An analytic toy model for relativistic accretion in Kerr spacetime

TL;DR

This paper introduces an analytical relativistic model for axisymmetric accretion onto Kerr black holes, capturing the effects of frame-dragging and providing a benchmark for numerical simulations of accretion flows.

Contribution

It presents a novel analytic approach to describe all orbit types in relativistic accretion, including a simple scheme for density calculation, and explores the coupling between black hole spin and infalling matter.

Findings

Analytic expressions for all orbit types in Kerr spacetime.

Benchmarking tool for relativistic hydrodynamics codes.

Insights into spin-angular momentum coupling effects.

Abstract

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 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 collapsar-like 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.