The H i mass function of group galaxies in the ALFALFA survey

We present the HI mass function (HIMF) of group galaxies based on combining four popular optically defined galaxy group catalogs from SDSS (Berlind et al, Tempel et al, Yang et al, and Lim et al) with knowledge of the neutral atomic gas (HI) content of the galaxies measured by the ALFALFA survey. We significantly improve on the statistical foundation of previous work: the four HIMFs we construct from each of the four group catalogs have approximately two to three orders of magnitude more groups and two orders of magnitude more HI detected galaxies contributing the mass function than previous attempts to measure the group HIMF. Broadly speaking, we find the group HIMF differs from the global HIMF by having an approximately flat low mass slope, and a knee mass which is marginally higher than the global HIMF. More strictly speaking, we find there is no universal group galaxy HIMF: the different methods of constructing group catalogs lead to differences in the group HIMF. Thus a comparison of the HIMF between different groups or group catalogs requires a comparison between how the groups were constructed before the results can be interpreted. Indeed, the attempt to construct a universal group HIMF has shed light on the caveats of existing group catalogs as they are compared to one another.