 of this problem.

Nonetheless, having expressed these [*caveats*]{}, it is still of some interest to estimate what ${\cal T}$ and ${\cal R}$ may be in radiation-dominated accretion disks in order to make some contact with the classical theory. To do so we make the suspect identification discussed in the preceding paragraph: we suppose that the shear viscosity in all directions is given by the Shakura-Sunayev $\alpha$. If so, ${\cal T} \simeq 10 \alpha^{-2}$, independent of radius (or anything else). Within the radiation-dominated regime, the Rayleigh number is similarly constant: ${\cal R} \sim O(10) (\kappa/\kappa_T)^2$. Interestingly, the critical ${\cal R}$ for $10 < {\cal T} < 10^5$ is $\sim 10^3$ – $10^4$ (Chandrasekhar 1961). Thus, if the most appropriate analog to ordinary fluid viscosity is correctly estimated by this means, the strong convective instability we find might be quenched; however, as we have stressed, it is by no means clear that this analogy applies.

Implications
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We have shown that if an accretion disk is placed in the Shakura-Sunyaev radiation-dominated equilibrium, the growth rate of the convective instability is hardly affected by large changes in parameters such as the opacity or the way in which the local dissipation might be perturbed. This behavior is, perhaps, not surprising, when one considers that the convective instability is essentially dynamical, whereas the opacity and dissipation rates pertain to the (rather more slowly accomplished) thermal balance.

Given that the Shakura-Sunyaev equilibrium is unstable to convection for all reasonable parameters, we can hardly expect that it describes the actual state of radiation pressure-dominated disks. One’s first guess might be that what happens instead is that entropy is redistributed so as to make the disks at most marginally unstable to convection (Bisnovatyi-Kogan & Blinnikov 1977). If the entropy distribution is at most weakly unstable to convection, then departures from hydrostatic equilbrium should be small, 