Comptonization in Ultra-Strong Magnetic Fields: Numerical Solution to the Radiative Transfer Problem

We consider the radiative transfer problem in a plane-parallel slab of thermal electrons in the presence of an ultra-strong magnetic field (B approximately greater than B(sub c) approx. = 4.4 x 10(exp 13) G). Under these conditions, the magnetic field behaves like a birefringent medium for the propagating photons, and the electromagnetic radiation is split into two polarization modes, ordinary and extraordinary, that have different cross-sections. When the optical depth of the slab is large, the ordinary-mode photons are strongly Comptonized and the photon field is dominated by an isotropic component. Aims. The radiative transfer problem in strong magnetic fields presents many mathematical issues and analytical or numerical solutions can be obtained only under some given approximations. We investigate this problem both from the analytical and numerical point of view, provide a test of the previous analytical estimates, and extend these results with numerical techniques. Methods. We consider here the case of low temperature black-body photons propagating in a sub-relativistic temperature plasma, which allows us to deal with a semi-Fokker-Planck approximation of the radiative transfer equation. The problem can then be treated with the variable separation method, and we use a numerical technique to find solutions to the eigenvalue problem in the case of a singular kernel of the space operator. The singularity of the space kernel is the result of the strong angular dependence of the electron cross-section in the presence of a strong magnetic field. Results. We provide the numerical solution obtained for eigenvalues and eigenfunctions of the space operator, and the emerging Comptonization spectrum of the ordinary-mode photons for any eigenvalue of the space equation and for energies significantly lesser than the cyclotron energy, which is on the order of MeV for the intensity of the magnetic field here considered. Conclusions. We derived the specific intensity of the ordinary photons, under the approximation of large angle and large optical depth. These assumptions allow the equation to be treated using a diffusion-like approximation

Numerical solution of the radiative transfer equation: X-ray spectral formation from cylindrical accretion onto a magnetized neutron star

Predicting the emerging X-ray spectra in several astrophysical objects is of great importance, in particular when the observational data are compared with theoretical models. To this aim, we have developed an algorithm solving the radiative transfer equation in the Fokker-Planck approximation when both thermal and bulk Comptonization take place. The algorithm is essentially a relaxation method, where stable solutions are obtained when the system has reached its steady-state equilibrium. We obtained the solution of the radiative transfer equation in the two-dimensional domain defined by the photon energy E and optical depth of the system tau using finite-differences for the partial derivatives, and imposing specific boundary conditions for the solutions. We treated the case of cylindrical accretion onto a magnetized neutron star. We considered a blackbody seed spectrum of photons with exponential distribution across the accretion column and for an accretion where the velocity reaches its maximum at the stellar surface and at the top of the accretion column, respectively. In both cases higher values of the electron temperature and of the optical depth tau produce flatter and harder spectra. Other parameters contributing to the spectral formation are the steepness of the vertical velocity profile, the albedo at the star surface, and the radius of the accretion column. The latter parameter modifies the emerging spectra in a specular way for the two assumed accretion profiles. The algorithm has been implemented in the XSPEC package for X-ray spectral fitting and is specifically dedicated to the physical framework of accretion at the polar cap of a neutron star with a high magnetic field (> 10^{12} G), which is expected to be typical of accreting systems such as X-ray pulsars and supergiant fast X-ray transients.Comment: 13 pages, 20 figures, accepted for publication in A&

A search for pulsars around Sgr A* in the first Event Horizon Telescope data set

In 2017 the Event Horizon Telescope (EHT) observed the supermassive black hole at the center of the Milky Way, Sagittarius A* (Sgr A*), at a frequency of 228.1 GHz (λ = 1.3 mm). The fundamental physics tests that even a single pulsar orbiting Sgr A* would enable motivate searching for pulsars in EHT data sets. The high observing frequency means that pulsars—which typically exhibit steep emission spectra—are expected to be very faint. However, it also negates pulse scattering, an effect that could hinder pulsar detections in the Galactic center. Additionally, magnetars or a secondary inverse Compton emission could be stronger at millimeter wavelengths than at lower frequencies. We present a search for pulsars close to Sgr A* using the data from the three most sensitive stations in the EHT 2017 campaign: the Atacama Large Millimeter/submillimeter Array, the Large Millimeter Telescope, and the IRAM 30 m Telescope. We apply three detection methods based on Fourier-domain analysis, the fast folding algorithm, and single-pulse searches targeting both pulsars and burst-like transient emission. We use the simultaneity of the observations to confirm potential candidates. No new pulsars or significant bursts were found. Being the first pulsar search ever carried out at such high radio frequencies, we detail our analysis methods and give a detailed estimation of the sensitivity of the search. We conclude that the EHT 2017 observations are only sensitive to a small fraction (≲2.2 of the pulsars that may exist close to Sgr A*, motivating further searches for fainter pulsars in the region

