2003ApJ...584..228P

We present the analysis of the H I survey of isolated galaxies described in the first two papers in this series. This survey found 13 gas-rich companions around 10 of the 41 galaxies observed. In this paper, we present numerous pieces of evidence that the number of companions detected is less than expected by cold dark matter models of galaxy formation or H I observations of the population of galaxies in the field. We discuss the implications of these data for galaxy formation and the evolution of the properties of these companions. A statistical analysis of the observed distribution of the ensemble of companions with respect to the primary galaxies implies that, in general, these companions are on circular orbits and not eccentric orbits. While individual companions may be on eccentric orbits, the majority of the orbits are circular and, therefore, fairly stable. In fact, on the basis of the observed separations, both spatial and in velocity space, only those companions currently interacting with the galaxy they orbit should be accreted in the next few Gyr, and only half of the companies will be accreted in less than a Hubble time. Of the close companions, only UGC 260A and UGC 11152A appear to be significantly affecting the morphology of the primary galaxy. The remaining companions have too little mass and are too far away from the main galaxies to have any current effect on their morphology. None of these companions are massive enough to destroy the disk of the isolated galaxy when they are accreted, but instead will represent a minor merger that will supply a large amount of H I to fuel future star formation in these galaxies and produce small effects on the morphology. All of which implies that we are seeing nothing more than the tail end of the galaxy formation process. We have also compared the cumulative velocity distribution function of our companions with the predictions of cold dark matter and other galaxy formation models. Our data are only consistent with cold dark matter models when generous, but not unreasonable, correction factors are applied for nondetections of gas-poor galaxies. Models that suppress observable satellite galaxies, such as warm dark matter models or those that prevent neutral gas from accumulating in dark matter halos, would better explain our observed population of companions. Finally, we compare the H I mass function (MF) for companions to isolated galaxies with the H I MF from the work of others. Our H I MF is consistent with a variety of faint-end slopes up to α~-1.3. Such a slope argues against the Blitz et al. model for high-velocity clouds.