High-order schemes for non-ideal $3+1$ GRMHD: a study of the kinematic dynamo process in accretion tori

TL;DR

This paper introduces high-order implicit-explicit Runge-Kutta schemes within the ECHO code to simulate dynamo effects in accretion disks around black holes, revealing magnetic field amplification and cyclic behavior similar to solar phenomena.

Contribution

It is the first astrophysical application of the ECHO code with a generalized Ohm law, demonstrating advanced numerical schemes in 3+1 GRMHD for dynamo studies.

Findings

Magnetic fields are strongly amplified in accretion tori.

The dynamo process reproduces solar-like butterfly diagrams.

Field evolution timescales depend on dynamo and resistivity parameters.

Abstract

We present the first astrophysical application of the ECHO code in its recent version supplemented by a generalized Ohm law, namely a kinematic study of dynamo effects in thick accretion disks. High-order \emph{implicit-explicit} Runge-Kutta time-stepping routines are implemented and validated within $3+1$ \emph{General Relativistic MagnetoHydroDynamics} (GRMHD). The scheme is applied to a differentially rotating torus orbiting a Kerr black hole, where the mean-field dynamo process leads to strong amplification of seed magnetic fields. We show that the interplay between the toroidal and poloidal components occurs qualitatively in the same fashion as in the Sun, butterfly diagrams are reproduced, and a typical time-scale for the field evolution is found, depending on the dynamo and resistivity numbers, which could explain periodicities as observed in several accreting systems.