1 Introduction

The flow parameters of jets in extragalactic radio sources have hitherto proven difficult to determine because of the absence of unambiguous diagnostics. Most progress has been made in the estimation of velocities, particularly where these are thought to be relativistic. The idea that jets in low-luminosity, i.e. FRI (Fanaroff & Riley 1974), radio galaxies have relativistic speeds rests on five main arguments:

1. evidence for relativistic motion on parsec scales in BL Lac objects, coupled with the hypothesis that they are FRI radio galaxies observed at small angles to the line of sight (Urry & Padovani 1995);

2. measurement of apparent proper motions with speeds up to at least $c$ in M87 (Biretta, Zhou & Owen 1995);

3. modelling of relativistic flows, which demonstrates the feasibility of deceleration on kiloparsec scales in realistic galactic atmospheres (Bicknell 1994;  Komissarov 1994; Bowman, Leahy & Komissarov , 1996);

4. the interpretation of correlated depolarization asymmetry and jet sidedness in FRI sources (Morganti et al.1997) as a consequence of Doppler beaming and foreground Faraday rotation (Laing 1998);

5. observations of brightness and width asymmetries in FRI jets which decrease with distance from the nucleus and are correlated with fractional core flux, implying that they decelerate and are faster on-axis than at their edges ( Laing 1993, Laing 1996; Hardcastle et al 1997; Laing et al. 1999).

This paper reports a detailed study of the applicability of decelerating relativistic jet models to the well-resolved kiloparsec-scale structures in the nearby FRI radio galaxy 3C31. Our intention is to deconvolve the emission mechanism (synchrotron radiation from a magnetized relativistic flow) from the radio data, without embodying specific preconceptions about the poorly known internal physics. We construct sophisticated three-dimensional models of the effects of relativistic aberration on the appearance of intrinsically symmetric magnetized jets and we fit these models to the observed total and polarized intensity distributions in 3C31. The aim is to derive robust estimates of the velocity field, the emissivity (combining relativistic particle density and magnetic field strength) and the three-dimensional ordering of the magnetic field (purely geometrical factors independent of its strength). We regard this as a necessary first step: realistic physical models capable of being compared with observations are not yet available. We are able to reproduce many of the observed features of the jets and we conclude that our models now provide a way to obtain key constraints on the intrinsic properties of extragalactic radio jets.

Section 2 describes new VLA imaging of the jets in 3C31 that provides a high-quality data set suitable for detailed fitting by our models. Section 3 first reviews the principles underlying the relativistic jet models, and then goes on to describe how we adjust their parameters to fit the radio intensity and polarization data. Section 4 critically discusses the model fits and reviews the main features of the inferred jet velocity field, magnetic structure and emissivity distribution. Section 5 discusses more general implications, including: specific problems associated with reproducing the properties of the jets in the region closest to the galactic nucleus; the reasons for the sudden onset of deceleration; evidence for interaction between the jet and the surrounding medium and the applicability of adiabatic models.

Section 6 illustrates how the jets in 3C31 should appear if orientated at other angles to the line of sight and outlines the applicability of the model to other FRI sources, including those orientated at a small angle to the line of sight. Section 7 summarizes our conclusions regarding the kinematics, emissivity and field structure of the three distinct regions of the jet and their implications for future work.

Throughout this paper, we adopt a Hubble constant H₀ = 70 km s$^{-1}$Mpc$^{-1}$.

2002-06-13