We extend our previous numerical simulation of accretion disks with shock waves when cooling e ects are also included. We consider bremsstrahlung and other power law processes: / T 2 to mimic cooling in our simulation. We employ Smoothed Particle Hydrodynamics technique as in the past. We observe that for a given angular momentum of the ow, the shock wave undergoes a steady,
Results of numerical simulations of shock solutions in a geometrical thin accretion disk around a Kerr black hole (BH) are presented. Using the smoothed particle hydrodynamics (SPH) technique, the in uence of the central object is included by means of an e ective potential, which is known to mimic the external Kerr geometry very well.We rst present the theory of standing shock formation in accretion disks around a Kerr black hole, and show that the results of our numerical simulation agree very well with the theoretical results. Using the pseudo-potential, our analysis gives at least a semi-quantitative impression into what a true general relativistic computation might reveal. The location of the shocks is found to be di erent for the co-rotating and the counter-rotating ows. Compared to accretion in the vicinity of a non-rotating BH, the position of the shock is shifted inwards for prograde accretion and outwards for retrograde accretion. We nd that the shocks in an inviscid ow are very stable. We also remove the ambiguity prevalent regarding the location and stability of shocks in adiabatic ows. Finally we sketch some of the astrophysical consequences of our ndings in relation to accretion disks in Active Galactic Nuclei (AGN) and Quasars.
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