Searcharxiv⌕ Search

arXiv subjects

Alexander A. Mushtukov

Publications and source records attributed to Alexander A. Mushtukov.

At least 19 recordsLinked to original sources

Magnetospheric birefringence breaks the rotating-vector model and depolarises X-ray pulsars

Accreting X-ray pulsars have long been expected to show large linear polarisation below the cyclotron resonance. In the standard picture, this follows from two facts: radiative opacities in the strongly magnetised neutron star environment depend strongly on polarisation mode, and the emission comes from compact polar regions. The emerging radiation should therefore be locally polarised and add almost coherently, with a polarisation angle tracing the projected magnetic field as in the rotating-vector model. Recent X-ray polarimetric observations, instead, show modest polarisation fractions and position angle swings that often depart from this simple picture. Here we show that propagation through the magnetosphere of an accreting neutron star can naturally produce both effects. Using general-relativistic ray tracing and Stokes-parameter transport, we find that photons emitted from compact polar regions acquire ray-dependent polarisation angle offsets in two ways. First, nearly field-aligned trajectories can cross local non-adiabatic pockets inside the QED birefringent region. Second, photons that intersect the plasma-loaded accretion flow accumulate additional phase shifts between plasma normal modes. Both effects broaden the distribution of polarisation angles across the ray bundle and reduce the hotspot-integrated linear polarisation, while also producing systematic deviations from rotating-vector-model expectations. Magnetospheric propagation should therefore be treated as part of the polarimetric transfer problem in accreting X-ray pulsars, and may help explain the observed low polarisation fractions and anomalous angle swings.

astro-ph.HE↗

Real-time observations of the transition to the quiescent state in an accreting magnetised neutron star: No propeller required?

The final stages of outbursts in transient X-ray pulsars (XRPs), which are characterised by a significant decline in the mass accretion rate, provide valuable insight into the physics of the accretion disc and its interaction with the strong magnetic field of the neutron star (NS). In particular, the `propeller effect', or centrifugal inhibition of accretion, has been proposed as a key mechanism governing both the onset luminosity and the timescale of the rapid transition to the quiescent state. In addition, it offers an independent method for estimating the magnetic field strength of the NS. On the other hand, the decrease in the mass accretion rate itself is driven by processes occurring in the accretion flow at larger distances from the NS. Recovering the information encoded in the light curve therefore requires sensitive high-cadence X-ray monitoring capable of capturing the rapid and often unpredictable transition from the accreting regime to the quiescent regime. In this study, we present the results of the first comprehensive monitoring campaign that tracks the entire transition to quiescence in the transient XRP 4U 0115+63 utilising observations by the NICER X-ray telescope. We show that the observed behaviour can be explained by the thermal-viscous disc instability model (DIM), with the emission observed immediately after an outburst possibly arising from the ongoing accretion from the recombined (`cold') disc and the subsequent quiescent emission being produced by the cooling NS. We further applied this model to a larger sample of XRPs encompassing a broad range of physical parameters. Ultimately, our findings indicate that the temporal behaviour of XRPs, including the quiescent state, can be consistently explained within the DIM framework without requiring the propeller effect as the primary mechanism governing the observed transition.

astro-ph.HE↗

Probing the emission geometry of the X-ray pulsar 2S 1417$-$624 during a weak outburst with NICER, IXPE, and NuSTAR

