  We have examined the luminosity-size relationship as a function of
environment for 12150 SDSS galaxies with precise visual classifications from
the catalog of Nair & Abraham (2010a). Our analysis is subdivided into
investigations of early-type galaxies and late-type galaxies. Early-type
galaxies reveal a surprisingly tight luminosity-size relation. The dispersion
in luminosity about the fiducial relation is only ~0.14 dex (0.35 mag), even
though the sample contains galaxies which differ by a factor of almost 100 in
luminosity. The dispersion about the luminosity-size relation is comparable to
the dispersion about the fundamental plane, even though the luminosity-size
relation is fundamentally simpler and computed using purely photometric
parameters. The key contributors to the dispersion about the luminosity-size
relation are found to be color and central concentration. Expanding our
analysis to the full range of morphological types, we show that the slope, zero
point, and scatter about the luminosity-size relation is independent of
environmental density. Our study thus indicates that whatever process is
building galaxies is doing so in a way that preserves fundamental scaling laws
even as the typical luminosity of galaxies changes with environment. However,
the distribution of galaxies along the luminosity-size relation is found to be
strongly dependent on galaxy environment. This variation is in the sense that,
at a given morphology, larger and more luminous galaxies are rarer in sparser
environments. Our analysis of late-type galaxy morphologies reveals that
scatter increases towards later Hubble types. Taken together, these results
place strong constraints on conventional hierarchical models in which galaxies
are built up in an essentially stochastic way.
