2.3. Interactions with the extragalactic medium
One general feature of beam models (and, indeed, of any model which invokes ram pressure confinement of extended components) is that the maximum surface brightness attainable by the hot-spots is correlated with the density of the external medium. It is hard to quantify this relation precisely: it depends on the value of V, and on the fraction of the internal pressure that is provided by the relevant relativistic electrons and magnetic fields. It would, however, be a serious embarrassment to any such model if Cygnus A (or any other powerful double with equally intense "hot spots") were found to be definitely not in a cluster; though there is no such difficulty with a source such as 3C 236, where the internal energy density is ~ 100 times lower and can therefore be confined (for the same V) by a proportionately more rarefied external medium.
We suggest that this consideration is relevant to two important features of the data:
(i) As described by Willis (these proceedings), Gavazzi and Perola find that the most powerful sources (P 1025 Wm-2 Hz-1 ster-1) have linear sizes in the range 100-250 kps (for H = 100 km s-1 Mpc-1). The upper cut-off could be related to the scale height of the gas in a cluster of galaxies: even if the parent galaxy were sited in the centre of a cluster, and even if the central activity persisted, the beams would no longer be ploughing into dense gas (and would therefore no longer form Cygnus A-type hot-spots at the "working surface") when their distance exceeded a scale-height. (Note, however, that there are other possible interpretations of the observed correlation between P and linear size. For instance, there may be some reason why instabilities always broaden the beam before it penetrates beyond a certain distance).
(ii) The overall linear extent of double sources, and the compactness of their hot spots, may depend systematically on redshift, though the existing data are still tentative and ambiguous. Any such dependence may arise from (a) changes with epoch in the scale height of cluster gas, and (b) changes in the gas density in the source environment. As regards (b), the assumption has often been made that the relevant gas density scales just as (1 + z)3; but we wish to emphasise that things may be much less straightforward. The gas density in clusters may not have decreased at all between z 2 and the present epoch. Indeed it may even have increased, owing to infall, ejection from galaxies, etc; and we cannot exclude the possibility that the gas density surrounding strong extended sources at z 2 is typically lower than that for Cygnus A. Data from HEAO B may illuminate this question, but at the moment we cannot say whether hot spots should be systematically more or less compact in sources at large redshifts. If, as suggested in (i), the distribution of overall linear size depends on the scale height of cluster gas, this also may depend on z in an uncertain way. It is of course already quite widely appreciated that extended sources may be influenced by inverse Compton losses on the microwave background ( (1 + z)4) and by any dependence on cosmic epoch of the typical central power-supply and collimation mechanism. These cumulative uncertainties will certainly make it a long time before extended sources can constitute a worthwhile tool for "geometrical" cosmology.