  We report the first detection of the intrinsic velocity dispersion of the
Arches cluster - a young (~2 Myr), massive (~10,000 Solar Mass) starburst
cluster located near the Galactic center. This was accomplished using proper
motion measurements within the central region of the cluster, obtained with the
laser guide star adaptive optics system at Keck Observatory over a 3 year time
baseline (2006-2009). This uniform dataset results in proper motion
measurements that are improved by a factor ~5 over previous measurements from
heterogeneous instruments, yielding internal velocity dispersion estimates 0.15
+/- 0.01 mas/yr, which corresponds to 5.4 +/- 0.4 km/s at a distance of 8.4
kpc.
  Projecting a simple model for the cluster onto the sky to compare with our
proper motion dataset, in conjunction with surface density data, we estimate
the total present-day mass of the cluster to be 15,000 (+7400 -6000) Solar
masses. The mass in stars observed within a cylinder of radius R=0.4 pc is
found to be 9000 (+4000 -3500) Solar Masses at formal 3-sigma confidence. This
mass measurement is free from assumptions about the mass function of the
cluster, and thus may be used to check mass estimates from photometry and
simulation. When we conduct this check, we find that the present-day mass
function of the Arches cluster is likely either top-heavy or truncated at
low-mass, or both.
  Collateral benefits of our data and analysis include: 1. cluster membership
probabilities, which may be used to extract a clean cluster sample for future
photometric work; 2. a refined estimate of the bulk motion of the Arches
cluster with respect to the field, which we find to be 172 +/- 15 km/s, which
is slightly slower than suggested by previous VLT-Keck measurements; and 3. a
velocity dispersion estimate for the field itself, which is likely dominated by
the inner galactic bulge and the nuclear disk.
