Oblique Shock Breakout from a Uniform Density Medium

Abstract

The emergence of a shock from a medium with a free surface is an important process in various astrophysical phenomena. It generates the first light associated with explosions like supernovae and Gamma Ray Bursts. Most previous works considered planar or spherical geometries, where the shock front is parallel to the surface, and emerges simultaneously from all points. Here we study the hydrodynamics of an oblique planar shock breaking out from the planar surface of a uniform density ideal gas with adiabatic index $\gamma$. We obtain an analytic solution to the flow as a function of the angle between the plane of the shock and the surface $\beta$. We find steady state solutions (in a frame moving with the intersection point of the shock and the surface) up to some critical angle (${\beta }_{max}=63.4$ degress for $\gamma =5/3$ and ${\beta }_{max}=69.3$ degrees for $\gamma =4/3$). We show how this analytic solution can be used in more complicated geometries where the shock is not planar, giving the exact profile of the outermost breakout ejecta. We apply our analytical results to a few realistic problems, such as underwater explosions, detonation under the surface of an asteroid, or off center detonations in a uniform sphere.

arXiv comment10 pages, 10 figures. Accepted for publication in Physics of Fluids

References in corpus (9)

• The Expulsion of Stellar Envelopes in Core-Collapse Supernovae
• An extremely luminous X-ray outburst at the birth of a supernova
• Early supernovae light-curves following the shock-breakout
• From Shock Breakout to Peak and Beyond: Extensive Panchromatic Observations of the Type Ib Supernova 2008D associated with Swift X-ray Transient 080109
• The metamorphosis of Supernova SN2008D/XRF080109: a link between Supernovae and GRBs/Hypernovae
• Relativistic shock breakouts - a variety of gamma-ray flares: from low luminosity gamma-ray bursts to type Ia supernovae
• Oblique Shock Breakout in Supernovae and Gamma-Ray Bursts: I. Dynamics and Observational Implications
• Oblique Shock Breakout in Supernovae and Gamma-Ray Bursts: II. Numerical Solutions For Non-Relativistic Pattern Speeds
• Asymptotic Steady State Solution to a Bow Shock with an Infinite Mach Number

Cited by in corpus (6)

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• Partial Stellar Explosions -- Ejected Mass and Minimal Energy
• Bolometric light curves of aspherical shock breakout
• Wave-Driven Shocks in Stellar Outbursts: Dynamics, Envelope Heating, and Nascent Blastwaves
• Revisiting GRB 060218: new insights into low-luminosity gamma-ray bursts from a revised shock breakout model
• Van der Waals shock polars with multiple or supersonic critical points