We report the first detection of the intrinsic velocity dispersion of the Arches cluster - a young ( \sim 2 Myr ) , massive ( 10 ^ { 4 } M _ { \odot } ) starburst cluster located only 26 pc in projection from the Galactic center .
This was accomplished using proper motion measurements within the central 10 ^ { \prime \prime } \times 10 ^ { \prime \prime } 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 \sim 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 \pm 0.01 mas yr ^ { -1 } , which corresponds to 5.4 \pm 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 dataset , 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 } \times 10 ^ { 4 } M _ { \odot } .
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 } \times 10 ^ { 4 } M _ { \odot } 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 .
Photometric mass estimates assuming an initially Salpeter mass function ( \Gamma _ { 0 } = 1.35 , or \Gamma \sim 1.0 at present , where dN / d ( \log M ) \propto M ^ { \Gamma } ) suggest a total cluster mass M _ { cl } \sim ( 4 - 6 ) \times 10 ^ { 4 } M _ { \odot } and projected mass ( \sim 2 \leq M ( R < 0.4 ~ { } { pc } ) \leq 3 ) \times 10 ^ { 4 } M _ { \odot } .
Photometric mass estimates assuming a globally top-heavy or strongly truncated present-day mass function ( PDMF , with \Gamma \sim 0.6 ) yield mass estimates closer to M ( R < 0.4 ~ { } { pc } ) \sim 1 - 1.2 \times 10 ^ { 4 } M _ { \odot } .
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 : ( i ) cluster membership probabilities , which may be used to extract a clean cluster sample for future photometric work ; ( ii ) a refined estimate of the bulk motion of the Arches cluster with respect to the field , which we find to be 172 \pm 15 km s ^ { -1 } , which is slightly slower than suggested by previous VLT-Keck measurements ; and ( iii ) a velocity dispersion estimate for the field itself , which is likely dominated by the inner galactic bulge and the nuclear disk .