μ-PhotoZ: Photometric Redshifts by Inverting the Tolman Surface Brightness Test

Surface brightness is a fundamental observational parameter of galaxies. We show, for the first time in detail, how it can be used to obtain photometric redshifts for galaxies, the μ-PhotoZ method. We demonstrate that the Tolman surface brightness relation, μ ∝ (1 + z)^-4, is a powerful tool for determining galaxy redshifts from photometric data. We develop a model using μ and a color percentile (ranking) measure to demonstrate the μ-PhotoZ method. We apply our method to a set of galaxies from the SHELS survey, and demonstrate that the photometric redshift accuracy achieved using the surface brightness method alone is comparable with the best color-based methods. We show that the μ-PhotoZ method is very effective in determining the redshift for red galaxies using only two photometric bands. We discuss the properties of the small, skewed, non-Gaussian component of the error distribution. We calibrate μ_r, (r - i) from the SDSS to redshift and tabulate the result, providing a simple but accurate look-up table to estimate the redshift of distant red galaxies.