We model non-thermal emission spectrum of the extremely sub-Eddington X-ray binary system A0620-00. It is believed that this non-thermal emission is produced by a radiatively inefficient "quiescent" accretion onto a stellar-mass black hole present in the system. We post-process GRMHD simulations with multiwavelength, fully polarized, relativistic radiative transfer calculations to predict broadband spectra and emission polarization levels for a range of electron models and accretion rates. We find that a model with strong coupling of electrons and ions in the accretion disk and accretion rate of only $\dot{M}=3\times10^{-13} [M_\odot yr^{-1}]$ is able to recover the observed X-ray spectral slope as well as the excess of linear polarization detected in the source in NIR/optical bands. Our models constrain the spectral properties of a putative relativistic jet produced in this system. In addition we show that the magnetized winds from our hot accretion flow carry away a small fraction of the orbital angular momentum of the binary unable to explain the observed rapid orbital decay of the system. Similar to the present GRMHD simulations are often used to explain emission from sub-Eddington supermassvie black holes in Sgr A* or M87; the present simulations allow us to test whether some aspects of the quiescent black hole accretion are scale invariant.
We study the low angular momentum accretion of matter onto Schwarzschild or Kerr black hole using fully relativistic numerical simulations. Our aim is to include the rotation of both the gas and the black hole and the presence of the magnetic field into the picture. We compare resulting structure of transonic flow with results of 1D pseudo-Newtonian semi-analytical computations of non-magnetized flow.
We investigate a relativistic fluid jet driven by radiation from a shocked accretion disc around a non-rotating black hole approximated by Paczyński-Wiita potential. The sub-Keplerian and Keplerian accretion rates control the shock location and therefore, the radiation field around the accretion disc. We compute the radiative moments with full special relativistic transformation. The effect of a fraction of radiation absorbed by the black hole has been approximated, over and above the special relativistic transformations. We show that the radiative moments around a super massive black hole are…
We discuss the problem of the formation of a large-scale magnetic field in the accretion disks around black holes, taking into account the non-uniform vertical structure of the disk. The high electrical conductivity of the outer layers of the disk prevents the outward diffusion of the magnetic field. This implies a stationary state with a strong magnetic field in the inner parts of the accretion disk close to the black hole, and zero radial velocity at the surface of the disk. Structure of advective accretion disks is investigated, and conditions for formation of optically thin regions in cent…
We consider a temporal response of relativistically broadened line spectrum of iron from black hole accretion irradiated by an X-ray echo under strong gravity. The physical condition of accreting gas is numerically calculated in the context of general relativistic hydrodynamics under steady-state, axisymmetry in Kerr geometry. With the onset of a point-like X-ray flare of a short finite duration just above the accretion surface, the gas is assumed to be ionized to produce a neutral iron fluorescent line. Using a fully relativistic ray-tracing approach, the response of line photons due to the X…
Current state-of-the-art simulations of accretion flows onto black holes require a significant level of numerical sophistication, in order to allow the three-dimensional modelling of relativistic magnetised plasma in a regime of strong gravity. We present here a new version of the GRMHD code \texttt{ECHO} developed in collaboration with the Max Planck Computing and Data Facility (MPCDF) and the Leibniz Rechenzentrum (LRZ), which employs a hybrid multidimensional MPI-OpenMP coupled with the production of MPI-HDF5 output files. The code's high degree of parallelisation has been crucial for the s…
We investigated flow in Schwarzschild metric, around a non-rotating black hole and obtained self-consistent accretion - ejection solution in full general relativity. We covered the whole of parameter space in the advective regime to obtain shocked, as well as, shock-free accretion solution. We computed the jet streamline using von - Zeipel surfaces and projected the jet equations of motion on to the streamline and solved them simultaneously with the accretion disc equations of motion. We found that steady shock cannot exist {for $α\gsim0.06$} in the general relativistic prescription, but is lo…
Relativistic jets are launched from black hole (BH) X-ray binaries and active galactic nuclei when the disk accretion rate is below a certain limit (i.e., when the ratio of the accretion rate to the Eddingtion accretion rate, $\dot{m}$, is below about 0.01) but quenched when above. We propose a new paradigm to explain this observed coupling between the jet and the accretion disk by investigating the extraction of the rotational energy of a BH when it is surrounded by different types of accretion disk. At low accretion rates (e.g., when $\dot{m}\lesssim0.1$), the accretion near the event horizo…
