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Recent observations of X-ray pulsars (XRPs) performed by the Imaging X-ray Polarimetry Explorer (IXPE) have made it possible to investigate the intricate details of these objects in a new way, thanks to the added value of X-ray polarimetry. Here we present the results of the IXPE observations of SMC X-1, a member of the small group of XRPs displaying super-orbital variability. SMC X-1 was observed by IXPE three separate times during the high state of its super-orbital period. The observed luminosity in the 2-8 keV energy band of $L=2\times10^{38}$ erg/s makes SMC X-1 the brightest XRP ever observed by IXPE. We detect significant polarization in all three observations, with values of the phase-averaged polarization degree (PD) and polarization angle (PA) of $3.2\pm0.8$% and $97\deg\pm8\deg$ for Observation 1, $3.0\pm0.9$% and $90\deg\pm8\deg$ for Observation 2, and $5.5\pm1.1$% and $80\deg\pm6\deg$ for Observation 3, for the spectro-polarimetric analysis. The observed PD shows an increase over time with decreasing luminosity, while the PA decreases in decrements of 10\deg. The phase-resolved spectro-polarimetric analysis reveals significant detection of polarization in three out of seven phase bins, with the PD ranging between 2% and 10%, and a corresponding range in the PA from $\sim$70\deg\ to $\sim$100\deg. The pulse-phase resolved PD displays an apparent anti-correlation with the flux. Using the rotating vector model, we obtain constraints on the pulsar's geometrical properties for the individual observations. The position angle of the pulsar displays an evolution over time supporting the idea that we observe changes related to different super-orbital phases. Scattering in the wind of the precessing accretion disk may be responsible for the behavior of the polarimetric properties observed during the high-state of SMC X-1's super-orbital period., Comment: 11 pages, 11 figures, submitted to A&A

Discovery of pulsations from a number of ultra-luminous X-ray (ULX) sources proved that accretion onto neutron stars can produce luminosities exceeding the Eddington limit by a couple of orders of magnitude. The conditions necessary to achieve such high luminosities as well as the exact geometry of the accretion flow in the neutron star vicinity are, however, a matter of debate. The pulse phase-resolved polarization measurements that became possible with the launch of the IXPE can be used to determine the pulsar geometry and its orientation relative to the orbital plane. They provide an avenue to test different theoretical models of ULX pulsars. In this paper we present the results of three IXPE observations of the first Galactic ULX pulsar Swift J0243.6+6124 during its 2023 outburst. We find strong variations of the polarization characteristics with the pulsar phase. The average polarization degree increases from about 5% to 15% as the flux dropped by a factor of three in the course of the outburst. The polarization angle (PA) as function of the pulsar phase shows two peaks in the first two observations, but changes to a characteristic sawtooth pattern in the remaining data set. This is not consistent with a simple rotating vector model. Assuming the existence of an additional constant polarized component, we were able to fit the three observations with a common rotating vector model and obtain constraints on the pulsar geometry. In particular, we find the pulsar angular momentum inclination with respect to the line-of-sight of 15-40 deg, the magnetic obliquity of 60-80 deg, and the pulsar spin position angle of -50 deg, which differs from the constant component PA of about 10 deg. Combining these X-ray measurements with the optical PA, we find evidence for a 30 deg misalignment between the pulsar spin and the binary orbital axis., Comment: 13 pages, 10 figures, submitted to A&A

In an accreting X-ray pulsar, a neutron star accretes matter from a stellar companion through an accretion disk. The high magnetic field of the rotating neutron star disrupts the inner edge of the disc, funneling the gas to flow onto the magnetic poles on its surface. Hercules X-1 is in many ways the prototypical X-ray pulsar; it shows persistent X-ray emission and it resides with its companion HZ Her, a two-solar-mass star, at about 7~kpc from Earth. Its emission varies on three distinct timescales: the neutron star rotates every 1.2~seconds, it is eclipsed by its companion each 1.7~days, and the system exhibits a superorbital period of 35~days which has remained remarkably stable since its discovery. Several lines of evidence point to the source of this variation as the precession of the accretion disc, the precession of the neutron star or both. Despite the many hints over the past fifty years, the precession of the neutron star itself has yet not been confirmed or refuted. We here present X-ray polarization measurements with the Imaging X-ray Polarimetry Explorer (IXPE) which probe the spin geometry of the neutron star. These observations provide direct evidence that the 35-day-period is set by the free precession of the neutron star crust, which has the important implication that its crust is somewhat asymmetric fractionally by a few parts per ten million. Furthermore, we find indications that the basic spin geometry of the neutron star is altered by torques on timescale of a few hundred days., Comment: 37 pages

Spectro-polarimetric signatures of accretion disks in X-ray binaries and active galactic nuclei contain information about the masses and spins of their central black holes, as well as the geometry of matter close to the compact objects. This information can be extracted using the means of X-ray polarimetry. In this work, we present a fast analytical ray-tracing technique for polarized light \textsc{artpol} that helps obtain the spinning black hole parameters from the observed properties. This technique can replace the otherwise time-consuming numerical ray-tracing calculations. We show that \textsc{artpol} proves accurate for Kerr black holes with dimensionless spin parameter $a\leq0.94$ while being over four orders of magnitude faster than direct ray-tracing calculations. This approach opens broad prospects for directly fitting the spectro-polarimetric data from the \textit{Imaging X-ray Polarimetry Explorer}., Comment: Submitted to Astronomy & Astrophysics

