Radiation‐driven Warping. II. Nonisothermal Disks

Recent work by Pringle and by Maloney, Begelman & Pringle has shown thatgeometrically thin, optically thick, accretion disks are unstable to warpingdriven by radiation torque from the central source. In this paper we generalizethe study of radiation-driven warping to include general power-law surfacedensity distributions, $\Sigma\propto R^{-\delta}$. We consider the range$\delta=3/2$ (isothermal disks) to $\delta=-3/2$, which corresponds to aradiation-pressure-supported disk; this spans the range of surface densitydistributions likely to be found in real astrophysical disks. There is acritical minimum size for unstable disks. The critical radius and thesteady-state precession rate depend only weakly on $\delta$. The case$\delta=1$ divides the solutions into two qualitatively different regimes.Nonlinear effects must be important if the warp extends to the disk inner edgefor $\delta \ge 1$, but for $\delta < 1$ nonlinearity will be important only ifthe warp amplitude is large at the origin. The effects of shadowing of thecentral source by the warp will thus be very different in the two regimes of$\delta.$ In real accretion disks the outer boundary condition is likely to bedifferent from the zero-crossing condition that we have assumed. In accretiondisks around massive black holes in active galactic nuclei, the disk willprobably become optically thin before the outer disk boundary is reached, whilein X-ray binaries, there will be an outer disk region (outside thecircularization radius) in which the inflow velocity is zero but angularmomentum is still transported. We show that in both these cases the solutionsare similar to the zero-crossing eigenfunctions.Comment: 43 pages, 16 figures, to appear in The Astrophysical Journa