The effect of suspended particles on Jean's criterion for gravitational instability

The effect that the proper inclusion of suspended particles has on Jeans' criterion for the self-gravitational instability of an unbounded nonrotating adiabatic gas cloud is examined by formulating the appropriate model system, introducing particular physically plausible equations of state and constitutive relations, performing a linear stability analysis of a uniformly expanding exact solution to these governing equations, and exploiting the fact that there exists a natural small material parameter for this problem given by N sub 1/n sub 1, the ratio of the initial number density for the particles to that for the gas. The main result of this investigation is the derivation of an altered criterion which can substantially reduce Jeans' original critical wavelength for instability. It is then shown that the existing discrepancy between Jeans' theoretical prediction using and actual observational data relevant to the Andromeda nebula M31 can be accounted for by this new criterion of assuming suspended particles of a reasonable grain size and distribution to be present.