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 Physics , 2001, DOI: 10.1086/324717 Abstract: We consider the radial structure of radiatively inefficient hydrodynamic accretion flows around black holes. We show that low-viscosity flows consist of two zones: an outer convection-dominated zone and an inner advection-dominated zone. The transition between these two zones occurs at ~50 Schwarzschild radii.
 Sandip K. Chakrabarti Physics , 1996, DOI: 10.1016/0370-1573(95)00057-7 Abstract: We describe astrophysical processes around a black hole keeping primarily the physics of accretion in mind. In Section 1, we briefly discuss the formation, evolution and detection of black holes. We also discuss the difference of flow properties around a black hole and a Newtonian star. In Section 2, we present past and present developments in the study of spherically accreting flows. We study the properties of Bondi flow with and without radiative transfer. In the presence of significant angular momentum, which is especially true in a binary system, matter will be accreted as a thin Keplerian disk. In Section 3, we discuss a large number of models of these disks including the more popular standard disk model. We present magnetized disk models as well. Since the angular momentum is high in these systems, rotational motion is the most dominant component compared to the radial or the vertical velocity components. In Section 4, we study thick disk models which are of low angular momentum but still have no significant radial motion. The accretion rates could be very high causing the flow to become radiation dominated and the disk to be geometrically thick. For low accretion rates, ion pressure supported disks are formed. In Section 5, we extensively discuss the properties of transonic flows which has with sub-Keplerian angular momentum. In the absence of shock discontinuities, these sub-Keplerian flows are basically advecting, similar to Bondi flows, close to the black holes, though far away they match Keplerian or sub-Keplerian disks. In presence of shocks, the post-shock flow becomes rotation dominated similar to thick disks. In Section 6, we present results of important numerical simulations of accretion flows. Significant results from the studies of evolution of viscous transonic flows are reported. In Section 7, we discuss some observational evidences of the black hole accretion. We also present a detailed model of a generalized accretion disk and present its spectra and compare with observations. In Section 8, we summarize the review and make concluding remarks.
 Physics , 2003, DOI: 10.1086/375773 Abstract: We report on the second phase of our study of slightly rotating accretion flows onto black holes. We consider magnetohydrodynamical (MHD) accretion flows with a spherically symmetric density distribution at the outer boundary, but with spherical symmetry broken by the introduction of a small, latitude-dependent angular momentum and a weak radial magnetic field. We study accretion flows by means of numerical 2D, axisymmetric, MHD simulations with and without resistive heating. Our main result is that the properties of the accretion flow depend mostly on an equatorial accretion torus which is made of the material that has too much angular momentum to be accreted directly. The torus accretes, however, because of the transport of angular momentum due to the magnetorotational instability (MRI). Initially, accretion is dominated by the polar funnel, as in the hydrodynamic inviscid case, where material has zero or very low angular momentum. At the later phase of the evolution, the torus thickens towards the poles and develops a corona or an outflow or both. Consequently, the mass accretion through the funnel is stopped. The accretion of rotating gas through the torus is significantly reduced compared to the accretion of non-rotating gas (i.e., the Bondi rate). It is also much smaller than the accretion rate in the inviscid, weakly rotating case.Our results do not change if we switch on or off resistive heating. Overall our simulations are very similar to those presented by Stone, Pringle, Hawley and Balbus despite different initial and outer boundary conditions. Thus, we confirm that MRI is very robust and controls the nature of radiatively inefficient accretion flows.
