Estimate of the total kinetic power and age of extragalactic jet by its cocoon dynamics: The case of Cygnus A

Abstract

We examine the constraints imposed on the total kinetic power ($L_{\mathrm{j}}$) and the age ($t_{\mathrm{age}}$) of relativistic jets in FR II radio sources in a new way. We solve the dynamical expansion of its cocoon embedded in the intra-cluster medium (ICM) and obtain the analytic solution of its physical quantities in terms of $L_{\mathrm{j}}$ and $t_{\mathrm{age}}$. The estimate of $L_{\mathrm{j}}$ and $t_{\mathrm{age}}$ is done by the comparison of the model and the observed shape of the cocoon. The analysis is focused on Cygnus A and we find that (i) the source age is $3\mathrm{Myr}<t_{\mathrm{age}}<30\mathrm{Myr}$ and (ii) the total kinetic power of the jet is estimated as $0.2\times 10^{46}\mathrm{erg}{\mathrm{s}}^{-1}<L_{\mathrm{j}}<1\times 10^{48}\mathrm{erg}{\mathrm{s}}^{-1}$ which is larger than 1% of the Eddington luminosity of Cygnus A.

6 pages, 4 figures; MNRAS accepted, final version