We report on Imaging X-ray polarimetry explorer (IXPE) observations of the Be-transient X-ray pulsar LS V +44 17/RX J0440.9+4431 made at two luminosity levels during the giant outburst in January--February 2023. Considering the observed spectral variability and changes in the pulse profiles, the source was likely caught in supercritical and subcritical states with significantly different emission-region geometry, associated with the presence of accretion columns and hot spots, respectively. We focus here on the pulse-phase-resolved polarimetric analysis and find that the observed dependencies of the polarization degree and polarization angle (PA) on the pulse phase are indeed drastically different for the two observations. The observed differences, if interpreted within the framework of the rotating vector model (RVM), imply dramatic variations in the spin axis inclination, the position angle, and the magnetic colatitude by tens of degrees within the space of just a few days. We suggest that the apparent changes in the observed PA phase dependence are predominantly related to the presence of an unpulsed polarized component in addition to the polarized radiation associated with the pulsar itself. We then show that the observed PA phase dependence in both observations can be explained with a single set of RVM parameters defining the pulsar's geometry. We also suggest that the additional polarized component is likely produced by scattering of the pulsar radiation in the equatorial disk wind., Comment: 10 pages, 7 figures, accepted in A&A

The phase- and energy-resolved polarization measurements of accreting X-ray pulsars (XRPs) allow us to test different theoretical models of their emission, and they also provide an avenue to determine the emission region geometry. We present the results of the observations of the XRP GX 301-2 performed with the Imaging X-ray Polarimetry Explorer (IXPE). A persistent XRP, GX 301-2 has one of the longest spin periods known: $\sim$680s. A massive hyper-giant companion star Wray 977 supplies mass to the neutron star via powerful stellar winds. We did not detect significant polarization in the phase-averaged data when using spectro-polarimetric analysis, with the upper limit on the polarization degree (PD) of 2.3% (99% confidence level). Using the phase-resolved spectro-polarimetric analysis, we obtained a significant detection of polarization (above 99% confidence level) in two out of nine phase bins and a marginal detection in three bins, with a PD ranging between $\sim$3% and $\sim$10% and a polarization angle varying in a very wide range from $\sim$0 degree to $\sim$160 degree. Using the rotating vector model, we obtained constraints on the pulsar geometry using both phase-binned and unbinned analyses, finding excellent agreement. Finally, we discuss possible reasons for a low observed polarization in GX 301-2., Comment: 10 pages, 10 figures, accepted for publication in A&A

Accreting X-ray pulsars (XRPs) are presumably ideal targets for polarization measurements, as their high magnetic field strength is expected to polarize the emission up to a polarization degree of ~80%. However, such expectations are being challenged by recent observations of XRPs with the Imaging X-ray Polarimeter Explorer (IXPE). Here we report on the results of yet another XRP, EXO 2030+375, observed with IXPE and contemporarily monitored with Insight-HXMT and SRG/ART-XC. In line with recent results obtained with IXPE for similar sources, analysis of the EXO 2030+375 data returns a low polarization degree of 0%-3% in the phase-averaged study and variation in the range 2%-7% in the phase-resolved study. Using the rotating vector model we constrain the geometry of the system and obtain a value for the magnetic obliquity of ~$60^{\circ}$. Considering also the estimated pulsar inclination of ~$130^{\circ}$, this indicates that the magnetic axis swings close to the observer line of sight. Our joint polarimetric, spectral and timing analysis hint to a complex accreting geometry where magnetic multipoles with asymmetric topology and gravitational light bending significantly affect the observed source behavior., Comment: A&A accepted. Proofs version

The radiation from accreting X-ray pulsars was expected to be highly polarized, with some estimates for the polarization degree of up to 80%. However, phase-resolved and energy-resolved polarimetry of X-ray pulsars is required in order to test different models and to shed light on the emission processes and the geometry of the emission region. Here we present the first results of the observations of the accreting X-ray pulsar Vela X-1 performed with the Imaging X-ray Polarimetry Explorer (IXPE). Vela X-1 is considered to be the archetypal example of a wind-accreting high-mass X-ray binary system, consisting of a highly magnetized neutron star accreting matter from its supergiant stellar companion. The spectro-polarimetric analysis of the phase-averaged data for Vela X-1 reveals a polarization degree (PD) of 2.3$\pm$0.4% at the polarization angle (PA) of -47.3$\pm$5.4 deg. A low PD is consistent with the results obtained for other X-ray pulsars and is likely related to the inverse temperature structure of the neutron star atmosphere. The energy-resolved analysis shows the PD above 5 keV reaching 6-10%, and a 90 deg difference in the PA compared to the data in the 2-3 keV range. The phase-resolved spectro-polarimetric analysis finds a PD in the range 0-9% with the PA varying between -80 and 40 deg., Comment: 12 pages, 7 figures, ApJ Letters, submitted

Central compact objects (CCOs) are neutron stars found close to the center of some supernova remnants. A certain number of them are presumably covered by carbon envelopes. Their unpulsed thermal X-ray emission can originate either from the entire surface covered by a carbon atmosphere or alternatively from a nonuniformly emitting hydrogen atmosphere. However, the latter scenario appears unlikely given the available upper limits on the amplitude of pulsations. Here we explore a possibility to further discriminate between the two scenarios using X-ray polarimetric observations. We compute the polarization degree (PD) for nonmagnetized pure-carbon and pure-hydrogen atmospheres with effective temperatures of between 1 and 6 MK and find that it can reach up to 25% and 40% for hydrogen and carbon atmospheres, respectively, in the photon energy band 1-10 keV. However, given the available constraints on possible inhomogeneities of the temperature distribution deduced from models of the X-ray spectrum of the CCO in HESS J1731-347, the integrated PD appears to be very low for both carbon (<0.25%) and hydrogen (a few percent) compositions in the energy band of 2-8 keV covered by the recently launched Imaging X-ray Polarimetry Explorer. We therefore conclude that polarization from CCOs is not expected to be detectable by current facilities, but future detection would strongly support nonuniform hydrogen composition models., Comment: 10 pages, 16 figures. accepted to be published by A&A, corrected after the language Editor remarks, misprints in some numbers were corrected, a new version of Fig.15

