Polarimetric images of accreting black holes encode important information about laws of strong gravity and relativistic motions of matter. Recent advancements in instrumentation have enabled such studies of two objects: the supermassive black holes M87* and Sagittarius A*. Light coming from these sources is produced by a synchrotron mechanism whose polarization is directly linked to magnetic field lines, and propagates toward the observer in a curved spacetime. We studied the distortions of the gas image by employing the analytical ray-tracing technique for polarized light ARTPOL, which is adapted for the case of synchrotron emission. We derived analytical expressions for fast conversion of the intensity or flux, polarization degree, and polarization angle from the local coordinates to those of the observer. We placed an emphasis on the nonzero matter elevation above the equatorial plane and noncircular matter motions. Applications of the developed formalism include static polarimetric imaging of the black hole vicinity and dynamic polarimetric signatures of matter close to the compact object.

X-ray polarimetry is a fine tool for probing the accretion geometry and physical processes operating in the proximity of compact objects, such as black holes and neutron stars. Recent discoveries made by the Imaging X-ray Polarimetry Explorer question our understanding of the accretion picture. The observed high levels of X-ray polarization in X-ray binaries and active galactic nuclei are challenging to achieve within the conventional scenarios. We investigate the possibility that a fraction (or even all) of the observed polarized signal arises from scattering in the equatorial accretion disk winds, the slow and extended outflows, which are often detected in these systems via spectroscopic means. We find that wind scattering can reproduce the levels of polarization that are observed in these sources.

We present the first X-ray spectropolarimetric results for Cygnus X-1 in its soft state from a campaign of five IXPE observations conducted during 2023 May-June. Companion multiwavelength data during the campaign are likewise shown. The 2-8 keV X-rays exhibit a net polarization degree PD = 1.99% ± 0.13% (68% confidence). The polarization signal is found to increase with energy across the Imaging X-ray Polarimetry Explorer’s (IXPE) 2-8 keV bandpass. The polarized X-rays exhibit an energy-independent polarization angle of PA = −25.°7 ± 1.°8 east of north (68% confidence). This is consistent with being aligned to Cyg X-1’s au-scale compact radio jet and its parsec-scale radio lobes. In comparison to earlier hard-state observations, the soft state exhibits a factor of 2 lower polarization degree but a similar trend with energy and a similar (also energy-independent) position angle. When scaling by the natural unit of the disk temperature, we find the appearance of a consistent trend line in the polarization degree between the soft and hard states. Our favored polarimetric model indicates that Cyg X-1’s spin is likely high (a * ≳ 0.96). The substantial X-ray polarization in Cyg X-1's soft state is most readily explained as resulting from a large portion of X-rays emitted from the disk returning and reflecting off the disk surface, generating a high polarization degree and a polarization direction parallel to the black hole spin axis and radio jet. In IXPE’s bandpass, the polarization signal is dominated by the returning reflection emission. This constitutes polarimetric evidence for strong gravitational lensing of X-rays close to the black hole.

Spectro-polarimetric signatures of accretion disks in X-ray binaries and active galactic nuclei contain information on the masses and spins of their central black holes, as well as the geometry of matter in proximity to the compact objects. This information can be extracted by means of X-ray polarimetry. In this work, we present a fast analytical ray-tracing technique for polarized light (artpol) that helps us to obtain the spinning black hole parameters from the observed properties. This technique can replace the otherwise time-consuming numerical ray-tracing calculations for any optically thick or geometrically thin accretion flow. For the purposes of illustration, we considered a standard optically thick, geometrically thin accretion disk in the equatorial plane of the Kerr black hole. We show that artpol proves accurate for dimensionless spin parameter a ≤ 0.94 with a speed that is over four orders of magnitude faster than direct ray-tracing calculations. This approach opens up broader prospects for direct fittings of the spectro-polarimetric data from the Imaging X-ray Polarimetry Explorer.

The accretion of matter by compact objects can be inhibited by radiation pressure if the luminosity exceeds a critical value known as the Eddington limit. The discovery of ultraluminous X-ray sources has shown that accretion can proceed even when the apparent luminosity considerably exceeds this limit. A high apparent luminosity might be produced due to the geometric beaming of 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 measured the X-ray polarization in the Galactic X-ray binary Cygnus X-3 (Cyg X-3). We found high, >20%, nearly energy-independent linear polarization orthogonal to the direction of the radio ejections. These properties unambiguously indicate the presence of a collimating outflow from the X-ray binary Cyg X-3 and constrain its half-opening angle to less than or similar to 15 degrees. Thus, the source can be used as a laboratory for studying the supercritical accretion regime. This finding underscores the importance of X-ray polarimetry in advancing our understanding of accreting sources.

