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We present a uniform analysis of the stellar initial mass function (IMF) fromintegrated light spectroscopy of 15 compact stellar systems (11 globularclusters in M31 and 4 ultra compact dwarfs in the Virgo cluster, UCDs) and twobrightest Coma cluster galaxies (BCGs), covering a wide range of metallicities($-$1.7 $<$ [Fe/H] $<$ 0.01) and velocity dispersions (7.4 km~s$^{-1}$ $<\sigma <$ 275 km~s$^{-1}$). The S/N $\sim 100$ \AA$^{-1}$ Keck LRIS spectra arefitted over the range $4000<\lambda/\mbox{\AA}<10,000$ with flexible,full-spectrum stellar population synthesis models. We use the models to fitsimultaneously for ages, metallicities, and individual elemental abundances ofthe population, allowing us to decouple abundance variations from variations inIMF slope. We show that compact stellar systems do not follow the same trendswith physical parameters that have been found for early-type galaxies. Mostglobular clusters in our sample have an IMF consistent with that of the MilkyWay, over a wide range of [Fe/H] and [Mg/Fe]. There is more diversity among theUCDs, with some showing evidence for a bottom-heavy IMF, but with no clearcorrelation with metallicity, abundance, or velocity dispersion. The two ComaBCGs have similar velocity dispersion and metallicity, but we find the IMF ofNGC~4874 is consistent with that of the Milky Way while NGC~4889 presentsevidence for a significantly bottom-heavy IMF. For this sample, the IMF appearsto vary between objects in a way that is not explained by a singlemetallicity-dependent prescription.

Initial mass function variability from the integrated light of diverse stellar systems