## Abstract

The α 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 Lν. Turbulence and the use of α implies that (1) field line stretching gives a magnetic pressure α2/6 of the total pressure generally, and a one-to-one relation between α and the pressure ratio for thin discs, and (2) large turbulent scales in advection-dominated accretion flows (ADAFs) predict a lower Lν precision than thin discs for a given observation duration and central mass. The allowed variability (or RPE) at frequency ν increases with the size of the contributing region. For X-ray binary ADAFs, the RPE ∼ 5 per cent at R ≤ 1000 Schwarzchild radii (Rs) for averages over ≳1000 s. However, current data for galaxies like NGC 4258 and M87 give RPEs in Lν of 50–100 per cent even at R ≤ 100 RS. 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.