We study the rich globular cluster (GC) system in the center of the massive
cluster of galaxies Abell 1689 (z=0.18), one of the most powerful gravitational
lenses known. With 28 HST/ACS orbits in the F814W bandpass, we reach magnitude
I_814=29 with >90% completeness and sample the brightest ~5% of the GC system.
Assuming the well-known Gaussian form of the GC luminosity function (GCLF), we
estimate a total population of N(GC_total) = 162,850 GCs within a projected
radius of 400kpc. As many as half may comprise an intracluster component. Even
with the sizable uncertainties, which mainly result from the uncertain GCLF
parameters, this is by far the largest GC system studied to date. The specific
frequency S_N is high, but not uncommon for central galaxies in massive
clusters, rising from S_N~5 near the center to ~12 at large radii. Passive
galaxy fading would increase S_N by ~20% at z=0. We construct the radial mass
profiles of the GCs, stars, intracluster gas, and lensing-derived total mass,
and we compare the mass fractions as a function of radius. The estimated mass
in GCs, M(GC_total)=3.9x10^10 Msun, is comparable to ~80% of the total stellar
mass of the Milky Way. The shape of the GC mass profile appears intermediate
between those of the stellar light and total cluster mass. Despite the extreme
nature of this system, the ratios of the GC mass to the baryonic and total
masses, and thus the GC formation efficiency, are typical of those in other
rich clusters when comparing at the same physical radii. The GC formation
efficiency is not constant, but varies with radius, in a manner that appears
similar for different clusters; we speculate on the reasons for this similarity
in profile.Comment: 13 pages, 11 figures; accepted for publication in Ap
