Diffusion coefficient of a passive contaminant in a local MHD model of a turbulent accretion disc

We calculate the radial diffusion coefficient for a passive contaminant in an accretion disc which is turbulent due to the action of the magnetorotational instability. Numerical magnetohydrodynamic (MHD) simulations are used to follow the evolution of a local patch of the disc using the shearing box formalism. A separate continuity equation for the mass fraction of contaminant is integrated along with the MHD system, and radial profiles of this fraction are obtained as a function of time. Solutions of a linear diffusion equation are fitted to the numerical measured profiles of the contaminant, treating the diffusion coefficient D as the fitting parameter. At early times, the value of D is found to vary; however, once the contaminant is spread over scales comparable to the box size, it saturates at a steady value. The ratio of D to the transport coefficient of angular momentum due to shear stress is small. If D can be used as a proxy for the turbulent magnetic diffusivity, the effective magnetic Prandtl number P-eff=nu/D (where nu is the coefficient of 'effective viscosity' associated with shear stress) would be large.