Jeans instability in flattened thin disks

Taking into consideration the mass spectrum in a flattened differentially rotating disk, we calculate the critical parameters for local instability relative to small radial perturbations. We investigate the stability conditions in the general case when different relationships between element mass and random velocity may exist in different regions of the mass spectrum. In particular, we find some interesting results for the case of no relationship between the above quantities in which the effects of the mass spectrum on the stability conditions appear more clearly. [Copyright &y& Elsevier]