Highly-collimated, magnetically-dominated jets around rotating black holes

TL;DR

This paper introduces a new perturbative method for modeling highly-collimated, magnetically-dominated jets around rotating black holes, aligning well with numerical simulations and providing insights into jet stability and structure.

Contribution

The paper presents a novel perturbative approach to construct self-consistent, highly-collimated jet solutions around rotating black holes, differing from traditional methods by avoiding direct nonlinear equation solving.

Findings

Jet solutions are highly collimated and approach a magnetic cylinder.

The solutions are helically twisted due to black hole spin.

Jet power matches well with numerical simulations.

Abstract

In this paper, we propose a general method for perturtative solutions to Blandford-Znajek mechanism. Instead of solving the nonlinear Grad-Shafranov equation directly, we introduce an alternative way to determine relevant physical quantities based on the horizon boundary condition and the convergence requirement. Both the angular velocity $\Omega$ of magnetic field lines, the toroidal magnetic field $B^\phi$ and the total electric current $I$ are self-consistently specified according to our method. As an example, stationary axisymmetric and force-free jet models around rotating black holes are self-consistently constructed according to the method we proposed. This jet solution distinguishes itself from prior known analytic solutions in that it is highly collimated and asymptotically approaches a magnetic cylinder. This jet solution is helically twisted, since toroidal magnetic field is generated when the black hole spin is taken into account. For a given magnetic flux threading the black hole, the jet power and energy extraction rate of the collimated jet are compared with previous solutions. We find that our new solution agrees better with current state-of-the-art numerical simulation results. Some interesting properties of the collimated jet and effects of field line rotation on the jet stability are also briefly discussed.