Based on public data released from the UVES commissioning at the VLT/Kueyen telescope, ESO, Paranal, Chile.

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Tables A.1, A.2 and A.3 are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/373/757

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... $\Lambda = 0$

Recent measurements from high-z supernovae favor the non-zero cosmological constant (Perlmutter et al. 1999). When we use the mass density $\Omega_{{\rm m}} \sim 0.3$ and the cosmological constant energy density $\Omega_{\Lambda} \sim 0.7$ for the flat universe as the results from the supernova study favor (Perlmutter et al. 1999), the line number density for the non-evolving forest can still be approximated by a single power-law dn/d $z \propto (1+z)^{\sim 0.71}$ at 0 < z < 4.5with a slight steepening at z < 1: At z > 1, dn/d $z \propto (1+z)^{\sim 0.59}$ , while z < 1, dn/d $z \propto (1+z)^{\sim 1.15}$ .

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...1999)

It should be noted that Davé et al. (1999) assume the QSO-dominated Haardt-Madau UV background without He II reionization. No other scaling laws between $N_H{\sc i}$ and $\delta$ as a function of z from simulations under different UV backgrounds are found in the literature.

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... $z \sim 3$

Note that Ricotti et al. (2000) found that $\delta=0$ corresponds to $N_H{\sc i} = 5.62 \times 10^{12}~{\rm cm}^{-2}$ at z = 2.85 with He II reionization at $z \sim 3$ , almost a factor of 10 smaller than the column density calculated by Eq. (7). This discrepancy indicates the importance of using the correct ionizing background in simulations to constrain the temperature of the IGM.

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