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When a black hole is accreting well below the Eddington rate, a geometricallythick, radiatively inefficient state of the accretion disk is established.There is a limited number of closed-form physical solutions for geometricallythick (non-selfgravitating) toroidal equilibria of perfect fluids orbiting aspinning black hole, and these are predominantly used as initial conditions forsimulations of accretion in the aforementioned mode. However, different initialconfigurations might lead to different results and thus observationalpredictions drawn from such simulations.  We expand the known equilibria by a number of closed multiparametricsolutions with various possibilities of rotation curves and geometric shapes.Then, we ask whether choosing these as initial conditions influences the onsetof accretion and the asymptotic state of the disk.  We investigate a set of examples from the derived solutions in detail; weanalytically estimate the growth of the magneto-rotational instability (MRI)from their rotation curves and evolve the analytically obtained tori using the2D magneto-hydrodynamical code HARM. Properties of the evolutions are thenstudied through the mass, energy, and angular-momentum accretion rates.  The rotation curve has a decisive role in the numerical onset of accretion inaccordance with our analytical MRI estimates: In the first few orbital periods,the average accretion rate is linearly proportional to the initial MRI rate inthe toroids. The final state obtained from any initial condition within thestudied class after an evolution of $\gtrsim 10$ orbital periods is mostlyqualitatively identical and the quantitative properties vary within a singleorder of magnitude. The average values of the energy of the accreted fluid havean irregular dependency on initial data, and in some cases fluid with energiesmany times its rest mass is systematically accreted.

astronomy and astrophysics

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