Fluctuations, dissipation and turbulence in accretion discs

In this paper, we relate dissipational processes in accretion discs to large-scale correlated fluctuations in the velocity and magnetic field components. The radial-azimuthal (Rφ) component of the correlation stress tensor for velocity and magnetic fluctuations is responsible for transport within the disc. Under steady conditions, the Rφ component of the stress tensor scales with disc radius R and surface density Σ as 1/(R^3/2Σ). This component of the stress tensor can also be related in a simple way to the local radiative flux density. This latter relation is observationally sensitive to surface irradiation, but the former scaling law is expected to be very robust. Both results are examples of fluctuation-dissipation relations for accretion discs. Eclipse mapping and Doppler tomography techniques in cataclysmic variables and X-ray binary systems may soon be able to test these types of theoretical predictions. Molecular viscosity serves only as an energy sink, not as a source of any turbulent transport, thermalizing the high-wavenumber end of the power spectrum. The same is true of microscopic resistivity with respect to magnetic field fluctuations. This implies that an explicit representation for the viscosity or resistivity is not essential for large-scale numerical modelling of accretion disc turbulence.