Unbiased estimates of galaxy scaling relations from photometric redshift surveys

Many physical properties of galaxies correlate with one another, and these correlations are often used to constrain galaxy formation models. Such correlations include the color-magnitude relation, the luminosity-size relation, the Fundamental Plane, etc. However, the transformation from observable (e.g. angular size, apparent brightness) to physical quantity (physical size, luminosity), is often distance-dependent. Noise in the distance estimate will lead to biased estimates of these correlations, thus compromising the ability of photometric redshift surveys to constrain galaxy formation models. We describe two methods which can remove this bias. One is a generalization of the V_max method, and the other is a maximum likelihood approach. We illustrate their effectiveness by studying the size-luminosity relation in a mock catalog, although both methods can be applied to other scaling relations as well. We show that if one simply uses photometric redshifts one obtains a biased relation; our methods correct for this bias and recover the true relation.