Origin of the galaxy HI size-mass relation
  We analytically derive the observed size-mass relation of galaxies' atomic
hydrogen (HI), including limits on its scatter, based on simple assumptions
about the structure of HI discs. We trial three generic profiles for HI surface
density as a function of radius. Firstly, we assert that HI surface densities
saturate at a variable threshold, and otherwise fall off exponentially with
radius or, secondly, radius squared. Our third model assumes the total gas
surface density is exponential, with the HI fraction at each radius depending
on local pressure. These are tested against a compilation of 110 galaxies from
the THINGS, LITTLE THINGS, LVHIS, and Bluedisk surveys, whose HI surface
density profiles are well resolved. All models fit the observations well and
predict consistent size-mass relations. Using an analytical argument, we
explain why processes that cause gas disc truncation - such as ram-pressure
stripping - scarcely affect the HI size-mass relation. This is tested with the
IllustrisTNG(100) cosmological, hydrodynamic simulation and the Dark Sage
semi-analytic model of galaxy formation, both of which capture radially
resolved disc structure. For galaxies with m_*>10^9 M_solar and m_HI>10^8
M_solar, both simulations predict HI size-mass relations that align with
observations, show no difference between central and satellite galaxies, and
show only a minor, second-order dependence on host halo mass for satellites.
Ultimately, the universally tight HI size-mass relation is mathematically
inevitable and robust. Only by completely disrupting the structure of HI discs,
e.g. through overly powerful feedback, could a simulation predict the relation
poorly.
