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We report the first detection of the intrinsic velocity dispersion of theArches cluster - a young (~2 Myr), massive (~10,000 Solar Mass) starburstcluster located near the Galactic center. This was accomplished using propermotion measurements within the central region of the cluster, obtained with thelaser guide star adaptive optics system at Keck Observatory over a 3 year timebaseline (2006-2009). This uniform dataset results in proper motionmeasurements that are improved by a factor ~5 over previous measurements fromheterogeneous 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 8.4kpc.  Projecting a simple model for the cluster onto the sky to compare with ourproper motion dataset, in conjunction with surface density data, we estimatethe total present-day mass of the cluster to be 15,000 (+7400 -6000) Solarmasses. The mass in stars observed within a cylinder of radius R=0.4 pc isfound to be 9000 (+4000 -3500) Solar Masses at formal 3-sigma confidence. Thismass measurement is free from assumptions about the mass function of thecluster, and thus may be used to check mass estimates from photometry andsimulation. When we conduct this check, we find that the present-day massfunction of the Arches cluster is likely either top-heavy or truncated atlow-mass, or both.  Collateral benefits of our data and analysis include: 1. cluster membershipprobabilities, which may be used to extract a clean cluster sample for futurephotometric work; 2. a refined estimate of the bulk motion of the Archescluster with respect to the field, which we find to be 172 +/- 15 km/s, whichis slightly slower than suggested by previous VLT-Keck measurements; and 3. avelocity dispersion estimate for the field itself, which is likely dominated bythe inner galactic bulge and the nuclear disk.

Proper motions of the Arches cluster with Keck-LGS Adaptive Optics: the first kinematic mass measurement of the Arches