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The ACS Fornax Cluster Survey VII. Half-Light Radii of Globular Clusters in Early-Type Galaxies

We measure the half-light radii of globular clusters (GCs) in 43 galaxies from the ACS Fornax Cluster Survey (ACSFCS). We use these data to extend previous work in which the environmental dependencies of the half-light radii of GCs in early type galaxies in the ACS Virgo Cluster Survey (ACSVCS) were studied, and a corrected mean half-light radius (corrected for the observed environmental trends) was suggested as a reliable distance indicator. This work both increases the sample size for the study of the environmental dependencies, and adds leverage to the study of the corrected half-light radius as a possible distance indicator (since Fornax lies at a larger distance than the Virgo cluster). We study the environmental dependencies of the size of GCs using both a Principal Component Analysis as well as 2D scaling relations. We largely confirm the environmental dependencies shown in Jordan et al. (2005), but find evidence that there is a residual correlation in the mean half-light radius of GC systems with galaxy magnitude, and subtle differences in the other correlations - so there may not be a universal correction for the half-light radii of lower luminosity galaxy GC systems. The main factor determining the size of a GC in an early type galaxy is the GC color. Red GCs have <r_h> = 2.8+/-0.3 pc, while blue GCs have <r_h> = 3.4+/-0.3 pc. We show that for bright early-type galaxies (M_B < -19 mag), the uncorrected mean half-light radius of the GC system is by itself an excellent distance indicator (with error ~11%), having the potential to reach cosmologically interesting distances in the era of high angular resolution adaptive optics on large optical telescopes.