All Figures

$\begin{figure} \par\includegraphics[clip=,width=8.5cm]{8780hhi.ps}\\ \includegraphics[clip=,width=8.5cm]{8780hhis.ps} \end{figure}$ Figure 1: Top panel: neutral hydrogen column density distributions of DLAs in the overall UVES sample $\mathcal{S}$ (solid), the sub-sample of H₂-bearing systems $\mathcal{S}$ $_{\rm H2}$ (grey), and that of the systems with $\log f>-4.5$ ( $\mathcal{S}$ $_{\rm HF}$ ; dark grey). The distribution from the SDSS-DR5 sample (dotted; Prochaska et al. 2005) is represented with a different scaling (right axis) so that the area of both histograms are the same. The inset shows the cumulative distributions from sample $\mathcal{S}$ (solid line), sub-sample $\mathcal{S}$ $_{\rm HF}$ (dashed), and the SDSS-DR5 sample (dotted). Bottom panel: the above $\log N(\mbox{H {\sc i}})$ distributions are corrected for the bias in favour of large $N(\mbox{H {\sc i}})$ column densities (see text) by scaling the numbers separately for $20\le\log N(\mbox{H {\sc i}})<20.8$ and $\log N(\mbox{H {\sc i}})\ge 20.8$ to match the SDSS-DR5 distribution.
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In the text

$\begin{figure} \par\includegraphics[clip=,width=8.5cm]{8780hixh.ps}\\ \includegraphics[clip=,width=8.5cm]{8780hixf.ps} \end{figure}$ Figure 2: Logarithm of the total neutral hydrogen column density in the UVES sample versus metallicity ( top panel) or depletion factor ( bottom panel). Filled squares indicate systems in which H₂ is detected. The lack of systems with both a high metallicity and a large H I column density is seen in all DLA samples. There is no correlation between $N(\mbox{H {\sc i}})$ and [X/H] or [X/Fe].
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In the text

$\begin{figure} \par\includegraphics[clip=,width=8.5cm]{8780hxh.ps} \end{figure}$ Figure 3: The metallicity distribution of DLAs in the overall UVES sample ( $\mathcal{S}$ ; solid) is compared to that from the Keck sample (dotted; Prochaska et al. 2007), adequately scaled (right axis) so that the area of both histograms are the same. The distributions are similar. Distributions from sub-samples $\mathcal{S}$ $_{\rm H2}$ (grey) and $\mathcal{S}$ $_{\rm HF}$ (dark grey) are also shown. It is clear from this and the Kolmogorov-Smirnov test probability (inset) that the distributions from H₂-bearing systems are skewed towards high metallicities.
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In the text

$\begin{figure} \par\includegraphics[clip=,width=8.5cm]{8780hih2.ps} \end{figure}$ Figure 4: Molecular fraction versus total hydrogen ( $\mbox{H {\sc i}}+$ H₂) column density for sample $\mathcal{S}$ (the filled squares correspond to H₂ detections, i.e., sub-sample $\mathcal{S}$ $_{\rm H2}$ ), lines of sight through the SMC (blue dots, top panel; Tumlinson et al. 2002), the LMC (red triangles, middle panel; Tumlinson et al. 2002) and the Galactic disk (green diamonds, bottom panel; Savage et al. 1977). Upper limits are marked by unfilled symbols with downward arrows.
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In the text

$\begin{figure} \par\includegraphics[clip=,width=8.8cm,bb=28 390 600 750]{8780fxh.ps} \end{figure}$ Figure 5: Logarithm of the molecular fraction, f=2N(H₂)/(2N(H $_2)+N(\mbox{H {\sc i}})$ , versus metallicity, [X/H $]=\log N($ X)/N(H $)-\log~ ({\rm X/H})_\odot$ with X = Zn, S or Si. Filled squares indicate systems in which H₂is detected. The horizontal (resp. vertical) dashed line indicates the separation between what we somewhat arbitrarily call high and low molecular fractions, $\log f=-4.5$ (resp. high and low metallicities, [X/H]=-1.3).
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In the text

