Dark matter constraints with stacked gamma rays scales with the number of galaxies

Low-surface-brightness galaxies (LSBGs) are interesting targets for searches of dark matter emission due to their low baryonic content. However, predicting their expected dark matter emissivities is difficult because of observational challenges in their distance measurements. Here we present a stacking method that makes use of catalogs of LSBGs and maps of unresolved gamma-ray emission measured by the Fermi Gamma-Ray Space Telescope. We show that, for relatively large number of LSBGs, individual distance measurements to the LSBGs are not necessary, instead the overall distance distribution of the population is sufficient in order to impose dark matter constraints. Further, we demonstrate that the effect of the covariance between two galaxies located closely -- at an angular distance comparable to the size of the Fermi point spread function -- is negligibly small. As a case in point, we apply our pipeline to a sample of 800 faint LSBGs discovered by Hyper Suprime-Cam and find that, the 95 per cent confidence level upper limits on the dark matter annihilation cross-section scales with inverse of the number LSBGs. In light of this linear dependence with the number of objects, we argue this methodology could provide extremely powerful limits if it is applied to the more than 105 LSBGs readily available with the Legacy Survey of Space and Time.