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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 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 ip = 15°–40°, the magnetic obliquity of θp = 60°–80°, and the pulsar spin position angle of χp ≈ −50°, which significantly differs from the constant component PA of about 10°. Combining these X-ray measurements with the optical PA, we find evidence for at least a 30° misalignment between the pulsar angular momentum and the binary orbital axis. [ABSTRACT FROM AUTHOR]

Accreting stellar-mass black holes represent unique laboratories for studying matter and radiation under the influence of extreme gravity. They are highly variable sources going through different accretion states, showing various components in their X-ray spectra from the thermal emission of the accretion disc dominating in the soft state to the up-scattered Comptonisation component from an X-ray corona in the hard state. X-ray polarisation measurements are particularly sensitive to the geometry of the X-ray scatterings and can thus constrain the orientation and relative positions of the innermost components of these systems. The IXPE mission has observed about a dozen stellar-mass black holes with masses up to 20 solar masses in X-ray binaries with different orientations and in various accretion states. The low-inclination sources in soft states have shown a low fraction of polarisation. On the other hand, several sources in soft and hard states have revealed X-ray polarisation higher than expected, which poses significant challenges for theoretical interpretation, with 4U 1630–47 being one of the most puzzling sources. IXPE has measured the spin of three black holes via the measurement of their polarisation properties in the soft emission state. In each of the three cases, the new results agree with the constraints from the spectral observations. The polarisation observations of the black hole X-ray transient Swift J1727.8–1613 across its entire outburst has revealed that the soft-state polarisation is much weaker than the hard-state polarisation. Remarkably, the observations furthermore show that the polarisation of the bright hard state and that of the 100 times less luminous dim hard state are identical within the accuracy of the measurement. For sources with a radio jet, the electric field polarisation tends to align with the radio jet, indicating the equatorial geometry of the X-ray corona, e.g., in the case of Cyg X–1. In the unique case of Cyg X–3, where the polarisation is perpendicular to the radio jet, the IXPE observations reveal the presence and geometry of obscuring material hiding this object from our direct view. The polarisation measurements acquired by the IXPE mission during its first 2.5 years have provided unprecedented insights into the geometry and physical processes of accreting stellar-mass black holes, challenging existing theoretical models and offering new avenues for understanding these extreme systems. [ABSTRACT FROM AUTHOR]

Polarimetry provides an avenue for probing the geometry and physical mechanisms producing optical radiation in many astrophysical objects, including stellar binary systems. We present the results of multiwavelength (BVR) polarimetric studies of a sample of historical black hole X-ray binaries, observed during their outbursts or in the quiescent (or near-quiescent) state. We surveyed both long- and short-period systems, located at different Galactic latitudes. We performed careful analysis of the interstellar polarization in the direction on the sources to reliably estimate the intrinsic source polarization. Intrinsic polarization was found to be small (<0.2 per cent) in sources observed in bright soft states (MAXI J0637−430 and 4U 1957+115). It was found to be significant in the rising hard state of MAXI J1820+070 at the level of ∼0.5 per cent and negligible in the decaying hard state and during its failed outbursts, while Swift J1357.2−0933  showed its absence in the rising hard state. Three (XTE J1118+480 , V4641 Sgr , V404 Cyg) sources observed during quiescence show no evidence of significant intrinsic polarization, while MAXI J1820+070  is the only black hole X-ray binary which showed substantial (>5 per cent) intrinsic quiescent-state polarization with a blue spectrum. The absence of intrinsic polarization at the optical wavelengths puts constraints on the potential contribution of non-stellar (jet, hot flow, accretion disc) components to the total spectra of black hole X-ray binaries. [ABSTRACT FROM AUTHOR]