We report results from a multi-mission observational campaign of the transient X-ray pulsar 2S~1417$-$624 during its 2025 outburst, using data from NICER, IXPE, and NuSTAR. Phase-averaged and phase-resolved spectroscopy with NICER and NuSTAR reveal that a typical broken power-law model with a high-energy cut-off well describes the broadband spectra. Several spectral parameters, however, show clear and systematic modulations with pulse phase, indicating variations in the physical conditions of the emitting plasma over the neutron star's rotation. IXPE provides the first polarimetric measurements of this source, yielding a phase-averaged polarization degree (PD) of $4.8 \pm 1.2$% and a polarization angle (PA) of ${17}^{\circ} \pm {7}^{\circ}$, both quoted at the $1σ$ confidence level. Fitting the phase-resolved PA with the rotating vector model (RVM) gives a magnetic obliquity of $θ= 69_{-29}^{+13}$ deg, indicating a significantly inclined magnetic geometry that may approach a quasi-orthogonal configuration. In addition, using the unbinned photon-by-photon method, we obtain a PD of $5.9 \pm 1.2$% across the pulse phase, together with a pulsar geometry consistent with that inferred from the binned analysis, assuming the variable PA predicted by the RVM. A simultaneous RVM fit across the three energy bands, 2--5 keV, 5--6 keV, and 6--8 keV, provides the strongest constraints on the geometrical parameters, yielding $θ= {84}_{-6}^{+4}$ deg. Together, these findings demonstrate pronounced phase-dependent spectral and polarization variability, offering valuable constraints on the geometry and emission processes within the accretion region of this transient X-ray pulsar.

astro-ph.HE↗

Magnetospheric flows in X-ray pulsars II: Heating, cooling and ionization degree at sub-critical accretion

Magnetospheric accretion flows in X-ray pulsars shape their spectra, polarization, and variability. We model the thermal balance of the flow enveloping the neutron star magnetosphere in the sub-critical regime ($L \lesssim 10^{37}\,\mathrm{erg\,s^{-1}}$), where radiation forces do not control the dynamics and single Compton scatterings dominate. The energy budget includes Compton heating by surface X-rays, compressional (adiabatic) heating in the converging flow, and radiative cooling dominated by free-free emission and contributed also by cyclotron emission. We show that the interplay of these processes leads to efficient cooling of the flow in the inner magnetosphere. We compute the flow temperature profile as a function of luminosity and find that near the stellar surface the temperature can fall to a few tens of eV at $L < 10^{35}\,\mathrm{erg\,s^{-1}}$. Under such conditions, the accreting plasma, modelled here as pure hydrogen, is no longer fully ionized. In the strong magnetic fields typical for X-ray pulsars, such temperatures permit partial recombination of electrons and protons into neutral hydrogen. As a result, a significant fraction of the flow becomes weakly ionized, while external illumination ionizes this gas only partially within a geometrically thin layer immediately above the neutron star surface. This implies that magnetospheric accretion at low luminosities proceeds through a partially ionized medium, in contrast to the commonly assumed fully ionized flow.

astro-ph.HE↗

Detection and luminosity-dependent evolution of the high-energy hump in the Be/X-ray pulsar 1A 1118-61

Context. Accreting X-ray pulsars exhibit strong luminosity-dependent changes in their broad-band spectra. At high luminosities, their spectra are usually described by a power-law continuum with a high-energy cutoff, whereas low-luminosity observations have revealed a two-hump spectral morphology. Aims. We aim to trace the luminosity-dependent spectral evolution of the Be/X-ray pulsar 1A 1118-61 and to constrain the luminosity range over which the high-energy hump becomes clearly distinguishable. Methods. We use dense SRG/ART-XC and Insight-HXMT monitoring, together with three broad-band NuSTAR observations of 1A 1118-61 obtained during its 2026 outburst, to trace the luminosity-dependent evolution of the spectral shape. The ART-XC data follow the decay from a peak luminosity of $\simeq7\times10^{37}$ erg s$^{-1}$ to a low-luminosity plateau at $\simeq(3$-$8)\times10^{35}$ erg s$^{-1}$ in the 4-35 keV band, while the NuSTAR observations provide broad-band spectra during the bright phase, the decline, and the plateau. We describe the continuum with a phenomenological two-component Comptonization model. Results. As the source faded, the broad-band continuum developed a distinct high-energy hump, giving rise to a two-hump morphology with broad maxima near $\sim$10 keV and $\sim$30-40 keV. The ART-XC monitoring constrains the transition to this morphology to $L_{4-35}\simeq(0.8$-$1.8)\times10^{36}$ erg s$^{-1}$. We also find a break in the luminosity dependence of the flux ratio between the two continuum humps around $L_{4-35}\sim10^{37}$ erg s$^{-1}$. A cyclotron line at $\simeq55$ keV is detected in the high-energy hump, with no significant luminosity dependence of its centroid energy. We discuss this behavior in the context of resonant interactions in the magnetized accretion flow.

