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We present the methodology and data behind the photometric redshift data base of the Sloan Digital Sky Survey (SDSS) Data Release 12. We adopt a hybrid technique, empirically estimating the redshift via local regression on a spectroscopic training set, then fitting a spectrum template to obtain K-corrections and absolute magnitudes. The SDSS spectroscopic catalogue was augmented with data from other, publicly available spectroscopic surveys to mitigate target selection effects. The training set is comprised of 1976 978 galaxies, and extends up to redshift z ≈ 0.8, with a useful coverage of up to z ≈ 0.6. We provide photometric redshifts and realistic error estimates for the 208 474 076 galaxies of the SDSS primary photometric catalogue. We achieve an average bias of Δznorm = 5.84 × 10-5, a standard deviation of σ(Δznorm) = 0.0205, and a 3σ outlier rate of Po = 4.11 per cent when cross-validating on our training set. The published redshift error estimates and photometric error classes enable the selection of galaxies with high-quality photometric redshifts. We also provide a supplementary error map that allows additional, sophisticated filtering of the data. [ABSTRACT FROM AUTHOR]

We discuss the construction of a photometric redshift catalogue of luminous red galaxies (LRGs) from the Sloan Digital Sky Survey (SDSS), emphasizing the principal steps necessary for constructing such a catalogue: (i) photometrically selecting the sample, (ii) measuring photometric redshifts and their error distributions, and (iii) estimating the true redshift distribution. We compare two photometric redshift algorithms for these data and find that they give comparable results. Calibrating against the SDSS and SDSS–2dF (Two Degree Field) spectroscopic surveys, we find that the photometric redshift accuracy isfor redshifts less than 0.55 and worsens at higher redshift (∼ 0.06 for). These errors are caused by photometric scatter, as well as systematic errors in the templates, filter curves and photometric zero-points. We also parametrize the photometric redshift error distribution with a sum of Gaussians and use this model to deconvolve the errors from the measured photometric redshift distribution to estimate the true redshift distribution. We pay special attention to the stability of this deconvolution, regularizing the method with a prior on the smoothness of the true redshift distribution. The methods that we develop are applicable to general photometric redshift surveys. [ABSTRACT FROM AUTHOR]