A VLA survey of rich clusters of galaxies - IV. An analysis of the results

We present a detailed analysis of the results of a two-frequency VLA survey with scaled arrays of 60 fields near 58 Abell clusters. The sample of sour ces is complete to a flux density of 2.0 mJy at 1.5 GHz, from which we chos e two sub-samples of radio galaxies from clusters that had been surveyed co mpletely out to 0.24, and 0.51 times the Abell radius RA respectively. The following conclusions are drawn from these samples: (i) The sources are str ongly concentrated towards their cluster centres, showing a power-law varia tion of surface density with radius, with an exponent of similar to-16. Eac h cluster contains an average of two radio galaxies. (ii) The ratios of flu x density and surface brightness in the lobes of cluster and background dou bles are very similar, as are their spectral indices; the ratios of compone nt area are significantly different. (iii) The lobes of cluster doubles hav e spectra that steepen with radio power, but a less significant relationshi p is found between spectral index and surface brightness. (iv) Relationship s are found between source area and radio power, optical luminosity and r/R -A, spectral index and r/R-A, and between radio power and optical luminosit y. (v) We define three polarisation classes on the basis of the presence or absence of observable polarisation at 4.9 and 1.5 GHz; the physical parame ters vary systematically across the classes. (vi) Depolarisation in sources that are partially polarised at both frequencies (Class I) is predominantl y caused by tangled fields; sources that are polarised at only the higher f requency (Class II) or at neither frequency (Class III) are depolarised by a combination of tangled fields and differential Faraday rotation. The rms dispersion in the scale size of the tangled fields within the radio plasma is similar to 5 kpc. (vii) Differential Faraday depolarisation in Classes I and II suggests that thermal electrons are entrained in the radio plasma w ith densities in the range 1.1-2.3x10(-4) cm(-3) (viii) The magnetic fields in Class I doubles (with minimum Faraday rotation) favour directions predo minantly parallel to the major axis of the double. (ix) The univariate frac tional luminosity function suggests that an early-type cluster galaxy with M-R less than or equal to -21.0 has a probability of similar to 0.02 of cre ating a radio source with P-1.5 less than or equal to 10(24.9) W Hz(-1). (x ) The integrated bivariate fractional luminosity function shows that higher luminosity cluster galaxies are more likely to form radio sources, althoug h in each bin of absolute magnitude the fraction of radio sources decreases with increasing radio power. (xi) The average lifetime of a cluster source of similar to 2x10(6) yr is consistent with the travel-time of the plasma at similar to 3000 kms(-1) from a once-only acceleration site near the cent re of the host galaxy. (xii) The confinement of the radio lobes can be easi ly accomplished by the static pressure of the hot intra-cluster gas and/or ram pressure generated by the passage of the galaxy through the gas. (xiii) Radio powers of cluster sources and optical luminosities of their hosts ar e both independently correlated with cluster X-ray luminosity. This suggest s that radio power is maintained by the confining pressure of the hot gas, but the cause of the optical correlation is unknown. (xiv) Finally, core po wers in cluster radio galaxies are of the same order as those in non-cluste r sources, indicating that the hot intra-cluster gas does not provide an ex tra fuel supply for the nuclear engine.