The PAU Survey: narrowband photometric redshifts using Gaussian processes

We study the performance of the hybrid template-machine-learning photometric redshift (photo-z) algorithm Delight on a subset of the early data release of the Physics of the Accelerating Universe Survey (PAUS). We calibrate the fluxes of the 40 PAUS narrowbands with 6 broadband fluxes (uBVriz) in the COSMOS field using three different methods, including a new method which utilises the correlation between the apparent size and overall flux of the galaxy. We use a rich set of empirically derived galaxy spectral templates as guides to train the Gaussian process, and we show that our results are competitive with other standard photometric redshift algorithms, including the bespoke template-based BCNz2 previously applied to PAUS, lowering the photo-z 68th percentile error to $\sigma_{68}\approx 0.009(1+z)$ without any quality cut for galaxies with $i_\mathrm{auto}<22.5$. We use the combined Delight and BCNz2 results to identify a small number of tentative catastrophic failures among the secure spectroscopic redshift measurements in zCOSMOS. In the process, we introduce performance metrics derived from the results of both algorithms which improves the photo-z quality such that it achieves $\sigma_{68}<0.0035(1+z)$ at a magnitude of $i_\mathrm{auto}<22.5$ while keeping 50 per cent objects of the galaxy sample.