A Separable Solution for the Oscillatory Structure of Plasma in Accretion Disks

TL;DR

This paper introduces a separable analytical approach to modeling plasma oscillations in accretion disks, revealing that ring-like density structures can form even with minimal magnetic pressure, through both analytical and numerical methods.

Contribution

It presents a novel separable solution method for the plasma equilibrium equations in accretion disks, enabling analytical and numerical analysis of oscillatory density profiles.

Findings

Ring-like density profiles can form with small magnetic pressure.

Analytical solutions are obtained in the small magnetic pressure limit.

Numerical integration confirms the analytical results.

Abstract

We provide a new analysis of the system of partial differential equations describing the radial and vertical equilibria of the plasma in accretion disks. In particular, we show that the partial differential system can be separated once a definite, oscillatory (or hyperbolic) form for the radial dependence of the relevant physical quantities is assumed. The system is thus reduced to an ordinary differential system in the vertical dimensionless coordinate. The resulting equations can be integrated analytically in the limit of small magnetic pressure. We complete our analysis with a direct numerical integration of the more general case. The main result is that a ring-like density profile (i.e., radial oscillations in the mass density) can appear even in the limit of small magnetic pressure.