Exploring the Correlations between Globular Cluster Populations and Supermassive Black Holes in Giant Galaxies

This paper presents an analysis of the correlation between the number of globular clusters (N_GC) in giant galaxies and the mass of the galaxies' central supermassive black hole (M_SMBH). I construct a sample of 20 elliptical, spiral, and S0 galaxies with known SMBH masses and with accurately-measured globular cluster system properties derived from wide-field imaging studies. The coefficients of the best-fitting N_GC-M_SMBH relation for the early-type galaxies are consistent with those from previous work but in some cases have smaller relative errors. I examine the correlation between N_GC and M_SMBH for various subsamples and find that elliptical galaxies show the strongest correlation while S0 and pseudobulge galaxies exhibit increased scatter. I also compare the quality of the fit of the numbers of metal-poor globular clusters versus SMBH mass and the corresponding fit for metal-rich globular clusters. I supplement the 20-galaxy sample with ten additional galaxies with reliable N_GC determinations but without measured M_SMBH. I use this larger sample to investigate correlations between N_GC and host galaxy properties like total galaxy luminosity and stellar mass and bulge luminosity and mass. I find that the tightest correlation is between N_GC and total galaxy stellar mass. This lends support to the notion that N_GC and M_SMBH are not directly linked but are correlated because both quantities depend on the host galaxy potential. Finally, I use the N_GC-M_SMBH relation derived from the 20-galaxy sample to calculate predicted M_SMBH values for the ten galaxies with accurate N_GC measurements but without measured SMBH masses.