A model for the surface brightness of a turbulent, low Mach number jet. II - The global energy budget and radiative losses

Abstract

Detailed consideration is given to the energy balance in extragalactic radio sources, in particular the Fanaroff-Riley class I radio sources whose morphology is likely to be due to jets being stopped by entrain-ment of the surrounding medium. It is shown that the ratio, k, of the lobe synchrotron plus inverse Compton luminosity to the jet energy flux can be estimated if there exist spectral index variations across the lobe from which an age can be determined and if the ratio EJE L of relativistic electron energy to total lobe energy is known. It is argued that in class I sources EJE L mainly depends upon the initial composition of plasma ejected from the core and the dilution by thermal material entrained along the jet. If the relativistic electron energy is at least comparable to the relativistic proton energy and the lobe is approximately in equipartition, then 0.1 < EJE l < 0.25. The value of k, combined with the dependence of the energy flux along the jet and expressions for the energy flux across an arbitrary section of the jet, can be used to estimate the jet velocity. For low Mach numbers (M^ <00, where M c is the central Mach number) the energy flux is dominated by the enthalpy flux, and estimates of the velocity are virtually independent of estimates of the thermal density which are uncertain at present. For « 10 upper limits on the jet velocity may be obtained by ignoring the Mach number dependence of the energy flux. Spectral index variations in jets of arbitrary nonrelativistic velocity are also considered since this provides a means of determining whether a jet is dissipative over a given region or not. It is shown that if an injected power-law electron distribution evolves nondissipatively, the cutoff frequency downstream is proportional to the parameter (v 0 Bq 3/2) 2 (v 0 and B 0 are jet velocity and magnetic field at a fiducial point) times an easily calculated angular function which depends upon the variation of jet velocity. The parameter v 0 Bq 3/2 can be estimated from relations derived from the source energy balance and the surface brightness of the jet, without recourse to separate estimates of velocity and magnetic field. The theory is applied to further the analysis of the northern jet in 3C 31. It is also shown, using a compilation of jet data by Bridle, that a feasible explanation for the transition from class I to class II sources at P^Ughz^ Ï0 25 WHz-1 is that the jets in the class I sources have a Mach number < 2 in the region before they start to expand most rapidly. Laboratory data of Lau are advanced to support the view that light, supersonic jets with Mach numbers less than ~2, will become fully turbulent, entrain, and become subsonic or transonic in typical elliptical galaxy atmospheres. The deceleration of class I jets and their more rapid expansion rates combine to make the perpendicular magnetic field dominate in these sources.