New closed analytical solutions for geometrically thick fluid tori around black holes: Numerical evolution and the onset of the magneto-rotational instability

TL;DR

This paper introduces new analytical solutions for thick fluid tori around black holes, investigates how initial conditions affect accretion and MRI onset, and demonstrates that final disk states are largely similar despite initial differences.

Contribution

It expands the set of known equilibrium solutions for thick accretion disks and analyzes their influence on MRI development and disk evolution.

Findings

Rotation curves critically influence MRI onset and early accretion rates.

Final disk states are qualitatively similar after ~10 orbital periods.

Accreted fluid energy can vary widely, sometimes exceeding rest mass energy.

Abstract

When a black hole is accreting well below the Eddington rate, a geometrically thick, radiatively inefficient state of the accretion disk is established. There is a limited number of closed-form physical solutions for geometrically thick (non-selfgravitating) toroidal equilibria of perfect fluids orbiting a spinning black hole, and these are predominantly used as initial conditions for simulations of accretion in the aforementioned mode. However, different initial configurations might lead to different results and thus observational predictions drawn from such simulations. We expand the known equilibria by a number of closed multiparametric solutions with various possibilities of rotation curves and geometric shapes. Then, we ask whether choosing these as initial conditions influences the onset of accretion and the asymptotic state of the disk. We investigate a set of examples from the derived solutions in detail; we analytically estimate the growth of the magneto-rotational instability (MRI) from their rotation curves and evolve the analytically obtained tori using the 2D magneto-hydrodynamical code HARM. Properties of the evolutions are then studied through the mass, energy, and angular-momentum accretion rates. The rotation curve has a decisive role in the numerical onset of accretion in accordance with our analytical MRI estimates: In the first few orbital periods, the average accretion rate is linearly proportional to the initial MRI rate in the toroids. The final state obtained from any initial condition within the studied class after an evolution of $\gtrsim 10$ orbital periods is mostly qualitatively identical and the quantitative properties vary within a single order of magnitude. The average values of the energy of the accreted fluid have an irregular dependency on initial data, and in some cases fluid with energies many times its rest mass is systematically accreted.