 Physics , 2015, DOI: 10.1093/mnras/stv2397 Abstract: The metal-poor gas continuously accreting onto the discs of spiral galaxies is unlikely to arrive from the intergalactic medium (IGM) with exactly the same rotation velocity as the galaxy itself and even a small angular momentum mismatch inevitably drives radial gas flows within the disc, with significant consequences to galaxy evolution. Here we provide some general analytic tools to compute accretion profiles, radial gas flows and abundance gradients in spiral galaxies as a function of the angular momentum of accreting material. We generalize existing solutions for the decomposition of the gas flows, required to reproduce the structural properties of galaxy discs, into direct accretion from the IGM and a radial mass flux within the disc. We then solve the equation of metallicity evolution in the presence of radial gas flows with a novel method, based on characteristic lines, which greatly reduces the numerical demand on the computation and sheds light on the crucial role of boundary conditions on the abundance profiles predicted by theoretical models. We also discuss how structural and chemical constraints can be combined to disentangle the contributions of inside-out growth and radial flows in the development of abundance gradients in spiral galaxies. Illustrative examples are provided throughout with parameters plausible for the Milky Way. We find that the material accreting on the Milky Way should rotate at 70-80 per cent of the rotational velocity of the disc, in agreement with previous estimates.
 Dimitrios Psaltis Physics , 2000, DOI: 10.1086/323329 Abstract: I study the formation of Comptonization spectra in spherically symmetric, fast moving media in a flat spacetime. I analyze the mathematical character of the moments of the transfer equation in the system-frame and describe a numerical method that provides fast solutions of the time-independent radiative transfer problem that are accurate in both the diffusion and free-streaming regimes. I show that even if the flows are mildly relativistic (V~0.1, where V is the electron bulk velocity in units of the speed of light), terms that are second-order in V alter the emerging spectrum both quantitatively and qualitatively. In particular, terms that are second-order in V produce power-law spectral tails, which are the dominant feature at high energies, and therefore cannot be neglected. I further show that photons from a static source are upscattered by the bulk motion of the medium even if the velocity field does not converge. Finally, I discuss these results in the context of radial accretion onto and outflows from compact objects.
 Physics , 2015, Abstract: In this paper, we investigate the Michel-type accretion onto a static spherically symmetric black hole. We first show that, for a perfect fluid, this type of accretion yields a formula for the pressure that is the sign-inverse of the Legendre transform of the energy density, which in turn yields a first order differential equation for the determination of thermodynamic state functions. We formulate the problem in terms of a Hamiltonian dynamical system. Using the isothermal and polytropic equations of state, we show that the standard method employed for tackling the accretion problem has masked some important properties of the fluid flow. Contrary to what is generally stated in the literature, we determine new analytical solutions that are neither transonic nor supersonic as the fluid approaches the horizon(s); rather, they remain subsonic for all values of the radial coordinate. Moreover, the three-dimensional speed vanishes and the pressure diverges on the horizon(s), resulting in a flowout of the fluid under the effect of its own pressure. This is in favor of an earlier prediction that pressure-dominant regions form near the horizon. This result does not depend on the form of the metric and it applies to a neighborhood of any horizon where the time coordinate is timelike. For anti-de Sitter-like f(R) black holes we discuss the stability of the critical flow and determine separatrix heteroclinic orbits. We show that the polytropic test fluid has no global solutions for the class of f(R) gravity we consider in this work and its subsonic flow is almost non-relativistic. For de Sitter-like f(R) black holes with two horizons, we construct polytropic cyclic, non-homoclinic, physical flows connecting the two horizons. These flows become non-relativistic for Hamiltonian values higher than the critical value allowing for a good estimate of the proper period of the flow.
