Self-Similar Dynamics of a Relativistically Hot Gas

Abstract

In the presence of self-gravity, we investigate the self-similar dynamics of a relativistically hot gas with or without shocks in astrophysical processes of stellar core collapse, formation of compact objects, and supernova remnants with central voids. The model system is taken to be spherically symmetric and the conservation of specific entropy along streamlines is adopted for a relativistic hot gas. In terms of equation of state, this leads to a polytropic index $\gamma =4/3$. The conventional polytropic gas of $P=\kappa {\rho }^{\gamma }$, where $P$ is the thermal pressure, $\rho$ is the mass density, $\gamma$ is the polytropic index, and $\kappa$ is a global constant, is included in our theoretical model framework. Two qualitatively different solution classes arise according to the values of a simple power-law scaling index $a$, each of which is analyzed separately and systematically. We obtain new asymptotic solutions that exist only for $\gamma =4/3$. Global and asymptotic solutions in various limits as well as eigensolutions across sonic critical lines are derived analytically and numerically with or without shocks. By specific entropy conservation along streamlines, we extend the analysis of Goldreich & Weber for a distribution of variable specific entropy with time $t$ and radius $r$ and discuss consequences in the context of a homologous core collapse prior to supernovae. As an alternative rebound shock model, we construct an Einstein-de Sitter explosion with shock connections with various outer flows including a static outer part of a singular polytropic sphere (SPS). Under the joint action of thermal pressure and self-gravity, we can also construct self-similar solutions with central spherical voids with sharp density variations along their edges.

21 pages, 15 figures, accepted for publication in MNRAS

References in corpus (5)

• New Self-Similar Solutions of Polytropic Gas Dynamics
• Envelope Expansion with Core Collapse. III. Similarity Isothermal Shocks in a Magnetofluid
• Self-Similar Dynamics of a Magnetized Polytropic Gas
• Magnetohydrodynamic Rebound Shocks of Supernovae
• Self-Similar Shocks in Polytropic Gas Flows around Star-Forming Regions

Cited by in corpus (5)

• Dynamic Evolution of a Quasi-Spherical General Polytropic Magnetofluid with Self-Gravity
• Self-Similar Polytropic Champagne Flows in H II Regions
• General Polytropic Magnetofluid under Self-Gravity: Voids and Shocks
• Dynamic Evolution Model of Isothermal Voids and Shocks
• Self-Similar Shocks and Winds in Galaxy Clusters