Predicting the Resolved WALLABY Velocity Function

The velocity function of local disk galaxies — their number density as a function of their rotation velocity — is a key statistical constraint on cosmological galaxy formation because its properties depend on both the dark matter halo velocity function as well as on how galaxies of different masses are embedded in those halos. The HI velocity function is particularly powerful in this context because the extended HI layers of disk galaxies contain most of their angular momentum. HI velocity functions have insofar been measured from spatially unresolved single-dish surveys, but their interpretation is complicated by the unknown gas distribution within each galaxy: this is particularly true at the low-V end, where hypotheses to explain the strong discrepancy from the collisionless dark matter halo relation range from blaming measurement errors, to invoking large non-circular flows, to positing that the narrow HI widths of many local disk galaxies belie high masses. The Australian SKA Pathfinder (ASKAP) WALLABY survey is set to revolutionize this field by delivering the first HI velocity function built from spatially resolved observations over a cosmological volume. Its properties depend both on the galaxy population resolved by WALLABY and how reliably those detections can be kinematically modelled. We generate the first detailed predictions for the resolved WALLABY velocity function by simulating realistic HI detections and assessing how well they can be modelled with state-of-the-art tools. We predict that axisymmetric HI disks resolved by as few as 3.5 telescope beams across their major axes can be reliably modelled at most inclinations. WALLABY will therefore measure the resolved galaxy velocity function down to VHI ~ 30 km/s, well into the regime where current observations and collisionless simulation predictions are discrepant.