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Astron. Astrophys. 340, 335-342 (1998)

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1. Introduction

Ly[FORMULA] absorption line forests in QSO spectra come from intervening absorbers, or clouds, with neutral hydrogen column densities ranging from about [FORMULA] to [FORMULA] cm-2 at high red-shifts. Since the size of the Ly[FORMULA] clouds at high red-shift is as large as 100-200 h-1 Kpc, and their velocity dispersion is as low as [FORMULA] 100 km s-1 (Bechtold et al. 1994, Dinshaw et al. 1995, Fang et al. 1996), it is generally believed that the Ly[FORMULA] forests are due to the absorption of pre-collapsed clouds in the density field of the universe. Ly[FORMULA] clouds are probably fair tracers of the cosmic density field on large scales and therefore, the clustering behavior of the Ly[FORMULA] clouds should be useful for testing models of structure formation of the universe.

More importantly, unlike other high redshift objects, Ly[FORMULA] forests do not show significant power in their two-point correlation functions. Aside from very small scales [FORMULA] km/s, all results drawn from the two-point correlation function of the Ly[FORMULA] absorption lines have failed to detect clustering (Webb, 1987, Weymann 1993, Hu et al. 1995, Cristiani et al. 1997). The power spectrum of the 1-D spatial distribution of the Ly[FORMULA] absorbers is found to be flat on scales in velocity space of [FORMULA] 600 to 30,000 km s-1 (Pando & Fang 1998). This result indicates that the distribution of the Ly[FORMULA] clouds may still be in the linear or quasilinear evolutionary stages on scales larger than a few h-1 Mpc. Indeed, it is found that simulations of popular models using the linear or log-normal approximation fit well with the second order statistical properties of Ly[FORMULA] forests (Bi, Ge & Fang 1995, Bi & Davidson 1997). Therefore, the Ly[FORMULA] clouds may contain information of cosmic clustering in the linear or quasilinear evolutionary stages.

It is known that even though the evolution of the power spectrum during the quasi-linear regime does not significantly differ from the linear regime, the density perturbations on different scales will no longer evolve mutually independently because of the power transfer of perturbations via mode coupling. For popular models, like the cold dark matter model, the mode-mode coupling of the quasi-linear evolution leads to a power transfer from large scales to small ones (Suto & Sasaki 1991). Numerical studies show that the power transfer is already significant on scales of about 50 h-1 Mpc at redshift [FORMULA] (Jing et al. 1995). Thus, there should exist non-Gaussianity on scales of a few 10 h-1 Mpc which is the "remnant" of the mode-mode coupling of the quasi-linear evolution.

This theory is supported by works based on methods other than the two-point correlation function. For instance, the distribution of nearest neighbor Ly[FORMULA] line intervals is found to be definitely different from a Poisson process (Duncan, Ostriker, & Bajtlik 1989; Liu and Jones 1990). A study using the Kolmogorov-Smirnoff (K-S) statistics, finds that Ly[FORMULA] absorbers show a deviation from a uniform random distribution at the [FORMULA] significance level (Fang, 1991). Some observations also indicate the existence of [FORMULA] Mpc void (Dobrzycki & Bechtold 1991), and deviation from uniform distribution on larger scales (Crotts 1987, 1989.) However, this individual structure cannot be used for a statistical analysis. Using a method based on cluster identification, many structures have been systematically identified and formed into an ensemble. It is found that the abundance of the identified "clusters" with respect to the richness are significantly different from a Gaussian process (Pando & Fang 1996, hereafter PF). Recently, we have also found that the Ly[FORMULA] forest line distribution shows significant scale-scale correlations. As a consequence models which predict a Gaussian process for the evolution of the Ly[FORMULA] clouds are ruled out, and the halos hosting the clouds must have gone through a "history" dependent merging process during their formation (Pando et al. 1998.)

In this paper, we will continue to develop the description of the non-Gaussianity of the Ly[FORMULA] line distribution. The emphasis of this paper will be to detect the non-Gaussian spectrum, and to show its ability to discriminate among models of Ly[FORMULA] cloud formation which are degenerate at second order.

In Sect. 2, we will describe the observed and simulated samples of Ly[FORMULA] forests, and the problems related to their large scale structure detection. In Sect. 3, the DWT technique of non-Gaussian spectrum detection will be discussed. The results of this analysis for real and simulated samples are discussed in Sect. 4. We will show that the distributions of Ly[FORMULA] forest lines are significantly different from Gaussian distributions. Additionally, we show that the non-Gaussian spectrum is a powerful tool for distinguishing between models.

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© European Southern Observatory (ESO) 1998

Online publication: November 9, 1998