  We determine the near-infrared Fundamental Plane (FP) for $\sim10^4$
early-type galaxies in the 6dF Galaxy Survey (6dFGS). We fit the distribution
of central velocity dispersion, near-infrared surface brightness and half-light
radius with a three-dimensional Gaussian model using a maximum likelihood
method. For the 6dFGS $J$ band sample we find a FP with
$R_{e}$\,$\propto$\,$\sigma_0^{1.52\pm0.03}I_{e}^{-0.89\pm0.01}$, similar to
previous near-IR determinations and consistent with the $H$ and $K$ band
Fundamental Planes once allowance is made for differences in mean colour. The
overall scatter in $R_e$ about the FP is $\sigma_r$,=,29%, and is the
quadrature sum of an 18% scatter due to observational errors and a 23%
intrinsic scatter. Because of the distribution of galaxies in FP space,
$\sigma_r$ is not the distance error, which we find to be $\sigma_d$,=,23%.
Using group richness and local density as measures of environment, and
morphologies based on visual classifications, we find that the FP slopes do not
vary with environment or morphology. However, for fixed velocity dispersion and
surface brightness, field galaxies are on average 5% larger than galaxies in
higher-density environments, and the bulges of early-type spirals are on
average 10% larger than ellipticals and lenticulars. The residuals about the FP
show significant trends with environment, morphology and stellar population.
The strongest trend is with age, and we speculate that age is the most
important systematic source of offsets from the FP, and may drive the other
trends through its correlations with environment, morphology and metallicity.
