Stellar mass-gap as a probe of halo assembly history and concentration: youth hidden among old fossils

We investigate the use of the halo mass-gap statistic --- defined as the logarithmic difference in mass between the host halo and its most massive satellite subhalo --- as a probe of halo age and concentration. A cosmological N-body simulation is used to study N ~25, 000 group/cluster sized halos in the mass range 10^12.5 < M_halo/M_sol < 10^14.5. In agreement with previous work, we find that halo mass-gap is related to halo formation time and concentration. On average, older and more highly concentrated halos have larger halo mass-gaps, and this trend is stronger than the mass-concentration relation over a similar dynamic range. However, there is a large amount of scatter owing to the transitory nature of the satellite subhalo population, which limits the use of the halo mass-gap statistic on an object-by-object basis. For example, we find that 20% of very large halo mass-gap systems (akin to "fossil groups") are young, and have likely experienced a recent merger between a massive satellite subhalo and the central subhalo. We relate halo mass-gap to the observable stellar mass-gap via abundance matching. Using a galaxy group catalog constructed from the Sloan Digital Sky Survey Data Release 7, we find that the star formation and structural properties of galaxies at fixed mass show no trend with stellar mass-gap. This is despite a variation in halo-age of ~2.5 Gyr over ~1.2 dex in stellar mass-gap. Thus, we find no evidence to suggest that the halo formation history significantly affects galaxy properties.