We perform 1D/2D/3D relativistic hydrodynamical simulations of accretion flows with low angular momentum, filling the gap between spherically symmetric Bondi accretion and disc-like accretion flows. Scenarios with different directional distributions of angular momentum of falling matter and varying values of key parameters such as spin of central black hole, energy and angular momentum of matter are considered. In some of the scenarios the shock front is formed. We identify ranges of parameters for which the shock after formation moves towards or outwards the central black hole or the long las…
We have analyzed AstroSat observations of the galactic micro-quasar system GRS 1915+105, when the system exhibited C-type Quasi-periodic Oscillations (QPOs) in the frequency range of 3.4-5.4 Hz. The broad band spectra (1-50 keV) obtained from simultaneous LAXPC and SXT can be well described by a dominant relativistic truncated accretion disk along with thermal Comptonization and reflection. We find that while the QPO frequency depends on the inner radii with a large scatter, a much tighter correlation is obtained when both the inner radii and accretion rate of the disk are taken into account. …
In this paper we present a fully relativistic study of axisymmetric magnetohydrodynamic Bondi--Hoyle accretion onto a moving Kerr black hole. The equations of general relativistic magnetohydrodynamics are solved using high resolution shock capturing methods. In this treatment we consider the ideal MHD limit. The parameters of interest in this study are the adiabatic constant $Γ$, the asymptotic speed of sound $c_{s}^{\infty}$, and the plasma beta parameter $β_{P}$. We focus the investigation on the parameter regime in which the flow is supersonic, or when $v_\infty \ge c_{s}^{\infty}$. In some…
We use analytic estimates and numerical simulations of test particles interacting with magnetohydrodynamic (MHD) turbulence to show that subsonic MHD turbulence produces efficient second-order Fermi acceleration of relativistic particles. This acceleration is not well-described by standard quasi-linear theory but is a consequence of resonance broadening of wave-particle interactions in MHD turbulence. We provide momentum diffusion coefficients that can be used for astrophysical and heliospheric applications and discuss the implications of our results for accretion flows onto black holes. In pa…
We briefly summarize the method of simulating Sgr A* polarized sub-mm spectra from the accretion flow and fitting the observed spectrum. The dynamical flow model is based on three-dimensional general relativistic magneto hydrodynamic simulations. Fully self-consistent radiative transfer of polarized cyclo-synchrotron emission is performed. We compile a mean sub-mm spectrum of Sgr A* and fit it with the mean simulated spectra. We estimate the ranges of inclination angle theta=42-75deg, mass accretion rate Mdot=(1.4-7.0)*10^{-8}Msun/yr, and electron temperature Te=(3-4)*10^{10}K at 6M. We discus…
We describe HEROIC, an upgraded version of the relativistic radiative post-processor code HERO described in a previous paper, but which now Includes Comptonization. HEROIC models Comptonization via the Kompaneets equation, using a quadratic approximation for the source function in the short characteristics radiation solver. It employs a simple form of accelerated lambda iteration to handle regions of high scattering opacity. In addition to solving for the radiation field, HEROIC also solves for the gas temperature by applying the condition of radiative equilibrium. We present benchmarks and te…
A Kerr black hole (BH) surrounded by a neutrino-dominated accretion flow (NDAF) is one of plausible candidates of the central engine in gamma-ray bursts. The accretion material might inherit and restructure strong magnetic fields from the compact object mergers or massive collapsars. The magnetic coupling (MC) process between a rapid rotating BH and an accretion disc is one of possible magnetic configurations that transfers the energy and angular momentum from the BH to the disc. In this paper, we investigate one-dimensional global solutions of NDAFs with MC (MCNDAFs), taking into account gene…
The nearby accreting neutron star binary Sco X-1 is the closest example of ongoing relativistic jet production at high Eddington ratios. Previous radio studies have revealed that alongside mildly relativistic, radio-emitting ejecta, there is at times a much faster transfer of energy from the region of the accretion flow along the jet. The nature of this ultrarelativistic flow remains unclear and while there is some evidence for a similar phenomenon in other systems which might contain neutron stars, it has never been observed in a confirmed black hole system. We have compared these previous ra…
In this work we revisit the steady state, spherically symmetric gas accretion problem from the non-relativistic regime to the ultra-relativistic one. We first perform a detailed comparison between the Bondi and Michel models, and show how the mass accretion rate in the Michel solution approaches a constant value as the fluid temperature increases, whereas the corresponding Bondi value continually decreases, the difference between these two predicted values becoming arbitrarily large at ultra-relativistic temperatures. Additionally, we extend the Michel solution to the case of a fluid with an e…
We describe the implementation of sophisticated numerical techniques for general-relativistic magnetohydrodynamics simulations in the Athena++ code framework. Improvements over many existing codes include the use of advanced Riemann solvers and of staggered-mesh constrained transport. Combined with considerations for computational performance and parallel scalability, these allow us to investigate black hole accretion flows with unprecedented accuracy. The capability of the code is demonstrated by exploring magnetically arrested disks.
