There is a well known disparity between the evolution the star formation rate density , \psi _ { * } , and the abundance of neutral hydrogen ( H i ) , the raw material for star formation .
Recently , however , we have shown that \psi _ { * } may be correlated with the fraction of cool atomic gas , as traced through the 21-cm absorption of H i .
This is expected since star formation requires cold ( T \sim 10 K ) gas and so this could address the issue of why the star formation rate density does not trace the bulk atomic gas .
The data are , however , limited to redshifts of z \stackrel { < } { { } _ { \sim } } 2 , where both \psi _ { * } and the cold gas fraction exhibit a similar steep climb from the present day ( z = 0 ) , and so it is unknown whether the cold gas fraction follows the same decline as \psi _ { * } at higher redshift .
In order to address this , we have used unpublished archival observations of 21-cm absorption in high redshift damped Lyman- \alpha absorption systems to increase the sample at z \stackrel { > } { { } _ { \sim } } 2 .
The data suggest that the cold gas fraction does exhibit a decrease , although this is significantly steeper than \psi _ { * } at z \sim 3 .
This is , however , degenerate with the extents of the absorbing galaxy and the background continuum emission and upon removing these , via canonical evolution models , we find the mean spin temperature of the gas to be \left < T _ { spin } \right > \approx 3000 K , compared to the \approx 2000 K expected from the \psi _ { * } T _ { spin } \approx 100 M _ { \odot } yr ^ { -1 } Mpc ^ { -3 } K fit at z \stackrel { < } { { } _ { \sim } } 2 .
These temperatures are consistent with the observed high neutral hydrogen column densities , which require T \stackrel { < } { { } _ { \sim } } 4000 K in order for the gas not to be highly ionised .