  Observations indicate that some extended outer disks have a sharp cut off in
the surface density of neutral hydrogen when this approaches the value of $\sim
2\times 10^{19}$ cm$^{-2}$. In this paper we model these HI edges as places
where the ratio of neutral to ionized hydrogen drops rapidly due to ionizing
radiation. We use two different models for the vertical distribution of gas
above the outer galactic plane: in the first model we derive the density from
the ideal gas law while in the second model we insert a macroscopic pressure
term and derive the density as for an isothermal slab. We consider two
different sources of ionizing photons: external fluxes of different intensity
and spectral index due to quasars, and a monochromatic UV flux due to neutrino
decays. We find that galaxies which have a smaller gas scale height should show
outer HI disks to a lower column density and smoother HI edges. The sharpness
of the HI-HII transition and the total column density at which the medium is
50$\%$ ionized, are strongly correlated. We present several model fits to the
HI sharp edge observed in M33. If today's UV background is dominated by
attenuated quasar light, which gives $\sim 10^{-14}$ H ionizations s$^{-1}$, a
large gas scale height or equivalently a nearly spherical halo is preferred. If
ionizing photons from decaying neutrinos are responsible for the sharp edge, a
flat dark matter halo, is required.
