The proper motion of the Arches cluster with Keck laser-guide star adaptive optics

We present the first measurement of the proper motion of the young, compact Arches cluster near the Galactic center from near-infrared adaptive optics (AO) data taken with the recently commissioned laser-guide star (LGS) at the Keck 10 m telescope. The excellent astrometric accuracy achieved with LGS-AO provides the basis for a detailed comparison with VLT/NAOS-CONICA data taken 4.3 yr earlier. Over the 4.3 yr baseline, a spatial displacement of the Arches cluster with respect to the field population is measured to be 24.0 +/- 2.2 mas, corresponding to a proper motion of 5.6 +/- 0.5 mas yr(-1) or 212 +/- 29 km s(-1) at a distance of 8 kpc. In combination with the known line-of-sight velocity of the cluster, we derive a three-dimensional (3D) space motion of 232 +/- 30 km s(-1) of the Arches relative to the field. The large proper motion of the Arches cannot be explained with any of the closed orbital families observed in gas clouds in the bar potential of the inner Galaxy, but would be consistent with the Arches being on a transitional trajectory between x1 and x2 orbits. We investigate a cloud-cloud collision as the possible origin for the Arches cluster. The integration of the cluster orbit in the potential of the inner Galaxy suggests that the cluster passes within 10 pc of the supermassive black hole only if its true GC distance is very close to its projected distance. A contribution of young stars from the Arches cluster to the young stellar population in the inner few parsecs of the GC thus appears increasingly unlikely. The measurement of the 3D velocity and orbital analysis provides the first observational evidence that Arches-like clusters do not spiral into the GC. This confirms that no progenitor clusters to the nuclear cluster are observed at the present epoch.