The radio properties of a complete, X-ray selected sample of nearby, massive elliptical galaxies

We investigate the radio properties of a complete sample of nearby, massive, X-ray bright elliptical and S0 galaxies. Our sample contains 18 galaxies with ROSAT All-Sky Survey X-ray fluxes F-X,F- 0.1-2.4 keV > 3 x 10(-12) erg s(-1) cm(-2), within a distance of 100 Mpc. For these galaxies, we have completed (18/18) Very Large Array (VLA) radio and Chandra X-ray coverage. Nuclear radio emission is detected from 17/18 of the galaxies. Ten of the galaxies exhibit extended radio emission; of these 10, all but one also exhibit clear evidence of interaction of the radio source with the surrounding, X-ray emitting gas. Among the seven galaxies with unresolved radio sources, one has clear, and one has small, cavity-like features in the Chandra X-ray images; a third has a disturbed X-raymorphology. Using a radio luminosity limit equivalent to L-1.4 GHz > 10(23) W Hz(-1) to calculate the radio-loud fraction, we find that this misses the majority of the radio detected galaxies in the sample. We determine integrated radio-to-X-ray flux ratios for the galaxies, GRX, which are shown to span a large range (a factor of 100). We calculate the mass-weighted cooling times within 1 kpc, and find hints for an anticorrelation with the radio luminosity. We also calculate limits on k/f, where k is the ratio of the total particle energy to that of relativistic electrons radiating in the range 10 MHz-10 GHz and f is the volume filling factor of the plasma in the cavity. The k/f distribution is also broad, reflecting previous results for larger galaxy clusters. Lowering the X-ray flux limit, at the expense of less complete VLA and Chandra coverage, increases the size of our sample to 42 galaxies. Nuclear radio activity is detected in at least 34/42 of this extended sample.