SPIDER - III. Environmental Dependence of the Fundamental Plane of
  Early-type Galaxies
  We analyse the Fundamental Plane (FP) relation of $39,993$ early-type
galaxies (ETGs) in the optical (griz) and $5,080$ ETGs in the Near-Infrared
(YJHK) wavebands, forming an optical$+$NIR sample of $4,589$ galaxies. We focus
on the analysis of the FP as a function of the environment where galaxies
reside. We characterise the environment using the largest group catalogue,
based on 3D data, generated from SDSS at low redshift ($z < 0.1$). We find that
the intercept $``c''$ of the FP decreases smoothly from high to low density
regions, implying that galaxies at low density have on average lower
mass-to-light ratios than their high-density counterparts. The $``c''$ also
decreases as a function of the mean characteristic mass of the parent galaxy
group. However, this trend is weak and completely accounted for by the
variation of $``c''$ with local density. The variation of the FP offset is the
same in all wavebands, implying that ETGs at low density have younger
luminosity-weighted ages than cluster galaxies, consistent with the
expectations of semi-analytical models of galaxy formation. We measure an age
variation of $\sim 0.048$~dex ($\sim 11\%$) per decade of local galaxy density.
This implies an age difference of about $32 \%$ ($\sim 3 \, Gyr$) between
galaxies in the regions of highest density and the field. We find the
metallicity decreasing, at $\sim 2$~$\sigma$, from low to high density. We also
find $2.5 \, \sigma$ evidence that the variation in age per decade of local
density augments, up to a factor of two, for galaxies residing in massive
relative to poor groups. (abridged)
