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5 Discussion

The expected number of DLAS (N(H I $) > 2\times
10^{20}$ cm-2) and LLS ( $2 \times 10^{17} < N($H I $) <
2\times 10^{20}$ cm-2) in the redshift interval covered by our 7 spectra as computed from their number density as a function of redshift - $N(z)_{\rm DLAS} \simeq 0.055(1+z)^{1.11}$, $N(z)_{\rm LLS} \simeq 0.27(1+z)^{1.55}$ (Storrie-Lombardi & Wolfe 2000)- is of 1 and 9, respectively. We detect 3 DLASs and 8 LLSs indicating that our lines of sight are not strongly biased toward an overabundance of high column density systems.

The investigation of the nearby lines of sight at the redshift of each of the previous systems, gives the following results. Of the three DLASs: 2 coincide with metal systems with C IV rest equivalent width $W_{\rm r}(\lambda1548)>
0.5$ Å, and 1 is at less than 1000 km s-1 from the emission redshift of the paired QSO, which in turn is marking the presence of a high matter density peak (see Ellison et al. 2001). The transverse spatial separation over which these coincidences happen varies between $\sim $5 and 9 h-1 Mpc.

  \begin{figure}
\par\includegraphics[width=8.8cm,height=8cm,clip]{MS2352f15.eps} %
\end{figure} Figure 15: Summary of the observed coincidences as a function of redshift. The dotted lines mark the redshift range of the observed Lyman-$\alpha $ forests. The angular separations of the quasars are reported between the solid vertical lines. The symbols are: open square for metal systems, solid square for LLS with $2\times 10^{17} < N({\rm HI})< 2\times 10^{20}$ cm-2 and star for DLAS with $N({\rm HI})> 2\times 10^{20}$ cm-2. The big open circles mark the emission redshift of the quasars.

As for the 8 LLSs: 4 of them form two coinciding pairs at $z_{\rm a} \sim 2.03$ and 2.12 in the spectra of UM680 and UM681, their transverse spatial separations are $\sim $920 and 940 h-1 kpc, respectively. The LLS at $z_{\rm a} \sim 2.38$ in the spectrum of Q2138-4427 shows a coinciding metal system in the spectrum of Q2139-4434 at a transverse spatial separation $\sim $$9\ h^{-1}$ Mpc. However, only low-ionisation transitions are observed and no C IV. Furthermore, the H I Lyman-$\alpha $ of the latter system is outside our spectral range . The remaining 3 Lyman limit systems have corresponding Lyman-$\alpha $ absorptions without associated metals within 3000 km s-1.

In summary, we measure a coincidence within 1000 km s-1 between high density systems, in 5 cases out of 10. We exclude the coincidence at $z \sim 2.38$ in the triplet, since it was not possible to determine the H I column density of the metal system. Figure 15 shows a pictorial description of the observed coincidences as a function of redshift; while in Table 4 we report the main properties of the matching absorption systems.

In order to approximately compute the significance of our result, we consider the number density of C IV systems with rest equivalent width $W_{\rm r} > 0.3$ Å as a function of redshift (Steidel 1990). The chance probability (in the hypothesis of null clustering) to detect a C IV absorption line within 1000 km s-1, between z =2 and 3, is ${\cal P}_{\rm exp} \simeq
0.004$. If we assume that a binomial random process rules the detection or the non-detection of a coincidence, the a posteriori probability in the studied case is < $2.5 \times 10^{-10}$. The clustering signal is indeed highly significant.

Going back to our sample, the two coincidences in the spectra of UM680, UM681 at $\sim $$1\ h^{-1}$ Mpc are closely related to the emitting quasars. As recently claimed for associated absorption lines (e.g. Srianand & Petitjean 2000; de Kool et al. 2001; Hamann et al. 2001), the observed absorption systems could arise in gas expelled by a galactic "superwind'' in a luminous starburst associated with the formation of the quasar itself. Superwinds contain cool dense clouds which justify the presence of low ionisation lines, embedded in a hot ($\sim $107 K) X-ray-emitting plasma (see Heckman et al. 1996, and references therein). In low redshift galaxies, outflow velocities of 102-103 km s-1 and column densities $N(H) \sim {\rm few}\ \times 10^{21}$ cm-2 have been measured which are consistent with the observed values.

The remaining three coincident systems involve DLASs and are characterized by larger QSO pair separations. Damped systems at high redshifts are thought to arise in large disks (e.g. Wolfe 1995) or in multiple protogalactic clumps (Haehnelt et al. 1998; Ledoux et al. 1998; McDonald & Miralda-Escudé 1999). In either case they trace high matter density peaks and they are possibly associated with Lyman-break galaxies (Møller et al. 2002). The representation of these kind of objects in hydrodynamical simulations (e.g. Jenkins et al. 1998; Cen 1998) shows that they lie in knots of $\sim $$1\ h^{-1}$ Mpc scale from which filaments several Mpc in length depart in a spider-like structure. Star formation takes place in the central condensation but also in some denser blobs of matter along the filaments. The correlation on large scales observed around the DLAS in our sample finds a likely explanation in this scenario (see the discussion in Francis et al. 2001b). For comparison, Lyman break galaxies at $z \sim 3$, which are thought to have masses $M \sim 10^{11}~M_{\odot}$, show correlation lengths $r_0 \sim 2\ h^{-1}$ Mpc (Giavalisco et al. 1998; Porciani & Giavalisco 2001; Arnouts et al. 2002).


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