Wiener filtering and multi-tracer techniques for dark matter cross-correlations between gamma-ray emission and galaxy catalogs

Cross-correlations between a gravitational tracer of dark matter and the contribution to the unresolved gamma-ray background (UGRB) from the radiation produced by the annihilation of the particles responsible for the dark matter, have been established as a powerful tool to investigate the particle physics nature of dark matter. Cross-correlations of the UGRB with galaxy catalogs, cluster catalogs and weak lensing have indeed been measured. In this paper we study statistical techniques that could improve the sensitivity of the cross-correlation techniques on the bounds that can be set to the particle dark matter physical properties. The two methods that we investigate are the application of a Wiener filter and the exploitation of the full multi-tracer information. After identifying the optimal strategies, we show that the adoption of a Wiener filter in the cross-correlation analysis can improve the sensitivity to the dark matter annihilation rate by a factor of 2/2.5 as compared to the standard analysis where no filter is applied. The inclusion of the full multi-tracer information can improve the sensitivity up to a factor of 5 for dark matter masses below about 50 GeV, the Wiener filter remaining the best option for heavier dark matter.