Nonaxisymmetric instabilities in self-gravitating disks. II. Linear and quasi-linear analyses

• DOI: 10.1007/s10509-014-1994-8
• Publication Date: 2014-06-19T04:12:23Z
• Authors: Kathryn Z. Hadley; Paul Fernandez; James N. Imamura; Erik Keever; Rebecka Tumblin; William Dumas
• Keywords: Mass ratio; Oscillation (cell signaling)

We studied global nonaxisymmetric hydrodynamic instabilities in an extensive collection of hot, self-gravitating polytropic disk systems, systems that covered a wide expanse of the parameter space relevant to protostellar and protoplanetary systems. We examined equilibrium disk models varying three parameters: the ratio of the inner to outer equatorial radii, the ratio of star mass to disk mass, and the rotation law exponent $q$. We took the polytropic index $n$ = 1.5 and examined the exponents $q =$ 1.5 and 2, and the transitional one $q$ = 1.75. For each of these sets of parameters, we examined models with inner to outer radius ratios from 0.1 to 0.75, and star mass to disk mass ratios from 0 to 10$^3$. We numerically calculated the growth rates and oscillation frequencies of low-order nonaxisymmetric disk modes, modes with azimuthal dependence $\propto$ e$^{im��}$. Low-$m$ modes are found to dominate with the character and strength of instability strongly dependent on disk self-gravity. Representatives of each mode type are examined in detail, and torques and mass transport rates are calculated.