New Self-Similar Solutions of Polytropic Gas Dynamics

Abstract

We explore semi-complete self-similar solutions for the polytropic gas dynamics involving self-gravity under spherical symmetry, examine behaviours of the sonic critical curve, and present new asymptotic collapse solutions that describe `quasi-static' asymptotic behaviours at small radii and large times. These new `quasi-static' solutions with divergent mass density approaching the core can have self-similar oscillations. Earlier known solutions are summarized. Various semi-complete self-similar solutions involving such novel asymptotic solutions are constructed, either with or without a shock. In contexts of stellar core collapse and supernova explosion, a hydrodynamic model of a rebound shock initiated around the stellar degenerate core of a massive progenitor star is presented. With this dynamic model framework, we attempt to relate progenitor stars and the corresponding remnant compact stars: neutron stars, black holes, and white dwarfs.

17 pages, 11 figures, Accepted for publication in MNRAS

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Cited by in corpus (30)

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• Dynamic Evolution of a Quasi-Spherical General Polytropic Magnetofluid with Self-Gravity
• Self-Similar Shocks in Polytropic Gas Flows around Star-Forming Regions
• Self-Similar Dynamics of a Relativistically Hot Gas
• Magnetohydrodynamic Rebound Shocks of Supernovae
• Magnetized massive stars as magnetar progenitors
• Self-Similar Dynamics of a Magnetized Polytropic Gas
• Thermal structure of a protostellar envelope
• An Imaging and Spectral Study of Ten X-Ray Filaments around the Galactic Center
• Self-Similar Polytropic Champagne Flows in H II Regions
• Perturbation Analysis of a General Polytropic Homologously Collapsing Stellar Core
• Relativistic Self-similar Dynamic Collapses of Black Holes in General Polytropic Spherical Clouds
• 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
• Dynamic Voids Surrounded by Shocked Conventional Polytropic Gas Envelopes
• Collisional interaction limits between dark matters and baryons in `cooling flow' clusters
• Molecular Line Profiles of Collapsing Gas Clouds
• Adiabatic Perturbations in Homologous Conventional Polytropic Core Collapses of a Spherical Star
• Intermediate-Mass Black Holes in Globular Clusters
• On the self-similar motion of a gravitating Chaplygin fluid
• Self-Similar Shocks and Winds in Galaxy Clusters
• Spherically-symmetric, cold collapse: the exact solutions and a comparison with self-similar solutions
• Magnetohydrodynamic Model of Equatorial Plasma Torus in Planetary Nebulae
• A Three-Dimensional Magnetohydrodynamic Model of Planetary Nebula Jets, Knots, and Filaments
• Vanishing viscosity limit for Riemann solutions to a $2\times 2$ hyperbolic system with linear damping
• Supermassive Black Holes in Galactic Bulges
• Homologous Gravitational Collapse in Lagrangian Coordinate: Planetary System in Protostar and Cavity in Pre-Supernova
• Delta shock solution to the generalized one-dimensional zero-pressure gas dynamics system with linear damping
• Mass and Mean Velocity Dispersion Relations for Supermassive Black Holes in Galactic Bulges