The Dependence of Globular Cluster Number on Density for Abell Cluster Central Galaxies

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 $S_N$ in these galaxies with other galaxy and cluster properties and puts forth an interpretation of these results. $S_N$ 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 $S_N$. Taken together, the scaling of $S_N$ 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.