An improved method for constructing models of self-gravitating tori around black holes

TL;DR

This paper presents a highly accurate numerical method for constructing self-gravitating torus models around black holes, capable of filling their Roche lobe, and investigates the limits of specific angular momentum in these models.

Contribution

It introduces an improved self-consistent-field method in compactified coordinates for modeling self-gravitating tori around black holes, with detailed analysis of angular momentum constraints.

Findings

Models with constant specific angular momentum filling their Roche lobe are limited by l<4M_BH.

The numerical code is highly accurate and robust.

Results scale with the black hole mass.

Abstract

General-relativistic models of self-gravitating tori around black holes are constructed with a self-consistent-field method in compactified coordinates. The numerical code is highly accurate and robust, allowing for the construction of models that exactly fill their Roche lobe, when a cusp exists. As a first application, we focus on self-consistent models with cusp, having different values of constant specific angular momentum. Scaling all results with the mass of the black hole, we find evidence that models with constant specific angular momentum that can fill their Roche lobe are still limited by $l<4M_{\rm BH}$ (as is the case for models constructed in a fixed background metric) even for heavy tori.