The X-ray radiation produced on the surface of accreting magnetised neutron stars is expected to be strongly polarised. A swing of the polarisation vector with the pulsar phase gives a direct measure ...of the source inclination and magnetic obliquity. In the case of rapidly rotating millisecond pulsars, the relativistic motion of the emission region causes additional rotation of the polarisation plane. Here, we develop a relativistic rotating vector model, where we derive analytical expression for the polarisation angle as a function of the pulsar phase accounting for relativistic aberration and gravitational light bending in the Schwarzschild metric. We show that in the case of fast pulsars the rotation of the polarisation plane can reach tens of degrees, strongly influencing the observed shape of the polarisation angle’s phase dependence. The rotation angle grows nearly linearly with the spin rate but it is less sensitive to the neutron star radius. Overall, this angle is large even for large spots. Our results have implications with regard to the modelling of X-ray polarisation from accreting millisecond pulsars that are to be observed with the upcoming Imaging X-ray Polarimeter Explorer and the enhanced X-ray Timing and Polarimetry mission. The X-ray polarisation may improve constraints on the neutron star mass and radius coming from the pulse profile modelling.
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We propose new analytic formulae describing light bending in the Schwarzschild metric. For an emission radii above the photon orbit at the 1.5 Schwarzschild radius, the formulae have an accuracy of ...better than 0.2% for the bending angle and 3% for the lensing factor for any trajectories that turn around a compact object by less than about 160°. In principle, they can be applied to any emission point above the horizon of the black hole. The proposed approximation can be useful for problems involving emission from neutron stars and accretion discs around compact objects when fast accurate calculations of light bending are required. It can also be used to test the codes that compute light bending using exact expressions via elliptical integrals.
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Abstract
Recent X-ray polarimetric data on the prototypical black hole X-ray binary Cyg X-1 from the Imaging X-ray Polarimetry Explorer present tight constraints on accretion geometry in the hard ...spectral state. Contrary to general expectations of a low, ≲1% polarization degree (PD), the observed average PD was found to be a factor of 4 higher. Aligned with the jet position angle on the sky, the observed polarization favors geometry of the X-ray emission region stretched normally to the jet in the accretion disk plane. The high PD is, however, difficult to reconcile with the low orbital inclination of the binary
i
≈ 30°. We suggest that this puzzle can be explained if the emitting plasma is outflowing with a mildly relativistic velocity ≳0.4
c
. Our radiative transfer simulations show that Comptonization in the outflowing medium elongated in the plane of the disk and radiates X-rays with the degree and direction of polarization consistent with observations at
i
≈ 30°.
The GeV-range spectra of blazars are shaped not only by non-thermal emission processes internal to the relativistic jet but also by external pair-production absorption on the thermal emission of the ...accretion disc and the broad-line region (BLR). For the first time, we compute here the pair-production opacities in the GeV range produced by a realistic BLR accounting for the radial stratification and radiation anisotropy. Using photoionization modelling with the cloudy code, we calculate a series of BLR models of different sizes, geometries, cloud densities, column densities and metallicities. The strongest emission features in the model BLR are Ly alpha and He ii Ly alpha . Contribution of recombination continua is smaller, especially for hydrogen, because Ly continuum is efficiently trapped inside the large optical depth BLR clouds and converted to Lyman emission lines and higher order recombination continua. The largest effects on the gamma-ray opacity are produced by the BLR geometry and localization of the gamma-ray source. We show that when the gamma-ray source moves further from the central source, all the absorption details move to higher energies and the overall level of absorption drops because of decreasing incidence angles between the gamma-rays and BLR photons. The observed positions of the spectral breaks can be used to measure the geometry and the location of the gamma-ray emitting region relative to the BLR. Strong dependence on geometry means that the soft photons dominating the pair-production opacity may be actually produced by a different population of BLR clouds than the bulk of the observed broad line emission.
We study the effects of the mutual interaction of hot plasma and cold medium in black hole binaries in their hard spectral state. We consider a number of different geometries. In contrast to previous ...theoretical studies, we use a modern energy-conserving code for reflection and reprocessing from cold media. We show that a static corona above an accretion disc extending to the innermost stable circular orbit produces spectra not compatible with those observed. They are either too soft or require a much higher disc ionization than that observed. This conclusion confirms a number of previous findings, but disproves a recent study claiming an agreement of that model with observations. We show that the cold disc has to be truncated in order to agree with the observed spectral hardness. However, a cold disc truncated at a large radius and replaced by a hot flow produces spectra which are too hard if the only source of seed photons for Comptonization is the accretion disc. Our favourable geometry is a truncated disc coexisting with a hot plasma either overlapping with the disc or containing some cold matter within it, also including seed photons arising from cyclo-synchrotron emission of hybrid electrons, i.e. containing both thermal and non-thermal parts.
