LOG-POISSON HIERARCHICAL CLUSTERING OF COSMIC NEUTRAL HYDROGEN AND Lyα TRANSMITTED FLUX OF QSO ABSORPTION SPECTRUM

In this paper, we study the non-Gaussian features of the mass density field of neutral hydrogen fluid and the Ly alpha transmitted flux of QSO absorption spectrum from the point of view of self-similar log-Poisson hierarchy. It has been recently shown that, in the scale range, from the onset of nonlinear evolution to dissipation, the velocity and mass density fields of cosmic baryon fluid are extremely well described by the She-Leveque's scaling formula, which is due to the log-Poisson hierarchical cascade. Since the mass density ratio between ionized hydrogen and total hydrogen is not uniform in space, the mass density field of the neutral hydrogen component is not given by a similar mapping of total baryon fluid. Nevertheless, we show, with hydrodynamic simulation samples of the concordance. CDM universe, that the mass density field of neutral hydrogen is also well described by the log-Poisson hierarchy. We then investigate the field of Lya transmitted flux of QSO absorption spectrum. Due to redshift distortion, Lya transmitted flux fluctuations no longer show all features of the log-Poisson hierarchy. However, some non-Gaussian features predicted by the log-Poisson hierarchy are not affected by the redshift distortion. We test these predictions with the high resolution and high signal-to-noise ratio data of the quasar's Lya absorption spectra. All results given by real data, including beta-hierarchy, high-order moments and scale-scale correlation, are found to be consistent with the log-Poisson hierarchy. We compare the log-Poisson hierarchy with the popular log-normal model of the Lya transmitted flux. The latter is found to yield too strong non-Gaussianity at high orders, while the log-Poisson hierarchy is in agreement with observed data.