At a projected distance of \sim 26 pc from Sgr A* , the Arches cluster provides insight to star formation in the extreme Galactic Center ( GC ) environment .
Despite its importance , many key properties such as the cluster ’ s internal structure and orbital history are not well known .
We present an astrometric and photometric study of the outer region of the Arches cluster ( R > 6.25 ” ) using HST WFC3IR .
Using proper motions we calculate membership probabilities for stars down to F153M = 20 mag ( \sim 2.5 M _ { \odot } ) over a 120 ” x 120 ” field of view , an area 144 times larger than previous astrometric studies of the cluster .
We construct the radial profile of the Arches to a radius of 75 ” ( \sim 3 pc at 8 kpc ) , which can be well described by a single power law .
From this profile we place a 3 \sigma lower limit of 2.8 pc on the observed tidal radius , which is larger than the predicted tidal radius ( 1 – 2.5 pc ) .
Evidence of mass segregation is observed throughout the cluster and no tidal tail structures are apparent along the orbital path .
The absence of breaks in the profile suggests that the Arches has not likely experienced its closest approach to the GC between \sim 0.2 – 1 Myr ago .
If accurate , this constraint indicates that the cluster is on a prograde orbit and is located front of the sky plane that intersects Sgr A* .
However , further simulations of clusters in the GC potential are required to interpret the observed profile with more confidence .