Relativistic Hydrodynamics of a Free Expansion and a Shock Wave in OneDimension  SuperLight Expansion of Extragalactic Radio Sources
Abstract
Dynamical evolution of a relativistic explosion resulting from a large amount of energy release in a homogenous medium is studied using the Khalatnikov equation describing relativistic, hydrodynamic, planar flow. The early phase of the explosion is idealized to two stages: a free expansion and a shock wave stage. By the hodograph transformation inverting the dependent and independent variables, the hydrodynamic equations for the relativistic flow are reduced to secondorder linear equations in a velocityenthalpy space and they are solved by the method of Laplace transformation. The propagation laws and flow structures of the relativistic expansion are obtained at each stage. In the free expansion stage, the flow with a sufficiently high sound velocity forms a thin shell of the energy density in the comoving frame at the front and accelerates the front. In the shock wave stage, the Lorentz factor of the shock front decreases logarithmically with time. The transition time from a free expansion to a shock wave stage suggests that the superlight expansion observed in extragalactic radio sources has no spherical geometry but must be confined to a narrow cone.
 Publication:

Astrophysics and Space Science
 Pub Date:
 October 1980
 DOI:
 10.1007/BF00639150
 Bibcode:
 1980Ap&SS..72..447Y
 Keywords:

 Explosions;
 Extragalactic Radio Sources;
 Hydrodynamics;
 Relativity;
 Shock Wave Propagation;
 Enthalpy;
 Flow Equations;
 Laplace Transformation;
 Two Dimensional Flow;
 Velocity Distribution;
 Astrophysics