Radio sources in low-luminosity active galactic nuclei - IV. Radio luminosity function, importance of jet power, and radio properties of the complete Palomar sample

We present the completed results of a high resolution radio imaging survey of all (similar to 200) low-luminosity active galactic nuclei (LLAGNs) and AGNs in the Palomar Spectroscopic Sample of all (similar to 488) bright northern galaxies. The high incidences of pc-scale radio nuclei, with implied brightness temperatures greater than or similar to 10(7) K, and sub-parsec jets argue for accreting black holes in greater than or similar to 50% of all LINERs and low-luminosity Seyferts; there is no evidence against all LLAGNs being mini-AGNs. The detected parsec-scale radio nuclei are preferentially found in massive ellipticals and in type 1 nuclei (i.e. nuclei with broad Ha emission). The radio luminosity function (RLF) of Palomar Sample LLAGNs and AGNs extends three orders of magnitude below, and is continuous with, that of "classical" AGNs. We find marginal evidence for a low-luminosity turnover in the RLF; nevertheless LLAGNs are responsible for a significant fraction of present day mass accretion. Adopting a model of a relativistic jet from Falcke & Biermann, we show that the accretion power output in LLAGNs is dominated by the kinetic power in the observed jets rather than the radiated bolometric luminosity. The Palomar LLAGNs and AGNs follow the same scaling between jet kinetic power and narrow line region (NLR) luminosity as the parsec to kilo-parsec jets in powerful radio galaxies. Eddington ratios l(Edd) (= L-Emitted/ L-Eddington) of <= 10(-1)- 10(-5) are implied in jet models of the radio emission. We find evidence that, in analogy to Galactic black hole candidates, LINERs are in a "low/hard" state ( gas poor nuclei, low Eddington ratio, ability to launch collimated jets) while low-luminosity Seyferts are in a "high" state ( gas rich nuclei, higher Eddington ratio, less likely to launch collimated jets). In addition to dominating the radiated bolometric luminosity of the nucleus, the radio jets are energetically more significant than supernovae in the host galaxies, and are potentially able to deposit sufficient energy into the innermost parsecs to significantly slow the gas supply to the accretion disk.