The redshift distribution of cosmological samples: a forward modeling approach

Determining the redshift distribution $n(z)$ of galaxy samples is essential for several cosmological probes including weak lensing. For imaging surveys, this is usually done using photometric redshifts estimated on an object-by-object basis. We present a new approach for directly measuring the global $n(z)$ of cosmological galaxy samples, including uncertainties, using forward modeling. Our method relies on image simulations produced using UFig (Ultra Fast Image Generator) and on ABC (Approximate Bayesian Computation) within the $MCCL$ (Monte-Carlo Control Loops) framework. The galaxy population is modeled using parametric forms for the luminosity functions, spectral energy distributions, sizes and radial profiles of both blue and red galaxies. We apply exactly the same analysis to the real data and to the simulated images, which also include instrumental and observational effects. By adjusting the parameters of the simulations, we derive a set of acceptable models that are statistically consistent with the data. We then apply the same cuts to the simulations that were used to construct the target galaxy sample in the real data. The redshifts of the galaxies in the resulting simulated samples yield a set of $n(z)$ distributions for the acceptable models. We demonstrate the method by determining $n(z)$ for a cosmic shear like galaxy sample from the 4-band Subaru Suprime-Cam data in the COSMOS field. We also complement this imaging data with a spectroscopic calibration sample from the VVDS survey. We compare our resulting posterior $n(z)$ distributions to the one derived from photometric redshifts estimated using 36 photometric bands in COSMOS and find good agreement. This offers good prospects for applying our approach to current and future large imaging surveys.