X-ray polarimetry is a unique way to probe the geometrical configuration of highly magnetized accreting neutron stars (X-ray pulsars). GRO J1008$-$57 is the first transient X-ray pulsar observed at two different flux levels by the Imaging X-ray Polarimetry Explorer (IXPE) during its outburst in November 2022. We find the polarization properties of GRO J1008$-$57 to be independent of its luminosity, with the polarization degree varying between nondetection and about 15% over the pulse phase. Fitting the phase-resolved spectro-polarimetric data with the rotating vector model allowed us to estimate the pulsar inclination (130 deg, which is in good agreement with the orbital inclination), the position angle (75 deg) of the pulsar spin axis, and the magnetic obliquity (74 deg). This makes GRO J1008$-$57 the first confidently identified nearly orthogonal rotator among X-ray pulsars. We discuss our results in the context of the neutron star atmosphere models and theories of the axis alignment of accreting pulsars., Comment: 11 pages, 7 figures, A&A, in press

Geometry and dynamical structure of emission regions in accreting pulsars are shaped by the interplay between gravity, radiation, and strong magnetic field, which significantly affects the opacities of a plasma and radiative pressure under such extreme conditions. Quantitative consideration of magnetic plasma opacities is, therefore, an essential ingredient of any self-consistent modeling of emission region structure of X-ray pulsars. We present results of computations of the Rosseland and Planck mean opacities of a strongly magnetized plasma with a simple chemical composition,namely the solar hydrogen/helium mix. We consider all relevant specific opacities of the magnetized plasma including vacuum polarization effect and contribution of electron-positron pairs where the pair number density is computed in the thermodynamic equilibrium approximation. The magnetic Planck mean opacity determines the radiative cooling of an optically thin strongly magnetized plasma. It is by factor of three smaller than non-magnetic Planck opacity at $k_{\rm B}T < 0.1\,E_{\rm cyc}$ and increases by a factor of $10^2 - 10^4$ at $k_{\rm B}T > 0.3\,E_{\rm cyc}$ due to cyclotron thermal processes. We propose a simple approximate expression which has sufficient accuracy for the magnetic Planck opacity description. We provide the Rosseland opacity in a tabular form computed in the temperature range 1 - 300 keV, magnetic field range $3 \times 10^{10} - 10^{15}$ G, and a broad range of plasma densities. We demonstrate that the scattering on the electron-positron pairs increases the Rosseland opacity drastically at temperatures >50 keV in the case of mass densities typical for accretion channel in X-ray pulsars., Comment: 14 pages, 12 figures, accepted for publication in MNRAS, added with data files and an interpolation code together with their description

Cen X-3 is the first X-ray pulsar discovered 50 years ago. Radiation from such objects is expected to be highly polarized due to birefringence of plasma and vacuum associated with propagation of photons in presence of the strong magnetic field. Here we present results of the observations of Cen X-3 performed with the Imaging X-ray Polarimetry Explorer. The source exhibited significant flux variability and was observed in two states different by a factor of ~20 in flux. In the low-luminosity state no significant polarization was found either in pulse phase-averaged (with the 3$\sigma$ upper limit of 12%) or phase-resolved data (the 3$\sigma$ upper limits are 20-30%). In the bright state the polarization degree of 5.8$\pm$0.3% and polarization angle of $49.6\deg\pm1.5\deg$ with significance of about 20$\sigma$ was measured from the spectro-polarimetric analysis of the phase-averaged data. The phase-resolved analysis showed a significant anti-correlation between the flux and the polarization degree as well as strong variations of the polarization angle. The fit with the rotating vector model indicates a position angle of the pulsar spin axis of about 49$\deg$ and a magnetic obliquity of 17$\deg$. The detected relatively low polarization can be explained if the upper layers of the neutron star surface are overheated by the accreted matter and the conversion of the polarization modes occurs within the transition region between the upper hot layer and a cooler underlying atmosphere. A fraction of polarization signal can also be produced by reflection of radiation from the neutron star surface and the accretion curtain., Comment: Submitted to ApJL. 18 pages, 12 figures

Using observations of X-ray pulsar Her X-1 by the Imaging X-ray Polarimetry Explorer, we report on a highly significant ($>17\sigma$) detection of the polarization signal from an accreting neutron star. The observed degree of the linear polarization of $\sim$10\% is found to be far below theoretical expectations for this object, and stays low throughout the spin cycle of the pulsar. Both the polarization degree and the angle exhibit variability with pulse phase, which allowed us to measure the pulsar spin position angle 57(2) deg and the magnetic obliquity 12(4) deg, which is an essential step towards detailed modelling of the intrinsic emission of X-ray pulsars. Combining our results with the optical polarimetric data, we find that the spin axis of the neutron star and the angular momentum of the binary orbit are misaligned by at least $\sim$20 deg, which is a strong argument in support of the models explaining stability of the observed super-orbital variability with the precession of the neutron star., Comment: 31 pages 7 figures, published

