Compact high-velocity clouds (CHVCs) are the most distant of the HVCs in the Local Group model and would have HI volume densities of order 0.0003/cm^3. Clouds with these volume densities and the observed neutral hydrogen column densities will be largely ionized, even if exposed only to the extragalactic ionizing radiation field. Here we examine the implications of this process for models of CHVCs. We have modeled the ionization structure of spherical clouds (with and without dark matter halos) for a large range of densities and sizes, appropriate to CHVCs over the range of suggested distances, exposed to the extragalactic ionizing photon flux. Constant-density cloud models in which the CHVCs are at Local Group distances have total (ionized plus neutral) gas masses roughly 20-30 times larger than the neutral gas masses, implying that the gas mass alone of the observed population of CHVCs is about 40 billion solar masses. With a realistic (10:1) dark matter to gas mass ratio, the total mass in such CHVCs is a significant fraction of the dynamical mass of the Local Group, and their line widths would exceed the observed FWHM. Models with dark matter halos fare even more poorly; they must lie within approximately 200 kpc of the Galaxy. We show that exponential neutral hydrogen column density profiles are a natural consequence of an external source of ionizing photons, and argue that these profiles cannot be used to derive model-independent distances to the CHVCs. These results argue strongly that the CHVCs are not cosmological objects, and are instead associated with the Galactic halo.
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