Analytical techniques for polarimetric imaging of accretion flows in Schwarzschild metric

Emission from an accretion disc 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 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 disc is strongly affected by the gravitational field of the compact object and relativistic velocities of the matter. The straightforward calculation of the observed polarization signatures involves computationally expensive ray-tracing technique. At the same time, having fast computational routines for direct data fitting becomes increasingly important in light of the currently observed images of the accretion flow around supermassive black hole in M87 by the Event Horizon Telescope, infrared polarization signatures coming from Sgr A*, as well as for 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 polarization plane in 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 high accuracy using approximate light-bending formula, lifting the need for the pre-computed tabular models in fitting routines.Comment: 14 pages, 11 figure

Oblate Schwarzschild approximation for polarized radiation from rapidly rotating neutron stars

We have developed a complete theory for the calculation of the observed Stokes parameters for radiation emitted from the surface of a rapidly rotating neutron star (NS) using the oblate Schwarzschild approximation. We accounted for the rotation of the polarization plane due to relativistic effects along the path from the stellar surface to the observer. The results were shown to agree with those obtained by performing full numerical general relativistic ray-tracing with the \textsc{arcmancer} code. We showed that the obtained polarization angle (PA) profiles may differ substantially from those derived for a spherical star. We demonstrated that assuming incorrect shape for the star can lead to biased constraints for NS parameters when fitting the polarization data. Using a simplified model, we also made a rough estimate of how accurately the geometrical parameters of an accreting NS can be determined using the X-ray polarization measurements of upcoming polarimeters like the Imaging X-ray Polarimeter Explorer (IXPE) or the enhanced X-ray Timing and Polarimetry (eXTP) mission.Comment: 11 pages, 10 figures, accepted in A&

Polarized radiation from an accretion shock in accreting millisecond pulsars using exact Compton scattering formalism

Pulse profiles of accreting millisecond pulsars can be used to determine neutron star (NS) parameters, such as their masses and radii, and therefore provide constraints on the equation of state of cold dense matter. Information obtained by the Imaging X-ray Polarimetry Explorer (IXPE) can be used to decipher pulsar inclination and magnetic obliquity, providing ever tighter constraints on other parameters. In this paper, we develop a new emission model for accretion-powered millisecond pulsars based on thermal Comptonization in an accretion shock above the NS surface. The shock structure was approximated by an isothermal plane-parallel slab and the Stokes parameters of the emergent radiation were computed as a function of the zenith angle and energy for different values of the electron temperature, the Thomson optical depth of the slab, and the temperature of the seed blackbody photons. We show that our Compton scattering model leads to a significantly lower polarization degree of the emitted radiation compared to the previously used Thomson scattering model. We computed a large grid of shock models, which can be combined with pulse profile modeling techniques both with and without polarization included. In this work, we used the relativistic rotating vector model for the oblate NS in order to produce the observed Stokes parameters as a function of the pulsar phase. Furthermore, we simulated the data to be produced by IXPE and obtained constraints on model parameters using nested sampling. The developed methods can also be used in the analysis of the data from future satellites, such as the enhanced X-ray Timing and Polarimetry mission.Comment: Accepted to A&A on 11 August 202

Neutron star parameter constraints for accretion-powered millisecond pulsars from the simulated IXPE data

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 accuracies in the measured time-dependent Stokes profiles integrated over all energy channels. We found that the measured relative errors depend strongly 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 $1/\sqrt{t}$, and spans the range from 30-90% with 200 ks exposure time to 20-60% with 500 ks exposure time (in 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 deg accuracy for most of the cases we considered. These measurements can be used to further constrain neutron star mass and radius when combined with modelling of the X-ray pulse profile.Comment: 12 pages, 11 figures, published in A&

Oblate Schwarzschild approximation for polarized radiation from rapidly rotating neutron stars

We have developed a complete theory for the calculation of the observed Stokes parameters for radiation emitted from the surface of a rapidly rotating neutron star (NS) using the oblate Schwarzschild approximation. We accounted for the rotation of the polarization plane due to relativistic effects along the path from the stellar surface to the observer. The results were shown to agree with those obtained by performing full numerical general relativistic ray-tracing with the ARCMANCER code. We showed that the obtained polarization angle profiles may differ substantially from those derived for a spherical star. We demonstrated that assuming incorrect shape for the star can lead to biased constraints for NS parameters when fitting the polarization data. Using a simplified model, we also made a rough estimate of how accurately the geometrical parameters of an accreting NS can be determined using the X-ray polarization measurements of upcoming polarimeters like the Imaging X-ray Polarimeter Explorer or the enhanced X-ray Timing and Polarimetry mission

