Generalized Grad-Shafranov equation for gravitational Hall-MHD equilibria

TL;DR

This paper develops a generalized Grad-Shafranov equation to describe gravitational Hall-MHD equilibria in accretion disks around compact objects, accounting for non-neutral plasmas and strong magnetic and gravitational fields.

Contribution

It extends previous models by formulating a GGS equation that includes space-time curvature effects for non-relativistic, Hall-MHD plasmas in accretion disks.

Findings

Derivation of a generalized Grad-Shafranov equation for G-Hall-MHD equilibria.

Application of the model to accretion disks with strong magnetic fields.

Insights into plasma behavior near compact objects.

Abstract

The consistent theoretical description of gravitational Hall-MHD (G-Hall-MHD) equilibria is of fundamental importance for understanding the phenomenology of accretion disks (AD) around compact objects (black holes, neutron stars, etc.). The very existence of these equilibria is actually suggested by observations, which show evidence of quiescent, and essentially non-relativistic, AD plasmas close to compact stars, thus indicating that accretion disks may be characterized by slowly varying EM and fluid fields. These (EM) fields, in particular the electric field, may locally be extremely intense, so that AD plasmas are likely to be locally non-neutral and therefore characterized by the presence of Hall currents. This suggests therefore that such equilibria should be described in the framework of the Hall-MHD theory. Extending previous approaches, holding for non-rotating plasmas or based on specialized single-species model equilibria which ignore the effect of space-time curvature, the purpose of this work is the formulation of a generalized Grad-Shafranov (GGS) equation suitable for the investigation of G-Hall-MHD equilibria in AD's where non-relativistic plasmas are present. For this purpose the equilibria are assumed to be generated by a strong axisymmetric stellar magnetic field and by the gravitating plasma characterizing the AD.