Jet launching from the Kerr black hole magnetosphere: An electrogeodesic approach

TL;DR

This work develops a fully analytic model of jet launching from a Kerr black hole by exploiting separable electrogeodesic motion in a Kerr monopole magnetosphere, addressing the gap between fluid/kinetic simulations and analytic particle dynamics.By constructing Maxwell fields from Kerr symmetries (Killing vectors and Killing-Yano tensors) and identifying magnetospheres that preserve the Carter constant, it yields closed-form integral solutions for charged-particle trajectories and acceleration.In the Kerr monopole case, particles are preferentially accelerated near the poles, with a well-defined jet opening produced by polar equilibrium conditions, magnetic frame-dragging that dominates gravitational drag, and a finite blueshift zone determining which ejecta are observed at infinity.The framework provides concrete, testable predictions for jet structure and dynamics, offering a tractable analytic baseline for kinetic jet modeling and comparisons with GR/MHD and PIC simulations.

Abstract

The launch of relativistic jets of plasma on astrophysical to cosmological scales are observed in a variety of astrophysical sources, from active galactic nuclei to X-rays binaries. While these jets can be reproduced by the general relativistic magneto-hydrodynamic (GRMHD) and particle-in-cells (GRPIC) simulations of the dynamical Kerr magnetosphere, the development of analytic models to describe the physics of the jets has remained limited. A key challenge is to analytically describe the individual trajectories of accelerated charged particles which ultimately build up the jet and emit radiation. In this work, we provide a first simple but fully analytical model of jet launching from the Kerr magnetosphere based on the motion of charged particles. To that end, we use the integrability of electrogeodesic motion in the Kerr monopole magnetosphere to study the ejection of charged particles near the poles. This enables us to derive (i) a criterion for the rotation axis to constitute a stable latitunal equilibrium position, thereby representing an idealized jet, (ii) the expression for the magnetic frame-dragging effect, and (iii) the condition for an asymptotic observer to measure blueshifted particles emanating from the black hole surroundings. Our study reveals that particles can be accelerated only in a specific region whose maximal radius depends on the spin and magnetization of the black hole. Alongside these results, we provide a detailed review of the construction of test magnetospheres from (explicit and hidden) symmetries of the Kerr geometry and the condition for the separability of the electrogeodesic motion in a test magnetosphere, which serves as a basis for the model we study in this work.

Figures (4)

• Figure 1: Effective potential $V(\theta)$ governing the latitudal motion for $\ell= - \kappa {\mathcal{P}}$. The plots are performed for $\beta = 8$ and for various values of $\varepsilon$ ensuring a stable equilibrium at $\theta = 0$, according to Eq. \ref{['theta_0_stable']}, i.e. $\varepsilon < 3$ (left panel) or $\varepsilon > 5$ (right panel). Notice that in all cases, $\theta=0$ is a (local) minimum of $V$ and that the marginal cases $\varepsilon=3$ and $\varepsilon=5$ are included in the plots.
• Figure 2: Effective potential $V(\theta)$ governing the latitudal motion for $\ell= - \kappa {\mathcal{P}}$ and $\beta=8$. Contrary to Fig. \ref{['pot_stable_theta_0']}, the chosen values of $\varepsilon$ are such that the equilibrium position at $\theta = 0$ is unstable: it corresponds to a local maximum of $V(\theta)$. According to Eq. \ref{['theta_0_stable']} with $\beta=8$, these values are in the range $3 < \varepsilon < 5$ (the marginal cases $\varepsilon=3$ and $\varepsilon=5$ are included in the plots). Notice that a stable equilibrium position occurs at $\theta = \theta_* \in (0,\pi/2)$.
• Figure 3: Redshift factor $z$ along the Northern rotation axis ($\theta=0$) as a function of the emission radius $r_{\rm em}$, for various values of the ratio $\beta/\varepsilon$ and for $a/M=0.1$ (top figures) and $a/M=0.5$ (bottom figures). Since $z$ is diverging for $r \to r_+$ (the horizon), the plots in the left figures start at $r = 1.01 \, r_+$.
• Figure 4: Same as Fig. \ref{['z_r_em_010_050']} but for $a/M=0.9$ (top figures) and $a/M=0.98$ (bottom figures).