Log-Poisson Non-Gaussianity of Ly$\alpha$ Transmitted Flux Fluctuations
  at High Redshift
  We investigate the non-Gaussian features of the IGM at redshift $z\sim 5 - 6$
using Ly$\alpha$ transmitted flux of quasar absorption spectra and cosmological
hydrodynamic simulation of the concordance $\Lambda$CDM universe. We show that
the neutral hydrogen mass density field and Ly$\alpha$ transmitted flux
fluctuations possess all the non-Gaussian features predicted by the log-Poisson
hierarchy, which depends only on two dimensionless parameters $\beta$ and
$\gamma$, describing, respectively, the intermittence and singularity of the
random fields. We find that the non-Gaussianity of the Ly$\alpha$ 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 $\beta$ 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.
