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

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 L_ν. Turbulence and the use of α implies that (1) field line stretching gives a magnetic pressure ≳ α^2/6 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 L_ν 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 (R_s) for averages over ≳1000 s. However, current data for galaxies like NGC 4258 and M87 give RPEs in L_ν of 50–100 per cent even at R ≤ 100 R_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.