TY - JOUR
T1 - Energy-conserving Relativistic Corrections to Strong-shock Propagation
AU - Coughlin, Eric R.
N1 - Publisher Copyright:
© 2019. The American Astronomical Society. All rights reserved..
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2019/8/1
Y1 - 2019/8/1
N2 - Astrophysical explosions are accompanied by the propagation of a shockwave through an ambient medium. Depending on the mass and energy involved in the explosion, the shock velocity V can be nonrelativistic (V ≪ c, where c is the speed of light), ultrarelativistic (V ≃ c), or moderately relativistic (V ∼ few × 0.1c). While self-similar energy-conserving solutions to the fluid equations that describe the shock propagation are known in the nonrelativistic (the Sedov-Taylor blastwave) and ultrarelativistic (the Blandford-McKee blastwave) regimes, the finite speed of light violates scale invariance and self-similarity when the flow is only mildly relativistic. By treating relativistic terms as perturbations to the fluid equations, here we derive the , energy-conserving corrections to the nonrelativistic Sedov-Taylor solution for the propagation of a strong shock. We show that relativistic terms modify the post-shock fluid velocity, density, pressure, and the shock speed itself, the latter being constrained by global energy conservation. We derive these corrections for a range of post-shock adiabatic indices γ (which we set as a fixed number for the post-shock gas) and ambient power-law indices n, where the density of the ambient medium ρ a into which the shock advances declines with spherical radius r as ρ a ∝ r -n. For Sedov-Taylor blastwaves that terminate in a contact discontinuity with diverging density, we find that there is no relativistic correction to the Sedov-Taylor solution that simultaneously satisfies the fluid equations and conserves energy. These solutions have implications for relativistic supernovae, the transition from ultra- to subrelativistic velocities in gamma-ray bursts, and other high-energy phenomena.
AB - Astrophysical explosions are accompanied by the propagation of a shockwave through an ambient medium. Depending on the mass and energy involved in the explosion, the shock velocity V can be nonrelativistic (V ≪ c, where c is the speed of light), ultrarelativistic (V ≃ c), or moderately relativistic (V ∼ few × 0.1c). While self-similar energy-conserving solutions to the fluid equations that describe the shock propagation are known in the nonrelativistic (the Sedov-Taylor blastwave) and ultrarelativistic (the Blandford-McKee blastwave) regimes, the finite speed of light violates scale invariance and self-similarity when the flow is only mildly relativistic. By treating relativistic terms as perturbations to the fluid equations, here we derive the , energy-conserving corrections to the nonrelativistic Sedov-Taylor solution for the propagation of a strong shock. We show that relativistic terms modify the post-shock fluid velocity, density, pressure, and the shock speed itself, the latter being constrained by global energy conservation. We derive these corrections for a range of post-shock adiabatic indices γ (which we set as a fixed number for the post-shock gas) and ambient power-law indices n, where the density of the ambient medium ρ a into which the shock advances declines with spherical radius r as ρ a ∝ r -n. For Sedov-Taylor blastwaves that terminate in a contact discontinuity with diverging density, we find that there is no relativistic correction to the Sedov-Taylor solution that simultaneously satisfies the fluid equations and conserves energy. These solutions have implications for relativistic supernovae, the transition from ultra- to subrelativistic velocities in gamma-ray bursts, and other high-energy phenomena.
KW - gamma-ray burst: general
KW - hydrodynamics
KW - methods: analytical
KW - shock waves
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U2 - 10.3847/1538-4357/ab29e6
DO - 10.3847/1538-4357/ab29e6
M3 - Article
AN - SCOPUS:85071947012
VL - 880
JO - Astrophysical Journal
JF - Astrophysical Journal
SN - 0004-637X
IS - 2
M1 - 108
ER -