Pressure Support vs. Thermal Broadening in the Lyman-alpha Forest II:
  Effects of the Equation of State on Transverse Structure
  We examine the impact of gas pressure on the transverse coherence of
high-redshift (2 <= z <= 4) Lyman-alpha forest absorption along neighboring
lines of sight that probe the gas Jeans scale (projected separation Delta r <=
500 kpc/h comoving; angular separation Delta theta <= 30"). We compare
predictions from two smoothed particle hydrodynamics (SPH) simulations that
have different photoionization heating rates and thus different
temperature-density relations in the intergalactic medium (IGM). We also
compare spectra computed from the gas distributions to those computed from the
pressureless dark matter. The coherence along neighboring sightlines is
markedly higher for the hotter, higher pressure simulation, and lower for the
dark matter spectra. We quantify this coherence using the flux
cross-correlation function and the conditional distribution of flux decrements
as a function of transverse and line-of-sight (velocity) separation. Sightlines
separated by Delta theta <= 15" are ideal for probing this transverse
coherence. Higher pressure decreases the redshift-space anisotropy of the flux
correlation function, while higher thermal broadening increases the anisotropy.
In contrast to the longitudinal (line-of-sight) structure of the Lya forest,
the transverse structure on these scales is dominated by pressure effects
rather than thermal broadening. With the rapid recent growth in the number of
known close quasar pairs, paired line-of-sight observations offer a promising
new route to probe the IGM temperature-density relation and test the
unexpectedly high temperatures that have been inferred from single sightline
analyses.
