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

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2. Ly[FORMULA] samples and problems

In PF, we looked at two popular data sets of Ly[FORMULA] forests. The first compiled by Lu, Wolfe and Turnshek (1991, hereafter LWT) contains [FORMULA] 950 lines from the spectra of 38 QSO that exhibit neither broad absorption lines nor metal line systems. The second set is from Bechtold (1994, hereafter JB), which contains [FORMULA] 2800 lines from 78 QSO's spectra, in which 34 high red-shift QSOs were observed at moderate resolution. In this paper, we augment those data sets with two observations using the Keck telescope: 1) Hu et al. (1995, hereafter HKCSR) observed 4 QSO's with a total of 1056 lines and column density in the range [FORMULA] cm-2 at extremely high S/N; 2) Kirkman and Tytler (1997, hereafter KT) obtained the highest quality spectra published to date from QSO HS 1946+7658 with 466 Ly[FORMULA] forest lines. A typical sample is shown in Fig. 1, which is a 1-D histogram of the spatial distribution of Ly[FORMULA] absorption lines of QSO-0142.

[FIGURE] Fig. 1. The Ly[FORMULA] forest line distribution of sample Q0142 and a typical realization of its randomization.

It is well known that the number density of the Ly[FORMULA] absorption lines increases with red-shift. The number density of lines with rest equivalent width W greater than a threshold [FORMULA] can approximately be described as


where [FORMULA] is the number density extrapolated to zero red-shift, and [FORMULA] the index of evolution. LWT finds that [FORMULA] and [FORMULA] for lines with [FORMULA] Å. KT finds [FORMULA] while JB finds that [FORMULA] for [FORMULA] Å and [FORMULA] for [FORMULA] Å.

Like other Ly[FORMULA] forest data, these data sets have failed to reveal structures in their distribution on scales [FORMULA] km/s when subjected to a two point correlation analysis (Hu et al. 1995.) Using the discrete wavelet transform spectrum estimator, the Fourier power spectrum of the 1-dimensional (1-D) spatial distribution of these data is found to be almost flat on scales from 2 to about 100 h-1 Mpc (Pando & Fang 1998). For comparison, Fig. 1 also shows a randomized sample which is produced by a random shifting of the lines of QSO-0142. Obviously, one cannot simply distinguish the real sample and its random counterpart by inspection. In fact, when analyzed by second order statistics, the real data are still indistinguishable from randomized samples.

These results indicate that 2nd order statistical techniques, i.e. the two-point correlation function and the power spectrum, are not even qualitatively sufficient to describe the clustering features of these samples. Higher order measures are not a correction to lower order descriptions, but crucial in describing the Ly[FORMULA] forest traced matter field.

This conclusion is strengthened by studying simulated samples. Typically, simulated density fields for pre-collapsed clouds are generated as perturbations with a linear or linear log-normal spectrum given by models such as the cold dark matter model (SCDM), the cold plus hot dark matter model (CHDM), and the low density flat cold dark matter model (LCDM). The baryonic matter distribution is then produced by assuming that the baryonic matter traces the dark matter distribution on scales larger than the Jeans length of the baryonic gas, but is smooth over structures on scales less than the Jeans length. The simulated Ly[FORMULA] absorption spectrum can be calculated as the absorption of neutral hydrogen in the baryonic gas. The effects of the observational instrumental point-spread-function, along with Poisson and background noises can also be simulated properly (Bi, Ge & Fang 1995, hereafter BGF; Bi & Davidson 1997).

Within a reasonable set of parameters, the simulated samples are found to fit with observational measurements such as the number density of Ly[FORMULA] clouds, the distribution of equivalent widths, the red-shift-dependence of the width distributions and clustering. Regardless the details of the simulation, these samples should contain structures because the effects of gravitational collapse have been considered, and baryonic matter does not distribute uniformly random, but traces the structure of dark matter. However, as is the case with observations, the simulated samples show no power in their two-point correlations (see Fig. 11 of BGF), and their 1-D spectra are rather flat on scales less than 100 h-1 Mpc. These results clearly show that higher order measures are necessary in describing the statistical features of the 1-D distributions of the Ly[FORMULA] clouds.

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© European Southern Observatory (ESO) 1998

Online publication: November 9, 1998