X-ray measurements of the external medium support arguments that low-power FRI jets slow through entrainment of this gas.
For the few low-power radio galaxies with heavily studied, straight, radio jets and counterjets (and so lying relatively close to the plane of the sky and presumably in relatively relaxed environments), kinematic models have been constructed to fit the jet-counterjet asymmetry [131, 38, 39, 132]. Typically, the jets start fast (relativistic) and relatively faint with a small opening angle. Then they go through a flaring region where they steadily broaden and are typically bright both in radio and X-ray (Fig. 1), and finally the opening angle changes and the jet becomes fainter, particularly at X-ray energies (e.g. 221). It is in this final region, beyond that shown for NGC 315 in Figure 1, that the jets are modelled as decelerating steadily as they collect mass from the external medium or stellar winds . Buoyancy forces are then important for much of the flow further downstream, as the jets adjust to changes in the density of the external medium, causing deflections from straight-line motion.
In ongoing work, these kinematic models are being extended into dynamical models, based on conservation laws for mass, momentum, and energy , and are being tested for self consistency with the density and pressure of the external medium. For one source so far, 3C 31, excellent self consistency has been found . This lends confidence to an understanding of the basic flow behaviour of these sources.
Deceleration via mass entrainment is consistent with a range of observational evidence at radio frequencies , and naturally leads to the outer parts of the jet (sheath) being decelerated before the inner (spine). Applied to more central regions, the consequence that emission from a slower sheath becomes relatively more important in jets at larger angle to the line of sight then resolves difficulties in models that unify BL Lac objects with FRI radio galaxies (e.g. 48).
It has been known since the Einstein and ROSAT X-ray observatories that the minimum pressure in low-power FRI jets (calculated without relativistic protons) is normally below that of the external X-ray-emitting medium (e.g. 149, 121, 77, 216). The model for 3C 31  demonstrates that entrainment of the external medium explains the jet dynamics in the deceleration region, and pressure balance can be achieved by adding relativistic protons (with neutrality preserved by balancing proton and electron number densities) or extending the electron spectrum to lower energies (if electron-positron charge balance is enforced). Recent work  has claimed a greater pressure imbalance in FRI jets that are more in contact with external gas (less in contact with the plumes or lobes of older jet plasma), and speculates that the pressure is balanced by heated entrained material, with an entrainment rate or a heating efficiency that is higher where jets are in greater direct contact with the X-ray-emitting atmosphere. This seems in conflict with the entrainment model for the quasar PKS 1136-135 in the context of the beamed iC-CMB model, where a standard model would have the jets heavily embedded in old lobe plasma and yet where the estimated entrainment rate is an order of magnitude higher than for 3C 31 .
While the X-ray-emitting interstellar or intergalactic medium can thus be controlling the flow where FRI jets are decelerating, and indeed where buoyancy forces or an excess of gas pressure dominate (e.g. 215, 222), FRI radio jets are highly overpressured in their inner regions close to the nucleus (e.g. 130). Here the X-ray emission has yet to contribute in a significant way to the collimation debate.
The jets of FRII radio galaxies are not significantly in contact with the external medium for most of their length, so the external medium is unlikely to control jet collimation, although entrainment of external gas might be significant over their long propagation paths . Current uncertainties in the jet X-ray emission mechanism, and thus the particle content and energy, make direct comparison of the internal and external pressures difficult, except in the large-scale lobes if dynamical effects are ignored.