We investigate the aperiodic variability for a relatively large sample of accreting neutron stars and intermediate polars, focusing on the properties of the characteristic break commonly observed in power spectra of accreting objects. In particular, we investigate the relation of the break frequency and the magnetic field strength, both of which are connected to the size of the magnetosphere. We find that for the majority of objects in our sample the measured break frequency values indeed agree with estimated inner radii of the accretion disc, which allows to use observed break frequencies to independently assess the magnetic field strength and structure in accreting compact objects. As a special case, we focus on Hercules X-1 which is a persistent, medium-luminosity X-ray pulsar accreting from its low-mass companion. In the literature, it has been suggested that the complex pulse profiles, the spin-up behaviour and the luminosity-correlation of the cyclotron energy seen in Her X-1 can be explained with a complex magnetic field structure of the neutron star. Here, we connect the measured break frequency to the magnetospheric radius and show that the magnetic field strength derived assuming a dipole configuration is nearly an order of magnitude smaller than the magnetic field strength corresponding to the cyclotron energy. Accordingly, this discrepancy can be explained with the magnetic field having strong multipole components. The multipolar structure would also increase the accreting area on the neutron star surface, explaining why the critical luminosity for accretion column formation is puzzlingly high in this source., Comment: 10 pages, 3 figures

Compton scattering is a key process shaping spectra formation and accretion flow dynamics in accreting strongly magnetized neutron stars. A strong magnetic field affects the scattering cross section and makes it dependent on photon energy, momentum, and polarization state. Using Monte Carlo simulations, we investigate statistical features of Compton scattering of polarized X-ray radiation in a strong magnetic field. Our analysis is focused on photon gas behaviour well inside the scattering region. We take into account the resonant scattering at the fundamental cyclotron frequency, thermal distribution of electrons at the ground Landau level, and bulk velocity of the electron gas. We show that (i) the photons scattered around the cyclotron energy by the electron gas at rest tend to acquire the final energy close to the cyclotron one with a very small dispersion measure; (ii) the redistribution of photons within the Doppler core of cyclotron resonance differs significantly from the complete redistribution; (iii) the efficiency of momentum transfer from photons to the electron gas is affected by the temperature of electron gas both for photons at cyclotron energy and below it; (iv) the momentum transfer from photons to the electron gas of non-zero bulk velocity is more efficient in the case of magnetic scattering., Comment: 18 pages, 13 figures, accepted for publication in Phys.Rev.D

Cataclysmic variables (CVs) are the most numerous population among the Galactic objects emitting in hard X-rays. Most probably, they are responsible for the extended hard X-ray emission of the Galactic ridge and the central Galactic regions. Here we consider the sample of CVs detected in the all-sky hard X-ray Swift/BAT survey which were also detected by Gaia and thus have reliable distance estimates. Using these data, we derive accurate estimates for local number density per solar mass (\rho_M = 1.37^{+0.3}_{-0.16} x 10^{-5} M_sun^{-1}) and luminosity density per solar mass (\rho_L = 8.95^{+0.15}_{-0.1} x 10^{26} erg s^{-1} M_sun^{-1}) for objects in the sample. These values appear to be in good agreement with the integrated Galactic ridge X-ray emission and Nuclear Stellar Cluster luminosities. Analysis of the differential luminosity functions d\rho_M/d(\log_{10} L_x) and d\rho_L/d(\log_{10} L_x) confirms that there are two populations of hard X-ray emitting CVs. Intermediate polars dominate at luminosities L > 10^{33} erg s^{-1}, whereas non-magnetic CVs and polars are much more numerous but have lower luminosities on average. As a consequence, the contribution of these populations to the observed hard X-ray luminosity is almost equivalent., Comment: 10 pages, 4 figures, 4 tables. Accepted for publication in MNRAS

(abridged version) We present a detailed spectroscopic and timing analysis of X-ray observations of the bright radio-to-gamma-ray emitting pulsar PSR B0656+14, which were obtained simultaneously with eROSITA and XMM-Newton during the Calibration and Performance Verification phase of the Spektrum-Roentgen-Gamma mission (SRG) for 100 ks. Using XMM-Newton and NICER we firstly established an X-ray ephemeris for the time interval 2015 to 2020, which connects all X-ray observations in this period without cycle count alias and phase shifts. The mean eROSITA spectrum clearly reveals an absorption feature originating from the star at 570 eV with a Gaussian sigma of about 70 eV, tentatively identified earlier in a long XMM-Newton observation (Arumugasamy et al. 2018). A second absorption feature, described here as an absorption edge, occurs at 260-265 eV. It could be of atmospheric or of instrumental origin. These absorption features are superposed on various emission components, phenomenologically described as the sum of hot (120 eV) and cold (65 eV) blackbody components, both of photospheric origin, and a power-law with photon index Gamma=2. The phase-resolved spectroscopy reveals that the Gaussian absorption line at 570 eV is clearly present throughout ~60% of the spin cycle. The visibility of the line strength coincides in phase with the maximum flux of the hot blackbody. We also present three families of model atmospheres: a magnetised atmosphere, a condensed surface, and a mixed model, which were applied to the mean observed spectrum and whose continuum fit the observed data well. The atmosphere model, however, predicts too short distances. For the mixed model, the Gaussian absorption may be interpreted as proton cyclotron absorption in a field as high as 10^14 G, which is significantly higher than that derived from the moderate observed spin-down., Comment: Submitted to A&A for the Special Issue: The Early Data Release of eROSITA and Mikhail Pavlinsky ART-XC on the SRG Mission. 21 pages, 13 figures, 13 tables

