UV background fluctuations and three-point correlations in the large-scale clustering of the Lyman α forest

Using the Lyman α (Lyα) Mass Association Scheme, we make theoretical predictions for the three-dimensional three-point correlation function (3PCF) of the Lyα forest at redshift z = 2.3. We bootstrap results from the (100 h^-1 Mpc)³ Horizon hydrodynamic simulation to a (1 h^-1 Gpc)³N-body simulation, considering both a uniform ultraviolet background (UVB) and a fluctuating UVB sourced by quasars with a comoving n_q ≈ 10^-5h³ Mpc^-3 placed either in massive haloes or randomly. On scales of 10-30 h^-1 Mpc, the flux 3PCF displays hierarchical scaling with the square of the two-point correlation function (2PCF), but with an unusual value of Q ≡ ζ₁₂₃/(ξ₁₂ξ₁₃ + ξ₁₂ξ₂₃ + ξ₁₃ξ₂₃) ≈ -4.5 that reflects the low bias of the Lyα forest and the anticorrelation between mass density and transmitted flux. For halo-based quasars and an ionizing photon mean free path of λ = 300 h^-1 Mpc comoving, UVB fluctuations moderately depress the 2PCF and 3PCF, with cancelling effects on Q. For λ = 100 or 50 h^-1 Mpc, UVB fluctuations substantially boost the 2PCF and 3PCF on large scales, shifting the hierarchical ratio to Q ≈ -3. We scale our simulation results to derive rough estimate of the detectability of the 3PCF in current and future observational data sets for the redshift range z = 2.1-2.6. At r = 10 and 20 h^-1 Mpc, we predict a signal-to-noise ratio (SNR) of ∼9 and ∼7, respectively, for both Baryon Oscillation Spectroscopic Survey (BOSS) and extended BOSS (eBOSS), and ∼37 and ∼25 for Dark Energy Spectroscopic Instrument (DESI). At r = 40 h^-1 Mpc the predicted SNR is lower by a factor of ∼3-5. Measuring the flux 3PCF would provide a novel test of the conventional paradigm of the Lyα forest and help separate the contributions of UVB fluctuations and density fluctuations to Lyα forest clustering, thereby solidifying its foundation as a tool of precision cosmology.