Beltrami state in black-hole accretion disk: A magnetofluid approach

TL;DR

This paper demonstrates that black-hole accretion disk plasmas can reach Beltrami-Bernoulli equilibria, with space-time curvature significantly affecting magnetic and velocity profiles, revealing complex plasma-gravity interactions.

Contribution

It introduces a magnetofluid framework showing how relativistic effects influence Beltrami states in black-hole accretion disks, highlighting new oscillatory scales.

Findings

Space-time curvature alters magnetic and velocity decay rates.

Velocity profiles deviate from geodesic predictions.

Helicity invariants induce a new oscillatory length scale.

Abstract

Using the magnetofluid unification framework, we show that the accretion disk plasma (embedded in the background geometry of a blackhole) can relax to a class of states known as the Beltrami-Bernoulli (BB) equilibria. Modeling the disk plasma as a Hall MHD system, we find that the space-time curvature can significantly alter the magnetic/velocity decay rate as we move away from the compact object; the velocity profiles in BB states, for example, deviate substantially from the predicted corresponding geodesic velocity profiles. These departures imply a rich interplay of plasma dynamics and general relativity revealed by examining the corresponding Bernoulli condition representing "homogeneity" of total energy. The relaxed states have their origin in the constraints provided by the two helicity invariants of Hall MHD. These helicities conspire to introduce a new oscillatory length scale into the system that is strongly influenced by relativistic and thermal effects.