Shocked similarity collapses and flows in star formation processes

We propose self-similar shocked flow models for certain dynamical evolution phases of young stellar objects (YSOs), `champagne flows' of H {\sevenrm II} regions surrounding OB stars and shaping processes of planetary nebulae (PNe). We analyze an isothermal fluid of spherical symmetry and construct families of similarity shocked flow solutions featured by: 1. either a core expansion with a finite central density or a core accretion at constant rate with a density scaling $\propto r^{-3/2}$; 2. a shock moving outward at a constant speed; 3. a preshock gas approaching a constant speed at large $r$ with a density scaling $\propto r^{-2}$. In addition to testing numerical codes, our models can accommodate diverse shocked flows with or without a core collapse or outflow and an envelope expansion or contraction. As an application, we introduce our model analysis to observations of Bok globule B335.