| Abstract
| - We present the results of three separate searches for H i 21-cm absorption in a total of 12 damped Lyman α absorption systems (DLAs) and sub-DLAs over the redshift range zabs= 0.86-3.37. We find no absorption in the five systems for which we obtain reasonable sensitivities and add the results to those of other recent surveys in order to investigate factors which could have an effect on the detection rate. We provide evidence that the mix of spin temperature/covering factor ratios seen at low redshift may also exist at high redshift, with a correlation between the 21-cm line strength and the total neutral hydrogen column density, indicating a roughly constant spin temperature/covering factor ratio for all of the DLAs searched. Also, by considering the geometry of a flat expanding Universe together with the projected sizes of the background radio emission regions, we find, for the detections, that the 21-cm line strength is correlated with the size of the absorber. For the non-detections, it is apparent that larger absorbers (covering factors) are required in order to exhibit 21-cm absorption, particularly if these DLAs do not arise in spiral galaxies. We also suggest that the recent zabs= 2.3 detection towards TXS 0311+430 arises in a spiral galaxy, but on the basis of a large absorption cross-section and high metallicity, rather than a low spin temperature.
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