Microphysical dissipation, turbulence and magnetic fields in hyper-accreting discs

Hyper-accreting discs occur in compact-object mergers and collapsars, and may power gamma-ray bursts (GRBs). We calculate the microscopic viscosity and resistivity of plasma in these discs, and discuss the implications for their global structure and evolution. In the neutrino-cooled innermost regions, the viscosity is provided mainly by mildly degenerate electrons, while the resistivity is modified from the Spitzer value due to the effects of both relativity and degeneracy. The plasma behaves as an almost ideal MHD fluid. Among the non-ideal MHD effects the Hall term is relatively the most important, while the magnetic Prandtl number, Pr (the ratio of viscosity to resistivity), is typically larger than unity: 10 < Pr < 6000. The outer radiatively inefficient regions also display high Pr. Numerical simulations of the magneto-rotational instability indicate that the saturation level and angular momentum transport efficiency may be greatly enhanced at high Pr. If this behaviour persists in the presence of a strong Hall effect we would expect that hyper-accreting discs should be strongly magnetised and highly variable. The expulsion of magnetic field that cannot be dissipated at small scales may also favour a magnetic outflow. We note the similaries between the Prandtl number in hyper-accreting discs and X-ray binary discs, which suggests that a comparison between late-time activity in GRBs and X-ray binary accretion states may be fruitful. Our results imply that the behavior of high Prandtl number MHD flows needs to be considered in studies of hyper-accreting discs.