# Demonstration of a magnetic Prandtl number disc instability from first principles

## TL;DR

This paper demonstrates from first principles that the magnetic Prandtl number can induce a thermal-viscous instability in accretion discs, potentially explaining state transitions in black hole binaries.

## Contribution

First self-consistent MHD simulation showing that the magnetic Prandtl number dependence causes a thermal-viscous instability in accretion discs.

## Key findings

- The $oldsymbol{
m extit{ extbf{α}}}$-Pm dependence persists with increased resolution.
- The Pm dependence can lead to a local thermal-viscous instability.
- The instability manifests as an unstable limit cycle in the disc.

## Abstract

Understanding what determines the strength of MHD turbulence in accretion discs is a question of fundamental theoretical and observational importance. In this work we investigate whether the dependence of the turbulent accretion disc stress ($\alpha$) on the magnetic Prandtl number (Pm) is sufficiently sensitive to induce thermal-viscous instability using 3D MHD simulations. We first investigate whether the $\alpha$-Pm dependence, found by many previous authors, has a physical or numerical origin by conducting a suite of local shearing-box simulations. We find that a definite $\alpha$-Pm dependence persists when simultaneously increasing numerical resolution and decreasing the absolute values of both the viscous and resistive dissipation coefficients. This points to a physical origin of the $\alpha$-Pm dependence. Using a further set of simulations which include realistic turbulent heating and radiative cooling, and by giving Pm a realistic physical dependence on the plasma temperature and density, we demonstrate that the $\alpha$-Pm dependence is sufficiently strong to lead to a local instability. We confirm that the instability manifests itself as an unstable limit cycle by mapping the local thermal-equilibrium curve of the disc. This is the first self-consistent MHD simulation demonstrating the Pm instability from first principles. This result is important because a physical Pm instability would lead to the global propagation of heating and cooling fronts and a transition between disc states on timescales compatible with the observed hard/soft state transitions in black hole binaries.