arXiv subjects

Alexander A. Mushtukov

Publications and source records attributed to Alexander A. Mushtukov.

At least 37 records · Page 2Linked to original sources

arXiv2024

Flickering pulsations in bright X-ray pulsars: the evidence of gravitationally lensed and eclipsed accretion column

It is expected that extreme mass accretion rate onto strongly magnetised neutron star results in appearance of accretion columns above stellar surface. For a distant observer, rotation of a star results in periodic variations of X-ray flux. Because the mass accretion rate fluctuates around the average value, the pulse profiles are not stable and demonstrate fluctuations as well. In the case of bright X-ray pulsars, however, pulse fluctuations are not solely attributed to variations in the mass accretion rate. They are also influenced by the variable height of the columns, which is dependent on the mass accretion rate. This study delves into the process of pulse profile formation in bright X-ray pulsars, taking into account stochastic fluctuations in the mass accretion rate, the corresponding variations in accretion column geometry and gravitational bending. Our analysis reveals that potential eclipses of accretion columns by a neutron star during their spin period should manifest specific features in pulse profile variability. Applying a novel pulse profile analysis technique, we successfully detect these features in the bright X-ray transient V0332+53 at luminosities $\gtrsim 2\times 10^{38}\,{\rm erg\,s^{-1}}$. This detection serves as compelling evidence for the eclipse of an accretion column by a neutron star. Detection of the eclipse places constraints on the relation between neutron star mass, radius and accretion column height. Specifically, we can establish an upper limit on the accretion column height, which is crucial for refining theoretical models of extreme accretion.

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arXiv2024

Coupling of radiation and magnetospheric accretion flow in ULX pulsars: radiation pressure and photon escape time

The accretion flow within the magnetospheric radius of bright X-ray pulsars can form an optically thick envelope, concealing the central neutron star from the distant observer. Most photons are emitted at the surface of a neutron star and leave the system after multiple reflections by the accretion material covering the magnetosphere. Reflections cause momentum to be transferred between photons and the accretion flow, which contributes to the radiative force and should thus influence the dynamics of accretion. We employ Monte Carlo simulations and estimate the acceleration along magnetic field lines due to the radiative force as well as the radiation pressure across magnetic field lines. We demonstrate that the radiative acceleration can exceed gravitational acceleration along the field lines, and similarly, radiation pressure can exceed magnetic field pressure. Multiple reflections of X-ray photons back into the envelope tend to amplify both radiative force along the field lines and radiative pressure. We analyze the average photon escape time from the magnetosphere of a star and show that its absolute value is weakly dependent on the magnetic field strength of a star and roughly linearly dependent on the mass accretion rate being $\sim 0.1\,{\rm s}$ at $\dot{M}\sim 10^{20}\,{\rm g\,s^{-1}}$. At high mass accretion rates, the escape time can be longer than free-fall time from the inner disc radius.

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arXiv2023

Apparent luminosity and pulsed fraction affected by gravitational lensing of accretion columns in bright X-ray pulsars

The luminosity of X-ray pulsars is their key parameter determining the geometry and physical conditions of the accretion flow both on the spatial scales of a binary system and on much smaller scales of emitting regions located close to the stellar surface. Traditionally, the luminosity of X-ray pulsars is estimated out of the X-ray energy flux averaged over the pulsed period and the estimated distance to the source. Due to the anisotropy of X-ray emission, the luminosity estimated on the base of the observed pulse profile can differ from the actual one. Super-critical X-ray pulsars with accretion columns are of particular interest because the X-ray flux from columns is a matter of strong gravitational lensing by a neutron star. Using toy model of an accretion column, we simulate beam patterns in super-critical X-ray pulsars, construct theoretical pulse profiles for different geometries and mutual orientations of pulsars and distant observers and show that despite strong light bending, the typical deviation of the apparent luminosity from the actual one is $\sim 20\%$ only, and in $\sim 90\%$ of cases, the apparent luminosity $0.8 L\lesssim L_{\rm app}\lesssim 1.25 L$. However, the shape of the pulse profiles is strongly affected by the geometry of the emitting region. We show that the appearance and growth of accretion columns tend to be accompanied by an increase of observed pulsed fraction, which is in agreement with the recent observations of bright X-ray transients.

