Hydrodynamic jets , underdense with respect to their environment by a factor of up to 10 ^ { 4 } , were computed in axisymmetry as well as in 3D .
They finally reached a size of up to 220 jet radii , corresponding to a 100 kpc sized radio galaxy .
The simulations are ” bipolar ” , involving both jets .
These are injected into a King type density profile with small stochastic density variations .
The back-reaction of the cocoons on the beams in the center produces armlength asymmetries of a few percent , with the longer jets on the side with the higher average density .
Two distinguishable bow shock phases were observed : an inner elliptical part , and a later cylindrical , cigar-like phase , which is known from previous simulations .
The sideways motion of the inner elliptical bow shock part is shown to follow the law of motion for spherical blast waves also in the late phase , where the aspect ratio is high , with good accuracy .
X-ray emission maps are calculated and the two bow shock phases are shown to appear as rings and elongated or elliptical regions , depending on the viewing angle .
Such structures are observed in the X-ray data of several radio galaxies ( e.g .
in Abell 2052 and Hercules A ) , the best example being Cygnus A .
In this case , an elliptical bow shock is infered from the observations , a jet power of 10 ^ { 47 } erg/s is derived , and the Lorentz factor can be limited to \Gamma > 10 .
Based on the simulation results and the comparison to the observations , the emission line gas producing the alignment effect in radio galaxies at high redshift is suggested to be cooled gas entrained over the cocoon boundary .