Precise photometric redshifts with a narrow-band filter set: The PAU Survey at the William Herschel Telescope

The Physics of the Accelerating Universe (PAU) survey at the William Herschel Telescope (WHT) will use a new optical camera (PAUCam) with a large set of narrow-band filters to perform a photometric galaxy survey with a quasi-spectroscopic redshift precision of \sigma(z)/(1 + z) ~ 0.0035 and map the large-scale structure of the universe in three dimensions up to i_AB < 22.5-23.0. In this paper we present a detailed photo-z performance study using photometric simulations for 40 equally-spaced 12.5-nm-wide (FWHM) filters with a ~25% overlap and spanning the wavelength range from 450 nm to 850 nm, together with a ugrizY broad-band filter system. We then present the migration matrix r_ij, containing the probability that a galaxy in a true redshift bin j is measured in a photo-z bin i, and study its effect on the determination of galaxy auto- and cross-correlations. Finally, we also study the impact on the photo-z performance of small variations of the filter set in terms of width, wavelength coverage, etc., and find a broad region where slightly modified filter sets provide similar results, with the original set being close to optimal.