Weighing the Giants - II. Improved calibration of photometry from stellar colours and accurate photometric redshifts

We present improved methods for using stars found in astronomical exposures to calibrate both star and galaxy colours as well as to adjust the instrument flat-field. By developing a spectroscopic model for the Sloan Digital Sky Survey (SDSS) stellar locus in colour-colour space, synthesizing an expected stellar locus, and simultaneously solving for all unknown zero-points when fitting to the instrumental locus, we increase the calibration accuracy of stellar locus matching. We also use a new combined technique to estimate improved flat-field models for the Subaru SuprimeCam camera, forming 'star flats' based on the magnitudes of stars observed in multiple positions or through comparison with available measurements in the SDSS catalogue. These techniques yield galaxy magnitudes with reliable colour calibration (less than or similar to 0.01-0.02 mag accuracy) that enable us to estimate photometric redshift probability distributions without spectroscopic training samples. We test the accuracy of our photometric redshifts using spectroscopic redshifts z(s) for similar to 5000 galaxies in 27cluster fields with at least five bands of photometry, as well as galaxies in the Cosmic Evolution Survey (COSMOS) field, finding sigma((z(p) - z(s))/(1 + z(s))) approximate to 0.03 for the most probable redshift z(p). We show that the full posterior probability distributions for the redshifts of galaxies with five-band photometry exhibit good agreement with redshifts estimated from thirty-band photometry in the COSMOS field. The growth of shear with increasing distance behind each galaxy cluster shows the expected redshift-distance relation for a flat Lambda cold dark matter (Lambda-CDM) cosmology. Photometric redshifts and calibrated colours are used in subsequent papers to measure the masses of 51 galaxy clusters from their weak gravitational shear and determine improved cosmological constraints. We make our PYTHON code for stellar locus matching publicly available at http://big-macs-calibrate.googlecode.com; the code requires only input catalogues and filter transmission functions.