Neutrino-dominated Accretion Flows with Magnetic Prandtl Number-dependent MRI-driven Turbulence

Abstract

We investigate the stability of a neutrino-dominated accretion flow (NDAF), which is expected to be formed in the gravitational collapse of a massive star or the merger of a neutron star binary, based on the variable- α prescription. Recent magnetohydrodynamic simulations shows that the viscosity parameter α is proportional to the power of the magnetic Prandtl number Pm =  ν / η , where ν and η are the kinematic viscosity and electric resistivity of the fluid, respectively. In the inner region of a hyperaccretion flow, the viscosity and resistivity are carried by mildly, relativistically degenerated electrons. We fit the dependence of the magnetic Prandtl number on density and temperature by a simple analytic form, and derive the condition for an NDAF to be dynamically unstable. As demonstrations we perform simple one-dimensional simulations of NDAFs with variable- α and show that the mass accretion becomes highly time-variable in the unstable branch. This mechanism may account for the rapid variability observed in the prompt emission of gamma-ray bursts. The mass ejection from a hyperaccretion flow due to viscous heating, which makes a kilonova/macronova emission in the merger of a neutron star binary, is also briefly discussed.