TY - JOUR

T1 - The non-relativistic interiors of ultra-relativistic explosions

T2 - Extension to the Blandford-McKee solutions

AU - Faran, Tamar

AU - Sari, Re'em

N1 - Publisher Copyright:
© 2021 Author(s).

PY - 2021/2/1

Y1 - 2021/2/1

N2 - The hydrodynamics of an ultrarelativistic flow, enclosed by a strong shock wave, are described by the well-known Blandford-McKee solutions in spherical geometry. These solutions, however, become inaccurate at a distance ∼R/2 behind the shock wave, where R is the shock radius, as the flow approaches Newtonian velocities. In this work, we find a new self-similar solution that is an extension to the Blandford-McKee solutions and that describes the interior part of the blast wave, where the flow reaches mildly relativistic to Newtonian velocities. We find that the velocity profile of the internal part of the flow does not depend on the value of the shock Lorentz factor, Γ, and is accurate from r = 0 down to a distance of R/Γ2 behind the shock. Despite the fact that the shock wave is in causal contact with the entire flow behind it, a singular point appears in the equations. Nevertheless, the solution is not required to pass through the singular point: for ambient density that decreases slowly enough, ρ ∞ r-k with k < 1 2 (5 - 10) ≅ 0.92, a secondary shock wave forms with an inflow toward the origin.

AB - The hydrodynamics of an ultrarelativistic flow, enclosed by a strong shock wave, are described by the well-known Blandford-McKee solutions in spherical geometry. These solutions, however, become inaccurate at a distance ∼R/2 behind the shock wave, where R is the shock radius, as the flow approaches Newtonian velocities. In this work, we find a new self-similar solution that is an extension to the Blandford-McKee solutions and that describes the interior part of the blast wave, where the flow reaches mildly relativistic to Newtonian velocities. We find that the velocity profile of the internal part of the flow does not depend on the value of the shock Lorentz factor, Γ, and is accurate from r = 0 down to a distance of R/Γ2 behind the shock. Despite the fact that the shock wave is in causal contact with the entire flow behind it, a singular point appears in the equations. Nevertheless, the solution is not required to pass through the singular point: for ambient density that decreases slowly enough, ρ ∞ r-k with k < 1 2 (5 - 10) ≅ 0.92, a secondary shock wave forms with an inflow toward the origin.

UR - http://www.scopus.com/inward/record.url?scp=85101761591&partnerID=8YFLogxK

U2 - 10.1063/5.0037299

DO - 10.1063/5.0037299

M3 - Article

AN - SCOPUS:85101761591

SN - 1070-6631

VL - 33

JO - Physics of Fluids

JF - Physics of Fluids

IS - 2

M1 - 0037299

ER -