Three- and two-point spatial correlations of IGM at $z\sim 2$: Cloud based analysis using simulations

Ly$\alpha$ forest absorption spectra decomposed into multiple Voigt profile components (clouds) allow us to study clustering of intergalactic medium (IGM) as a function of HI column density ($N_{\rm HI}$). Here, we explore the transverse three-point correlation ($\zeta$) of these Ly$\alpha$ clouds using mock triplet spectra obtained from hydrodynamical simulations at $z \sim 2$ on scales of 1-5 $h^{-1}$cMpc. We find $\zeta$ to depend strongly on $N_{\rm HI}$ and scale and weakly on angle ($\theta$) of the triplet configuration. We show that the "hierarchical ansatz" is applicable for scales $\ge~ 3h^{-1}$cMpc, and obtain a median reduced three-point correlation (Q) in the range 0.2-0.7. We show, $\zeta$ is influenced strongly by the thermal and ionization state of the gas. As found in the case of galaxies, the influence of physical parameters on Q is weaker compared to that of $\zeta$. We show difference in $\zeta$ and Q between different simulations are minimized if we use appropriate $N_{\rm HI}$ cut-offs corresponding to a given baryon over-density ($\Delta$) using the measured $N_{\rm HI}~vs~\Delta$ relationship obtained from individual simulations. Additionally, we see the effect of pressure broadening on $\zeta$ in a model with artificially boosted heating rates. However, for models with realistic thermal and ionization histories the effect of pressure broadening on $\zeta$ is weak and sub-dominant compared to other local effects. We find strong redshift evolution shown by $\zeta$, mainly originating from the redshift evolution of thermal and ionization state of the IGM. We discuss the observational requirements for the detection of three-point correlation, specifically, in small intervals of configuration parameters and redshift.