Turbulent viscosity in clumpy accretion disks II supernova driven turbulence in the Galaxy

Abstract

An analytical model for a turbulent clumpy gas disk is presented where turbulence is maintained by the energy input due to supernovae. Expressions for the disk parameters, global filling factors, molecular fractions, and star formation rates are given as functions of the Toomre parameter $Q$, the ratio between the cloud size and the turbulent driving length scale $δ$, the mass accretion rate within the disk $\dot{M}$, the constant of molecule formation $α$, the disk radius, the angular velocity, and its radial derivative. Two different cases are investigated: a dominating stellar disk and a self-gravitating gas disk in $z$ direction. The turbulent driving wavelength is determined in a first approach by energy flux conservation, i.e. the supernovae energy input is transported by turbulence to smaller scales where it is dissipated. The results are compared to those of a fully gravitational model. For Q=1 and $δ=1$ both models are consistent with each other. In a second approach the driving length scale is directly determined by the size of supernovae remnants. Both models are applied to the Galaxy and can reproduce its integrated and local gas properties. The influence of thermal and magnetic pressure on the disk structure is investigated. We infer $Q \sim 1$ and $\dot{M} \sim 0.05 - 0.1 M_{\odot} yr ^{-1}$ for the Galaxy.