This work introduces a novel formalism to investigate the role of the spin of astrophysical black holes in determining the behaviour of matter falling onto such accretors. Equations describing the general relativistic hydrodynamic accretion flow in the Kerr metric are formulated, and stationary solutions for such flow equations are provided. The accreting matter may become multi-transonic, allowing a stationary shock to form for certain initial boundary conditions. Such a shock determines the disc geometry and can drive strong outflows. The properties of matter extremely close to the event hor…
We present a new, approximate method for modelling the acceleration and collimation of relativistic jets in the presence of gravity. This method is self-similar throughout the computational domain where gravitational effects are negligible and, where significant, self-similar within a flux tube. These solutions are applicable to jets launched from a small region (e.g., near the inner edge of an accretion disk). As implied by earlier work, the flow can converge onto the rotation axis, potentially creating a collimation shock. In this first version of the method, we derive the gravitational cont…
By performing 2.5-dimensional general relativistic radiation magnetohydrodynamic simulations, we demonstrate supercritical accretion onto a non-rotating, magnetized neutron star, where the magnetic field strength of dipole fields is $10^{10}$ G on the star surface. We found the supercritical accretion flow consists of two parts; the accretion columns and the truncated accretion disk. The supercritical accretion disk, which appears far from the neutron star, is truncated at around $\sim 3R_*$ ($R_*=10^6$ cm is the neutron star radius), where the magnetic pressure via the dipole magnetic fields …
Black hole X-ray binaries are ideal environments to test the accretion phenomena in the presence of strong gravitational potentials. KERRBB held an important place in the X-ray spectral continuum method for measuring the black hole spin modeling the emission from the innermost regions of the accretion disk. In this work, we present the results of X-ray spectral analysis using publicly available RXTE data of GRO J1655-40 obtained during the 2005 outburst with the two relativistic accretion disk models, KERRBB and KYNBB. Our analysis showed that both models provide identical results with black h…
We study the relativistic accretion flow around a generic stationary axisymmetric space-time and obtain an effective potential ($Φ^{\rm eff}$) that accurately mimics the general relativistic features of Kerr black hole having spin $0\le a_k <1$. Considering the accretion disc confined around the equatorial plane of a rotating black hole and using the relativistic equation of state, we examine the properties of the relativistic accretion flow and compare it with the same obtained form semi-relativistic as well as non-relativistic accretion flows. Towards this, we first investigate the transonic…
We present a relativistic model for the stationary axisymmetric accretion flow of a rotating cloud of non-interacting particles falling onto a Kerr black hole. Based on a ballistic approximation, streamlines are described analytically in terms of timelike geodesics, while a simple numerical scheme is introduced for calculating the density field. A novel approach is presented for describing all of the possible types of orbit by means of a single analytic expression. This model is a useful tool for highlighting purely relativistic signatures in the accretion flow dynamics coming from a strong gr…
High luminosity accretion onto a strongly magnetized neutron star results in a radiation pressure dominated, magnetically confined accretion column. We investigate the dynamics of these columns using two-dimensional radiative relativistic magnetohydrodynamic simulations, restricting consideration to modest accretion rates where the height of the column is low enough that Cartesian geometry can be employed. The column structure is dynamically maintained through high-frequency oscillations of the accretion shock at $\simeq 10-25$~kHz. These oscillations arise because it is necessary to redistrib…
We model, for the first time, the Bondi-Hoyle accretion of a fluid with velocity gradients onto a Kerr black hole, by numerically solving the fully relativistic hydrodynamics equations. Specifically, we consider a supersonic ideal gas, which has velocity gradients perpendicular to the relative motion. We measure the mass and specific angular accretion rates to illustrate whether the fluid presents unstable patterns or not. The initial parameters, we consider in this work, are the velocity gradient $ε_{v}$, the black hole spin $a$, the asymptotic Mach number ${\cal M}_{\infty}$ and adiabatic in…
We present bhlight, a numerical scheme for solving the equations of general relativistic radiation magnetohydrodynamics (GRRMHD) using a direct Monte Carlo solution of the frequency-dependent radiative transport equation. bhlight is designed to evolve black hole accretion flows at intermediate accretion rate, in the regime between the classical radiatively efficient disk and the radiatively inefficient accretion flow (RIAF), in which global radiative effects play a sub-dominant but non-negligible role in disk dynamics. We describe the governing equations, numerical method, idiosyncrasies of ou…
