Estimating Luminosity Function Constraints from High-Redshift Galaxy
  Surveys
  The installation of the Wide Field Camera 3 (WFC3) on the Hubble Space
Telescope (HST) will revolutionize the study of high-redshift galaxy
populations. Initial observations of the HST Ultra Deep Field (UDF) have
yielded multiple z>~7 dropout candidates. Supplemented by the Great Observatory
Origins Deep Survey (GOODS) Early Release Science (ERS) and further UDF
pointings, these data will provide crucial information about the most distant
known galaxies. However, achieving tight constraints on the z~7 galaxy
luminosity function (LF) will require even more ambitious photometric surveys.
Using a Fisher matrix approach to fully account for Poisson and cosmic sample
variance, as well as covariances in the data, we estimate the uncertainties on
LF parameters achieved by surveys of a given area and depth. Applying this
method to WFC3 z~7 dropout galaxy samples, we forecast the LF parameter
uncertainties for a variety of model surveys. We demonstrate that performing a
wide area (~1 deg^2) survey to H_AB~27 depth or increasing the UDF depth to
H_AB~30 provides excellent constraints on the high-z LF when combined with the
existing UDF GO and GOODS ERS data. We also show that the shape of the matter
power spectrum may limit the possible gain of splitting wide area (>~0.5 deg^2)
high-redshift surveys into multiple fields to probe statistically independent
regions; the increased root-mean-squared density fluctuations in smaller
volumes mostly offset the improved variance gained from independent samples.
