The ACS Virgo Cluster Survey.: X.: Half-light radii of globular clusters in early-type galaxies:: Environmental dependencies and a standard ruler for distance estimation

We have measured half-light radii, r(h), for thousands of globular clusters (GCs) belonging to the 100 early-type galaxies observed in the ACS Virgo Cluster Survey and the elliptical galaxy NGC 4697. An analysis of the dependencies of the measured half-light radii on both the properties of the GCs themselves and their host galaxies reveals that, in analogy with GCs in the Galaxy but in a milder fashion, the average half-light radius increases with increasing galactocentric distance or, alternatively, with decreasing galaxy surface brightness. For the first time, we find that the average half-light radius decreases with the host galaxy color. We also show that there is no evidence for a variation of rh with the luminosity of the GCs. Finally, we find in agreement with previous observations that the average rh depends on the color of GCs, with red GCs being similar to 17% smaller than their blue counterparts. We show that this difference is probably a consequence of an intrinsic mechanism, rather than projection effects, and that it is in good agreement with the mechanism proposed by Jordan. We discuss these findings in light of two simple pictures for the origin of the r(h) of GCs and show that both lead to a behavior in rough agreement with the observations. After accounting for the dependencies on galaxy color, galactocentric radius, and underlying surface brightness, we show that the average GC half-light radii r(h) can be successfully used as a standard ruler for distance estimation. We outline the methodology, provide a calibration for its use, and discuss the prospects for this distance estimator with future observing facilities. We find r(h) = 2.7 +/- 0.35 pc for GCs with (g - z) = 1.2 mag in a galaxy with color (g - z)(gal) = 1.5 mag and at an underlying surface z-band brightness of mu(z) = 21 mag arcsec(-2). Using this technique, we place an upper limit of 3.4 Mpc on the 1 sigma line-of-sight depth of the Virgo Cluster. Finally, we examine the form of the rh distribution for our sample galaxies and provide an analytic expression that successfully describes this distribution.