Emission from an accretion disk around compact objects, such as neutron stars and black holes, is expected to be significantly polarized. The polarization can be used to put constraints on the geometrical and physical parameters of the compact sources – their radii, masses, and spins – as well as to determine the orbital parameters. The radiation escaping from the innermost parts of the disk is strongly affected by the gravitational field of the compact object and the relativistic velocities of the matter. The straightforward calculation of the observed polarization signatures involves a computationally expensive ray-tracing technique. At the same time, having fast computational routines for direct data fitting is becoming increasingly important in light of the currently observed images of the accretion flow around the supermassive black hole in M 87 by the Event Horizon Telescope and infrared polarization signatures coming from Sgr A*, as well as the upcoming X-ray polarization measurements by the Imaging X-ray Polarimetry Explorer and enhanced X-ray Timing and Polarimetry mission. In this work, we obtain an exact analytical expression for the rotation angle of the polarization plane in the Schwarzschild metric accounting for the effects of light bending and relativistic aberration. We show that the calculation of the observed flux, polarization degree, and polarization angle as a function of energy can be performed analytically with a high level of accuracy using an approximate light-bending formula, eliminating the need for the precomputed tabular models in fitting routines.

The observational signatures of black holes in x-ray binary systems depend on their masses, spins, accretion rate, and the misalignment angle between the black hole spin and the orbital angular momentum. We present optical polarimetric observations of the black hole x-ray binary MAXI J1820+070, from which we constrain the position angle of the binary orbital. Combining this with previous determinations of the relativistic jet orientation. which traces the black hole spin, and the inclination of the orbit, we determine a lower limit of 40 degrees on the spin-orbit misalignment angle. The misalignment must originate from either the binary evolution or black hole formation stages. If other x-ray binaries have similarly large misalignments, these would bias measurements of black hole masses and spins from x-ray observations.

We present the results of a detailed investigation of the poorly studied X-ray pulsar 2S 1845−024 based on data obtained at the NuSTAR observatory during the type I outburst in 2017. Neither pulse phase-averaged nor phase-resolved spectra of the source show evidence for a cyclotron absorption feature. We also used data obtained from other X-ray observatories (Swift, XMM-Newton and Chandra) to study the spectral properties as a function of orbital phase. The analysis reveals a high hydrogen column density for the source reaching ∼10²⁴ cm⁻² around periastron. Using high-quality Chandra data we were able to obtain an accurate localization of 2S 1845−024 at RA = 18^h48^m16.^s8 and Dec = −2°25′25.″1 (J2000), which allowed us to use infrared (IR) data to roughly classify the optical counterpart of the source as an OB supergiant at a distance of ≳15 kpc.

The enhanced x-ray timing and polarimetry mission (eXTP) is a flagship observatory for x-ray timing, spectroscopy and polarimetry developed by an international consortium. Thanks to its very large collecting area, good spectral resolution and unprecedented polarimetry capabilities, eXTP will explore the properties of matter and the propagation of light in the most extreme conditions found in the universe. eXTP will, in addition, be a powerful x-ray observatory. The mission will continuously monitor the x-ray sky, and will enable multi-wavelength and multi-messenger studies. The mission is currently in phase B, which will be completed in the middle of 2022.

This work is devoted to the study of the broad-band 0.8–79 keV spectral and timing properties of the poorly studied X-ray pulsar XTE J1859+083 during its 2015 outburst based on the data from the NuSTAR and Swift observatories. We show that the source pulse profile has complex shape that depends on the energy band. Pulse fraction of XTE J1859+083 has constant value around 35 per cent in the broad energy band, this behaviour is atypical for X-ray pulsars. At the same time its energy spectrum is typical of this class of objects and has a power-law shape with an exponential cutoff at high energies. No cyclotron absorption line was discovered in the source spectrum. On the basis of indirect method and the absence of a cyclotron line, an estimation was made for the magnetic field strength as less than 5 × 10¹¹ G or belonging to the interval from 5 × 10¹² to 2.0×10¹³ G. Data from the NOT and SALT telescopes as well as optical and IR sky surveys allowed us also to study the nature of its optical companion. We have proposed and studied new possible candidates for the optical companion of XTE J1859+083 and the most likely candidate was identified. The results of the optical and IR photometry and spectroscopy of these possible companions showed that the system is a Be X-ray binary, showing Brγ, He I, and strong H α spectral lines. 

X-ray polarimetry has long been considered the 'holy grail' of X-ray astronomy. Fortunately, after a silence of more than 40 years, the field is now rejuvenating. In fact, an X-ray polarimeter onboard a Cube-sat nano-satellite has been recently successfully operated. IXPE, the Imaging X-ray Polarimetry Explorer, will be launched in 2021 while eXTP, containing a larger version of IXPE, is expected to be launched in 2027. Although at present it is difficult to predict the discoveries that, given their exploratory nature, IXPE and eXTP will obtain, the path for a follow-up mission can already be envisaged. In this paper we describe the scientific goals of such a follow-up mission, and present a medium-size mission profile that can accomplish this task.

