We study the stellar and dust properties of a well-defined sample of local
elliptical galaxies to investigate the relationship between host galaxy
properties and nuclear activity. We select a complete sample of 45 ellipticals
from the Palomar spectroscopic survey of nearby galaxies, which includes 20
low-luminosity active galactic nuclei classified as LINERs and 25 inactive
galaxies. Using a stellar population synthesis method, we compare the derived
stellar population properties of the LINER versus the inactive subsamples. We
also study the dust and stellar surface brightness distributions of the central
regions of these galaxies using high-resolution images obtained with the {\it
Hubble Space Telescope}. Relative to the inactive subsample, ellipticals
hosting LINERs share similar total optical and near-infrared luminosity,
central stellar velocity dispersions, and nuclear stellar populations as judged
from their luminosity-weighted ages and metallicities. LINERs, on the other
hand, have a larger fraction of core-type central surface brightness profiles
and a much higher frequency of circumnuclear dust structures. Our results
support the suggestion that LINERs are powered by low-luminosity AGNs rather
than by young or intermediate-age stars. Nuclear activity in nearby elliptical
galaxies seems to occur preferentially in those systems where sufficient cold
interstellar material has managed to accumulate, perhaps via cooling
condensations from hot gas.Comment: 8 pages, accepted by A&