We studied the variability of the linear polarization and brightness of the γ-ray binary LS I +61° 303. High-precision BVR photopolarimetric observations were carried out with the Dipol-2 polarimeter on the 2.2 m remotely controlled UH88 telescope at Mauna Kea Observatory and the 60 cm Tohoku telescope at Haleakala bservatory (Hawaii) over 140 nights in 2016−2019. We also determined the degree and angle of the interstellar polarization toward LS I +61° 303 using two out of four nearby field stars that have Gaia's parallaxes. After subtracting the interstellar polarization, we determined the position angle of the intrinsic polarization θ ≃ 11°, which can either be associated with the projection of the Be star's decretion disk axis on the plane of sky, or can differ from it by 90°. Using the Lomb-Scargle method, we performed timing analyses and period searches of our polarimetric and photometric data. We found statistically significant periodic variability of the normalized Stokes parameters q and u in all passbands. The most significant period of variability, PPol = 13.244 ± 0.012 d, is equal to one half of the orbital period Porb = 26.496 d. The fits of the polarization variability curves with Fourier series show a dominant contribution from the second harmonic which is typical for binary systems with circular orbits and nearly symmetric distribution of light scattering material with respect to the orbital plane. The continuous change of polarization with the orbital phase implies co-planarity of the orbit of the compact object and the Be star's decretion disk. Using a model of Thomson scattering by a cloud that orbits the Be star, we obtained constraints on the orbital parameters, including a small eccentricity e < 0.2 and periastron phase of ϕp ≈ 0.6, which coincides with the peaks in the radio, X-ray, and TeV emission. These constraints are independent of the assumption about the orientation of the decretion disk plane on the sky. We also extensively discuss the apparent inconsistency with the previous measurements of the orbital parameters from radial velocities. By folding the photometry data acquired during a three-year time span with the orbital period, we found a linear phase shift of the moments of the brightness maximum, confirming the possible existence of superorbital variability. [ABSTRACT FROM AUTHOR]

We describe the first complete polarimetric data set of the entire outburst of a low-mass black hole X-ray binary system and discuss the constraints for geometry and radiative mechanisms it imposes. During the decaying hard state, when the optical flux is dominated by the non-thermal component, the observed polarization is consistent with the interstellar values in all filters. During the soft state, the intrinsic polarization of the source is small, ∼0.15 per cent in B and V filters, and is likely produced in the irradiated disc. A much higher polarization, reaching ∼0.5 per cent in V and R filters, at a position angle of ∼25○ observed in the rising hard state coincides in time with the detection of winds in the system. This angle coincides with the position angle of the jet. The detected optical polarization is best explained by scattering of the non-thermal (hot flow or jet base) radiation in an equatorial wind. [ABSTRACT FROM AUTHOR]

Aims. The optical emission of black hole transients increases by several magnitudes during the X-ray outbursts. Whether the extra light arises from the X-ray heated outer disc, from the inner hot accretion flow, or from the jet is currently debated. Optical polarisation measurements are able to distinguish the relative contributions of these components. Methods. We present the results of BVR polarisation measurements of the black hole X-ray binary MAXI J1820+070 during the period of March-April 2018. Results. We detect small, ∼0.7%, but statistically significant polarisation, part of which is of interstellar origin. Depending on the interstellar polarisation estimate, the intrinsic polarisation degree of the source is between ∼0.3% and 0.7%, and the polarisation position angle is between ∼10 ° −30°. We show that the polarisation increases after MJD 58222 (2018 April 14). The change is of the order of 0.1% and is most pronounced in the R band. The change of the source Stokes parameters occurs simultaneously with the drop of the observed V-band flux and a slow softening of the X-ray spectrum. The Stokes vectors of intrinsic polarisation before and after the drop are parallel, at least in the V and R filters. Conclusions. We suggest that the increased polarisation is due to the decreasing contribution of the non-polarized component, which we associate with the the hot flow or jet emission. The low polarisation can result from the tangled geometry of the magnetic field or from the Faraday rotation in the dense, ionised, and magnetised medium close to the black hole. The polarized optical emission is likely produced by the irradiated disc or by scattering of its radiation in the optically thin outflow. [ABSTRACT FROM AUTHOR]