Correlating spectral and timing properties in the evolving jet of the micro blazar MAXI J1836-194

During outbursts, the observational properties of black hole X-ray binaries (BHXBs) vary on timescales of days to months. These relatively short timescales make these systems ideal laboratories to probe the coupling between accreting material and outflowing jets as a the accretion rate varies. In particular, the origin of the hard X-ray emission is poorly understood and highly debated. This spectral component, which has a power-law shape, is due to Comptonisation of photons near the black hole, but it is unclear whether it originates in the accretion flow itself, or at the base of the jet, or possibly the interface region between them. In this paper we explore the disk-jet connection by modelling the multi-wavelength emission of MAXI J1836-194 during its 2011 outburst. We combine radio through X-ray spectra, X-ray timing information, and a robust joint-fitting method to better isolate the jet's physical properties. Our results demonstrate that the jet base can produce power-law hard X-ray emission in this system/outburst, provided that its base is fairly compact and that the temperatures of the emitting electrons are sub-relativistic. Because of energetic considerations, our model favours mildly pair-loaded jets carrying at least 20 pairs per proton. Finally, we find that the properties of the X-ray power spectrum are correlated with the jet properties, suggesting that an underlying physical process regulates both.Comment: 17 pages, 10 figures, accepted for publication on MNRA

Combining timing characteristics with physical broad-band spectral modelling of black hole X-ray binary GX 339–4

GX 339–4 is a black hole X-ray binary that is a key focus of accretion studies, since it goes into outburst roughly every 2–3 yr. Tracking of its radio, infrared (IR), and X-ray flux during multiple outbursts reveals tight broad-band correlations. The radio emission originates in a compact, self-absorbed jet; however, the origin of the X-ray emission is still debated: jet base or corona? We fit 20 quasi-simultaneous radio, IR, optical, and X-ray observations of GX 339–4 covering three separate outbursts in 2005, 2007, 2010–2011, with a composite corona+jet model, where inverse Compton emission from both regions contributes to the X-ray emission. Using a recently proposed identifier of the X-ray variability properties known as power-spectral hue, we attempt to explain both the spectral and evolving timing characteristics, with the model. We find the X-ray spectra are best fit by inverse Compton scattering in a dominant hot corona (kT_e ∼ hundreds of keV). However, radio and IR-optical constraints imply a non-negligible contribution from inverse Compton scattering off hotter electrons (kT_e ≥ 511 keV) in the base of the jets, ranging from a few up to ∼50 per cent of the integrated 3–100 keV flux. We also find that the physical properties of the jet show interesting correlations with the shape of the broad-band X-ray variability of the source, posing intriguing suggestions for the connection between the jet and corona

Polarimetric geometric modeling for mm-VLBI observations of black holes

The Event Horizon Telescope (EHT) is a millimeter very long baseline interferometry (VLBI) array that has imaged the apparent shadows of the supermassive black holes M87* and Sagittarius A*. Polarimetric data from these observations contain a wealth of information on the black hole and accretion flow properties. In this work, we develop polarimetric geometric modeling methods for mm-VLBI data, focusing on approaches that fit data products with differing degrees of invariance to broad classes of calibration errors. We establish a fitting procedure using a polarimetric "m-ring" model to approximate the image structure near a black hole. By fitting this model to synthetic EHT data from general relativistic magnetohydrodynamic models, we show that the linear and circular polarization structure can be successfully approximated with relatively few model parameters. We then fit this model to EHT observations of M87* taken in 2017. In total intensity and linear polarization, the m-ring fits are consistent with previous results from imaging methods. In circular polarization, the m-ring fits indicate the presence of event-horizon-scale circular polarization structure, with a persistent dipolar asymmetry and orientation across several days. The same structure was recovered independently of observing band, used data products, and model assumptions. Despite this broad agreement, imaging methods do not produce similarly consistent results. Our circular polarization results, which imposed additional assumptions on the source structure, should thus be interpreted with some caution. Polarimetric geometric modeling provides a useful and powerful method to constrain the properties of horizon-scale polarized emission, particularly for sparse arrays like the EHT