Collisional dark matter density profiles around supermassive black holes

摘要: We solve the spherically symmetric time dependent relativistic Euler equations on a Schwarzschild background space-time for perfect fluid, where fluid models dark matter and is that of non-rotating supermassive black hole. consider obeys an ideal gas equation state as simple model with pressure. Assuming out equilibrium initial conditions we search late-time attractor type solutions, which found to show constant accretion rate non-zero pressure case, is, itself suffices produce stationary regimes. then analyze resulting density profile such solutions function A/r � . For different values adiabatic index find slopes profile, study in two regions: region one near hole, located from horizon up 50M 800M 1500M, hole 10 9 M⊙ corresponds 0.1pc. The depends or equivalently our findings are follows: shows κ < 1.5 limit pressure-less case ! 1.5; other hand, two, value 0.3 all cases studied. If these results be applied problem, conclusion that, cuspy only approaches non-cuspy at bigger scales within 1pc. These hand provide flat profiles presence central does not distort