astro-ph.HE↗

Rapid quasi-periodic reconfiguration of the accretion column in pulsar 1A 0535+262

Accretion onto strongly magnetized neutron stars is commonly interpreted using quasi-steady models, in which the accretion-column structure adjusts smoothly to the mass inflow rate. The cyclotron line in the X-ray spectrum, whose centroid energy traces the magnetic field strength and thus the height of the line-forming region, provides a key diagnostic of this structure. Whether this simple quasi-steady description remains valid on short dynamical timescales has remained uncertain. Here we show that, during a giant outburst of the X-ray pulsar 1A~0535+262, quasi-periodic hard X-ray flux variations are accompanied by synchronized oscillations of the cyclotron line energy, with amplitudes exceeding those expected from simple accretion-rate fluctuations. The anti-correlation between cyclotron energy and apparent flux provides direct spectral-timing evidence for rapid changes in the line-forming region, which we interpret as geometric reconfiguration of the accretion column. The variability emerges in the luminosity regime where radiation pressure becomes dynamically important. These results reveal limitations of a simple quasi-steady interpretation for this source and suggest that radiation-supported columns can enter intrinsically dynamical states in high-luminosity accreting pulsars.

astro-ph.HE↗

Discovery of a 0.8-mHz quasi-periodic oscillation in the transient X-ray pulsar SXP31.0 and associated timing transitions

We present the first broadband spectral and timing study of the Be/X-ray pulsar XTE J0111.2$-$7317 (SXP31.0) during the first major outburst since its discovery in 1998. This giant type II outburst, observed between April and September 2025, marks the source's return to activity after nearly three decades of quiescence. Using NuSTAR observations together with data from Swift/XRT and SRG/ART-XC, we followed the outburst's evolution, with the source reaching a bolometric luminosity of $L_{\rm bol} = 3.6 \times 10^{38}$ erg s$^{-1}$. The broadband spectra are well described by an absorbed cutoff power law, two blackbody components (hot and soft), and a narrow Fe K$α$ line. No cyclotron absorption features were detected in either the phase-averaged or phase-resolved spectra in the 5-50 keV band. Most notably, we report the discovery of a previously undetected quasiperiodic oscillation (QPO) at $0.8 \pm 0.1$ mHz, characterized by a fractional root-mean-square (rms) amplitude of 14% at a super-Eddington bolometric luminosity of $L_{\rm bol} = 2.5 \times 10^{38}$ erg s$^{-1}$. In contrast, the previously reported 1.27 Hz QPO was not detected. While the 0.8 mHz QPO is present, the pulsed fraction (PF) is low in soft X-rays, which is consistent with other super-Eddington pulsars exhibiting mHz QPOs; however, it rises above 20 keV to reach 35%. The QPO vanishes in subsequent observations coinciding with a sharp increase in the PF and a distinct change in pulse profile morphology. It was not observed in any follow-up observations at luminosities above or below its initial detection, suggesting it is a transient phenomenon.

astro-ph.HE↗

Discovery of energy-dependent phase variations in the polarization angle of Cen X-3

We present a detailed polarimetric analysis of Cen X-3 using \ixpe observations during its high state, revealing complex energy-dependent polarization behavior. While phase-averaged polarization shows marginal energy dependence, phase-resolved analysis reveals that the energy dependence of the polarization angle (PA) is strongly phase-dependent, with dramatic variations visible in a few specific phase intervals. We model this behavior using a two-component polarization framework consisting of a pulsed component governed by the Rotating Vector Model (RVM) and an additional phase-dependent component. By allowing the additional component's polarized flux to vary with pulse phase while fixing its PA, the observed complex behavior can be reconciled with a single set of RVM parameters across all energies. Spectroscopic analysis using \ixpe, \nicer and \nustar during the high state reveals phase-modulated intrinsic hydrogen column density and covering fraction, suggesting that the wind properties are modulated with pulse phase. Our findings indicate that phase-dependent scattering in the disk wind may significantly alter the observed polarization properties of X-ray pulsars.

