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
Tspin​∼100K 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
Tspin​∼1000K 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≈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.Comment: 11 pages, 9 figures, 1 table. Proof corrected versio