$\begin{figure} \par\includegraphics[clip=,width=8.6cm]{8780xfxh.ps} \end{figure}$ Figure 6: A correlation (5.3 $\sigma$ confidence level) exists in the overall UVES sample between dust-depletion factor, [X/Fe], and metallicity, [X/H], with X either Zn, S or Si.
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In the text

$\begin{figure} \par\includegraphics[clip=,width=8.8cm,bb=28 390 600 750]{8780hxf.ps} \end{figure}$ Figure 7: Distribution of depletion factors from the overall UVES sample ( $\mathcal{S}$ ; solid), sub-samples $\mathcal{S}$ $_{\rm H2}$ (grey) and $\mathcal{S}$ $_{\rm HF}$ (dark grey). It is clear from these histograms that the distribution of depletion factors for H₂-bearing systems is different from that of the overall sample. This shows clearly that H₂-bearing DLAs are more dusty than the rest of the DLAs. The probability that the two samples are drawn from the same parent population is indeed very small: $P_{\rm KS}($ $\mathcal{S}$ / $\mathcal{S}$ $_{\rm HF})\approx 10^{-3}$ .
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In the text

$\begin{figure} \par\includegraphics[clip=,width=8.8cm,bb=28 390 600 755]{8780h2fd.ps} \end{figure}$ Figure 8: H₂ column density, N(H₂), versus column density of iron into dust grains, N(Fe $)_{\rm dust}$ . The horizontal dotted line at $\log N$ (H₂) $\simeq$ 18.2 (resp. 14.3) shows the median $\log N$ (H₂) (resp. the median upper limit on $\log N($ H₂)) for the H₂-bearing DLAs from sub-sample $\mathcal{S}$ $_{\rm H2}$ (resp. the H₂-undetected systems from sub-sample $\mathcal{S}$ - $\mathcal{S}$ $_{\rm H2}$ ). There is a clear gap of about four orders of magnitude between the two values. The horizontal bar in the upper-left corner of the plot shows the typical uncertainty on the measured $\log N$ (Fe) $_{\rm dust}$ .
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In the text

$\begin{figure} \par\includegraphics[clip=,width=8.8cm,bb=28 390 600 755]{8780hdv.ps} \end{figure}$ Figure 9: Distribution of the velocity spread, $\Delta V$ , of low-ionisation metal line profiles (see Ledoux et al. 2006a, for details on the technique) from the overall UVES sample ( $\mathcal{S}$ , 77 systems, solid histogram), systems with detected molecular hydrogen ( $\mathcal{S}$ $_{\rm H2}$ , 13 systems, grey), and systems with $\log f>-4.5$ ( $\mathcal{S}$ $_{\rm HF}$ , ten systems, dark grey). It is apparent from this and the Kolmogorov-Smirnov test probability (inset) that the likelihood of finding H₂ is higher when $\Delta V$ is larger.
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In the text

$\begin{figure} \par\includegraphics[clip=,width=8.6cm,bb=42 390 600 755]{8780hz.... ... \includegraphics[clip=,width=8.6cm,bb=42 390 600 755]{8780fz.ps} \end{figure}$ Figure 10: Top panel: redshift distributions of DLAs in the overall UVES sample ( $\mathcal{S}$ , 77 systems, solid histogram), systems with detected molecular hydrogen ( $\mathcal{S}$ $_{\rm H2}$ , 13 systems, grey), and systems with $\log f>-4.5$ ( $\mathcal{S}$ $_{\rm HF}$ , ten systems, dark grey). The inset shows the cumulative distributions from sample $\mathcal{S}$ (solid) and sub-sample $\mathcal{S}$ $_{\rm HF}$ (dashed). The two distributions are statistically indistinguishable ( $P_{\rm KS}=0.98$ ). Bottom panel: logarithm of the molecular fraction, $\log f$ , versus absorber redshift. There is a slight trend for more constraining upper limits at higher redshift. This is not physical however but due to the higher signal-to-noise ratios achieved towards the red, together with the larger number of H₂ transitions covered by the spectra.
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In the text

$\begin{figure} \par\includegraphics[clip=,width=8.6cm]{8780xfxh.ps} \end{figure}$	Figure 6: A correlation (5.3 $\sigma$ confidence level) exists in the overall UVES sample between dust-depletion factor, [X/Fe], and metallicity, [X/H], with X either Zn, S or Si.
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