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Future weak lensing surveys potentially hold the highest statistical powerfor constraining cosmological parameters compared to other cosmological probes.The statistical power of a weak lensing survey is determined by the skycoverage, the inverse of the noise in shear measurements, and the galaxy numberdensity. The combination of the latter two factors is often expressed in termsof $n_{\rm eff}$ -- the "effective number density of galaxies used for weaklensing measurements". In this work, we estimate $n_{\rm eff}$ for the LargeSynoptic Survey Telescope (LSST) project, the most powerful ground-basedlensing survey planned for the next two decades. We investigate how thefollowing factors affect the resulting $n_{\rm eff}$ of the survey withdetailed simulations: (1) survey time, (2) shear measurement algorithm, (3)algorithm for combining multiple exposures, (4) inclusion of data from multiplefilter bands, (5) redshift distribution of the galaxies, and (6) masking andblending. For the first time, we quantify in a general weak lensing analysispipeline the sensitivity of $n_{\rm eff}$ to the above factors.  We find that with current weak lensing algorithms, expected distributions ofobserving parameters, and all lensing data ($r$- and $i$-band, covering 18,000degree$^{2}$ of sky) for LSST, $n_{\rm eff} \approx37$ arcmin$^{-2}$ beforeconsidering blending and masking, $n_{\rm eff} \approx31$ arcmin$^{-2}$ whenrejecting seriously blended galaxies and $n_{\rm eff} \approx26$ arcmin$^{-2}$when considering an additional 15% loss of galaxies due to masking. With futureimprovements in weak lensing algorithms, these values could be expected toincrease by up to 20%. Throughout the paper, we also stress the ways in which$n_{\rm eff}$ depends on our ability to understand and control systematiceffects in the measurements.

The Effective Number Density of Galaxies for Weak Lensing Measurements in the LSST Project