Reconstructing galaxy fundamental distributions and scaling relations from photometric redshift surveys. Applications to the SDSS early-type sample

Noisy distance estimates associated with photometric rather than spectroscopic redshifts lead to a mis-estimate of the luminosities, and produce a correlated mis-estimate of the sizes. We consider a sample of early-type galaxies from the SDSS DR6 for which both spectroscopic and photometric information is available, and apply the generalization of the V_max method to correct for these biases. We show that our technique recovers the true redshift, magnitude and size distributions, as well as the true size-luminosity relation. We find that using only 10% of the spectroscopic information randomly spaced in our catalog is sufficient for the reconstructions to be accurate within about 3%, when the photometric redshift error is dz = 0.038. We then address the problem of extending our method to deep redshift catalogs, where only photometric information is available. In addition to the specific applications outlined here, our technique impacts a broader range of studies, when at least one distance-dependent quantity is involved. It is particularly relevant for the next generation of surveys, some of which will only have photometric information.