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arXiv2023

X-ray polarimetry of the accreting pulsar GX 301-2

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.

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arXiv2023

Complex variations of X-ray polarization in the X-ray pulsar LS V +44 17/RX J0440.9+4431

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.

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arXiv2023

X-ray pulsar GRO J1008$-$57 as an orthogonal rotator

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.

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arXiv2023

RX J0440.9+4431: another supercritical X-ray pulsar

In the beginning of 2023 the Be transient X-ray pulsar RX J0440.9+4431 underwent a fist-ever giant outburst observed from the source peaking in the beginning of February and reaching peak luminosity of $\sim 4.3\times10^{37}$ erg s$^{-1}$. Here we present the results of a detailed spectral and temporal study of the source based on NuSTAR, INTEGRAL, Swift, and NICER observations performed during this period and covering wide range of energies and luminosities. We find that both the pulse profile shape and spectral hardness change abruptly around $\sim2.8\times10^{37}$ erg s$^{-1}$, which we associate with a transition to super-critical accretion regime and erection of the accretion column. The observed pulsed fraction decreases gradually with energy up to 20 keV (with a local minimum around fluorescence iron line), which is unusual for an X-ray pulsar, and then rises rapidly at higher energies with the pulsations significantly detected up to $\sim120$ keV. The broadband energy spectra of RX J0440.9+4431 at different luminosity states can be approximated with a two-hump model with peaks at energies of about 10-20 and 50-70 keV previously suggested for other pulsars without additional features. In particular an absorption feature around 30 keV previously reported and interpreted as a cyclotron line in the literature appears to be absent when using this model, so the question regarding the magnetic field strength of the neutron star remains open. Instead, we attempted to estimate field using several indirect methods and conclude that all of them point to a relatively strong field of around $B\sim 10^{13}$ G.

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arXiv2023

Bright X-ray pulsars as sources of MeV neutrinos in the sky

High mass accretion rate onto strongly magnetised neutron stars results in the appearance of accretion columns supported by the radiation pressure and confined by the strong magnetic field of a star. At mass accretion rates above $\sim 10^{19}\,{\rm g\,s^{-1}}$, accretion columns are expected to be advective. Under such conditions, a noticeable part of the total energy release can be carried away by neutrinos of a MeV energy range. Relying on a simple model of the neutrino luminosity of accreting strongly magnetised neutron stars, we estimate the neutrino energy fluxes expected from six ULX pulsars known up to date and three brightest Be X-ray transits hosting magnetised neutron stars. Despite the large neutrino luminosity expected in ULX pulsars, the neutrino energy flux from the Be X-ray transients of our Galaxy, SMC and LMC is dominant. However, the neutrino flux from the brightest X-ray transients is estimated to be below the isotropic background by two orders of magnitude at least, which makes impossible direct registration of neutrino emission from accreting strongly magnetised neutron stars nowadays.

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arXiv2023

IXPE observations of the quintessential wind-accreting X-ray pulsar Vela X-1

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.

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arXiv2023

Determination of X-ray pulsar geometry with IXPE polarimetry

Using observations of X-ray pulsar Her X-1 by the Imaging X-ray Polarimetry Explorer, we report on a highly significant ($>17σ$) 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.

