Very light jets. I. Axisymmetric parameter study and analytic approximation

Abstract

The propagation of extragalactic jets is studied by a series of twelve axisymmetric hydrodynamic simulations. Motivated by observational constraints, but unlike most previous simulations, the regime of jet to external medium density ( $\eta$) from 10-5 to 10-2 is explored, for Mach numbers ( M) between 2.6 and 26. The computational domain contained the bow shocks for the whole simulation time. The bow shocks are found to be spherical at source sizes below a critical value r1 (blastwave phase), which can reach up to 10 jet radii. After that, their aspect ratio rises slowly, as long as the bow shock stays supersonic. The cocoons expand typically to almost the same size as the bow shock, unless the Mach number is below approximately three. Low values for the aspect ratio and the cocoon-to-bow-shock width ratio is demanded by recent Chandra X-ray observations of the bow shock in the archetypical radio galaxy Cygnus A. Therefore, $\eta<10^{-3}$ and M<6, in this source. The numerical work is complemented by an analytic approach for the spherical phase. Extending previous work, the radial force balance could be integrated for arbitrary background density and energy input, which results in a global solution. The analytic results are shown to be consistent with the numerical work, and a lower limit to r1 can be calculated, which falls below the numerical results by a few jet radii. It is shown explicitely how a King density distribution changes the discussed aspects of the bow shock propagation. Because the jet head propagates very fast in the blastwave phase, it turns out that it is not possible to "frustrate" a jet by a high density environment. This is very important for the class of small radio galaxies (compact symmetric objects / GHz peaked sources): They have to be young. During its blastwave phase, a powerful jet can transfer typically 1060 erg to the environmental gas. This is enough to balance the radiative losses in a cooling flow, if one of the cluster galaxies harbours a powerful jet every 109 years.