Globular clusters and supermassive black holes in galaxies: further analysis and a larger sample
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We explore several correlations between various large-scale galaxy
properties, particularly total globular cluster population (N_GCS), the central
black hole mass (M_BH), velocity dispersion (nominally sigma_e), and bulge mass
(M_dyn). Our data sample of 49 galaxies, for which both N_GC and M_BH are
known, is larger than used in previous discussions of these two parameters and
we employ the same sample to explore all pairs of correlations. Further, within
this galaxy sample we investigate the scatter in each quantity, with emphasis
on the range of published values for sigma_e and effective radius (R_e). We
find that these two quantities in particular are difficult to measure
consistently and caution that precise intercomparison of galaxy properties
involving R_e and sigma_e is particularly difficult.
Using both chi^2 and Monte Carlo Markov Chain (MCMC) fitting techniques, we
show that quoted observational uncertainties for all parameters are too small
to represent the true scatter in the data. We find that the correlation between
M_dyn and N_GC is stronger than either the M_BH-sigma_e or M_BH-N_GC relations.
We suggest that this is because both the galaxy bulge population ans N_GC were
fundamentally established at an early epoch during the same series of
star-forming events. By contrast, although the seed for M_BH was likely formed
at a similar epoch, its growth over time is less similar from galaxy to galaxy
and thus less predictable.
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