Tracking the X-ray Polarization of the Black Hole Transient Swift J1727.8-1613 during a State Transition

We report on a campaign on the bright black hole X-ray binary Swift J1727.8$-$1613 centered around five observations by the Imaging X-ray Polarimetry Explorer (IXPE). This is the first time it has been possible to trace the evolution of the X-ray polarization of a black hole X-ray binary across a hard to soft state transition. The 2--8 keV polarization degree slowly decreased from $\sim$4\% to $\sim$3\% across the five observations, but remained in the North-South direction throughout. Using the Australia Telescope Compact Array (ATCA), we measure the intrinsic 7.25 GHz radio polarization to align in the same direction. Assuming the radio polarization aligns with the jet direction (which can be tested in the future with resolved jet images), this implies that the X-ray corona is extended in the disk plane, rather than along the jet axis, for the entire hard intermediate state. This in turn implies that the long ($\gtrsim$10 ms) soft lags that we measure with the Neutron star Interior Composition ExploreR (NICER) are dominated by processes other than pure light-crossing delays. Moreover, we find that the evolution of the soft lag amplitude with spectral state differs from the common trend seen for other sources, implying that Swift J1727.8$-$1613 is a member of a hitherto under-sampled sub-population.Comment: Submitted to ApJ. 20 pages, 8 figure

Dynamic behavior model of the ballastless railroad track segment considering wave processes

The paper is devoted to the modification of the dynamic behavior model of a flat orthotropic element under shock and vibrational impacts. The impacts were caused by solid cylindrical body for the case of ballastless railway construction. The suggested model allows simulating the element deformation in the upper structure of the ballast-free design track. The propagation of elastic waves moving with finite speeds, orthotropic properties of the foundation slab, which allow optimally selecting rod reinforcement are taken into account. The obtained analytical and graphical results make it possible to assess the influence of properties of the reinforced concrete slab, the underframe speed, the presence of defects in wheel sets or rail bars, as well as the characteristics of the technical content of the track section

Structure of Late Pleistocene and Holocene Sediments in the Petrozavodsk Bay, Lake Onego (NW Russia)

Here, we present new results from seismic, geological, and geochemical studies conducted in 2015–2019 in the Petrozavodsk Bay of Lake Onego, NW Russia. The aims of these investigations were to (i) to characterize the structure of Quaternary deposits and (ii) provide new evidence of modern geodynamic movements and gas-seepage in Holocene sediments. The structure of the recovered deposits was composed of lacustrine mud, silt and sands from the Holocene, limno-glacial clays (varved clays) from the Late Glacial–Interglacial Transition, and glacial deposits (till) from the Late Pleistocene. The thickness of these deposits varied in different parts of the bay. Many pockmarks created by gases escaping and reaching sediment-water interface were observed in these deposits. Such pockmarks can play a significant role in the geochemical and biological processes in the bottom sediment surface, and gases that escape might modify the physicochemical characteristics of the environment

Ultrasoft state of microquasar Cygnus X-3: X-ray polarimetry reveals the geometry of the astronomical puzzle

Cygnus X-3 is an enigmatic X-ray binary that is both an exceptional accreting system and a cornerstone for population synthesis studies. Prominent X-ray and radio properties follow a well-defined pattern, and yet the physical reasons for the state changes observed in this system are not known. Recently, the presence of an optically thick envelope around the central source in the hard state was revealed using the X-ray polarization data obtained with the Imaging X-ray Polarimetry Explorer (IXPE). In this work we analyse IXPE data obtained in the ultrasoft (radio quenched) state of the source. The average polarization degree (PD) of 11.9 ± 0.5% at a polarization angle (PA) of 94° ±1° is inconsistent with the simple geometry of the accretion disc viewed at an intermediate inclination. The high PD, the blackbody-like spectrum, and the weakness of fluorescent iron line imply that the central source is hidden behind the optically thick outflow, similar to the hard-state geometry, and its beamed radiation is scattered, by the matter located along the funnel axis, towards our line of sight. In this picture the observed PD is directly related to the source inclination, which we conservatively determine to lie in the range 26° < i < 28°. Using the new polarimetric properties, we propose a scenario that can be responsible for the cyclic behaviour of the state changes in the binary