The fate of the debris of tidal disruption by a massive black hole in a dense star cluster

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Abstract
The fate of the debris of tidal disruption by a massive black hole in a dense star cluster is investigated for a variety of conditions. When the mass of the hole Mh does not exceed some |${10}^{3}\,{M}_{\odot}$| it is argued that the fate of the debris is best discussed in terms of annular clouds (‘donuts’) whose equilibrium is governed by gravity, rotation and radiation pressure. These donuts are assumed to have a polytropic structure and their evolution and fate is studied for different viscosities. The evolution of the debris is mainly governed by the relative importance of viscous effects to cooling. The results may be summarized by saying that the more effective viscosity is the smaller the fraction of mass accreted. This is so because initially the stellar debris is very loosely bound so that a small fraction of the total mass present can provide, when accreted, enough radiation to blow the remainder away. If on the other hand the donut cools faster than viscosity can operate to produce accretion, then the matter becomes increasingly bound and more will eventually be accreted. The results suggest that the fraction of mass accreted per tidal disruption is small. This may constitute a serious obstacle for the growth of a small ‘seed’ black hole. An alternative mechanism of production of massive holes may be necessary to provide an explanation of QSO luminosities using black holes. When Mh is substantially larger (⁠|$\gtrsim\,{10}^{6}\,{M}_{\odot}$|⁠, say) then the rate of disruptions is such that an individual cloud stays around longer than the mean time between disruptions. Collisions between clouds govern the subsequent evolution and rate of accretion as in the ‘debris cloud’ model of Hills.

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