Total galaxy magnitudes and effective radii from Petrosian magnitudes and radii

Petrosian magnitudes were designed to help with the difficult task of determining a galaxy's total light. Although these magnitudes [taken here as the flux within 2R_P, with the inverted Petrosian index 1/η(R _P) = 0.2] can represent most of an object's flux, they do of course miss the light outside the Petrosian aperture (2R_P). The size of this flux deficit varies monotonically with the shape of a galaxy's light profile, i.e., its concentration. In the case of a de Vaucouleurs R^1/4 profile, the deficit is 0.20 mag; for an R^1/8 profile this figure rises to 0.50 mag. Here we provide a simple method for recovering total (Sérsic) magnitudes from Petrosian magnitudes using only the galaxy concentration (R₉₀/R₅₀ or R₈₀/R₂₀) within the Petrosian aperture. The corrections hold to the extent that Sérsic's model provides a good description of a galaxy's luminosity profile. We show how the concentration can also be used to convert Petrosian radii into effective half-light radii, enabling a robust measure of the mean effective surface brightness. Our technique is applied to the Sloan Digital Sky Survey Data Release 2 (SDSS DR2) Petrosian parameters, yielding good agreement with the total magnitudes, effective radii, and mean effective surface brightnesses obtained from the New York University Value-Added Galaxy Catalog Sérsic R^1/n fits by Blanton and coworkers. Although the corrective procedure described here is specifically applicable to the SDSS DR2 and DR3, it is generally applicable to all imaging data where any Petrosian index and concentration can be constructed.