H i 21-cm absorption at z∼ 3.39 towards PKS 0201+113

We report the Giant Metrewave Radio Telescope detection of H  i 21-cm absorption from the z ∼ 3.39 damped Lyman α absorber (DLA) towards PKS 0201+113, the highest redshift at which 21-cm absorption has been detected in a DLA. The absorption is spread over ∼115 km s⁻¹ and has two components, at   z = 3.387 144(17)  and   z = 3.386 141  (45). The stronger component has a redshift and velocity width in agreement with the tentative detection of Briggs, Brinks & Wolfe, but a significantly lower optical depth. The core size and DLA covering factor are estimated to be ≲100 pc and f ∼ 0.69, respectively, from a Very Long Baseline Array 328-MHz image. If one makes the conventional assumption that the H  i column densities towards the optical and radio cores are the same, this optical depth corresponds to a spin temperature of T _s∼[(955 ± 160) × ( f /0.69)] K. However, this assumption may not be correct, given that no metal-line absorption is seen at the redshift of the stronger 21-cm component, indicating that this component does not arise along the line of sight to the optical quasi-stellar object (QSO), and that there is structure in the 21-cm absorbing gas on scales smaller than the size of the radio core. We model the 21-cm absorbing gas as having a two-phase structure with cold dense gas randomly distributed within a diffuse envelope of warm gas. For such a model, our radio data indicate that, even if the optical QSO lies along a line of sight with a fortuitously high (∼50 per cent) cold gas fraction, the average cold gas fraction is low, ≲17 per cent, when averaged over the spatial extent of the radio core. Finally, the large mismatch between peak 21-cm and optical redshifts and the complexity of both profiles makes it unlikely that the z ∼ 3.39 DLA will be useful in tests of fundamental constant evolution.