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We examine the impact of gas pressure on the transverse coherence of high‐redshift  (2 ≤ z ≤ 4)  Lyman α (Lyα) forest absorption along neighbouring lines of sight that probe the gas Jeans scale (projected separation  Δ r  p ≤ 500  h  −1  kpc  comoving, angular separation  Δθ≲ 30 arcsec ). We compare predictions from two smoothed particle hydrodynamics 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 neighbouring 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  Δθ≲ 15 arcsec  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 Lyα 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.

Pressure support versus thermal broadening in the Lyman α forest – II. Effects of the equation of state on transverse structure