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&

The prototype X-ray binary GX 339-4:using TeV γ-rays to assess LMXBs as Galactic cosmic ray accelerators

Since the discovery of cosmic rays (CRs) over a century ago, their origin remains an open question. Galactic CRs with energy up to the knee ($10^{15}$ eV) are considered to originate from supernova remnants, but this scenario has recently been questioned due to lack of TeV $\gamma$-ray counterparts in many cases. Extragalactic CRs on the other hand, are thought to be associated with accelerated particles in the relativistic jets launched by supermassive accreting black holes at the center of galaxies. Scaled down versions of such jets have been detected in X-ray binaries hosting a stellar black hole (BHXBs). In this work, we investigate the possibility that the smaller-scale jets in transient outbursts of low-mass BHXBs could be sources of Galactic CRs. To better test this scenario, we model the entire electromagnetic spectrum of such sources focusing on the potential TeV regime, using the `canonical' low-mass BHXB GX 339-4 as a benchmark. Taking into account both the leptonic radiative processes and the $\gamma$-rays produced via neutral pion decay from inelastic hadronic interactions, we predict the GeV and TeV $\gamma$-ray spectrum of GX 339-4 using lower-frequency emission as constraints. Based on this test-case of GX 339-4 we investigate whether other, nearby low-mass BHXBs could be detected by the next-generation very-high-energy $\gamma$-ray facility the Cherenkov Telescope Array, which would establish them as additional and numerous potential sources of CRs in the Galaxy.Comment: 13 pages, 12 figures, accepted to MNRA

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