It has been recently discovered that the transition of X-ray pulsars to the low luminosity state ($L\lesssim10^{35}\,{\rm erg\,s^{-1}}$) is accompanied by a dramatic spectral change. Namely, the typical power-law-like spectrum with high energy cutoff transforms into a two-component structure with a possible cyclotron absorption feature on top of it. It was proposed that these spectral characteristics can be explained qualitatively by the emission of cyclotron photons in the atmosphere of the neutron star caused by collisional excitation of electrons to upper Landau levels and further comptonization of the photons by electron gas. The latter is expected to be overheated in a thin top layer of the atmosphere. In this paper, we perform Monte Carlo simulations of the radiative transfer in the atmosphere of an accreting neutron star while accounting for a resonant scattering of polarized X-ray photons by thermally distributed electrons. The spectral shape is shown to be strongly polarization-dependent in soft X-rays ($\lesssim 10\,{\rm keV}$) and near the cyclotron scattering feature. The results of our numerical simulations are tested against the observational data of X-ray pulsar A 0535+262 in the low luminosity state. We show that the spectral shape of the pulsar can be reproduced by the proposed theoretical model. The applications of the discovery to the observational studies of accreting neutron stars are discussed., Comment: 11 pages, 6 figures, accepted for publication in MNRAS

Neutron stars (NSs) in low-mass X-ray binaries rotate at frequencies high enough to significantly deviate from sphericity ($\nu_* \sim$ 200--600 Hz). We investigate the effects of rapid rotation on the observational appearance of a NS. We propose analytical formulae relating gravitational mass and equatorial radius of the rapidly rotating NS to the mass $M$ and radius $R$ of a non-rotating NS of the same baryonic mass using accurate fully relativistic computations. We compute spectra from an oblate rotating NS observed at different inclination angles using the modified oblate Schwarzschild (MOS) approximation, where light bending is computed in Schwarzschild metric, but frame dragging and quadrupole moment of a NS are approximately accounted for in the photon redshift calculations. We generalize the cooling tail method to the case of a rapidly rotating NS to obtain the most probable values of $M$ and $R$ of the corresponding non-rotating NS with the same baryonic mass. We approximate the local spectra from the NS surface by a diluted blackbody using previously computed NS atmosphere models. We show that the NS radius could be overestimated by 3--3.5 km for face-on stars of $R\approx 11$ km rotating at $\nu_* =$ 700 Hz if the version of the cooling tail method for a non-rotating NS is used. We apply the method to an X-ray burst observed from the NS rotating at $\nu_* \approx$ 532 Hz in SAX J1810.8$-$2609. The resulting radius of the non-rotating NS (assuming $M=1.5 M_\odot$) becomes $11.8\pm0.5$ km if it is viewed at inclination i=60 deg and $R=11.2\pm0.5$ km for a face-on view, which are smaller by 0.6 and 1.2 km than the radius obtained using standard cooling tail method ignoring rotation. The corresponding equatorial radii of these rapidly rotating NSs are 12.3$\pm 0.6$ km (for i=60 deg) and 11.6$\pm 0.6$\,km (for i=0 deg)., Comment: 17 pages, 16 figures, accepted for publication in Astronomy and Astrophysics

Black hole X-ray binaries show signs of non-thermal emission in the optical/near-infrared range. We analyze the optical/near-infrared SMARTS data on GX339$-$4 over the 2002--2011 period. Using the soft state data, we estimate the interstellar extinction towards the source and characteristic color temperatures of the accretion disk. We show that various spectral states of regular outbursts occupy similar regions on the color-magnitude diagrams, and that transitions between the states proceed along the same tracks despite substantial differences in the observed light curves morphology. We determine the typical duration of the hard-to-soft and soft-to-hard state transitions and the hard state at the decaying stage of the outburst to be one, two and four weeks, respectively. We find that the failed outbursts cannot be easily distinguished from the regular ones at their early stages, but if the source reaches 16 mag in $V$-band, it will transit to the soft state. By subtracting the contribution of the accretion disk, we obtain the spectra of the non-thermal component, which have constant, nearly flat shape during the transitions between the hard and soft states. In contrast to the slowly evolving non-thermal component seen at optical and near-infrared wavelengths, the mid-infrared spectrum is strongly variable on short timescales and sometimes shows a prominent excess with a cutoff below $10^{14}$ Hz. We show that the radio to optical spectrum can be modeled using three components corresponding to the jet, hot flow and irradiated accretion disk., Comment: Accepted for publication in Astronomy & Astrophysics, 19 pages, 6 tables, 18 figures

We computed accurate atmosphere models of rotation-powered millisecond pulsars in which the polar caps of a neutron star (NS) are externally heated by magnetospheric return currents. The external ram pressure, energy losses, and stopping depth of the penetrating charged particles were computed self-consistently with the atmosphere model, instead of assuming a simplified deep-heated atmosphere in radiative equilibrium. We used exact Compton scattering formalism to model the properties of the emergent X-ray radiation. The deep-heating approximation was found to be valid only if most of the heat originates from ultra-relativistic bombarding particles with Lorentz factors of $\gamma \gtrsim 100$. In the opposite regime, the atmosphere attains a distinct two-layer structure with an overheated optically thin skin on top of an optically thick cool plasma. The overheated skin strongly modifies the emergent radiation: it produces a Compton-upscattered high-energy tail in the spectrum and alters the radiation beaming pattern from limb darkening to limb brightening for emitted hard X-rays. This kind of drastic change in the emission properties can have a significant impact on the inferred NS pulse profile parameters as performed, for example, by Neutron star Interior Composition ExploreR. Finally, the connection between the energy distribution of the return current particles and the atmosphere emission properties offers a new tool to probe the exact physics of pulsar magnetospheres., Comment: 13 pages, 10 figures, published in A&A

