PROPER MOTIONS OF THE ARCHES CLUSTER WITH KECK LASER GUIDE STAR ADAPTIVE OPTICS: THE FIRST KINEMATIC MASS MEASUREMENT OF THE ARCHES

We report the first detection of the intrinsic velocity dispersion of the Arches cluster—a young (∼2 Myr), massive (104 M☉) starburst cluster located only 26 pc in projection from the Galactic center. This was accomplished using proper motion measurements within the central 10″ × 10″ of the cluster, obtained with the laser guide star adaptive optics system at Keck Observatory over a three-year time baseline (2006–2009). This uniform data set results in proper motion measurements that are improved by a factor ∼5 over previous measurements from heterogeneous instruments. By careful, simultaneous accounting of the cluster and field contaminant distributions as well as the possible sources of measurement uncertainties, we estimate the internal velocity dispersion to be 0.15 ± 0.01 mas yr−1, which corresponds to 5.4 ± 0.4 km s−1 at a distance of 8.4 kpc. Projecting a simple model for the cluster onto the sky to compare with our proper motion data set, in conjunction with surface density data, we estimate the total present-day mass of the cluster to be M(r < 1.0 pc) = 1.5+0.74−0.60 × 104 M☉. The mass in stars observed within a cylinder of radius R (for comparison to photometric estimates) is found to be M(R < 0.4 pc) = 0.90+0.40−0.35 × 104 M☉ at formal 3σ 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. Photometric mass estimates assuming an initially Salpeter mass function (Γ0 = 1.35, or Γ ∼ 1.0 at present, where dN/d(log M)∝MΓ) suggest a total cluster mass Mcl ∼ (4–6) × 104 M☉ and projected mass (∼ 2 ⩽ M(R < 0.4 pc) ⩽ 3) × 104 M☉. Photometric mass estimates assuming a globally top-heavy or strongly truncated present-day mass function (PDMF; with Γ ∼ 0.6) yield mass estimates closer to M(R < 0.4 pc) ∼ 1–1.2 × 104 M☉. Consequently, our results support a PDMF that is 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−1, which is slightly slower than suggested by previous measurements using one epoch each with the Very Large Telescope and the Keck telescope; and (3) a velocity dispersion estimate for the field itself, which is likely dominated by the inner Galactic bulge and the nuclear disk.