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.