Effects of overlapping sources on cosmic shear estimation: Statistical
  sensitivity and pixel-noise bias
  In Stage-IV imaging surveys, a significant amount of the cosmologically
useful information is due to sources whose images overlap with those of other
sources on the sky. The cosmic shear signal is primarily encoded in the
estimated shapes of observed galaxies and thus directly impacted by overlaps.
We introduce a framework based on the Fisher formalism to analyze effects of
overlapping sources (blending) on the estimation of cosmic shear. For the Rubin
Observatory Legacy Survey of Space and Time (LSST), we present the expected
loss in statistical sensitivity for the ten-year survey due to blending. We
find that for approximately 62% of galaxies that are likely to be detected in
full-depth LSST images, at least 1% of the flux in their pixels is from
overlapping sources. We also find that the statistical correlations between
measures of overlapping galaxies and, to a much lesser extent the higher shot
noise level due to their presence, decrease the effective number density of
galaxies, $N_{eff}$, by $\sim$18%. We calculate an upper limit on $N_{eff}$ of
39.4 galaxies per arcmin$^2$ in $r$ band. We study the impact of varying
stellar density on $N_{eff}$ and illustrate the diminishing returns of
extending the survey into lower Galactic latitudes. We extend the Fisher
formalism to predict the increase in pixel-noise bias due to blending for
maximum-likelihood (ML) shape estimators. We find that noise bias is sensitive
to the particular shape estimator and measure of ensemble-average shape that is
used, and properties of the galaxy that include redshift-dependent quantities
such as size and luminosity.
