Estimate of the Shakura-Sunyaev viscosity parameter in the Keplerian accretion disk from hydrodynamic turbulence

Recently, in a series of papers, Mukhopadhyay and his collaborators have argued for possible pure hydrodynamic turbulence in a Keplerian accretion disk. This is essentially important to solving the puzzle of the transport mechanism in cold accretion disk systems where the temperature could be lower than 5000 K, where magnetorotational instability seems not to be working to trigger turbulence. Here we quantify the corresponding instability and turbulence in terms of turbulent viscosity and obtain the famous Shakura-Shunyaev viscosity parameter, alpha. It is exciting that the range of alpha obtained from our analysis is 0.1 greater than or similar to alpha greater than or similar to 0.0001 for a realistic parameter region. This range also suggests that once the hydrodynamic instability described by Mukhopadhyay and his collaborators leads to turbulence-an effect which should exist in systems independent of being hot or cold-the effect may compete with the magnetohydrodynamic effect even in hot accretion disks and thus may be effective in transporting matter in hot gas systems as well