Dynamical models for jet deceleration in the radio galaxy 3C 31

We present a dynamical analysis of the flow in the jets of the low-luminosity radio galaxy 3C 31 based on our earlier geometrical and kinematic model and on estimates of the external pressure and density distributions from Chandra observations. We apply conservation of particles, energy and momentum to derive the variations of pressure and density along the jets and show that there are self-consistent solutions for deceleration by injection of thermal matter. We initially take the jets to be in pressure equilibrium with the external medium at large distances from the nucleus and the momentum flux to be Pi Phi/c, where Phi is the energy flux; we then progressively relax these constraints. With our initial assumptions, the energy flux is well determined: Phi approximate to 9-14 x 10(36) W. We infer that the jets are overpressured compared with the external medium at the flaring point (1.1 kpc from the nucleus) where they start to expand rapidly. Local minima in the density and pressure and maxima in the mass injection rate and Mach number occur at 3 kpc. Further out, the jets decelerate smoothly with a Mach number of approximate to1. The mass injection rate we infer is comparable with that expected from stellar mass loss throughout the cross-section of the jet close to the flaring point, but significantly exceeds it at large distances. We conclude that entrainment from the galactic atmosphere across the turbulent boundary layer of the jet is the dominant mass input process far from the nucleus, but that stellar mass loss may also contribute near the flaring point. The occurrence of a significant overpressure at the flaring point leads us to suggest that it is the site of a stationary shock system, perhaps caused by reconfinement of an initially free jet. Our results are compatible with a jet consisting of e(-)e(+) plasma on parsec scales that picks up thermal matter from stellar mass loss to reach the inferred density and mass flux at the flaring point, but we cannot rule out an e(-)p(+) composition with a low-energy cut-off.