UV Background Fluctuations and Three-Point Correlations in the Large Scale Clustering of the Lyman-alpha Forest

Abstract

Using the Ly$\alpha$ mass assignment scheme (LyMAS), we make theoretical predictions for the 3-dimensional 3-point correlation function (3PCF) of the Ly$\alpha$ forest at redshift $z=2.3$. We bootstrap results from the (100 $h^{-1} \mbox{ Mpc}$)${}^3$ Horizon hydrodynamic simulation to a (1 $h^{-1}$ Gpc)${}^3$ $N$-body simulation, considering both a uniform UV background (UVB) and a fluctuating UVB sourced by quasars with a comoving $n_q\approx 10^{-5}$ $h^3$ Mpc${}^{-3}$ placed either in massive halos or randomly. On scales of $10-30$ $h^{-1} \mbox{ Mpc}$, the flux 3PCF displays hierarchical scaling with the square of the 2PCF, but with an unusual value of $Q\equiv {\zeta }_{123}/({\xi }_{12}{\xi }_{13}+{\xi }_{12}{\xi }_{23}+{\xi }_{13}{\xi }_{23})\approx -4.5$ that reflects the low bias of the Ly$\alpha$ forest and the anti-correlation between mass density and transmitted flux. For halo-based quasars and an ionizing photon mean free path of $\lambda =300$ $h^{-1} \mbox{ Mpc}$ comoving, UVB fluctuations moderately depress the 2PCF and 3PCF, with cancelling effects on $Q$. For $\lambda =100$ $h^{-1} \mbox{ Mpc}$ or 50 $h^{-1} \mbox{ Mpc}$, UVB fluctuations substantially boost the 2PCF and 3PCF on large scales, shifting the hierarchical ratio to $Q\approx -3$. We scale our simulation results to derive rough estimate of the 3PCF detectability in observational data sets for the redshift range $z=2.1-2.6$. At $r=10$ $h^{-1} \mbox{ Mpc}$ and 20 $h^{-1} \mbox{ Mpc}$, we predict a signal-to-noise (SNR) of $\sim$ 9 and $\sim$ 7, respectively, for both BOSS and eBOSS, and $\sim$ 37 and $\sim$ 25 for DESI. At $r=40$ $h^{-1} \mbox{ Mpc}$ the predicted SNR is lower by $\sim$ 3$-$5 times. Measuring the flux 3PCF would be a novel test of the conventional paradigm of the Ly$\alpha$ forest and help separate the contributions of UVB fluctuations and density fluctuations to Ly$\alpha$ forest clustering.

arXiv commentSubmitted to MNRAS. 19 pages, 17 figures

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