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In Stage-IV imaging surveys, a significant amount of the cosmologicallyuseful information is due to sources whose images overlap with those of othersources on the sky. The cosmic shear signal is primarily encoded in theestimated shapes of observed galaxies and thus directly impacted by overlaps.We introduce a framework based on the Fisher formalism to analyze effects ofoverlapping sources (blending) on the estimation of cosmic shear. For the RubinObservatory Legacy Survey of Space and Time (LSST), we present the expectedloss in statistical sensitivity for the ten-year survey due to blending. Wefind that for approximately 62% of galaxies that are likely to be detected infull-depth LSST images, at least 1% of the flux in their pixels is fromoverlapping sources. We also find that the statistical correlations betweenmeasures of overlapping galaxies and, to a much lesser extent the higher shotnoise level due to their presence, decrease the effective number density ofgalaxies, $N_{eff}$, by $\sim$18%. We calculate an upper limit on $N_{eff}$ of39.4 galaxies per arcmin$^2$ in $r$ band. We study the impact of varyingstellar density on $N_{eff}$ and illustrate the diminishing returns ofextending the survey into lower Galactic latitudes. We extend the Fisherformalism to predict the increase in pixel-noise bias due to blending formaximum-likelihood (ML) shape estimators. We find that noise bias is sensitiveto the particular shape estimator and measure of ensemble-average shape that isused, and properties of the galaxy that include redshift-dependent quantitiessuch as size and luminosity.

Effects of overlapping sources on cosmic shear estimation: Statistical sensitivity and pixel-noise bias