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.

arXiv comment21 pages, 15 figures, accepted for publication in MNRAS

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• Magnetized massive stars as magnetar progenitors
• Self-Similar Polytropic Champagne Flows in H II Regions
• Relativistic Self-similar Dynamic Collapses of Black Holes in General Polytropic Spherical Clouds
• Perturbation Analysis of a General Polytropic Homologously Collapsing Stellar Core
• Three-dimensional Hydrodynamic Instabilities in Stellar Core Collapses
• General Polytropic Magnetofluid under Self-Gravity: Voids and Shocks
• Dynamic Evolution Model of Isothermal Voids and Shocks
• Molecular Line Profiles of Collapsing Gas Clouds
• Dynamic Voids Surrounded by Shocked Conventional Polytropic Gas Envelopes
• Adiabatic Perturbations in Homologous Conventional Polytropic Core Collapses of a Spherical Star
• Self-Similar Shocks and Winds in Galaxy Clusters
• Variable protostellar mass accretion rates in cloud cores