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The mean and the scatter of the HI content of a dark-matter halo as afunction of the halo mass are useful statistics that can be used to test modelsof structure and galaxy formation. We investigate the possibility ofconstraining this HI-halo mass relation (HIHMR) from intensity maps of theredshifted 21 cm line. In particular, we use the geometry and topology of thebrightness-temperature isocontours in a single frequency channel as quantifiedby the Minkowski functionals. First, we generate mock maps from a large N-bodysimulation considering the impact of thermal noise and foreground removal. Wethen use the Fisher information formalism to forecast constraints on aparametric model for the HIHMR. We consider a 20,000 deg$^2$ survey (originallyproposed for dark-energy science) conducted with the Square Kilometre ArrayPhase 1 (SKA-1) MID observatory operating in single-dish mode. For a channelbandwidth of 2 MHz, we show that an integration time of a few$\,\times\,10^4$ sper pointing is sufficient to image the smoothed HI distribution at redshift $z\simeq 1$ and to measure the HIHMR in a nearly optimal way from the Minkowskifunctionals. Tighter constraints on some of the parameters can be obtained byusing also an independent measurement of the mean HI density. Combining theresults from different frequency channels provides exquisite constraints on theevolution of the HIHMR, especially in the central frequency range of the datacube.

The HI-halo mass relation at redshift $z \sim 1$ from the Minkowski functionals of 21 cm intensity maps