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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.
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Multiwavelength observations of Galactic black hole transients have opened a new path to understanding the physics of the innermost parts of the accretion flows. While the processes giving rise to ...their X-ray continuum have been studied extensively, the emission in the optical and infrared (OIR) energy bands was less investigated and remains poorly understood. The standard accretion disc, which may contribute to the flux at these wavelengths, is not capable of explaining a number of observables: the infrared excesses, fast OIR variability and a complicated correlation with the X-rays. It was suggested that these energy bands are dominated by the jet emission; however, this scenario does not work in a number of cases. We propose here an alternative, namely that most of the OIR emission is produced by the extended hot accretion flow. In this scenario, the OIR bands are dominated by the synchrotron radiation from the non-thermal electrons. An additional contribution is expected from the outer irradiated part of the accretion disc heated by the X-rays. We discuss the properties of the model and compare them to the data. We show that the hot-flow scenario is consistent with many of the observed spectral data, at the same time naturally explaining X-ray timing properties, fast OIR variability and its correlation with the X-rays.
We present here the first convincing observational manifestation of a magnetar-like magnetic field in an accreting neutron star in binary system – the first pulsating ultraluminous X-ray source X−2 ...in the galaxy M82. Using the Chandra X-ray observatory data, we show that the source exhibit the bimodal distribution of the luminosity with two well-defined peaks separated by a factor of 40. This behaviour can be interpreted as the action of the ‘propeller regime’ of accretion. The onset of the propeller in a 1.37 s pulsar at luminosity of ∼1040 erg s−1 implies the dipole component of the neutron star magnetic field of ∼1014 G.
The accretion flow around X-ray pulsars with a strong magnetic field is funnelled by the field to relatively small regions close to the magnetic poles of the neutron star (NS), the hotspots. During ...strong outbursts regularly observed from some X-ray pulsars, the X-ray luminosity can be so high that the emerging radiation is able to stop the accreting matter above the surface via radiation-dominated shock, and the accretion column begins to rise. This border luminosity is usually called the ‘critical luminosity’. Here we calculate the critical luminosity as a function of the NS magnetic field strength B using the exact Compton scattering cross-section in a strong magnetic field. Influence of the resonant scattering and photon polarization is taken into account for the first time. We show that the critical luminosity is not a monotonic function of the B-field. It reaches a minimum of a few 1036 erg s−1 when the cyclotron energy is about 10 keV and a considerable amount of photons from a hotspot have energy close to the cyclotron resonance. For small B, this luminosity is about 1037 erg s−1, nearly independent of the parameters. It grows for the B-field in excess of 1012 G because of the drop in the effective cross-section of interaction below the cyclotron energy. We investigate how different types of the accretion flow and geometries of the accretion channel affect the results and demonstrate that the general behaviour of the critical luminosity on the B-field is very robust. The obtained results are shown to be in good agreement with the available observational data and provide a necessary ground for the interpretation of upcoming high-quality data from the currently operating and planned X-ray telescopes.
Recent observations of accreting black holes reveal the presence of quasi-periodic oscillations (QPO) in the optical power density spectra. The corresponding oscillation periods match those found in ...X-rays, implying a common origin. Among the numerous suggested X-ray QPO mechanisms, some may also work in the optical. However, their relevance to the broadband-optical through X-ray-spectral properties have not been investigated. For the first time, we discuss the QPO mechanism in the context of the self-consistent spectral model. We propose that the QPOs are produced by Lense-Thirring precession of the hot accretion flow, whose outer parts radiate in optical wavelengths. At the same time, its innermost parts are emitting X-rays, which explains the observed connection of QPO periods. We predict that the X-ray and optical QPOs should be either in phase or shifted by half a period, depending on the observer position. We investigate the QPO harmonic content and find that the variability amplitudes at the fundamental frequency are larger in the optical, while the X-rays are expected to have strong harmonics. We then discuss the QPO spectral dependence and compare the expectations to the existing data.
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