Exploring the correlations between globular cluster populations and supermassive black holes in giant galaxies

Abstract

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 GC 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 GCs versus SMBH mass and the corresponding fit for metal-rich GCs. I supplement the 20 galaxy sample with 10 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 10 galaxies with accurate $N_{GC}$ measurements but without measured SMBH masses.