On the possibility of laboratory simulation of quasi-spherical accretion onto black holes with a shallow-water experimental setup

Abstract

We describe the concept of a shallow-water setup for simulation of gas accretion onto a black hole in the mode of a quasi-spherical accretion. The bottom for the shallow-water container must have the funnel-shaped curvilinear concavo-convex shape. We calculate the configuration surface of the properly shaped bottom that simulates precisely the Newtonian or pseudo-Newtonian gravitational potentials. Like the spatial part of the Schwarzchild metric, the funnel's surface metric has a (removable) singularity at the finite distance from the funnel's center and places the certain funnel's depth which we call `gravitational length'. The gravitational length is analogous to the gravitational radius and defines the equivalent of the black hole's mass in the laboratory model. The mass equivalent corresponds to $\sim 0.367\cdot 10^{12}$ g for the funnel as deep as 5 cm. We define more precisely the inviscid shallow water equations for the arbitrary bottom curvature. We show that in general case the shallow water pressure obeys the non-barotropic equation of state. We suggest the schematic course for experiments for simulation of accretion in a thick accretion disk mode as well as the Bondi-Hoyle accretion.