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arXiv2022

Bright X-ray Pulsars: how outflows influence beaming, pulsations and pulse phase lags

Extreme accretion in X-ray pulsars (XRPs) results in radiation-driven outflows launched from the inner parts of the accretion disc. The outflows affect the apparent luminosity of the XRPs and their pulsations through the geometrical beaming. We model processes of geometrical beaming and pulse formation using Monte Carlo simulations. We confirm our earlier statement that strong amplification of luminosity due to the collimation of X-ray photons is inconsistent with a large pulsed fraction. Accounting for relativistic aberration due to possibly high outflow velocity ($\sim 0.2c$) does not affect this conclusion. We demonstrate that the beaming causes phase lags of pulsations. Within the opening angle of the accretion cavity formed by the outflows, phase lags tend to be sensitive to observers viewing angles. Variations in outflow geometry and corresponding changes of the phase lags might influence the detectability of pulsation in bright X-ray pulsars and ULXs. We speculate that the strong geometrical beaming is associated with large radiation pressure on the walls of accretion cavity due to multiple photons reflections. We expect that the mass loss rate limits geometrical beaming: strong beaming becomes possible only under sufficiently large fractional mass loss rate from the disc.

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arXiv2022

Mean opacities of a strongly magnetized high temperature plasma

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.

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arXiv2022

The X-ray polarimetry view of the accreting pulsar Cen X-3

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$σ$ upper limit of 12%) or phase-resolved data (the 3$σ$ upper limits are 20-30%). In the bright state the polarization degree of 5.8$\pm$0.3% and polarization angle of $49.6°\pm1.5°$ with significance of about 20$σ$ 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$°$ and a magnetic obliquity of 17$°$. 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.

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arXiv2022

Constraints on the magnetic field structure in accreting compact objects from aperiodic variability

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.

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arXiv2022

First characterization of a new High Mass X-ray Binary in LMC eRASSU J050810.4$-$660653 with SRG/ART-XC, NuSTAR and Swift

We report results of the first detailed spectral and temporal studies of the recently discovered Be/X-ray binary eRASSU J050810.4$-$660653 in LMC based on the data from the SRG/ART-XC, NuSTAR and Swift/XRT instruments obtained in December 2021 - May 2022 in a wide energy range of 0.5-79 keV. Pulsations with the period of $40.5781 \pm 0.0004$ s were found in the source light curve with the pulsed fraction monotonically increasing with the energy. An estimate of the orbital period of $\sim38$ days was obtained based on the long-term monitoring of the system. The source spectrum can be well approximated with a power-law model modified by an exponential cutoff at high energies. The pulse phase-resolved spectroscopy shows a strong variation of spectral parameters depending on the phase of a neutron star rotation. We have not found any features connected with the cyclotron absorption line both in the phase-averaged and phase-resolved spectra of eRASSU J050810.4$-$660653. However, the neutron star magnetic field was estimated around several $10^{13}$ G using different indirect methods. Discovered variations of the hardness ratio over the pulse phase is discussed in terms of physical and geometrical properties of the emitting region.

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arXiv2022

Statistical features of multiple Compton scattering in a strong magnetic field

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.

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arXiv2021

SRG/ART-XC, Swift, NICER and NuSTAR study of different states of the transient X-ray pulsar MAXI J0903-531

The results of the broadband spectral and timing study of the recently discovered transient X-ray pulsar MAXI J0903-531 in a wide range of luminosities differing by a factor of ~30 are reported. The observed X-ray spectrum in both states can be described as a classical pulsar-like spectrum consisting of the power-law with the high-energy cutoff. We argue that absence of the spectrum transformation to the two-hump structure expected at low fluxes points to a relatively weak magnetic field of the neutron star below (2-3)$\times10^{12}$ G. This estimate is consistent with other indirect constraints and non-detection of any absorption features which can be interpreted as a cyclotron absorption line. Timing analysis of the NuSTAR data revealed only slight variations of a single-peaked pulse profile of the source as a function of the energy band and mass accretion rate. In both intensity states the pulsed fraction increases from 40% to roughly 80% with the energy. Finally we were also able to obtain the orbital solution for the binary system using data from the Fermi/GBM, NICER and NuSTAR instruments.

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arXiv2021

Spectrum formation in X-ray pulsars at very low mass accretion rate: Monte-Carlo approach

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.

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