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this paper is a progress report on a project whose aim is to derive quantitative estimates for the physical parameters of jets .
we have developed techniques to derive the three - dimensional distributions of velocity , rest - frame emissivity and magnetic - field structure and hence to deduce the jet dynamics via a conservation - law approach .
our fundamental assumption is that jets may be approximated as intrinsically symmetrical , time - stationary , axisymmetric relativistic flows .
we model their observed radio synchrotron emission in total intensity and linear polarization , using the observed differences between approaching and receding jets to constrain velocity , emissivity and field .
we then combine this model of jet kinematics with a description of the surrounding igm and use conservation of energy , momentum and particles to estimate the internal pressure and density .
for this technique to work , we need sources with two - sided but asymmetrical and straight radio jets .
we then make deep observations with many resolution elements to derive total intensity and linear polarization , corrected for any faraday rotation .
we also require x - ray observations of the hot gas surrounding the radio source from which the external pressure and temperature may be derived . at present
, these requirements are met only by vla and _ chandra _ observations of nearby fri radio galaxies .
the first source to which we have applied these techniques in full is 3c31 : the kinematic model , x - ray observations and conservation - law analysis are described by @xcite , @xcite and @xcite , respectively .
the kinematic model requires the jets to be at @xmath0 52@xmath1 to the line of sight .
the jets may be divided into three distinct sections by geometry , velocity and emissivity variation : a well - collimated inner region , a flaring region in which the jets widen rapidly and then recollimate and a conical outer region . both deceleration ( from @xmath2 where the jet flares to @xmath3 at the end of the modelled region ) and
transverse velocity gradients are inferred .
the toroidal magnetic field component is larger than the longitudinal component almost everywhere and the radial component is small except at the edge of the jet in the flaring region , where the field is roughly isotropic , perhaps as a result of turbulent entrainment .
the beginning of the flaring region marks a discontinuity in emissivity and , probably , velocity .
the conservation - law analysis shows that the jets must be extremely light ( @xmath4kgm@xmath5 ) .
the entrainment rate has a local maximum where the expansion is fastest ; thereafter , it increases smoothly and monotonically .
the required entrainment could be provided by stellar mass loss close to the nucleus , but interaction with the external medium is required at larger distances . the jet is overpressured with respect to the surrounding medium where it flares , but the outer region is likely to be in pressure equilibrium .
the composition of the jet is not determined uniquely by this analysis , but an electron - positron jet with entrained thermal matter would be consistent with all of the available evidence .
we have applied simplified kinematic models to describe less detailed observations of a complete sample of fri radio galaxies from the b2 sample @xcite .
two of these , 0326 + 39 and 1553 + 24 , have been reobserved with the vla at 8.4ghz and modelled in detail ( canvin & laing , in preparation ) .
good fits were again obtained : we show a comparison between model and data for 0326 + 39 in fig .  [ 0326fig ] .
the basic picture of jet deceleration with tranverse velocity gradients holds for both sources , but there are interesting differences in the field structures : 1553 + 24 ( like 3c31 ) has a dominant toroidal component but the outer part of 0326 + 29 ( fig .  [ 0326fig ] ) has roughly equal radial and toroidal components , but no longitudinal field ( cf .
thus far , we have assumed that emissivity and field structure are independent of the velocity field .
this is appropriate if we aim to deduce the internal parameters without imposing preconceptions about the underlying physics , but to make further progress , we need to make additional assumptions .
the simplest approximation is that the jets are `` adiabatic '' in the sense defined by @xcite : the relativistic particles lose energy only by the adiabatic process and the magnetic field is convected passively with the flow . @xcite derived analytical relations for the surface - brightness of a relativistic jet with no transverse velocity gradient and either a transverse or longitudinal magnetic field .
we have generalized their approach to include shear and arbitrary initial field geometry , using a formalism based on that of @xcite .      in fig .
[ 3c31ad ] , we show the results of fitting adiabatic models to the outer regions of the jets in 3c31 , with initial conditions set as profiles of emissivity and field - ordering across the jet at the start of the region .
the models fit reasonably well , but can not accurately describe the observed polarization at the jet edges .
a likely possibility is that the velocity field is more complicated than the simple laminar flow we assume , and that some turbulent component is present , leading to changes in field ordering and strength which are not described by our model .
in contrast , adiabatic models fail completely in the inner and flaring regions .
this should not come as a surprise : the x - ray emission detected in these regions by @xcite is most likely to be synchrotron radiation , requiring significant particle acceleration .
we model jets in low - luminosity ( fri ) radio galaxies as intrinsically symmetrical , axisymmetric , decelerating relativistic flows with transverse velocity gradients . 
 this allows us to derive velocity fields and the three - dimensional distributions of magnetic - field ordering and rest - frame emissivity . 
 a conservation - law analysis , combining the kinematic model with x - ray observations of the surrounding igm , gives the profiles of internal density , pressure , mach number and entrainment rate along the jets . 
 we summarize our recently - published results on 3c31 and outline new work on other sources and adiabatic jet models .    ,    ,    galaxies : jets , radio continuum : galaxies , x - rays : galaxies , magnetic fields , polarization    98.62.n , 98.54.g