It is reasonable to expect that any difference in the radio properties of a sample of galaxies should be reflected in the radio luminosity function, either as a change in the shape or in the power cutoff, so it is instructive to see how the RLF for elliptical and S0 galaxies selected in different environments compares to the RLF derived for field galaxies. We note that galaxies with radio emission owe the radio activity primarily to an AGN-type mechanism, i.e. accretion from a central black hole, therefore when we compare the RLF for field and cluster ellipticals and S0s we test if the cluster environment affects the probability of such galaxy types developing a radio source of nuclear origin, i.e. a radio AGN.
This was first investigated by Fanti (1984), who obtained a RLF for ellipticals and SOs in rich Abell clusters with distance class D < 3 (z < 0.1), using 1.4 GHz interferometric data available in the literature. The most striking result is that the RLF for ellipticals and S0s in rich clusters and in the field does not differ. Even for cluster galaxies the only relevant parameter seems to be the optical magnitude, i.e. brighter galaxies have a higher probability of developing a radio galaxy within a given power range. The radial distribution of radio galaxies in rich clusters reveals a segregation effect, i.e. powerful radio sources are centrally peaked (more than 50% of radio galaxies with logPiAGHz ^ 24.5 are located within from the cluster centre), and the distribution flattens at lower powers. This could, at least in part, reflect the well known segregation in the optical, and could be interpreted as due to the fact that brighter galaxies, which have a higher probability of producing a powerful radio galaxy, tend to be more concentrated towards the cluster centre. As expected on the basis of these results, the RLF is also independent of the richness class of the clusters.
Those early results were more recently confirmed and reinforced by Ledlow & Owen (1996) on the basis of a much larger sample of cluster galaxies selected from the VLA 1.4 GHz survey of Abell clusters (Zhao et al. 1989; Owen et al. 1992, 1993) and coupled with R-band CCD photometry (Ledlow & Owen 1995). A total of 188 galaxies in Abell clusters were used to derive the local RLF, i.e. redshift z < 0.09 and radio power in the range logP (W Hz-1) from 22.4 to 25.6. Comparison between their RLF and the Auriemma et al. (1977) RLF shows no difference, either in shape or normalisation. Furthermore, no dependence is apparent on richness class, Bautz-Morgan or Rood-Sastry cluster class.
Thanks to the large number of galaxies and to the homogeneous optical information available for the whole sample, Ledlow & Owen (1996) carried out an accurate study of the bivariate RLF and confirmed that it depends only on the optical magnitude (Fig. 6.12). From their study it is confirmed that the RLF break P* depends on the optical luminosity L, following the law L2. This reflects a relevant result for elliptical galaxies, i.e. the power division between FRI and FRII radio galaxies is a function of the magnitude of the host galaxy (Owen & Ledlow 1994).
The universality of the local RLF for early type galaxies can be generalised also to merging clusters. Apparently, the enhanced probability of galaxy interaction in merging clusters has no effect on the probability of galaxies to develop a radio active AGN in their centres. The central cluster complexes in the Shapley Concentration, the largest concentration of merging clusters in the local Universe (Bardelli et al. 1998, 2000; Schindler 1996), were observed at radio wavelengths, and the results show that even this exceptionally unrelaxed environment seems not to increase the probability for elliptical galaxies to develop a radio source. In two out of the three merging complexes studied thus far, the RLF is consistent with the other environments, and for the remaining one it is lower (Venturi et al. 2001).
It is interesting to note that no evolution of the RLF has been found out to redshift z ~ 0.8 for logP1.4Giiz (W Hz-1) ~ 24 (Stocke et al. 1999). A deep radio survey of X-ray selected clusters with z < 0.8 shows that the global properties of radio galaxies in distant clusters, i.e. morphology, power range, core dominance, linear size and RLF, do not differ from those of rich nearby clusters.
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