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

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

1998-04-24

arxiv.org/abs/astro-ph/9804266v2

Astronomy and Astrophysics

Astrophysics

16 pages, TeX (minor changes to K_3 and alpha-beta relation) sub. to MNRAS

Scientific paper

10.1046/j.1365-8711.1998.01967.x

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.

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