Deep NuSTAR observation of X-ray pulsar A 0535+262, performed at a very low luminosity of $\sim7\times10^{34}$ erg s$^{-1}$, revealed the presence of two spectral components. We argue that the high-energy component is associated with cyclotron emission from recombination of electrons collisionally excited to the upper Landau levels. The cyclotron line energy of $E_{\rm cyc}=47.7\pm0.8$ keV was measured at the luminosity of almost an order of magnitude lower than what was achieved before. The data firmly exclude a positive correlation of the cyclotron energy with the mass accretion rate in this source., Comment: 5 pages, 3 figures, accepted by MNRAS Letters

The X-ray pulsar GRO J1744-28 is a unique source which shows both pulsations and type-II X-ray bursts, allowing studies of the interaction of the accretion disk with the magnetosphere at huge mass accretion rates exceeding $10^{19}$ g s$^{-1}$ during its super-Eddington outbursts. The magnetic field strength in the source, $B\approx 5\times 10^{11}$ G, is known from the cyclotron absorption feature discovered in the energy spectrum around 4.5 keV. Here, we explore the flux variability of the source in context of interaction of its magnetosphere with the radiation-pressure dominated accretion disk. Particularly, we present the results of the analysis of noise power density spectra (PDS) using the observations of the source in 1996-1997 by RXTE. Accreting compact objects commonly exhibit a broken power-law shape of the PDS with a break corresponding to the Keplerian orbital frequency of matter at the innermost disk radius. The observed frequency of the break can thus be used to estimate the size of the magnetosphere. We found, however, that the observed PDS of GRO J1744-28 differs dramatically from the canonical shape. Furthermore, the observed break frequency appears to be significantly higher than what is expected based on the magnetic field estimated from the cyclotron line energy. We argue that these observational facts can be attributed to the existence of the radiation-pressure dominated region in the accretion disk at luminosities above $\sim$2$\times 10^{37}$ erg s$^{-1}$. We discuss a qualitative model for the PDS formation in such disks, and show that its predictions are consistent with our observational findings. The presence of the radiation-pressure dominated region can also explain the observed weak luminosity-dependence of the inner radius, and we argue that the small inner radius can be explained by a quadrupole component dominating the magnetic field of the neutron star., Comment: 10 pages, 9 figures, accepted by A&A

In this White Paper we present the potential of the enhanced X-ray Timing and Polarimetry (eXTP) mission for studies related to Observatory Science targets. These include flaring stars, supernova remnants, accreting white dwarfs, low and high mass X-ray binaries, radio quiet and radio loud active galactic nuclei, tidal disruption events, and gamma-ray bursts. eXTP will be excellently suited to study one common aspect of these objects: their often transient nature. Developed by an international Consortium led by the Institute of High Energy Physics of the Chinese Academy of Science, the eXTP mission is expected to be launched in the mid 2020s., Comment: Accepted for publication on Sci. China Phys. Mech. Astron. (2019)

The hardness of the X-ray spectra of intermediate polars (IPs) is determined mainly by the white dwarf (WD) compactness (mass-radius ratio, M/R) and, thus, hard X-ray spectra can be used to constrain the WD mass. An accurate mass estimate requires the finite size of the WD magnetosphere R_m to be taken into the account. We suggested to derive it either directly from the observed break frequency in power spectrum of X-ray or optical lightcurves of a polar, or assuming the corotation. Here we apply this method to all IPs observed by NuSTAR (10 objects) and Swift/BAT (35 objects). For the dwarf nova GK Per we also observe a change of the break frequency with flux, which allows to constrain the dependence of the magnetosphere radius on the mass-accretion rate. For our analysis we calculated an additional grid of two-parameter (M and R_m/R) model spectra assuming a fixed, tall height of the accretion column H_sh/R=0.25, which is appropriate to determine WD masses in low mass-accretion IPs like EX\,Hya. Using the Gaia Data Release 2 we obtain for the first time reliable estimates of the mass-accretion rate and the magnetic field strength at the WD surface for a large fraction of objects in our sample. We find that most IPs accrete at rate of ~10^{-9} M_Sun/yr, and have magnetic fields in the range 1--10 MG. The resulting WD mass average of our sample is 0.79 +/- 0.16 M_Sun, which is consistent with earlier estimates., Comment: 14 pages, 16 figures, 4 tables, submitted to MNRAS

Thermonuclear X-ray bursts on the surface of neutron stars (NSs) can enrich photosphere with metals, which may imprint the photoionization edges on the burst spectra. We report here the discovery of absorption edges in the spectra of the type I X-ray burst from the NS low-mass X-ray binary GRS 1747$-$312 in Terzan 6 during observations by the Rossi X-ray Timing Explorer. We find that the edge energy evolves from $9.45\pm0.51$ keV to $\sim6$ keV and then back to $9.44\pm0.40$ keV during the photospheric radius expansion phase and remains at $8.06\pm0.66$ keV in the cooling tail. The photoionization absorption edges of hydrogen-like Ni, Fe or Fe/Ni mixture and the bound-bound transitions of metals may be responsible for the observed spectral features. The ratio of the measured absorption edge energy in the cooling tail to the laboratory value of hydrogen-like Ni(Fe) edge energy allows us to estimate the gravitational redshift factor $1+z=1.34\pm0.11$($1+z=1.15\pm0.09$). The evolution of the spectral parameters during the cooling tail are well-described by the metal-rich atmosphere models. The combined constraints on the NS mass and radius from the direct cooling method and the tidal deformability strongly suggest very high atmospheric abundance of the iron group elements and limit the distance to the source to $11\pm1$ kpc., Comment: matches the published version

