We used our database of VLT-UVES quasar spectra to build up a sample of 70
Damped Lyman-alpha (DLA) or strong sub-DLA systems with total neutral hydrogen
column densities of log N(HI)>20 and redshifts in the range 1.7<z_abs<4.3. For
each of the systems, we measured in an homogeneous manner the metallicities
relative to Solar, [X/H] (with X=Zn, or S or Si), and the velocity widths of
low-ionization line profiles, Delta V. We provide for the first time evidence
for a correlation between DLA metallicity and line profile velocity width,
which is detected at the 6.1sigma significance level. This confirms the trend
previously observed in a much smaller sample by Wolfe & Prochaska (1998). The
best-fit linear relation is [X/H]=1.55(\pm 0.12) log Delta V -4.33(\pm 0.23)
with Delta V expressed in km/s. The slope of the DLA velocity-metallicity
relation is the same within uncertainties between the higher (z_abs>2.43) and
the lower (z_abs<2.43) redshift halves of our sample. However, the two
populations of systems are statistically different. There is a strong redshift
evolution in the sense that the mean metallicity and mean velocity width
increase with decreasing redshift. We argue that the existence of a DLA
velocity-metallicity correlation, over more than a factor of 100 spread in
metallicity, is probably the consequence of an underlying mass-metallicity
relation for the galaxies responsible for DLA absorption lines. Assuming a
simple linear scaling of the galaxy luminosity with the mass of the dark-matter
halo, we find that the slope of the DLA velocity-metallicity relation is
consistent with that of the luminosity-metallicity relation derived for local
galaxies. [...] abridged.Comment: 10 pages, 4 figures, A&A in pres