The accreting millisecond X-ray pulsar Swift J1756.9-2508 launched into an outburst in April 2018 and June 2019 - 8.7 years after the previous period of activity. We investigated the temporal, timing, and spectral properties of these two outbursts using data from NICER, XMM-Newton, NuSTAR, INTEGRAL, Swift, and Insight-HXMT. The two outbursts exhibited similar broadband spectra and X-ray pulse profiles. For the first time, we report the detection of the pulsed emission up to similar to 100 keV that was observed by Insight-HXMT during the 2018 outburst. We also found the pulsation up to similar to 60 keV that was observed by NICER and NuSTAR during the 2019 outburst. We performed a coherent timing analysis combining the data from the two outbursts. The binary system is well described by a constant orbital period over a time span of similar to 12 years. The time-averaged broadband spectra are well fitted by the absorbed thermal Comptonization model COMPPS in a slab geometry with an electron temperature, kT(e)=40-50 keV, Thomson optical depth tau similar to 1.3, blackbody seed photon temperature kT(bb, seed)similar to 0.7-0.8 keV, and hydrogen column density of N-H similar to 4.2x10(22) cm(-2). We searched the available data for type-I (thermonuclear) X-ray bursts, but found none, which is unsurprising given the estimated low peak accretion rate (approximate to 0.05 of the Eddington rate) and generally low expected burst rates for hydrogen-poor fuel. Based on the history of four outbursts to date, we estimate the long-term average accretion rate at roughly 5x10(-12) M-circle dot yr(-1) for an assumed distance of 8 kpc. The expected mass transfer rate driven by gravitational radiation in the binary implies the source may be no closer than 4 kpc. Swift J1756.9-2508 is the third low mass X-ray binary exhibiting double outbursts, which are separated by much shorter intervals than what we typically see and are likely to result from interruption of the accretion flow from the disk onto the neutron star. Such behavior may have important implications for the disk instability model.

We study X-ray and soft gamma-ray spectra from the hard state of the accreting black-hole binary MAXI J1820+070. We perform an analysis of two joint spectra from NuSTAR and INTEGRAL, covering the range of 3-650 keV, and of an average joint spectrum over the rise of the hard state, covering the 3-2200 keV range. The spectra are well modeled by Comptonization of soft seed photons. However, the distributions of the scattering electrons are not purely thermal; we find they have substantial high-energy tails, well modeled as power laws. The photon tail in the average spectrum is detected well beyond the threshold for electron-positron pair production, 511 keV. This allows us to calculate the rate of the electron-positron pair production and put a lower limit on the size of the source from pair equilibrium. At the fitted Thomson optical depth of the Comptonizing plasma, the limit is about 4 gravitational radii. If we adopt the sizes estimated by us from the reflection spectroscopy of >20 gravitational radii, the fractional pair abundance becomes much less than unity. The low pair abundance is confirmed by the lack of both an annihilation feature and of a pair absorption cutoff above 511 keV in the average spectrum.

Kilohertz-scale quasi-periodic oscillations (kHz QPOs) are a distinct feature of the variability of neutron star low-mass X-ray binaries. Among all the variability modes, they are especially interesting as a probe for the innermost parts of the accretion flow, including the accretion boundary layer (BL) on the surface of the neutron star. All the existing models of kHz QPOs explain only part of their rich phenomenology. Here, we show that some of their properties can be explained by a very simple model of the BL that is spun up by accreting rapidly rotating matter from the disk and spun down by the interaction with the neutron star. In particular, if the characteristic time scales for the mass and the angular momentum transfer from the BL to the star are of the same order of magnitude, our model naturally reproduces the so-called parallel tracks effect, where the QPO frequency is correlated with luminosity at time scales of hours but becomes uncorrelated at time scales of days. The closeness of the two time scales responsible for mass and angular momentum exchange between the BL and the star is an expected outcome of the radial structure of the BL.

We have simulated the X-ray polarization data that can be obtained with the Imaging X-ray Polarimetry Explorer, when observing accretion-powered millisecond pulsars. We estimated the necessary exposure times for SAX J1808.4−3658 in order to obtain different accuracy in the measured time-dependent Stokes profiles integrated over all energy channels. We found that the measured relative errors strongly depend on the relative configuration of the observer and the emitting hotspot. The improvement in the minimum relative error in Stokes Q and U parameters as a function of observing time t scales as 1/√t, and it spans the range from 30–90% with a 200 ks exposure time to 20–60% with a 500 ks exposure time (in the case of data binned in 19 phase bins). The simulated data were also used to predict how accurate measurements of the geometrical parameters of the neutron star can be made when modelling only Q and U parameters, but not the flux. We found that the observer inclination and the hotspot co-latitude could be determined with better than 10° accuracy for most of the cases we considered. In addition, we show that the position of a secondary hotspot can also be constrained when the spot is not obscured by an accretion disc. These measurements can be used to further constrain the neutron star mass and radius when combined with modelling of the X-ray pulse profile.