http://arxiv.org/abs/2301.04085
Photometric redshifts are a key ingredient in the analysis and interpretation of large-scale structure (LSS) surveys. The accuracy and precision of these redshifts estimates is directly linked to the constraining power of photometric surveys. It is hence necessary to define precision and accuracy requirements for the redshift calibration to not to infer biased results in the final analysis. For weak gravitational lensing of the LSS the photometry culminates in the estimation of the source redshift distribution (SRD) in each of the tomographic bins used in the analysis. The focus has been on shifts of the mean of the SRDs and how well the calibration must be able to recover those. Since the estimated SRDs are usually given as a normalized histogram with corresponding errors, it would be advantageous to propagate these uncertainties accordingly to see whether the requirements of the given survey are indeed fulfilled. Here we propose the use of functional derivatives to calculate the sensitivity of the final observables, e.g. the lensing angular power spectrum, with respect to the SRD at a specific redshift. This allows the propagation of arbitrarily shaped small perturbations to the SRD, without having to run the whole analysis pipeline for each realization again. We apply our method to a EUCLID survey and demonstrate it with SRDs of the KV450 data set, recovering previous results. Lastly, we note that for cosmic shear moments of order larger than two will probably be not relevant when propagating redshift uncertainties.
R. Reischke
Wed, 11 Jan 23
44/80
Comments: 9 pages, 7 figures