Steady shocks around black holes produced by sub-Keplerian flows with negative energy

We discuss a special case of formation of axisymmetric shocks in the accretion flowof ideal gas onto a Schwarzschild black hole: when the total energy of the flow isnegative. The result of our analysis enlarges the parameter space for which thesesteady shocks are exhibited in the accretion of gas rotating around relativistic stellarobjects. Since keplerian disks have negative total energy, we guess that, in this energyrange, the production of the shock phenomenon might be easier than in the case ofpositive energy. So our outcome reinforces the view that sub-keplerian flows of mattermay significantly affect the physics of the high energy radiation emission from blackhole candidates. We give a simple procedure to obtain analytically the position ofthe shocks. The comparison of the analytical results with the data of 1D and 2Daxisymmetric numerical simulations confirms that the shocks form and are stable.