General relativistic magnetohydrodynamic Bondi-Hoyle accretion

Abstract

In this paper, we present a fully relativistic study of axisymmetric magnetohydrodynamic (MHD) Bondi–Hoyle accretion on to a moving Kerr black hole. The equations of general relativistic MHD are solved using high‐resolution shock‐capturing methods. In this treatment, we consider the ideal MHD limit. The parameters of interest in this study are the adiabatic constant Γ, the asymptotic speed of sound c∞s and the plasma β parameter βP. We focus the investigation on the parameter regime in which the flow is supersonic or when v∞≥c∞s. In some cases, subsonic asymptotic flows are considered for comparison purposes. We study the accretion rates of the total energy and momenta, as well as the hydrodynamic energy and momentum accretion rates. The models presented in this study exhibit a matter density depletion in the downstream region of the black hole which tends to vacuum (ρ0= 0) in convergence tests. This feature is due to the presence of the magnetic field, more specifically the magnetic pressure, and is not seen in previous purely hydrodynamic studies.

GRHydro: a new open-source general-relativistic magnetohydrodynamics code for the Einstein toolkit

“…An important aspect of any GRMHD scheme is the numerical method used to preserve the divergence free constraint. GRHydro implements both the hyperbolic divergence cleaning method (e.g., [43,44]) and a variant of the constrained transport method (e.g., [42,45,86]), which are both discussed in detail in section 4.4.…”

“…Divergence cleaning works by introducing a new field variable that both damps divergences and advects them off the grid through a hyperbolic equation modelled after the telegraph equation, driving numerical solutions towards zero divergence. Our implementation follows closely that of [43,44], with some minor differences. The new field variable ψ satisfies the evolution equation…”

“…A number of techniques have been designed to combat these, including 'divergence cleaning' [43,44,95], a method which introduces a new field that both damps and advects divergences off the grid, 'constrained transport' algorithms [42] that balance out fluxes exactly to maintain divergence-free magnetic fields to round-off accuracy, and magnetic vector potential methods that seek to achieve the same result [73,96]. Constrained transport methods are often difficult to implement in simulations that employ mesh refinement, since maintaining balance at refinement boundaries is algorithmically complex.…”

“…While the evolution equations themselves are easily cast into the same flux-conservative form as the other hydrodynamics equations, the primary challenge for evolving magnetic fields is numerically maintaining the divergence-free constraint of the magnetic field. For this, we have implemented a variant of the constrained transport approach [42] and a hyperbolic 'divergence cleaning' technique, similar to that discussed in [43,44].…”

Relativistic Bondi-Hoyle-Lyttleton accretion: A parametric study

“…Also, Penner (2011) has performed a parametric study of general relativistic magneto-hydrodynamic (GRMHD) BHL, again using HRSC methods on a Cartesian mesh. Dönmez et al (2011) have also investigated instabilities within Bondi-Hoyle flows, but in the thin-disc approximation.…”