Envelope expansion with core collapse – I. Spherical isothermal similarity solutions

摘要: We investigate self-similar dynamical processes in an isothermal self-gravitational fluid with spherical symmetry. With reference to the earlier complementary solution results of Larson, Penston, Shu, Hunter and Whitworth & Summers, we further explore 'semi-complete space' from initial instant t → 0 + a final stage +∞. These similarity solutions can describe accommodate physical radial inflow, core collapse, oscillations envelope expansion (namely, outflow or wind) contraction as well shocks. In particular, present new classes solutions, referred 'envelope collapse' (EECC) that feature concurrent interior collapse exterior expansion. The towards central approaches free-fall state radius r 0, while gradually constant flow speed There exists at least one stagnation surface zero separates travels outward speed, either subsonically supersonically, manner. Without crossing sonic critical line where travel non-linear disturbances relative is equal sound there continuous band infinitely many EECC only supersonic point for (ECCC) without point. Crossing twice analytically, are discrete more subsonic points. Such generally allow region between outer addition, obtained ECCC cross oscillations. all these surfaces resulting yet different speeds specified boundary shock conditions, it possible construct infinite number such which conceptually applicable various astrophysical problems involving gravitational collapses outflows. mention potential applications formation process protoplanetary nebulae connecting asymptotic giant branch phase planetary nebula H II clouds surrounding star regions, certain evolution galaxy clusters.