On estimating Lyα forest correlations between multiple sightlines

The next frontier of Ly alpha forest studies is the reconstruction of three-dimensional (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 re-ionization history. This study addresses the sensitivity of spectroscopic surveys to 3D correlations in the Lya 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 signal-to-noise ratio (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 approximate to 2 in a 1-angstrom 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 re-ionization history.