Nonaxisymmetric Instabilities in Self-Gravitating Disks. II Linear and Quasi-Linear Analyses

TL;DR

This paper investigates global nonaxisymmetric hydrodynamic instabilities in self-gravitating disks, analyzing how various parameters influence mode growth rates, frequencies, and mass transport, with implications for protostellar and protoplanetary systems.

Contribution

It provides a comprehensive linear and quasi-linear analysis of instabilities across a wide parameter space in self-gravitating disks, highlighting the role of self-gravity in mode behavior.

Findings

Low-m modes dominate instability behavior.

Growth rates and frequencies depend strongly on self-gravity.

Mass transport rates are quantified for different modes.

Abstract

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.