astro-ph.HE↗

Propeller effect in action: Unveiling quenched accretion in the transient X-ray pulsar 4U 0115+63

The Be/X-ray pulsar 4U 0115+63 underwent a type II outburst in 2023. After the outburst, similar to the outbursts in 2015 and 2017, the source decayed into a quiescent state. Two out of three XMM-Newton observations conducted after the 2023 outburst confirmed the source to be in a low-luminosity state at a level of $L_{\rm X} \sim 10^{33}\,\rm erg\,s^{-1}$. X-ray pulsations were detected at $\approx$0.277 Hz in both observations with a pulsed fraction exceeding 50%. The power density spectra show no significant low-frequency red noise in both observations, suggesting that the radiation is not driven by accretion. The energy spectra in this state can be described by a single blackbody component, with an emitting area smaller than the typical size of the polar caps during the accretion phase. Based on the timing and spectral properties, we suggest that the propeller effect is active during the quiescent state, resulting in a total quenching of accretion. We discuss possible mechanisms for the generation of pulsations in this regime and consider the scenario of neutron star crust cooling.

astro-ph.HE↗

Angle-dependent hardening of the reprocessed spectra in ULXs powered by accretion onto neutron stars

It is anticipated that mass accretion rates exceeding approximately $10^{19}\,{\rm g\,s^{-1}}$ in X-ray pulsars lead to radiation-driven outflows from super-critical accretion discs. The outflows launched from the disc influence the angular distribution of X-ray radiation, resulting in geometrical beaming. The beaming, in turn, impacts the apparent luminosity of the X-ray pulsar, detectability of pulsations, and the spectral composition of the X-ray flux. We employ a straightforward geometrical model of the outflows, perform Monte Carlo simulations, and model the spectra of radiation, reprocessed by the walls of the accretion cavity formed by the outflows. We consider the reprocessed emission only; direct pulsar emission is not included in our modelling. Our results demonstrate that the spectra of reprocessed radiation depend on the actual luminosity of the central engine, the geometry of the outflows, and the viewing angle - most notably on the latter, through changing visibility of the hotter wall regions near the disc plane. The high-energy part of the reprocessed spectrum depends strongly on viewing angle (harder at lower inclinations), while the soft flux varies comparatively little with inclination. In our model, this contrast is a prediction: variable ultra-luminous X-ray sources are expected to exhibit strong high-energy angle sensitivity together with comparatively modest soft-band variation, naturally arising if precession modulates the effective inclination.

astro-ph.HE↗

Gamma-ray lines, electron-positron annihilation, and possible radio emission in X-ray pulsars

Accretion onto neutron stars (NSs) in X-ray pulsars (XRPs) results in intense X-ray emission, and under specific conditions, high-energy nuclear interactions that produce gamma-ray photons at discrete energies. These interactions are enabled by the high free-fall velocities of accreting nuclei near the NS surface and give rise to characteristic gamma-ray lines, notably at 2.2 MeV, 5.5 MeV, and 67.5 MeV. We investigate the production mechanisms of these lines and estimate the resulting gamma-ray luminosities, accounting for the suppression effects of radiative deceleration in bright XRPs and the creation of electron-positron pairs in strong magnetic fields. The resulting annihilation of these pairs leads to a secondary emission line at $\sim 511$ keV. We also discuss the possibility that non-stationary pair creation in the polar cap region could drive coherent radio emission, though its detectability in accreting systems remains uncertain. Using a numerical framework incorporating general relativistic light bending and magnetic absorption, we compute the escape fraction of photons and distinguish between actual and apparent gamma-ray luminosities. Our results identify the parameter space - defined by magnetic field strength, accretion luminosity, and NS compactness - where these gamma-ray signatures may be observable by upcoming MeV gamma-ray missions. In particular, we highlight the diagnostic potential of detecting gravitationally redshifted gamma-ray lines and annihilation features for probing the mass-radius relation and magnetospheric structure of NSs.

