LeMMINGs IV: The X-ray properties of a statistically-complete sample of
  the nuclei in active and inactive galaxies from the Palomar sample
  All 280 of the statistically-complete Palomar sample of nearby (<120 Mpc)
galaxies dec > 20 degrees have been observed at 1.5 GHz as part of the LeMMINGs
e-MERLIN legacy survey. Here, we present Chandra X-ray observations of the
nuclei of 213 of these galaxies, including a statistically-complete sub-set of
113 galaxies in the declination range 40 degrees to 65 degrees. We observed
galaxies of all optical spectral types, including 'active' galaxies (e.g.,
LINERs and Seyferts) and 'inactive' galaxies like HII galaxies and absorption
line galaxies (ALG). The X-ray flux limit of our survey is
1.65$\times$10$^{-14}$~erg s$^{-1}$ cm$^{-2}$ (0.3$-$10 keV). We detect X-ray
emission coincident within 2-arcsec of the nucleus in 150/213 galaxies,
including 13/14 Seyferts, 68/77 LINERs, 13/22 ALGs and 56/100 HII galaxies, but
cannot completely rule out contamination from non-AGN processes in sources with
nuclear luminosities <10$^{39}$ erg s$^{-1}$. We construct an X-ray Luminosity
function (XLF) and find that the local galaxy XLF, when including all AGN
types, can be represented as a single power-law of slope $-0.54 \pm 0.06$. The
Eddington ratio of the Seyferts is usually 2-4 decades higher than that of the
LINERs, ALGs and HII galaxies, which are mostly detected with Eddington ratios
<10$^{-3}$. Using [O III] line measurements and BH masses from the literature,
we show that LINERs, HII galaxies and ALGs follow similar correlations to low
luminosities, suggesting that some 'inactive' galaxies may harbour AGN.