Weakly magnetized neutron stars in X-ray binaries show a complex phenomenology with several spectral components that can be associated with the accretion disk, the boundary, and/or a spreading layer, a corona, and a wind. Spectroscopic information alone, however, is not enough to distinguish these components. The analysis of the timing data revealed that most of the variability, and in particular, kilohertz quasi-period oscillations, are associated with the high-energy component that corresponds to the boundary and/or spreading layer. Additional information about the nature of the spectral components, and in particular, about the geometry of the emission region, can be provided by X-ray polarimetry. One of the objects of the class, a bright, persistent, and rather peculiar galactic Type I X-ray burster GX 13+1, was observed with the Imaging X-ray Polarimetry Explorer (IXPE) and the XMM-Newton. Using the XMM-Newton data, we obtained the best-fit values for the continuum spectral parameters and detected strong absorption lines associated with the accretion disk wind. IXPE data showed the source to be significantly polarized in the 2-8 keV energy band, with an overall polarization degree (PD) of 1.4%+/- 0.3% at a polarization angle (PA) of -2 degrees +/- 6 degrees (errors at the 68% confidence level). During the two-day long observation, we detected rotation of the PA by about 70 degrees with the corresponding changes in the PD from 2% to nondetectable and then up to 5%. These variations in polarization properties are not accompanied by visible spectral state changes of the source. The energy-resolved polarimetric analysis showed a significant change in polarization, from being strongly dependent on energy at the beginning of the observation to being almost constant with energy in the later parts of the observation. As a possible interpretation, we suggest a constant polarization component, strong wind scattering, or a different polarization of the two main spectral components with an individually peculiar behavior. The rotation of the PA suggests a misalignment of the neutron star spin from the orbital axis.

Black hole X-ray binaries exhibit different spectral and timing properties in different accretion states. The X-ray outburst of a recently discovered and extraordinarily bright source, Swift J1727.8-1613, has enabled the first investigation of how the X-ray polarization properties of a source evolve with spectral state. The 2-8 keV polarization degree was previously measured by the Imaging X-ray Polarimetry Explorer (IXPE) to be ≈4% in the hard and hard intermediate states. Here we present new IXPE results taken in the soft state, with the X-ray flux dominated by the thermal accretion disk emission. We find that the polarization degree has dropped dramatically to ≲1%. This result indicates that the measured X-ray polarization is largely sensitive to the accretion state and the polarization fraction is significantly higher in the hard state when the X-ray emission is dominated by upscattered radiation in the X-ray corona. The combined polarization measurements in the soft and hard states disfavor a very high or low inclination of the system.

We report two epochs of simultaneous near-infrared (IR) and X-ray observations of the low-mass X-ray binary black hole candidate Swift J1753.5-0127 with a subsecond time resolution during its long 2005-2016 outburst. Data were collected strictly simultaneously with VLT/ISAAC (K-S band, 2.2 mu m) and RXTE (2-15 keV) or XMM-Newton (0.7-10 keV). A clear correlation between the X-ray and the IR variable emission is found during both epochs but with very different properties. In the first epoch, the near-IR variability leads the X-ray by similar to 130 ms, which is the opposite of what is usually observed in similar systems. The correlation is more complex in the second epoch, with both anti-correlation and correlations at negative and positive lags. Frequency-resolved Fourier analysis allows us to identify two main components in the complex structure of the phase lags: the first component, characterised by a near-IR lag of a few seconds at low frequencies, is consistent with a combination of disc reprocessing and a magnetised hot flow; the second component is identified at high frequencies by a near-IR lag of approximate to 0.7 s. Given the similarities of this second component with the well-known constant optical/near-IR jet lag observed in other black hole transients, we tentatively interpret this feature as a signature of a longer-than-usual jet lag. We discuss the possible implications of measuring such a long jet lag in a radio-quiet black hole transient.

We report on the detection of X-ray polarisation in the black-hole X-ray binary Swift J1727.8-1613 during its dim hard spectral state by the Imaging X-ray Polarimetry Explorer (IXPE). This is the first detection of X-ray polarisation at the transition from the soft to the hard state in an X-ray binary. We find an averaged 2- 8 keV polarisation degree of (3.3 ± 0.4)% and a corresponding polarisation angle of 3 ±4, which matches the polarisation detected during the rising stage of the outburst, in September- October 2023, within 1σuncertainty. The observational campaign complements previous studies of this source and enables comparison of the X-ray polarisation properties of a single transient across the X-ray hardness-intensity diagram. The complete recovery of the X-ray polarisation properties, including the energy dependence, came after a dramatic drop in the X-ray polarisation during the soft state. The new IXPE observations in the dim hard state at the reverse transition indicate that the accretion properties, including the geometry of the corona, appear to be strikingly similar to the bright hard state during the outburst rise despite the X-ray luminosities differing by two orders of magnitude.

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 i(p)=15 degrees-40 degrees, the magnetic obliquity of theta(p) = 60 degrees-80 degrees, and the pulsar spin position angle of chi(p)approximate to-50 degrees, which significantly differs from the constant component PA of about 10 degrees. Combining these X-ray measurements with the optical PA, we find evidence for at least a 30 degrees misalignment between the pulsar angular momentum and the binary orbital axis.