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Study of Asymptotic Velocity in the Bondi-Hoyle Accretion Flows in the Domain of Kerr and 4-D Einstein-Gauss-Bonnet Gravities

Understanding the physical structures of the accreated matter very close to the black hole in quasars and active galactic nucleus (AGNs) is an important milestone to constrain the activities occurring in their centers. In this paper, we numerically investigate the effects of the asymptotic velocities on the physical structures of the accretion disk around the Kerr and Einstein-Gauss-Bonnet (EGB) rapidly rotating black holes. The Bondi-Hoyle accretion is considered with a falling gas towards the black hole in upstream region of the computational domain. The shock cones are naturally produced in the downstream part of the flow around both black holes. It is found that the structure of the cones and the amount of the accreated matter depend on asymptotic velocity $V_{\infty}$ (Mach number) and the types of the gravities (Kerr or EGB). Increasing the Mach number of the inflowing matter in the supersonic region causes the shock opening angle and accretion rates getting smaller because of the rapidly falling gas towards the black hole. The EGB gravity leads to an increase in the shock opening angle of the shock cones while the mass accretion rates $\dot{M}$ are decreasing in EGB gravity with a Gauss-Bonnet (GB) coupling constant $α$. It is also confirmed that accretion rates and drag forces are significantly altered in the EGB gravity. Our numerical simulation results could be used to identify the accreation mechanism and physical properties of the accretion disk and black hole in the observed $X-$ rays such as NGC $1313$ $X-1$ and $1313$ $X-2$ and MAXI $J1803-298$.