  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.
