Observations indicate that some extended outer disks have a sharp cuto
ff in the surface density of neutral hydrogen when this approaches the
value of approximately 2 x 10(19) cm-2. In this paper we model these
H I edges as places where the ratio of neutral to ionized hydrogen dro
ps rapidly due to ionizing radiation. We use two different models for
the vertical distribution of gas above the outer Galactic plane: in th
e first model we derive the density from the ideal gas law, while in t
he second model we insert a macroscopic pressure term and derive the d
ensity 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 dec
ays inside and outside the disk. We find that galaxies which have a sm
aller gas scale height, because of a higher dark matter density or a l
arger external pressure, should show outer H i disks to a lower column
density and smoother H I edges. The sharpness of the H I-H II transit
ion and the total column density at which the medium is 50% ionized, a
re strongly correlated, irrespective of the gas or photon flux model u
sed. We present several model fits to the H I sharp edge observed in t
he nearby galaxy M33. If today's UV background is dominated by attenua
ted quasar light and gives approximately 10(-14) H ionizations s-1, a
large gas scale height or equivalently a nearly spherical halo is pref
erred. If ionizing photons from decaying neutrinos are responsible for
the M33 sharp edge, then a thin outer H I disk, and consequently a fl
at dark matter halo, is required.