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 mu-PhotoZ method. We demonstrate that the Tolman surface brightness relation, mu proportional to ( 1+z)(-4), is a powerful tool for determining galaxy redshifts from photometric data. We develop a model using mu and a color percentile ( ranking) measure to demonstrate the mu-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 mu-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 mu(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.