We used our database of ESO VLT-UVES spectra of quasars to build up a sample of 67 Damped Lyman- \alpha ( DLA ) systems with redshifts 1.7 < z _ { abs } < 3.7 .
For each system , we measured average metallicities relative to Solar , [ X/H ] ( with either { X } = { Zn } , S or Si ) , and the velocity widths of low-ionization line profiles , W _ { 1 } .
We find that there is a tight correlation between the two quantities , detected at the 5 \sigma significance level .
The existence of such a correlation , over more than two orders of magnitude spread in metallicity , is likely to be the consequence of an underlying mass-metallicity relation for the galaxies responsible for DLA absorption lines .
The best-fit linear relation is [ { X } / { H } ] = 1.35 ( \pm 0.11 ) \log W _ { 1 } -3.69 ( \pm 0.18 ) with W _ { 1 } expressed in km s ^ { -1 } .
While the slope of this velocity-metallicity relation is the same within uncertainties between the higher and the lower redshift bins of our sample , there is a hint of an increase of the intercept point of the relation with decreasing redshift .
This suggests that galaxy halos of a given mass tend to become more metal-rich with time .
Moreover , the slope of this relation is consistent with that of the luminosity-metallicity relation for local galaxies .
The DLA systems having the lowest metallicities among the DLA population would therefore , on average , correspond to the galaxies having the lowest masses .
In turn , these galaxies should have the lowest luminosities among the DLA galaxy population .
This may explain the recent result that the few DLA systems with detected Ly \alpha emission have higher than average metallicities .