In this work, we present, for the first time, a numerical study of the Bondi-Hoyle accretion with density gradients in the fully relativistic regime. In this context, we consider accretion onto a Kerr Black Hole (BH) of a supersonic ideal gas, which has density gradients perpendicular to the relative motion. The set of parameters of interest in this study are the Mach number, M, the spin of the BH, a, and the density-gradient parameter of the gas, ρ . We show that, unlike in the Newtonian case, all the studied cases, especially those with density gradient, approach a stationary flow pattern. T…
Theoretical models for the production of relativistic jets from active galactic nuclei predict that jet power arises from the spin and mass of the central black hole, as well as the magnetic field near the event horizon. The physical mechanism mechanism underlying the contribution from the magnetic field is the torque exerted on the rotating black hole by the field amplified by the accreting material. If the squared magnetic field is proportional to the accretion rate, then there will be a correlation between jet power and accretion luminosity. There is evidence for such a correlation, but ina…
Matter makes a transition from non-relativistic to relativistic regime, as it falls onto a black hole. We employ a relativistic equation of state, abbreviated as RC, to study multi-species fluid flow around black holes. We show that pair-plasma fluid around a black hole is thermally not relativistic. In order to make it relativistic, a finite baryon loading is necessary. As a consequence of this, pair-plasma flow do not suffer centrifugal pressure driven shock in accretion. However, fluid with finite baryon content may undergo shock transition.
Standard accretion disc model relies upon several assumptions, the most important of which is geometrical thinness. Whenever this condition is violated, new physical effects become important such as radial energy advection and mass loss from the disc. These effects are important, for instance, for large mass accretion rates when the disc approaches its local Eddington limit. In this work, we study the upper limits for standard accretion disc approximation and find the corrections to the standard model that should be considered in any model aiming on reproducing the transition to super-Eddingto…
We study time evolution of sub-Keplerian transonic accretion flows onto black holes using a general relativistic numerical simulation code. We perform simulations around the black holes having non-zero rotation. We first compare one-dimensional simulation results with theoretical results and validate the performance of our code. Next, we present results of axisymmetric, two-dimensional simulation of advective flows. In the literature, there is no solution which describes steady shock solutions in two dimensions. However, our simulations produce these centrifugal force supported steady shock wa…
We present the global solutions of low angular momentum, inviscid, advective accretion flow around Kerr-Taub-NUT (KTN) black hole in presence and absence of shock waves. These solutions are obtained by solving the governing equations that describe the relativistic accretion flow in KTN spacetime which is characterized by the Kerr parameter ($a_{\rm k}$) and NUT parameter ($n$). During accretion, rotating flow experiences centrifugal barrier that eventually triggers the discontinuous shock transition provided the relativistic shock conditions are satisfied. In reality, the viability of shocked …
Theoretical models show that the power of relativistic jets of active galactic nuclei depends on the spin and mass of the central supermassive black holes, as well as the accretion. Here we report an analysis of archival observations of a sample of blazars. We find a significant correlation between jet kinetic power and the spin of supermassive black holes. At the same time, we use multiple linear regression to analyze the relationship between jet kinetic power and accretion, spin and black hole mass. We find that the spin of supermassive black holes and accretion are the most important contri…
The recent imaging of the M87 black hole at millimeter wavelengths by the Event Horizon Telescope (EHT) collaboration has triggered a renewed interest in numerical models for the accretion of magnetized plasma in the regime of general relativistic magnetohydrodynamics (GRMHD). Here non-ideal simulations, including both the resistive effects and, above all, the mean-field dynamo action due to sub-scale, unresolved turbulence, are applied for the first time to such systems in the fully nonlinear regime. Combined with the differential rotation of the disk, the dynamo process is able to produce an…
We present a novel analytic model of relativistic wind accretion on to a Schwarzschild black hole. This model constitutes a general relativistic extension of the classical model of wind accretion by Bondi, Hoyle, and Lyttleton (BHL). As in BHL, this model is based on the assumptions of steady state, axisymmetry, and ballistic motion. Analytic expressions are provided for the wind streamlines while simple numerical schemes are presented for calculating the corresponding accretion rate and density field. The resulting accretion rate is greater in the relativistic model when compared to the Newto…