astro-ph.HE↗

Probing the polarized emission from the accretion-powered pulsar 4U 1907+09 with IXPE

We present observations of the accretion-powered X-ray pulsar (XRP) 4U 1907+09, conducted with the Imaging X-ray Polarimetry Explorer (IXPE) that delivers the first high-quality polarization measurements of this source. 4U 1907+09 was observed twice during its brightest periods close to the periastron. We observe a stronger polarization in the first observation, with the phase-averaged polarization degree (PD) of $6.0 \pm 1.6\%$ and polarization angle (PA) of $69^\circ \pm 8^\circ$. In contrast, the second observation provides weaker constraints on the polarimetric properties, with a PD=$2.2 \pm 1.6\%$ and a PA=$46^\circ \pm 23^\circ$, as determined from the spectral-polarimetric analysis. Combining the data from both observations results in a PD=$3.7 \pm 1.1\%$ and a PA=$63^\circ \pm 9^\circ$. We detect an energy-dependent PA in the phase-averaged analyses with a significance of 1.7 $σ$. In the phase-resolved analyses, we observe a potential PA rotation by approximately $90^\circ$ between adjacent energy bands (4--5 and 5--6 keV) within the single phase bin of 0.25--0.375. We also investigate the influence of short flares on the polarization properties of this source. The results suggest that flares do not significantly affect the energy-phase-dependent PA, implying that the pulsar's geometry remains stable during flare events.

astro-ph.HE↗

Exploring polarization and geometry in the X-ray pulsar 4U 1538-52

The Imaging X-ray Polarimetry Explorer (IXPE) observations of accreting X-ray pulsars (XRPs) continue to provide novel insights into the physics and geometry of these sources. We present the first X-ray polarimetric study of the persistent wind-fed XRP 4U 1538-52, based on five IXPE observations totaling 360 ks, conducted in March and October 2024. We detect marginally significant polarization in the combined data set in the full 2--8 keV energy band, with a polarization degree (PD) of 3.0+-1.1% and polarization angle (PA) of -18 degrees. The energy-resolved analysis shows a clear energy dependence of the polarization properties, with a remarkable ~70 degrees switch in PA between low and high energies. Similarly, the pulse phase-resolved spectro-polarimetric analysis reveals different signatures at low and high energies. At low (2--3 keV) energies, the PD ranges between ~2% and ~18%, with the PA varying between -16 and 70 degrees. At higher (4--8 keV) energies, the PD varies between ~3% and ~12%, with a drastically different PA behavior. Fitting the rotating vector model to the pulse phase dependence of the PA at the lower energies, we constrain the geometric configuration of the pulsar. The analysis favors a high spin-axis inclination of >50 which agrees with both previous pulse-phase-dependent spectral fitting of the cyclotron line region and the known high orbital inclination of the binary system. The magnetic obliquity is estimated to be 30 degrees and the spin position angle to be 19 degrees. A sharp switch in PA around 3 keV presents a particular theoretical challenge, as it is not consistent with the right-angle switch that was only seen in one other pulsar Vela X-1.

astro-ph.HE↗

Revealing two orthogonally polarized spectral components in Vela X-1 with IXPE

Polarimetric observations of X-ray pulsars (XRPs) have provided us with the key to unlocking their geometrical properties. Thanks to the Imaging X-ray Polarimetry Explorer (IXPE) the geometries of several XRPs have been determined, providing new insights into their emission mechanisms and magnetic field structures. Previously, Vela X-1 has proven to be exceptional in demonstrating a clear energy dependence of its polarimetric properties, showing a 90$^{\circ}$ swing in the polarization angle (PA) between low and high energies. Due to the complex energy-dependent nature of the polarization properties, it was not possible to determine the pulsar geometry. In this work, we present the results of a detailed analysis of the pulse phase-resolved polarization properties of at different energies. By separating the polarimetric analysis into low and high energy ranges, we are able to disentangle the contributions of the soft and hard spectral components to the polarization, revealing the pulse phase dependence of polarization degree (PD) and PA in each energy band. The PA pulse phase dependence at high energies (5$-$8 keV) allows us, for the first time, to determine the pulsar geometry in Vela X-1. The fit with the rotating vector model gives an estimate for the pulsar spin position angle at around 127$^{\circ}$ and for the magnetic obliquity of 13$^{\circ}$. In order to explain the 90$^{\circ}$ swing in PA between high and low energies, we discuss two possible scenarios: a two-component spectral model and the vacuum resonance.