The classical limit on the accretion luminosity of a neutron star is given by the Eddington luminosity. The advanced models of accretion onto magnetized neutron stars account for the appearance of magnetically confined accretion columns and allow the accretion luminosity to be higher than the Eddington value by a factor of tens. However, the recent discovery of pulsations from ultraluminous X-ray source (ULX) in NGC 5907 demonstrates that the accretion luminosity can exceed the Eddington value up to by a factor of 500. We propose a model explaining observational properties of ULX-1 in NGC 5907 without any ad hoc assumptions. We show that the accretion column at extreme luminosity becomes advective. Enormous energy release within a small geometrical volume and advection result in very high temperatures at the bottom of accretion column, which demand to account for the energy losses due to neutrino emission which can be even more effective than the radiation energy losses. We show that the total luminosity at the mass accretion rates above $10^{21}\,{\rm g\,s^{-1}}$ is dominated by the neutrino emission similarly to the case of core-collapse supernovae. We argue that the accretion rate measurements based on detected photon luminosity in case of bright ULXs powered by neutron stars can be largely underestimated due to intense neutrino emission. The recently discovered pulsating ULX-1 in galaxy NGC 5907 with photon luminosity of $\sim 10^{41}\,{\rm erg\,s^{-1}}$ is expected to be even brighter in neutrinos and is thus the first known Neutrino Pulsar., Comment: 7 pages, 3 figures, 1 table, accepted for publication in MNRAS

The ultracompact low-mass X-ray binary 4U 1820-30 situated in the globular cluster NGC 6624 has an orbital period of only $\approx$11.4 min which likely implies a white dwarf companion. The observed X-ray bursts demonstrate a photospheric radius expansion phase and therefore are believed to reach the Eddington luminosity allowing us to estimate the mass and the radius of the neutron star (NS) in this binary. Here we re-analyse all Rossi X-ray Timing Explorer observations of the system and confirm that almost all the bursts took place during the hard persistent state of the system. This allows us to use the recently developed direct cooling tail method to estimate the NS mass and radius. However, because of the very short, about a second, duration of the cooling tail phases that can be described by the theoretical atmosphere models, the obtained constraints on the NS radius are not very strict. Assuming a pure helium NS atmosphere we found that the NS radius is in the range 10-12 km, if the NS mass is below 1.7 $M_\odot$, and in a wider range of 8-12 km for a higher 1.7-2.0 $M_\odot$ NS mass. The method also constrains the distance to the system to be 6.5$\pm$0.5 kpc, which is consistent with the distance to the cluster. For the solar composition atmosphere, the NS parameters are in strong contradiction with the generally accepted range of possible NS masses and radii., Comment: 9 pages, 9 figures, 2 tables, accepted for publication in MNRAS

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 $\gtrsim 10^{19}\,{\rm g\,s^{-1}}$ 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., Comment: 8 pages, 6 figures, accepted for publication in MNRAS

Determining neutron star (NS) radii and masses can help to understand the properties of matter at supra-nuclear densities. Thermal emission during thermonuclear X-ray bursts from NSs in low-mass X-ray binaries provides a unique opportunity to study NS parameters, because of the high fluxes, large luminosity variations and the related changes in the spectral properties. The standard cooling tail method uses hot NS atmosphere models to convert the observed spectral evolution during cooling stages of X-ray bursts to the Eddington flux F_Edd and the stellar angular size \Omega. These are then translated to the constraints on the NS mass M and radius R. Here we present the improved, direct cooling tail method that generalises the standard approach. First, we adjust the cooling tail method to account for the bolometric correction to the flux. Then, we fit the observed dependence of the blackbody normalization on flux with a theoretical model directly on the M-R plane by interpolating theoretical dependences to a given gravity, hence ensuring only weakly informative priors for M and R instead of F_Edd and \Omega. The direct cooling method is demonstrated using a photospheric radius expansion burst from SAX J1810.8--2609, which has happened when the system was in the hard state. Comparing to the standard cooling tail method, the confidence regions are shifted by 1 sigma towards larger radii, giving R=11.5-13.0 km at M=1.3-1.8 M_sun for this NS., Comment: 8 pages, 5 figures. Accepted for publications in MNRAS

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 anticorrelation of line energy with flux, which we interpret as a transition from super- to sub-critical accretion associated with the disappearance of the accretion column. Finally, we confirm and briefly discuss the orbital modulation observed in the outburst light curve of the source., Comment: added journal reference&doi for proper indexing

Cyclotron resonance scattering features observed in the spectra of some X-ray pulsars show significant changes of the line centroid energy with the pulsar luminosity. Whereas for bright sources above the so called critical luminosity these variations are established to be connected with the appearance of the high accretion column above the neutron star surface, at low, sub-critical luminosities the nature of the variations (but with the opposite sign) has not been discussed widely. We argue here that the cyclotron line is formed when the radiation from a hotspot propagates through the plasma falling with a mildly relativistic velocity onto the neutron star surface. The position of the cyclotron resonance is determined by the Doppler effect. The change of the cyclotron line position in the spectrum with luminosity is caused by variations of the velocity profile in the line-forming region affected by the radiation pressure force. The presented model has several characteristic features: (i) the line centroid energy is positively correlated with the luminosity; (ii) the line width is positively correlated with the luminosity as well; (iii) the position and the width of the cyclotron absorption line are variable over the pulse phase; (iv) the line has a more complicated shape than widely used Lorentzian or Gaussian profiles; (v) the phase-resolved cyclotron line centroid energy and the width are negatively and positively correlated with the pulse intensity, respectively. The predictions of the proposed theory are compared with the variations of the cyclotron line parameters in the X-ray pulsar GX 304-1 over a wide range of sub-critical luminosities as seen by the INTEGRAL observatory., Comment: 9 pages, 10 figures, 1 table, accepted for publication in MNRAS