We present not a literature review but a description, as detailed and consistent as possible, of two analytic models of disk accretion onto a rotating black hole: a standard relativistic disk and a twisted relativistic disk. Although one of these models is much older than the other, both are of topical current interest for black hole studies. The way the exposition is presented, the reader with only a limited knowledge of general relativity and relativistic hydrodynamics can --- with little or no use of additional sources -- gain good insight into many technical details lacking in the original…
We have calculated the relativistic reflection component of the X-ray spectra of accretion disks in active galactic nuclei (AGN). Our calculations have shown that the spectra can be significantly modified by the motion of the accretion flow and the gravity and rotation of the central black hole. The absorption edges in the spectra suffer severe energy shifts and smearing, and the degree of distortion depends on the system parameters, in particular, the inner radius of the accretion disk and the disk viewing inclination angles. The effects are significant. Fluorescent X-ray emission lines from …
We introduce a novel formalism to investigate the role of the spin angular momentum of astrophysical black holes in influencing the behaviour of low angular momentum general relativistic accretion. We propose a metric independent analysis of axisymmetric general relativistic flow, and consequently formulate the space and time dependent equations describing the general relativistic hydrodynamic accretion flow in the Kerr metric. The associated stationary critical solutions for such flow equations are provided and the stability of the stationary transonic configuration is examined using an elega…
In this work, we perform linear perturbation on general relativistic isothermal accretion onto a non-rotating astrophysical black hole to study the salient features of the corresponding emergent acoustic metric. For spherically symmetric accretion as well as for the axially symmetric matter flow for three different geometric configuration of matter, we perturb the velocity potential, the mass accretion rate, and the integral solution of the time independent part of the general relativistic Euler equation to obtain such acoustic geometry. We provide the procedure to locate the acoustic horizon …
We study time evolution of sub-Keplerian transonic accretion flows onto black holes using a general relativistic numerical simulation code. We perform simulations in Schwarzschild spacetime. We first compare one-dimensional simulation results with theoretical results and validate the performance of our code. Next, we present results of axisymmetric, two-dimensional simulation of advective flows. We find that even in this case, for which no complete theoretical analysis is present in the literature, steady state shock formation is possible.
In this paper we study the relativistic bulk tensor, shear tensor and the shear stress viscosity of the relativistic accretion disks around the rotating black holes. we calculate all non-zero components of the bulk tensor, shear tensor and shear stress viscosity in the equatorial plan in the BLF. We obtain the relations of the relativistic bulk tensor, shear tensor and shear stress viscosity in the terms of components of four velocity and derivatives, Christoffel symbols and metric components. To see the behaviorr of the components of relativistic bulk tensor, shear tensor and shear stress vis…
We linearly perturb advective isothermal transonic accretion onto rotating astrophysical black holes to study the emergence of the relativistic acoustic spacetime and to investigate how the salient features of such spacetime get influenced by the spin angular momentum of the black hole. We have perturbed three different quantities - the velocity potential, the mass accretion rate and the relativistic Bernoulli's constant to show that the acoustic metric obtained for these three cases are same up to a conformal factor. By constructing the required causal structures, it has been demonstrated tha…
Black hole accretion disks have been proposed as good candidates for a range of interesting nucleosynthesis, including the r-process. The presence of the black hole influences the neutrino fluxes and affects the nucleosynthesis resulting from the interaction of the emitted neutrinos and hot outflowing material ejected from the disk. We study the impact of general relativistic effects on the neutrinos emitted from black hole accretion disks. We present abundances obtained by considering null geodesics and energy shifts for two different disk models. We find that both the bending of the neutrino…
When an accretion disk falls prey to the runaway instability, a large portion of its mass is devoured by the black hole within a few dynamical times. Despite decades of effort, it is still unclear under what conditions such an instability can occur. The technically most advanced relativistic simulations to date were unable to find a clear sign for the onset of the instability. In this work, we present three-dimensional relativistic hydrodynamics simulations of accretion disks around black holes in dynamical space-time. We focus on the configurations that are expected to be particularly prone t…
