15-GHz radio emission from nearby low-luminosity active galactic nuclei
  We present a sub-arcsec resolution radio imaging survey of a sample of 76
low-luminosity active galactic nuclei (LLAGN) that were previously not detected
with the Very Large Array at 15 GHz. Compact, parsec-scale radio emission has
been detected above a flux density of 40 $\mu$Jy in 60% (45 of 76) of the LLAGN
sample. We detect 20 out of 31 (64%) low-ionization nuclear emission-line
region (LINER) nuclei, ten out of 14 (71%) low-luminosity Seyfert galaxies, and
15 out of 31 (48%) transition objects. We use this sample to explore
correlations between different emission lines and the radio luminosity. We also
populate the X-ray and the optical fundamental plane of black hole activity and
further refine its parameters. We obtain a fundamental plane relation of log
L$_\textrm{R}$ = $0.48\,(\pm0.04$) log L$_\textrm{X}$ + $0.79\,(\pm0.03$) log
$\textrm{M}$ and an optical fundamental plane relation of log L$_\textrm{R}$ =
$0.63\,(\pm 0.05)$ log L$_{[\rm O~III]}$ + $0.67\,(\pm 0.03)$ log $\textrm{M}$
after including all the LLAGN detected at high resolution at 15 GHz, and the
best-studied hard-state X-ray binaries (luminosities are given in erg s$^{-1}$
while the masses are in units of solar mass). Finally, we find conclusive
evidence that the nuclear 15 GHz radio luminosity function (RLF) of all the
detected Palomar Sample LLAGN has a turnover at the low-luminosity end, and is
best-fitted with a broken power law. The break in the power law occurs at a
critical mass accretion rate of 1.2$\times$10$^{-3}$ M$_{\odot}$/yr, which
translates to an Eddington ratio of $\rm \dot m_{Edd} \sim 5.1 \times 10^{-5}$,
assuming a black hole mass of 10$^9 M_{\odot}$. The local group stands closer
to the extrapolation of the higher-luminosity sources, and the classical
Seyferts agree with the nuclear RLF of the LLAGN in the local universe.
