On the local radio luminosity function of galaxies I. The Virgo cluster

We cross-correlate the galaxies brighter than m(B) = 18 in the Virgo cluste r with the radio sources in the NVSS survey (1.4 GHz), resulting in 180 rad io-optical identifications. We determine the radio luminosity function of t he Virgo galaxies, separately for the early- and late-types. Late-type gala xies develop radio sources with a probability proportional to their optical luminosity. In fact their radio/optical (R-B) distribution is gaussian, ce ntered at log R-B similar to -0.5, i.e. the radio luminosity is similar to 0.3 of the optical one. The probability of late-type galaxies to develop ra dio sources is almost independent of their detailed Hubble type, except for Sa (and S0+S0a) which are a factor of similar to 5 less frequent than late r types at any R-B. Giant elliptical galaxies feed "monster" radio sources with a probability s trongly increasing with mass. However the frequency of fainter radio source s is progressively less sensitive on the system mass. The faintest giant E galaxies (M-B = -17) have a probability of feeding low power radio sources similar to that of dwarf E galaxies as faint as M-B = -13.