  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. 
The Environmental Dependence of the Luminosity-Size Relation for   Galaxies