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]Comment: 29 pages, 25 figures, accepted by MNRAS. For additional material,
including higher-resolution figures and animations, see
http://www.cv.nrao.edu/~abridle/3c31free