 Roman V. Shcherbakov Physics , 2008, DOI: 10.1086/588609 Abstract: The first spherical accretion model was developed 55 years ago, but the theory is yet far from being complete. The real accretion flow was found to be time-dependent and turbulent. This paper presents the minimal MHD spherical accretion model that separately deals with turbulence. Treatment of turbulence is based on simulations of several regimes of collisional MHD. The effects of freezing-in amplification, dissipation, dynamo action, isotropization, and constant magnetic helicity are self-consistently included. The assumptions of equipartition and magnetic field isotropy are released. Correct dynamics of magnetized flow is calculated. Diffusion, convection, and radiation are not accounted for. Two different types of Radiatively Inefficient accretion flows are found: a transonic non-rotating flow (I), a flow with effective transport of angular momentum outward (II). Non-rotating flow has an accretion rate several times smaller than Bondi rate, because turbulence inhibits accretion. Flow with angular momentum transport has accretion rate about 10-100 times smaller than Bondi rate. The effects of highly helical turbulence, states of outer magnetization, and different equations of state are discussed. The flows were found to be convectively stable on average, despite gas entropy increases inward. The proposed model has a small number of free parameters and the following attractive property. Inner density in the non-rotating magnetized flow was found to be several times lower than density in a non-magnetized accretion. Still several times lower density is required to explain the observed low IR luminosity and low Faraday rotation measure of accretion onto Sgr A*.
 Physics , 1999, Abstract: Significant nucleosynthesis is possible in the centrifugal pressure-supported dense and hot region of the accretion flows which deviate from Keplerian disks around black holes. We compute composition changes and energy generations due to such nuclear processes. We use a network containing 255 species and follow the changes in composition. Highly viscous, high-accretion-rate flows deviate from a Keplerian disk very close to the black hole and the temperature of the flow is very small due to Compton cooling. No significant nucleosynthesis takes place in these cases. Low-viscosity and lower-accretion-rate hot flows deviate farther out and significant changes in composition are possible in these cases. We suggest that such changes in composition could be contributing to the metallicities of the galaxies. Moreover, the radial variation of the energy generation/absorption specifically due to proton capture and photo-dissociation reactions could cause instabilities in the inner regions of the accretion flows. For most of these cases sonic point oscillations may take place. We discuss the possibility of neutrino emissions.
 Physics , 2012, DOI: 10.1088/0004-637X/761/2/129 Abstract: Numerical simulations of hot accretion flow have shown that the mass accretion rate decreases with decreasing radius; consequently the density profile of accretion flow becomes flatter compared to the case of a constant accretion rate. This result has important theoretical and observational implications. However, because of technical difficulties, the radial dynamic range in almost all previous simulations usually spans at most two orders of magnitude. This small dynamical range, combined with the effects of boundary conditions, makes the simulation results suspectable. Especially, the radial profiles of density and accretion rate may not be precise enough to be used to compare with observations. In this paper we present a "two-zone" approach to expand the radial dynamical range from two to four orders of magnitude. We confirm previous results and find that from $r_s$ to $10^4r_s$ the radial profiles of accretion rate and density can be well described by $\dot{M}(r)\propto r^s$ and $\rho\propto r^{-p}$. The values of (s, p) are (0.48, 0.65) and (0.4, 0.85), for viscous parameter $\alpha=0.001$ and 0.01, respectively. We have looked up numerical simulation works in the literature and found that the values of $s$ and $p$ are all similar, no matter a magnetic field is included or not and what kind of initial conditions are adopted. The density profile we obtain is in good quantitative agreement with that obtained from the detailed observations and modeling to Sgr A* and NGC 3115. The origin of such a accretion rate profile will be investigated in a subsequent paper.
 Physics , 2000, Abstract: The evolution of an initially stellar dipole type magnetosphere interacting with an accretion disk is investigated numerically using the ideal MHD ZEUS-3D code in the 2D-axisymmetry option. The simulations last several thousands of Keplerian periods of the inner disk. A Keplerian disk is assumed as a boundary condition prescribing a mass inflow into the corona. Additionally, a stellar wind from a rotating central star is prescribed. Our major result is that the initially dipole type field develops into a spherically radial outflow pattern with two main components, a disk wind and a stellar wind component. These components evolve into a quasi- stationary final state. The poloidal field lines follow a conical distribution. As a consequence of the initial dipole, the field direction in the stellar wind is opposite to that in the disk wind. The maximum speed of the outflow is about the Keplerian speed at the inner disk radius. With the chosen mass flow rates and field strength we see almost no indication for a flow self-collimation.
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