A new method for extending solutions to the self-similar relativistic magnetohydrodynamics equations for black hole outflows

TL;DR

This paper introduces a novel integration scheme for relativistic magnetohydrodynamics equations, enabling detailed semi-analytical modeling of black hole jets, including features like counter-rotation and recollimation, across a broad parameter space.

Contribution

The authors develop a new method to solve self-similar MHD equations, allowing comprehensive exploration of jet solutions from the disk to downstream regions, including counter-rotation phenomena.

Findings

Jet solutions with Lorentz factors up to 10.

Identification of recollimation sites between 10^3 and 10^7 gravitational radii.

First semi-analytical model showing jet counter-rotation.

Abstract

The paradigm in which magnetic fields play a crucial role in launching/collimating outflows in many astrophysical objects continues to gain support. However, semi-analytical models including the effect of magnetic fields on the dynamics and morphology of jets are still missing due to the intrinsic difficulties in integrating the equations describing a collimated, relativistic flow in the presence of gravity. Only few solutions have been found so far, due to the highly nonlinear character of the equations together with the need to blindly search for singularities. These numerical problems prevented a full exploration of the parameter space. We present a new integration scheme to solve r-self-similar, stationary, axisymmetric magnetohydrodynamics equations describing collimated, relativistic outflows crossing smoothly all the singular points (Alfven point and modified slow/fast points). For the first time, we are able to integrate from the disk mid-plane to downstream of the modified fast point. We discuss an ensemble of jet solutions, emphasising trends and features that can be compared to observables. We present, for the first time with a semi-analytical MHD model, solutions showing counter-rotation of the jet for a substantial fraction of its extent. We find diverse jet configurations with bulk Lorentz factors up to 10 and potential sites for recollimation between $10^3-10^7$ gravitational radii. Such extended coverage of the intervals of quantities, such as magnetic-to-thermal energy ratios at the base or the heights/widths of the recollimation region, makes our solutions suitable for application to many different systems where jets are launched.