The Flux Auto- and Cross-Correlation of the Lyman-alpha Forest. II. Modelling Anisotropies with Cosmological Hydrodynamic Simulations

The isotropy of the Lyman-alpha forest in real-space uniquely provides a measurement of cosmic geometry at z > 2. The angular diameter distance for which the correlation function along the line of sight and in the transverse direction agree corresponds to the correct cosmological model. However, the Lyman-alpha forest is observed in redshift-space where distortions due to Hubble expansion, bulk flows, and thermal broadening introduce anisotropy. Similarly, a spectrograph's line spread function affects the autocorrelation and cross-correlation differently. In this the second paper of a series on using the Lyman-alpha forest observed in pairs of QSOs for a new application of the Alcock-Paczynski (AP) test, these anisotropies and related sources of potential systematic error are investigated with cosmological hydrodynamic simulations. Three prescriptions for galactic outflow were compared and found to have only a marginal effect on the Lyman-alpha flux correlation (which changed by at most 7% with use of the currently favored variable-momentum wind model vs. no winds at all). An approximate solution for obtaining the zero-lag cross-correlation corresponding to arbitrary spectral resolution directly from the zero-lag cross-correlation computed at full-resolution (good to within 2% at the scales of interest) is presented. Uncertainty in the observationally determined mean flux decrement of the Lyman-alpha forest was found to be the dominant source of systematic error; however, this is reduced significantly when considering correlation ratios. We describe a simple scheme for implementing our results, while mitigating systematic errors, in the context of a future application of the AP test.