Variability associated with αaccretion disc theory for standard and advection-dominated discs

The alpha turbulent viscosity formalism for accretion discs must be interpreted as a mean field theory, modelling a steady state only on spatial or time-scales greater than those of the turbulence. The extent of the scale separation determines the relative precision error (RPE) of the predicted luminosity L-nu. Turbulence and the use of alpha implies that (1) field line stretching gives a magnetic pressure greater than or similar to alpha(2)/6 of the total pressure generally, and a one-to-one relation between alpha and the pressure ratio for thin discs, and (2) large turbulent scales in advection-dominated accretion flows (ADAFs) predict a lower L-nu precision than thin discs for a given observation duration and central mass. The allowed variability (or RPE) at frequency nu increases with the size of the contributing region. For X-ray binary ADAFs, the RPE similar to 5 per cent at R less than or equal to 1000 Schwarzchild radii (R-s) for averages over greater than or similar to 1000 s. However, current data for galaxies like NGC 4258 and M87 give RPEs in L-nu of 50-100 per cent even at R less than or equal to 100R(s). More data are required, but systematic deviations from ADAF predictions are more significant than random deviations, and may constrain properties of the turbulence, the accretion mode, the assumption of a steady state or the accretion rate.