Accreting neutron stars can power a wide range of astrophysical phenomena including short- and long-duration gamma-ray bursts, ultra-luminous X-ray sources, and X-ray binaries. Numerical simulations are a valuable tool for studying the accretion-disk--magnetosphere interaction that is central to these problems, most clearly for the recently discovered transitional millisecond pulsars. However, magnetohydrodynamic (MHD) methods, widely used for simulating accretion, have difficulty in highly magnetized stellar magnetospheres, while force-free methods, suitable for such regions, cannot include t…
Dissipations, e.g. heat flow and bulk and shear viscosities, cause the transport of energy, momentum and angular momentum, which is the essence of accretion of matters onto celestial objects. Dissipations are usually described by the Fourier and Navier-Stokes laws ("classic laws" of dissipations). However the classic laws result in an infinitely fast propagation of dissipations. In relativistic formulation, the classic laws of dissipations violate the causality, and hence no relativistic theory of accretion flow onto celestial object is formulated. In this short report, we summarize the causal…
We revisit Bondi accretion - steady-state, adiabatic, spherical gas flow onto a Schwarzschild black hole at rest in an asymptotically homogeneous medium - for stiff polytropic equations of state (EOSs) with adiabatic indices $Γ> 5/3$. A general relativistic treatment is required to determine their accretion rates, for which we provide exact expressions. We discuss several qualitative differences between results for soft and stiff EOSs - including the appearance of a minimum steady-state accretion rate for EOSs with $Γ\geq 5/3$ - and explore limiting cases in order to examine these differences.…
In this Letter, we present a new self-consistent theory for the production of the relativistic outflows observed from radio-loud black hole candidates and active galaxies as a result of particle acceleration in hot, viscous accretion disks containing standing, centrifugally-supported isothermal shocks. This is the first work to obtain the structure of such disks for a relatively large value of the Shakura-Sunyaev viscosity parameter ($α=0.1$), and to consider the implications of the shock for the acceleration of relativistic particles in viscous disks. In our approach, the hydrodynamics and th…
Ultra high-energy cosmic rays from relativistic outflows in accretion induced collapse of white dwarfs
Fermi National Accelerator Laboratory（费米国家加速器实验室）；Kavli Institute for Cosmological Physics, University of Chicago（芝加哥大学卡弗里宇宙物理研究所）；Institute of Science Tokyo（东京科学大学）；The University of Tokyo（东京大学）；Virginia Tech（弗吉尼亚理工大学）
Linear perturbation of general relativistic accretion of low angular momentum hydrodynamic fluid onto a Kerr black hole leads to the formation of curved acoustic geometry embedded within the background flow. Characteristic features of such sonic geometry depend on the black hole spin. Such dependence can be probed by studying the correlation of the acoustic surface gravity $κ$ with the Kerr parameter $a$. The $κ- a$ relationship further gets influenced by the geometric configuration of the accretion flow structure. In this work, such influence has been studied for multitransonic shocked accret…
In this paper we solve the hydrodynamical equations of optically thin, steady state accretion disks around Kerr black holes. Here, fully general relativistic equations are used. We use a new method to calculate the shear tensor in the LNRF (Locally Non-Rotating Frame), BLF (Boyer-Lindquist Frame) and FRF (Fluid Rest Frame). We show that two components of shear tensor in the FRF are nonzero (in previous works only one nonzero component was assumed). We can use these tensors in usual transonic solutions and usual causal viscosity, but we derive solutions analytically by some simplifications. The…
We construct a general relativistic radiative transfer (RT) formulation, applicable to particles with or without mass in astrophysical settings. Derived from first principles, the formulation is manifestly covariant. Absorption and emission, as well as relativistic, geometrical and optical depth effects are treated self-consistently. The RT formulation can handle 3D geometrical settings and structured objects with variations and gradients in the optical depths across the objects and along the line-of-sight. The presence of mass causes the intensity variation along the particle bundle ray to be…
In previous work, we derived the most general solution of the collisionless Boltzmann equation describing the accretion of a kinetic gas into a Schwarzschild black hole background, and we gave explicit expressions for the corresponding observables (the current density and stress energy-momentum tensor) in terms of certain integrals over the distribution function. In this article, we numerically compute these integrals for the particular case of the steady-state, spherical symmetric accretion flows which, at infinity, are described by an equilibrium distribution function of given temperature. W…
