The Time Development of a Resonance Line in the Expanding Universe

The time-dependent spectral profile of a resonance line in a homogeneous expanding medium is studied by numerically solving an improved Fokker-Planck diffusion equation. The solutions are used to determine the time required to reach a quasi-static solution near the line center. A simple scaling law for this relaxation time is derived and is fitted to the numerical results. The results are applied to the case of Lyman alpha scattering during primordial recombination of hydrogen. For a wide range of cosmological models it is found that the relaxation times are smaller than the recombination timescale, although not by a very large factor. Thus the standard assumption of a quasi-static solution in cosmological recombination calculations is reasonably valid, and should not cause substantial errors in the solutions.Comment: 20 pages text and 10 figures, in 30 pages of uuencoded, compressed postscript. CFA preprint no. 375

μ\mu--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, $\mu \propto (1+z)^{-4}$, 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.Comment: Accepted for publication in the Astronomical Journa