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Log-Poisson Non-Gaussianity of Ly$α$ Transmitted Flux Fluctuations at High Redshift

We investigate the non-Gaussian features of the IGM at redshift $z\sim 5 - 6$ using Ly$α$ transmitted flux of quasar absorption spectra and cosmological hydrodynamic simulation of the concordance $Λ$CDM universe. We show that the neutral hydrogen mass density field and Ly$α$ transmitted flux fluctuations possess all the non-Gaussian features predicted by the log-Poisson hierarchy, which depends only on two dimensionless parameters $β$ and $γ$, describing, respectively, the intermittence and singularity of the random fields. We find that the non-Gaussianity of the Ly$α$ transmitted flux of quasars from $z=4.9$ to $z=6.3$ can be well reconstructed by the hydrodynamical simulation samples. Although the Gunn-Peterson optical depth and its variance underwent a significant evolution in the redshift range of $5 - 6$, the intermittency measured by $β$ is almost redshift-independent in this range. More interesting, the intermittency of quasar's absorption spectra on physical scales $0.1-1$ h$^{-1}$Mpc in redshift $5 - 6$ are found to be about the same as that on physical scales $1-10$ h$^{-1}$Mpc at redshifts $2 - 4$. Considering the Jeans length is less than 0.1 h$^{-1}$Mpc at $z\sim 5$, and $1$ h$^{-1}$Mpc at $z\sim 2$, these results imply that the nonlinear evolution in high and low redshifts will lead the cosmic baryon fluid to a state similar to fully developed turbulence. The log-Poisson high order behavior of current high redshift data of quasar's spectrum can be explained by uniform UV background in the redshift range considered. We also studied the log-Poisson non-Gaussianity by considering inhomogeneous background. With several simplified models of inhomogeneous background, we found the effect of the inhomogeneous background on the log-Poisson non-Gaussianity is not larger than 1-sigma.