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We present a simulation based analysis of \Lyal\ forest regions in the spectra of 17 QSOs. The spectra in the sample have medium-to-high resolution ($\sim$50\kms) and high ($>$5 per pixel in continuum) signal to noise ratio. All spectra were reduced in the same way.
Distributions of physical parameters of the \Lyal\ clouds, column density ($N$) and Doppler parameter ($b$) were approximated with the following functions: \begin{displaymath} \frac{d\N}{dN} \propto N^{-\beta} {\rm ~~and~~} \frac{d\N}{db} \propto \exp\left[-\frac{(b-\bsr)^2}{2\sigma_b^2} \right] \end{displaymath}
The aim of this study is to establish the parameters of the distributions of the \Lyal\ forest clouds minimizing the subjective part of the analysis. We achieved that using absorption spectra simulation software developed by us.
We constructed a grid of models of the spectra with different input parameters. Each set of simulated spectra consisted of 17 ``QSOs'', having identical: emission redshift, binning, continuum, resolution, and signal to noise ratios as the actual observed spectra. For each simulation, lists of resolution elements with significant absorption were generated. The distributions of (1) equivalent widths of these elements and (2) separations between them were then compared with respective distributions of analogical quantities derived from observed spectra, yielding acceptable ranges of parameters.
We obtain $\beta=1.4\pm0.1$ and $\bsr=30\pm15$\kms. The result for $\beta$ is quite interesting. It is lower than the values obtained with the analysis of line lists ($\beta=1.7-1.9$), but it is consistent with analysis by Press \& Rybicki (1993) and with curve of growth studies (Jenkins et al.\ 1991). Our result for \bsr, though consistent with values quoted in the literature, is of lower significance, as it is smaller than the resolution of our spectra.
