A simple analytical model of magnetic jets

TL;DR

This paper presents a simplified analytical model of magnetic jets around black holes, deriving magnetic field profiles and jet stability insights based on conservation laws and simulation data.

Contribution

It introduces a new analytical framework that combines conservation laws with simulation results to model magnetic jet profiles and stability around rotating black holes.

Findings

Poloidal magnetic field dominates over toroidal in the jet.

The model recovers the standard black hole power extraction formula.

Jets are predicted to be more stable to kink instabilities.

Abstract

We propose a simple analytical jet model of magnetic jets, in which radially-averaged profiles of main physical quantities are obtained based on conservation laws and some results of published GRMHD jet simulations. We take into account conversion of the magnetic energy flux to bulk acceleration in jets formed around rotating black holes assuming the mass continuity equation and constant jet power, which leads to the Bernoulli equation. For assumed profiles of the bulk Lorentz factor and the radius, this gives us the profile of the toroidal magnetic field component along the jet. We then consider the case where the poloidal field component is connected to a rotating black hole surrounded by an accretion disc. Our formalism then recovers the standard formula for the power extracted from a rotating black hole. We find that the poloidal field strength dominates over the toroidal one in the comoving frame up to large distances, which means that jets should be more stable to current-driven kink modes. The resulting magnetic field profiles can then be used to calculate the jet synchrotron emission.