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 Fx_(0.1-2.4 keV) > 3 x 10^(-12) erg/s/cm^2,
within a distance of 100 Mpc. For these galaxies, we have complete (18/18) 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
ten, 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-ray morphology.
Using a radio luminosity limit equivalent to L_(1.4 Ghz) > 10^(23) W/Hz 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
(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.
