Using 21-cm absorption surveys to measure the average HI spin temperature in distant galaxies

We present a statistical method for measuring the average HI spin temperature in distant galaxies using the expected detection yields from future wide-field 21cm absorption surveys. As a demonstrative case study we consider a simulated all-southern-sky survey of 2-h per pointing with the Australian Square Kilometre Array Pathfinder for intervening HI absorbers at intermediate cosmological redshifts between $z = 0.4$ and $1$. For example, if such a survey yielded $1000$ absorbers we would infer a harmonic-mean spin temperature of $\overline{T}_\mathrm{spin} \sim 100$K for the population of damped Lyman $α$ (DLAs) absorbers at these redshifts, indicating that more than $50$ per cent of the neutral gas in these systems is in a cold neutral medium (CNM). Conversely, a lower yield of only 100 detections would imply $\overline{T}_\mathrm{spin} \sim 1000$K and a CNM fraction less than $10$ per cent. We propose that this method can be used to provide independent verification of the spin temperature evolution reported in recent 21cm surveys of known DLAs at high redshift and for measuring the spin temperature at intermediate redshifts below $z \approx 1.7$, where the Lyman-$α$ line is inaccessible using ground-based observatories. Increasingly more sensitive and larger surveys with the Square Kilometre Array should provide stronger statistical constraints on the average spin temperature. However, these will ultimately be limited by the accuracy to which we can determine the HI column density frequency distribution, the covering factor and the redshift distribution of the background radio source population.