Gravitational Collapse and Star Formation in Logotropic and Nonisothermal Spheres

We present semianalytical similarity solutions for the inside out, expansion-wave collapse of initially virialized gas clouds with nonisothermal equations of state. Results are given for the family of negative-index polytropes (P ∝ ργ, γ ≤ 1), but we focus especially on the so-called logotrope, P/Pc = 1 + Aln(ρ/ρc). In a separate paper, we have shown this to be the best available phenomenological description of the internal structure and …