Variability Associated with Alpha Accretion Disc Theory for Standard and Advection Dominated Discs

The $\alpha$ turbulent viscosity formalism for accretion discs must be interpreted as a mean field theory. The extent to which the disc scale exceeds that of the turbulence determines the precision of the predicted luminosity $L_\nu$. The assumption of turbulence and use of $\a$ implies: (1) Field line stretching generates a magnetic pressure $\gsim \a^2/6$ of the total pressure generally, and a 1 to 1 relation between $\a$ and the pressure ratio when shearing instabilities dominate the viscosity. (2) Large eddy sizes and speeds in typical advection dominated accretion flows (ADAFs) lead to a lower precision in $L_\nu$ than for thin discs of a given total observation duration and central mass. The allowed variability (relative precision) at a particular frequency increases (decreases) with the size of the contributing region. For X-ray binary type ADAFs, the allowed variability is $\sim 5$% at $R \le 1000$ Schwarzchild radii for averages over $\gsim 1000$sec. But for large galactic nuclei like NGC 4258 and M87, the relative precision error can approach $50-100$ even at $R \le 100 R_S$ for currently available observation durations. More data are then required to compare with ADAF predictions.