An analytic toy model for relativistic accretion in Kerr spacetime
Abstract
We present a relativistic model for the stationary axisymmetric accretion flow of a rotating cloud of noninteracting particles falling on to 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 gravitational field with frame dragging. In particular, we explore the coupling due to this between the spin of the black hole and the angular momentum of the infalling matter. Moreover, we demonstrate how this analytic solution may be used for benchmarking general relativistic numerical hydrodynamics codes by comparing it against results of smoothed particle hydrodynamics simulations for a collapsarlike setup. These simulations are performed first for a ballistic flow (with zero pressure) and then for a hydrodynamical one where we measure the effects of pressure gradients on the infall, thus exploring the extent of applicability of the ballistic approximation.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 February 2013
 DOI:
 10.1093/mnras/sts316
 arXiv:
 arXiv:1207.0733
 Bibcode:
 2013MNRAS.429..925T
 Keywords:

 accretion;
 accretion discs;
 black hole physics;
 Astrophysics  High Energy Astrophysical Phenomena
 EPrint:
 15 pages, 8 figures, references and minor changes added to match version accepted for publication in MNRAS