A study of the globular cluster systems of 23 brightest, or central, galaxies
in 19 Abell clusters has recently been completed. This Letter presents some of
the newly discovered correlations of the globular cluster specific frequency
SN in these galaxies with other galaxy and cluster properties and puts forth
an interpretation of these results. SN is found to correlate strongly with
measures of the cluster density, such as the velocity dispersion of the cluster
galaxies and the cluster X-ray temperature and luminosity (especially ``local''
X-ray luminosity). Within a cluster, galaxies at smaller projected distances
from the X-ray center are found to have higher values of SN. Taken together,
the scaling of SN with cluster density and the relative constancy of central
galaxy luminosity suggest a scenario in which globular clusters form in
proportionate numbers to the available mass, but galaxy luminosity
``saturates'' at a maximum threshold, resulting in higher \sn\ values for
central galaxies in denser clusters as well as the suitability of these
galaxies as ``standard candles.'' Thus, these galaxies do not have too many
globular clusters for their luminosity; rather, they are underluminous for
their number of globular clusters.Comment: 10 pages, with 4 included postscript figures; AASTeX (aaspp4.sty); to
appear in ApJ Letter