Relativistic models and the jet velocity field in the radio galaxy 3C 31
  We show that the principal differences in appearance of the main and counter-jets within 30 arcsec of the nucleus of the low-luminosity radio galaxy 3C 31 can result entirely from the effects of relativistic aberration in two symmetrical, antiparallel, axisymmetric, time-stationary relativistic flows. We develop empirical parameterized models of the jet geometry and the three-dimensional distributions of the velocity, emissivity and magnetic-field structure and optimize their parameters by fitting the predicted synchrotron intensity and polarization to deep 8.4-GHz VLA observations. We conclude that the jets are at roughly 52 degrees to the line of sight, that they decelerate and that they have transverse velocity gradients. They have three regions with distinct kinematics: a narrow inner region; a flaring region of rapid expansion followed by recollimation and a conical outer region. There is a discontinuity in the flow between inner and flaring regions. The on-axis velocity is close to 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 has primarily toroidal and longitudinal components except in the flaring region, where there is a significant radial component at the jet edge. Simple adiabatic models fail in the inner and flaring regions. 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. [Abridged] 
R. A. Laing (1), A. H. Bridle (2) ((1) Oxford/RAL, (2) NRAO)