Viscous accretion and ejection from tori around black holes in general relativity

We systematically perform long-term (millions of Schwarzschild time) axisymmetric viscous hydrodynamics simulations for tori around black holes in general relativity supposing the super-Eddington accretion flow. The initial condition for the tori is modeled simply by the Fishbone-Moncrief torus with a constant specific angular momentum <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>j</a:mi></a:math> but with a wide variety of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>j</c:mi></c:math>. Such a torus may be a remnant after tidal disruption of ordinary stars near a relatively low-mass supermassive black hole or an outcome of an inflow of the matter with a low specific angular momentum. We find that, for a given density profile, the fraction of the mass infall onto the black hole is approximately proportional to <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mi>j</e:mi><e:mrow><e:mo>−</e:mo><e:mn>1</e:mn></e:mrow></e:msup></e:math>, indicating that only a minor fraction of the matter in the torus formed far from the black hole falls into the black hole, while the majority is ejected with the typical average velocity of a few percent of the speed of light. We also find that the mass ejection is driven only outside <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mo>≈</g:mo><g:mn>2</g:mn><g:msub><g:mrow><g:mi>r</g:mi></g:mrow><g:mrow><g:mi>ISCO</g:mi></g:mrow></g:msub></g:mrow></g:math>, where <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>r</i:mi><i:mrow><i:mi>ISCO</i:mi></i:mrow></i:msub></i:math> is the areal radius of the innermost stable circular orbit around black holes, which depends strongly on the black hole spin. We derive an approximate fitting formula for the spin dependence on the mass infall fraction as <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:mo>∝</k:mo><k:msubsup><k:mrow><k:mi>r</k:mi></k:mrow><k:mrow><k:mi>ISCO</k:mi></k:mrow><k:mrow><k:mn>0.7</k:mn></k:mrow></k:msubsup></k:mrow></k:math>, which suggests that the rapid growth of supermassive black holes proceeded primarily by the accretion of the matter with the angular momentum counterrotating with the black hole spin.