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 (~200) low-luminosity active galactic nuclei (LLAGNs) and AGNs in the Palomar Spectroscopic Sample. The high incidences of pc-scale radio nuclei, with T(brightness) >=10^7 K, and sub-parsec jets argue for accreting black holes in >=50% of all LINERs and low-luminosity Seyferts; there is no evidence against all LLAGNs being mini-AGNs. 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-power turnover in the RLF; nevertheless LLAGNs are responsible for a significant fraction of present day mass accretion. Adopting the jet model of Falcke & Biermann, we show that the accretion energy output in LLAGNs is dominated by the energy in the observed jets rather than the radiated bolometric luminosity. The Palomar LLAGNs and AGNs follow the same scaling between jet power and narrow line region (NLR) luminosity as the pc to kpc jets in powerful radio galaxies. Eddington ratios 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). The jets are energetically more significant than supernovae in the LLAGN host galaxies, and are potentially able to deposit sufficient energy into the innermost parsecs to significantly slow the gas supply to the accretion disk.