astro-ph.HE↗

Neutrino beaming in ultraluminous X-ray pulsars as a result of gravitational lensing by neutron stars

X-ray pulsars experiencing extreme mass accretion rates can produce neutrino emission in the MeV energy band. Neutrinos in these systems are emitted in close proximity to the stellar surface and subsequently undergo gravitational bending in the space curved by a neutron star. This process results in the formation of a distinct beam pattern of neutrino emission and gives rise to the phenomenon of neutrino pulsars. The energy flux of neutrinos, when averaged over the neutron star's pulsation period, can differ from the isotropic neutrino energy flux, which impacts the detectability of bright pulsars in neutrinos. We investigate the process of neutrino beam pattern formation, accounting for neutron star transparency to neutrinos and gravitational bending. Based on simulated neutrino beam patterns, we estimate the potential difference between the actual and apparent neutrino luminosity. We show that the apparent luminosity can greatly exceed the actual luminosity, albeit only in a small fraction of cases, depending on the specific equation of state and the mass of the star. For example, the amplification can exceed a factor of ten for $\approx0.05\%$ of typical neutron stars with mass of $1.4\,M_\odot$. Strong amplification is less probable for neutron stars of higher mass. In the case of strange stars, a fraction of high energy neutrinos can be absorbed and the beam pattern, as well as the amplification of apparent neutrino luminosity, depend on neutrino energy.

astro-ph.HE↗

Studying geometry of the ultraluminous X-ray pulsar Swift J0243.6+6124 using X-ray and optical polarimetry

Discovery of pulsations from a number of ULXs proved that accretion onto neutron stars can produce luminosities exceeding the Eddington limit by several 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 Imaging X-ray Polarimetry Explorer (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 in 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 a 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 significantly differs from the constant component PA of about 10 deg. Combining these X-ray measurements with the optical PA, we find evidence for at least a 30 deg misalignment between the pulsar angular momentum and the binary orbital axis.

astro-ph.HE↗

Cygnus X-3 revealed as a Galactic ultraluminous X-ray source by IXPE

The accretion of matter by compact objects can be inhibited by radiation pressure if the luminosity exceeds the critical value, known as the Eddington limit. Discovery of ultraluminous X-ray sources has shown that accretion can proceed even when the apparent luminosity significantly exceeds this limit. High apparent luminosity might be produced thanks to geometric beaming of the radiation by an outflow. The outflow half-opening angle, which determines the amplification due to beaming, has never been robustly constrained. Using the Imaging X-ray Polarimetry Explorer, we made the measurement of X-ray polarization in the Galactic X-ray binary Cyg X-3. We find high, over 20%, nearly energy-independent linear polarization, orthogonal to the direction of the radio ejections. These properties unambiguously indicate the presence of a collimating outflow in the X-ray binary Cyg~X-3 and constrain its half-opening angle, <15 degrees. Thus, the source can be used as a laboratory for studying the super-critical accretion regime. This finding underscores the importance of X-ray polarimetry in advancing our understanding of accreting sources.

astro-ph.HE↗

Probing the polarized emission from SMC X-1: the brightest X-ray pulsar observed by IXPE

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 $97°\pm8°$ for Observation 1, $3.0\pm0.9$% and $90°\pm8°$ for Observation 2, and $5.5\pm1.1$% and $80°\pm6°$ 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°. 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° to $\sim$100°. 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.

astro-ph.HE↗