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

We examine the constraints imposed on the total kinetic power (L j ) and the age (t age ) of relativistic jets in Fanaroff-Riley type II radio sources in a new way. We solve the dynamical expansion of its cocoon embedded in the intracluster medium and obtain the analytical solution of its physical quantities in terms of L j and t age . We estimate Lj and t age using a comparison of the model and the observed shape of the cocoon. The analysis focuses on Cygnus A and we find that (i) the source age is 3 < t age < 30 Myr and (ii) the total kinetic power of the jet is estimated as 0.2 x 10 46 < Lj < 1 x 10 48 erg s -1 , which is larger than 1 per cent of the Eddington luminosity of Cygnus A.