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 ultra-luminous 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 implies the dipole component of the neutron star magnetic field of ~$10^{14}$ G., Comment: 6 pages, 3 figures, 1 table, accepted by MNRAS

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 $10^{40}\,{\rm erg/s}$ for the magnetar-like magnetic field ($B\gtrsim 10^{14}\,{\rm G}$) and long spin periods ($P\gtrsim 1.5\,{\rm s}$). The relative narrowness of an area of feasible NS parameters which are able to provide higher luminosities leads to the conclusion that $L\simeq 10^{40}\,\,{\rm erg/s}$ 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 X-ray 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., Comment: 11 pages, 8 figures, accepted for publication in MNRAS

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., Comment: 11 pages, 16 figures, accepted for publication in MNRAS

Neutron star (NS) masses and radii can be estimated from observations of photospheric radius-expansion X-ray bursts, provided the chemical composition of the photosphere, the spectral colour-correction factors in the observed luminosity range, and the emission area during the bursts are known. By analysing 246 X-ray bursts observed by the Rossi X-ray Timing Explorer from 11 low-mass X-ray binaries, we find a dependence between the persistent spectral properties and the time evolution of the black body normalisation during the bursts. All NS atmosphere models predict that the colour-correction factor decreases in the early cooling phase when the luminosity first drops below the limiting Eddington value, leading to a characteristic pattern of variability in the measured blackbody normalisation. However, the model predictions agree with the observations for most bursts occurring in hard, low-luminosity, 'island' spectral states, but rarely during soft, high-luminosity, 'banana' states. The observed behaviour may be attributed to the accretion flow, which influences cooling of the NS preferentially during the soft state bursts. This result implies that only the bursts occurring in the hard, low-luminosity spectral states can be reliably used for NS mass and radius determination., Comment: 18 pages, 4 figures, accepted to MNRAS

Cyclotron resonance scattering features are observed in the spectra of some X-ray pulsars and show significant changes in the line energy with the pulsar luminosity. In a case of bright sources, the line centroid energy is anti-correlated with the luminosity. Such a behaviour is often associated with the onset and growth of the accretion column, which is believed to be the origin of the observed emission and the cyclotron lines. However, this scenario inevitably implies large gradient of the magnetic field strength within the line-forming region, and it 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 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. The idea is based on the facts that a substantial part of column luminosity is intercepted by the neutron star surface and the reflected radiation should contain absorption features. The reflection model is developed and applied 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., Comment: 6 pages, 3 figures, proceedings of the conference "Physics at the Magnetospheric Boundary", Geneva, June 2013

Emission of the neutron star surface potentially contains information about its size and thus of vital importance for high energy astrophysics. In spite of the wealth of data on the emission of luminous accreting neutron stars, the emission of their surfaces is hard to disentangle from their time averaged spectra. A recent X-ray transient source XTE J1701-462 has provided a unique dataset covering the largest ever observed luminosity range for a single source. In this paper, we extract the spectrum of the boundary layer between the inner part of the accretion disc and the neutron star surface with the help of maximally spectral model-independent method. We show compelling evidences that the energy spectrum of the boundary layer stays virtually the same over factor of 20 variations of the source luminosity. It is rather wide and cannot be described by a single temperature blackbody spectrum, probably because of the inhomogeneity of the boundary layer and a spread in the colour temperature. The observed maximum colour temperature of the boundary/spreading layer emission of kT~2.4-2.6 keV is very close to the maximum observed colour temperature in the photospheric radius expansion X-ray bursts, which is set by the limiting Eddington flux at the neutron star surface. Observed stability of the boundary layer spectrum and its maximum colour temperature strongly supports theoretical models of the boundary/spreading layers on surfaces of luminous accreting neutron stars, which assume the presence of a region emitting at the local Eddington limit. Variations in the luminosity in that case lead to changes in the size of this region, but affect less the spectral shape. Elaboration of this model will provide solid theoretical grounds for measurements of the neutron star sizes using the emission of the boundary/spreading layers of luminous accreting neutron stars., Comment: 7 pages, 7 figures, accepted for publication in MNRAS

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 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. We develop here the 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., Comment: 9 pages, 6 figures; version accepted to the Astrophysical Journal

We have investigated the influence of X-ray irradiation on the vertical structure of the outer accretion disk in low-mass X-ray binaries by performing a self-consistent calculation of the vertical structure and X-ray radiation transfer in the disk. Penetrating deep into the disk, the field of scattered X-ray photons with energy $E\gtrsim10$\,keV exerts a significant influence on the vertical structure of the accretion disk at a distance $R\gtrsim10^{10}$\,cm from the neutron star. At a distance $R\sim10^{11}$\,cm, where the total surface density in the disk reaches $\Sigma_0\sim20$\,g\,cm$^{-2}$, X-ray heating affects all layers of an optically thick disk. The X-ray heating effect is enhanced significantly in the presence of an extended atmospheric layer with a temperature $T_{atm}\sim(2\div3)\times10^6$\,K above the accretion disk. We have derived simple analytic formulas for the disk heating by scattered X-ray photons using an approximate solution of the transfer equation by the Sobolev method. This approximation has a $\gtrsim10$\,% accuracy in the range of X-ray photon energies $E<20$\,keV., Comment: 19 pages, 8 figures, published in Astronomy Letters