Relativistic models and the jet velocity field in the radio galaxy 3C 31

We compare deep Very Large Array (VLA) imaging of the total intensity and linear polarization of the inner jets in the nearby, low-luminosity radio galaxy 3C 31 with models of the jets as intrinsically symmetrical, decelerating relativistic flows. We show that the principal differences in appearance of the main and counter-jets within 30 arcsec of the nucleus can result entirely from the effects of relativistic aberration in two symmetrical, antiparallel, axisymmetric, time-stationary relativistic flows. We develop empirical parametrized models of the jet geometry and the three-dimensional distributions of the velocity, emissivity and magnetic-field structure. We calculate the synchrotron emission by integration through the models, accounting rigorously for relativistic effects and the anisotropy of emission in the rest frame. The model parameters are optimized by fitting to our 8.4-GHz VLA observations at resolutions of 0.25 and 0.75 arcsec full width at half maximum (FWHM), and the final quality of the fit is extremely good. The novel features of our analysis are that we model the two-dimensional brightness distributions at large number of independent data points rather than using one-dimensional profiles, we allow transverse as well as longitudinal variations of velocity, field and emissivity and we simultaneously fit total intensity and linear polarization. We conclude that the jets are ≈52° to the line of sight, that they decelerate and that they have transverse velocity gradients. Their magnetic field configuration has primarily toroidal and longitudinal components. The jets may be divided into three distinct parts, based not only on the geometry of their outer isophotes, but also on their kinematics and emissivity distributions: a well-collimated inner region; a flaring region of rapid expansion followed by recollimation and a conical outer region. The inner region is poorly resolved, but is best modelled as the sum of fast (0.8–0.9c) and much slower components. The transition between inner and flaring regions marks a discontinuity in the flow where the emissivity increases suddenly. The on-axis velocity stays fairly constant at ≈0.8c until the end of the flaring region, where it drops abruptly to ≈0.55c, thereafter falling more slowly to ≈0.25c at the end of the modelled region. Throughout the flaring and outer regions, the velocity at the edge of the jet is ≈0.7 of its on-axis value. The magnetic field in the flaring region is complex, with an essentially isotropic structure at the edge of the jet, but a more ordered toroidal + longitudinal configuration on-axis. In the outer region, the radial field vanishes and the toroidal component becomes dominant. We show that the emissivity and field structures are inconsistent with simple adiabatic models in the inner and flaring regions. We suggest that the discontinuity between the inner and flaring regions could be associated with a stationary shock structure and that the inferred transverse velocity profiles and field structure in the flaring region support the idea that the jets decelerate by entraining the external medium. We demonstrate the appearance of our model at other angles to the line of sight and argue that other low-luminosity radio galaxies resemble 3C 31 seen at different orientations.