A new method to perform data/model comparison in Fermi-LAT analysis

The analysis of Fermi Large Area Telescope (LAT) gamma-ray data in a given Region Of Interest (RoI) usually consists of performing a binned log-likelihood fit in order to determine the sky model that, after convolution with the instrument response, best accounts for the distribution of observed counts. While tools are available to perform such a fit, it is not easy to check the goodness-of-fit. The difficulty of the assessment of the data/model agreement is twofold. First of all, the observed and predicted counts are binned in three dimensions (two spatial dimensions and one energy dimension) and comparing two 3D maps is not straightforward. Secondly, gamma-ray source spectra generally decrease with energy as the inverse of the energy square. As a consequence the number of counts above several GeV generally falls into the Poisson regime, which precludes performing a simple $\chi^2$ test. We propose a method that overcomes these two obstacles by producing and comparing spatially integrated count spectra for data and model at each pixel of the analysed RoI. The comparison is performed following a log-likelihood approach that extends the $\chi^2$ test to histograms with low statistics. This method can take into account likelihood weights that are used to account for systematic uncertainties. We optimize the new method so that it provides a fast and reliable tool to assess the goodness-of-fit of Fermi-LAT data and we use it to check the latest gamma-ray source catalog on 10~years of data.