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Numerical analysis of the ultrarelativistic and magnetized Bondi--Hoyle problem Penner, Andrew Jason

Abstract

In this thesis, we present numerical studies of models for the accretion of fluids and magnetofluids onto rotating black holes. Specifically, we study three main scenarios, two of which treat accretion of an unmagnetized perfect fluid characterized by an internal energy sufficiently large that the rest-mass energy of the fluid can be ignored. We call this the ultrarelativistic limit, and use it to investigate accretion flows which are either axisymmetric or restricted to a thin disk. For the third scenario, we adopt the equations of ideal magnetohydrodyamics and consider axisymmetric solutions. In all cases, the black hole is assumed to be moving with fixed velocity through a fluid which has constant pressure and density at large distances. Because all of the simulated flows are highly nonlinear and supersonic, we use modern computational techniques capable of accurately dealing with extreme solution features such as shocks. In the axisymmetric ultrarelativistic case, we show that the accretion is described by steady-state solutions characterized by well-defined accretion rates which we compute, and are in reasonable agreement with previously reported results by Font and collaborators [1,2,3]. However, in contrast to this earlier work with moderate energy densities, where the computed solutions always had tail shocks, we find parameter settings for which the time-independent solutions contain bow shocks. For the ultrarelativistic thin-disk models, we find steady-state configurations with specific accretion rates and observe that the flows simultaneously develop both a tail shock and a bow shock. For the case of axisymmetric accretion using a magnetohydrodynamic perfect fluid, we align the magnetic field with the axis of symmetry. Preliminary results suggest that the resulting flows remain time-dependent at late times, although we cannot conclusively rule out the existence of steady-state solutions. Moreover, the flow morphology is different in the magnetic case: additional features are apparent that include an evacuated region near the symmetry axis and close to the black hole.

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