3.1 Assumptions

Our key assumption is that the bases of the two jets are intrinsically identical, antiparallel, axisymmetric, stationary flows. We model the jets using simple parameterized expressions for the variables which determine the synchrotron emission - velocity fields, emissivity variations and intrinsic magnetic field structures - and determine the free parameters of these expressions by fitting to the observed images.

We assume that the flow is laminar and that there are no discontinuous changes of direction. If there is a turbulent velocity component (as theoretical models suggest; Section 5.2), then our technique will determine an average bulk flow speed, weighted by the distribution of Doppler beaming factors in a given region. We also assume that the variations of velocity and emissivity are continuous and smooth unless our fitting procedure explicitly requires discontinuities (this turns out to be the case at one special location: see Section 3.3).

We allow both for longitudinal deceleration as inferred from the B2 sample data (Laing et al.1999) and for transverse velocity structure. The latter is required for two reasons. First, one class of model for relativistic jet deceleration invokes entrainment of the interstellar medium from the host galaxy across a boundary layer. A transverse velocity variation allows for the possibility that the relativistic particles near the edges of the jet move down the jet more slowly than those on the jet axis. Second, because the outer isophotes of the jets in FRI sources are usually more symmetric across the nucleus than those close to the jet axis ( Laing 1993, Laing 1996,  Hardcastle et al.1997; Laing et al. 1999), a transverse velocity variation is generally required to fit well-resolved jet brightness distributions. In order to quantify this effect, we consider two possible transverse structures. In the first (Laing 1993), a central fast spine with no transverse variation of velocity or emissivity is surrounded by a slower shear layer with gradients in both variables. In the second case, there is no distinct spine component, and the jet consists entirely of a shear layer with a truncated Gaussian transverse variation in velocity. We will refer to the two types as spine/shear-layer (SSL) and Gaussian models, respectively.

The significant linear polarization observed requires an anisotropic magnetic field. We assume that it is disordered on small scales, with negligible mean, and that the anisotropy is introduced by shear and compression. We consider large-scale ordering of the magnetic fields to be unlikely. The simplest ordered fields capable of generating the observed polarization (single helices) produce large changes in emission across the jets, which are not observed ( Laing 1981; Clarke, Norman & Burns 1989). More complex ordered configurations, such as those proposed by Königl & Choudhuri 1985, cannot be as easily dismissed on observational grounds, but the presence of a significant ordered longitudinal component is ruled out by flux conservation arguments (Begelman, Blandford & Rees 1984). In any case, our conclusions on the relative magnitudes of the field components would not be seriously affected (indeed, our calculations would be unchanged if one of the three field components is vector-ordered). We quantify the anisotropy using the ratios of the rms field components along three orthogonal directions.

The spectrum of the jets between 1.4 and 8.4 GHz at a resolution of 1.5 arcsec FWHM is accurately described by a power law with a spectral index $\alpha = 0.55$ ( $S_\nu \propto \nu^{-\alpha}$). The emission is therefore taken to be optically thin (we do not attempt to model the partially self-absorbed parsec-scale core). The corresponding electron energy distribution is $n(E)dE = n_0 E^{-(2\alpha+1)} dE = n_0 E^{-2.1} dE$. We assume an isotropic pitch-angle distribution relative to the field, so the degree of polarization, $p = (U^2+Q^2)^{1/2}/I$, has a maximum value of $p_0 = (3\alpha+3)/(3\alpha+5) = 0.70$.

2002-06-13