The flux auto- and cross-correlation of the Lyα forest.: II.: Modeling anisotropies with cosmological hydrodynamic simulations

The isotropy of the Ly 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 Ly 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 Ly alpha forest observed in pairs of quasi-stellar objects for a new application of the Alcock-Paczyn ski 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 Ly 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 Ly 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 Alcock-Paczyn ski test.