Self-similar Blast Wave for A Two-component Fluid with Variable Adiabatic Index

We propose a self-similar (SS) solution to hydrodynamic non-relativistic flow behind a spherical strong blast wave (BW) passing through a homogeneous plasma with efficient relativistic particle acceleration at the shock front. The flow is described by an ideal two-fluid model with a relativistic component so that the post-shock gas has an effective SS adiabatic index $γ$ varying from $5/3$ to $4/3$. This solution is calculated numerically and compared with the standard Sedov solution. We find that the BW center in our solution is dominated by the relativistic component with $γ=4/3$ for the divergence of expansion there, and the relativistic component dominates the interior for a moderate acceleration efficiency at the shock front. The overall efficiency of relativistic particle acceleration can be enhanced by a factor of $2$ due to the slower adiabatic energy loss rate of the relativistic component during expansion. Tendency of the dominance by the relativistic component may be common in expanding astrophysical two-fluid systems such as supernova remnants, lobes of radio galaxies.

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