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 \phi } .
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 .