The effects of Prandtl number on black hole accretion flows

Recent numerical simulations of MHD turbulence, under very different driving conditions, and by several different investigators, all indicate a sensitivity of the rms fluctuations to the ratio of the microscopic viscosity to resistivity. This dimensionless quantity is known as the magnetic Prandtl number Pm. In general, standard astrophysical accretion disks are characterized by Pm ≪ 1 throughout their radial extent, while low luminosity accretors (e.g. Sag A∗) have Pm ≫ 1. Here, we show that standard α models of black hole accretion disks have a transition radius, measured in tens of Schwarzschild radii, at which the flow goes from Pm ≪ 1 to Pm ≫ 1. Moreover, this transition may well be dynamically unstable, leading to a sort of two-phase “Prandtl number medium” We advance the idea that this is the physical reason underlying the change in the accretion properties of the inner regions of Keplerian disks, leading to a truncation of the cool disk (Pm ≪ 1) and the onset of hot, low density gas flow (Pm ≫ 1).