On Estimating Lyman-alpha Forest Correlations between Multiple
  Sightlines
  The next frontier of Lyman-alpha forest studies is the reconstruction of 3D
correlations from a dense sample of background sources. The measurement of 3D
correlations has the potential to improve constraints on fundamental
cosmological parameters, ionizing background models, and the reionization
history. This study addresses the sensitivity of spectroscopic surveys to 3D
correlations in the Lyman-alpha forest. We show that the sensitivity of a
survey to this signal can be quantified by just a single number, a
noise-weighted number density of sources on the sky. We investigate how the
sensitivity of a spectroscopic quasar (or galaxy) survey scales as a function
of its depth, area, and redshift. We propose a simple method for weighting
sightlines with varying S/N levels to estimate the correlation function, and we
show that this estimator generally performs nearly as well as the minimum
variance quadratic estimator. In addition, we show that the sensitivity of a
quasar survey to the flux correlation function is generally maximized if it
observes each field just long enough to achieve S/N ~ 2 in a 1 A pixel on an
L_* quasar while acquiring spectra for all quasars with L > L_*: Little is
gained by integrating longer on the same targets or by including fainter
quasars. We quantify how these considerations relate to constraints on the
angular diameter distance, the curvature of space-time, and the reionization
history.
