We present a study of cold gas absorption from a damped Lyman- \alpha absorber ( DLA ) at redshift z _ { abs } = 1.946 towards two lensed images of the quasar J144254.78+405535.5 at redshift z _ { \textsc { qso } } = 2.590 .
The physical separation of the two lines of sight at the absorber redshift is d _ { abs } = 0.7 kpc based on our lens model .
We observe absorption lines from neutral carbon and H _ { 2 } along both lines of sight indicating that cold gas is present on scales larger than d _ { abs } .
We measure column densities of H i to be \log N ( H \textsc { i } ) = 20.27 \pm 0.02 and 20.34 \pm 0.05 and of H _ { 2 } to be \log N ( H _ { 2 } ) = 19.7 \pm 0.1 and 19.9 \pm 0.2 .
The metallicity inferred from sulphur is consistent with Solar metallicity for both sightlines : [ { S / H } ] _ { A } = 0.0 \pm 0.1 and [ { S / H } ] _ { B } = -0.1 \pm 0.1 .
Based on the excitation of low rotational levels of H _ { 2 } , we constrain the temperature of the cold gas phase to be T = 109 \pm 20 and T = 89 \pm 25 K for the two lines of sight .
From the relative excitation of fine-structure levels of C i , we constrain the hydrogen volumetric densities in the range of 40 - 110 cm ^ { -3 } .
Based on the ratio of observed column density and volumetric density , we infer the average individual ‘ cloud ’ size along the line of sight to be l \approx 0.1 pc .
Using the transverse line-of-sight separation of 0.7 kpc together with the individual cloud size , we are able to put an upper limit to the volume filling factor of cold gas of f _ { vol } < 0.2 % .
Nonetheless , the projected covering fraction of cold gas must be large ( close to unity ) over scales of a few kpc in order to explain the presence of cold gas in both lines of sight .
Compared to the typical extent of DLAs ( \sim 10 - 30 kpc ) , this is consistent with the relative incidence rate of C i absorbers and DLAs .