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ABSTRACT Pulse profile modelling is a relativistic ray-tracing technique that can be used to infer masses, radii, and geometric parameters of neutron stars. In a previous study, we looked at the performance of this technique when applied to thermonuclear burst oscillations from accreting neutron stars. That study showed that ignoring the variability associated with burst oscillation sources resulted in significant biases in the inferred mass and radius, particularly for the high count rates that are nominally required to obtain meaningful constraints. In this follow-on study, we show that the bias can be mitigated by slicing the bursts into shorter segments where variability can be neglected, and jointly fitting the segments. Using this approach, the systematic uncertainties on the mass and radius are brought within the range of the statistical uncertainty. With about 106 source counts, this yields uncertainties of approximately 10 per cent for both the mass and radius. However, this modelling strategy requires substantial computational resources. We also confirm that the posterior distributions of the mass and radius obtained from multiple bursts of the same source can be merged to produce outcomes comparable to that of a single burst with an equivalent total number of counts. 

ABSTRACT We study the effects of the time-variable properties of thermonuclear X-ray bursts on modelling their millisecond-period burst oscillations. We apply the pulse profile modelling technique that is being used in the analysis of rotation-powered millisecond pulsars by the Neutron Star Interior Composition Explorer to infer masses, radii, and geometric parameters of neutron stars. By simulating and analysing a large set of models, we show that overlooking burst time-scale variability in temperatures and sizes of the hot emitting regions can result in substantial bias in the inferred mass and radius. To adequately infer neutron star properties, it is essential to develop a model for the time-variable properties or invest a substantial amount of computational time in segmenting the data into non-varying pieces. We discuss prospects for constraints from proposed future X-ray telescopes. 

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°, which is in good agreement with the orbital inclination), the position angle (75°) of the pulsar spin axis, and the magnetic obliquity (∼74°). 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. 

Accreting X-ray pulsars (XRPs) are presumed to be 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, namely, 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, an analysis of the EXO 2030+375 data returns a low polarization degree of 0%–3% in the phase-averaged study and a variation in the range of 2%–7% in the phase-resolved study. Using the rotating vector model, we constrained the geometry of the system and obtained a value of ∼60° for the magnetic obliquity. When considering the estimated pulsar inclination of ∼130°, this also indicates that the magnetic axis swings close to the observer’s line of sight. Our joint polarimetric, spectral, and timing analyses hint toward a complex accreting geometry, whereby magnetic multipoles with an asymmetric topology and gravitational light bending significantly affect the behavior of the observed source. 

Abstract 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. 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 spectropolarimetric analysis of the phase-averaged data for Vela X-1 reveals a polarization degree (PD) of 2.3% ± 0.4% at the polarization angle (PA) of −47.°3 ± 5.°4. 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° difference in the PA compared to the data in the 2–3 keV range. The phase-resolved spectropolarimetric analysis finds a PD in the range 0%–9% with the PA varying between −80° and 40°. 

Abstract The first X-ray pulsar, Cen X-3, was discovered 50 yr ago. Radiation from such objects is expected to be highly polarized due to birefringence of plasma and vacuum associated with propagation of photons in the 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 in either pulse phase-averaged (with a 3 σ upper limit of 12%) or phase-resolved (the 3 σ upper limits are 20%–30%) data. In the bright state, the polarization degree of 5.8% ± 0.3% and polarization angle of 49.°6 ± 1.°5 with a significance of about 20 σ were measured from the spectropolarimetric analysis of the phase-averaged data. The phase-resolved analysis showed a significant anticorrelation 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.