Analytic solutions to the accretion of a rotating finite cloud towards a central object - II. Schwarzschild spacetime

Abstract

We construct a general relativistic model for the accretion flow of a rotating finite cloud of non-interacting particles infalling onto a Schwarzschild black hole. The streamlines start at a spherical shell, where boundary conditions are fixed, and are followed down to the point at which they either cross the black hole horizon or become incorporated into an equatorial thin disc. Analytic expressions for the streamlines and the velocity field are given, in terms of Jacobi elliptic functions, under the assumptions of stationarity and ballistic motion. A novel approach allows us to describe all of the possible types of orbit with a single formula. A simple numerical scheme is presented for calculating the density field. This model is the relativistic generalisation of the Newtonian one developed by Mendoza, Tejeda, Nagel, 2009 and, due to its analytic nature, it can be useful in providing a benchmark for general relativistic hydrodynamical codes and for exploring the parameter space in applications involving accretion onto black holes when the approximations of steady state and ballistic motion are reasonable ones.

12 pages, 6 figures, references and minor changes added to match version accepted for publication in MNRAS

References in corpus (2)

• The Galactic Center Massive Black Hole and Nuclear Star Cluster
• Long duration gamma-ray bursts: hydrodynamic instabilities in collapsar disks

Cited by in corpus (13)

• Chaotic cold accretion on to black holes in rotating atmospheres
• An accurate Newtonian description of particle motion around a Schwarzschild black hole
• Geodesic motion in the space-time of a non-compact boson star
• Charged Q-balls and boson stars and dynamics of charged test particles
• Bondi-type accretion in the Reissner-Nordström-(anti-)de Sitter spacetime
• Michel accretion of a polytropic fluid with adiabatic index gamma > 5/3: Global flows versus homoclinic orbits
• Relativistic wind accretion on to a Schwarzschild black hole
• Relativistic dust accretion of charged particles in Kerr-Newman spacetime
• An analytic toy model for relativistic accretion in Kerr spacetime
• Choked accretion onto a Kerr black hole
• Kinetic equilibria of relativistic collisionless plasmas in the presence of non-stationary electromagnetic fields
• Relativistic Low Angular Momentum Accretion: Long Time Evolution of Hydrodynamical Inviscid Flows
• Spherical accretion in the Schwarzschild spacetime in the Newtonian analogous construct