We report the detection of 21-cm and molecular hydrogen absorption lines in the same damped Lyman- \alpha system ( with log N ( H i ) =21.36 \pm 0.10 ) at z _ { abs } =3.17447 towards SDSS J133724.69+315254.55 ( z _ { em } \sim 3.174 ) .
We estimate the spin temperature of the gas to be , T _ { S } = 600 ^ { +222 } _ { -159 } K , intermediate between the expected values for cold and warm neutral media .
This suggests that the H i absorption originates from a mixture of different phases .
The total molecular fraction is low , f _ { H _ { 2 } } =10 ^ { -7 } , and H _ { 2 } rotational level populations are not in equilibrium .
The average abundance of the \alpha -elements is , [ S/H ] = -1.45 \pm 0.22 .
Nitrogen and iron are found underabundant with respect to \alpha -elements by \sim 1.0 dex and \sim 0.5 dex respectively .
Using photoionization models we conclude that the gas , of mean density , { n _ { H } } \sim 2 cm ^ { -3 } , is located more than 270 kpc away from the QSO .
While the position of 21-cm absorption line coincides with the H _ { 2 } velocity profile , its centroid is shifted by \sim 2.7 \pm 1.0 km s ^ { -1 } with respect to the redshift measured from the H _ { 2 } lines .
However , the position of the strongest metal absorption component matches the position of the 21-cm absorption line within 0.5 km s ^ { -1 } .
From this , we constrain the variation of the combination of fundamental constants x = \alpha ^ { 2 } G _ { p } / \mu , \Delta x / x = - ( 1.7 \pm 1.7 ) \times 10 ^ { -6 } .
This system is unique as we can at the same time have an independent constrain on \mu using H _ { 2 } lines .
However , as the H _ { 2 } column density is low , only Werner band absorption lines are seen and , unfortunately , the range of sensitivity coefficients is too narrow to provide a stringent constraint : \Delta \mu / \mu \leq 4.0 \times 10 ^ { -4 } .
The Ultraviolet and Visual Echelle Spectrograph ( UVES ) spectrum reveals another DLA at z _ { abs } = 3.16768 with log N ( H i ) = 20.41 \pm 0.15 and low metallicity , [ Si/H ] = -2.68 \pm 0.11 , in which [ O/C ] \sim 0.18 \pm 0.18 and [ O/Si ] \sim 0 .
This shows that even in the very early stages of chemical evolution , the carbon or silicon to oxygen ratios can be close to solar .
Using Voigt profile fitting we derive log ( N ( D i ) / N ( H i ) ) = - ( 4.93 \pm 0.15 ) in this system .
This is a factor of two smaller than the value expected from the best fitted value of \Omega _ { b } from the Wilkinson Microwave Anisotropy Probe ( WMAP ) 5 year data .
This confirms the presence of astration of deuterium even at very low metallicity .