behind the envelope. Particularly, the optically thick accretion envelope results in a multi-color black-body spectrum originating from the magnetospheric surface. The spectrum and photon energy flux vary with the viewing angle, which gives rise to pulsations characterized by high pulsed fraction and typically smooth pulse profiles. The reprocessing of radiation due to interaction with the envelope leads to the disappearance of cyclotron scattering features from the spectrum. We speculate that the super-orbital variability of ultra-luminous X-ray sources powered by accreting neutron stars can be attributed to precession of the neutron star due to interaction of magnetic dipole with the accretion disc.

We present here the first convincing observational manifestation of a magnetar-like magnetic field in an accreting neutron star in binary system -the first pulsating ultraluminous X-ray source X-2 in the galaxy M82. Using the Chandra X-ray observatory data we show that the source exhibit the bimodal distribution of the luminosity with two well-defined peaks separated by a factor of 40. This behaviour can be interpreted as the action of the "propeller regime" of accretion. The onset of the propeller in a 1.37 s pulsar at luminosity of ∼ 10 40 erg s −1 implies the dipole component of the neutron star magnetic field of ∼ 10 14 G.

Cyclotron resonance scattering features observed in the spectra of some X-ray pulsars show significant changes of the line energy with the pulsar luminosity. At high luminosities, these variations are often associated with the onset and growth of the accretion column, which is believed to be the origin of the observed emission and of the cyclotron lines. However, this scenario inevitably implies a large gradient of the magnetic field strength within the line-forming region, which makes the formation of the observed line-like features problematic. Moreover, the observed variation of the cyclotron line energy is much smaller than could be anticipated for the corresponding luminosity changes. We argue here that a more physically realistic situation is that the cyclotron line forms when the radiation emitted by the accretion column is reflected from the neutron star surface, where the gradient of the magnetic field strength is significantly smaller. Here we develop a reflection model and apply it to explain the observed variations of the cyclotron line energy in a bright X-ray pulsar V 0332+53 over a wide range of luminosities.

Aims. We present the results of the monitoring programmes performed with the Swift/XRT telescope and aimed specifically to detect an abrupt decrease of the observed flux associated with a transition to the propeller regime in two well-known X-ray pulsars 4U 0115+63 and V 0332+53. Methods. Both sources form binary systems with Be optical companions and undergo so-called giant outbursts every 3-4 years. The current observational campaigns were performed with the Swift/XRT telescope in the soft X-ray band (0.5-10 keV) during the declining phases of the outbursts exhibited by both sources in 2015.Results. The transitions to the propeller regime were detected at the threshold luminosities of (1.4 ± 0.4) × 10 36 erg s −1 and (2.0 ± 0.4) × 10 36 erg s −1 for 4U 0115+63 and V 0332+53, respectively. Spectra of the sources are shown to be significantly softer during the low state. In both sources, the accretion at rates close to the aforementioned threshold values briefly resumes during the periastron passage following the transition into the propeller regime. The strength of the dipole component of the magnetic field required to inhibit the accretion agrees well with estimates based on the position of the cyclotron lines in their spectra, thus excluding presence of a strong multipole component of the magnetic field in the vicinity of the neutron star.

We report on the analysis of NuSTAR observations of the Be-transient X-ray pulsar V 0332+53 during the giant outburst in 2015 and another minor outburst in 2016. We confirm the cyclotron-line energy -luminosity correlation previously reported in the source and the line energy decrease during the giant outburst. Based on 2016 observations we find that a year later the line energy has increased again essentially reaching the pre-outburst values. We discuss this behaviour and conclude that it is likely caused by a change of the emission region geometry rather than previously suggested accretion-induced decay of the neutron stars magnetic field. At lower luminosities we find for the first time a hint of departure from the anti-correlation of line energy with flux, which we interpret as a transition from super-to sub-critical accretion associated with disappearance of the accretion column. Finally, we confirm and briefly discuss the orbital modulation observed in the outburst light curve of the source.

Aims. Magnetic field of accreting neutron stars determines their overall behavior including the maximum possible luminosity. Some models require an above-average magnetic field strength ( 10 13 G) in order to explain super-Eddington mass accretion rate in the recently discovered class of pulsating ultraluminous X-ray sources (ULX). The peak luminosity of SMC X-3 during its major outburst in 2016-2017 reached ∼ 2.5 × 10 39 erg s −1 comparable to that in ULXs thus making this source the nearest ULX-pulsar. Determination of the magnetic field of SMC X-3 is the main goal of this paper. Methods. SMC X-3 belongs to the class of transient X-ray pulsars with Be optical companions, and exhibited a giant outburst in July 2016 -March 2017. The source has been observed during the entire outburst with the Swift/XRT and Fermi/GBM telescopes, as well as the NuSTAR observatory. Collected data allowed us to estimate the magnetic field strength of the neutron star in SMC X-3 using several independent methods. Results. Spin evolution of the source during and between the outbursts and the luminosity of the transition to so-called propeller regime in the range of (0.3 − 7) × 10 35 erg s −1 imply relatively weak dipole field of (1 − 5) × 10 12 G. On the other hand, there is also evidence for much stronger field in the immediate vicinity of the neutron star surface. In particular, transition from super-to subcritical accretion regime associated with cease of the accretion column and very high peak luminosity favor an order of magnitude stronger field. This discrepancy makes SMC X-3 a good candidate to posses significant non-dipolar components of the field, and an intermediate source between classical X-ray pulsars and accreting magnetars which may constitute an appreciable fraction of ULX population.