We present a detailed analysis of the results of a two-frequency VLA survey with scaled arrays of 60 flelds near 58 Abell clusters. The sample of sources is complete to a ∞ux density of 2¢ 0 mJy at 1¢ 5 GHz, from which we chose two sub-samples of radio galaxies from clusters that had been surveyed completely 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 strongly concentrated towards their cluster centres, showing a power-law variation of surface density with radius, with an exponent of »i1¢ 6. Each cluster contains an average of two radio galaxies. (ii) The ratios of ∞ux density and surface brightness in the lobes of cluster and background doubles are very similar, as are their spectral indices; the ratios of component area are signiflcantly difierent. (iii) The lobes of cluster doubles have spectra that steepen with radio power, but a less signiflcant relationship is found between spectral index and surface brightness. (iv) Relationships are found between source area and radio power, optical luminosity and r/RA, spectral index and r/RA, and between radio power and optical luminosity. (v) We deflne three polarisation classes on the basis of the presence or absence of observable polarisation at 4¢ 9 and 1¢ 5 GHz; the physical parameters vary systematically across the classes. (vi) Depolarisation in sources that are partially polarised at both frequencies (Class I) is predominantly caused by tangled flelds; sources that are polarised at only the higher frequency (Class II) or at neither frequency (Class III) are depolarised by a combination of tangled flelds and difierential Faraday rotation. The rms dispersion in the scale size of the tangled flelds within the radio plasma is»5 kpc. (vii) Difierential Faraday depolarisation in Classes I and II suggests that thermal electrons are entrained in the radio plasma with densities in the range 1¢ 1{2¢ 3£10 i4 cm i3 . (viii) The magnetic flelds in Class I doubles (with minimum Faraday rotation) favour directions predominantly parallel to the major axis of the double. (ix) The univariate fractional luminosity function suggests that an early-type cluster galaxy with M R•i21¢ 0 has a probability of »0¢ 02 of creating a radio source with P 1¢ 5• 10 24¢ 9 WH z i 1 . (x) The integrated bivariate fractional luminosity function shows that higher luminosity cluster galaxies are more likely to form radio sources, although 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 »2£10 6 yr is consistent with the travel-time of the plasma at»3000 km s i1 from a once-only acceleration site near the centre of the host galaxy. (xii) The conflnement of the radio lobes can be easily 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 are both independently correlated with cluster X-ray luminosity. This suggests that radio power is maintained by the conflning pressure of the hot gas, but the cause of the ⁄ Paper I, Aust. J. Phys., 1989, 42, 633; Paper II, Aust. J. Phys., 1994, 47, 145; Paper III, Aust. J. Phys., 1996, 49, 977.
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