Demonstration of a magnetic Prandtl number disc instability from first principles - Potter, W; Balbus, S (Oxford University Press, 2017)
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 (α) on the magnetic Prandtl number (Pm) is sufficiently sensitive to induce thermal-viscous instability using 3D MHD simulations. We first investigate whether the α-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 α-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 α-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 α-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 could 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.