  We present new near-infrared spectroscopic observations of the outer edges of
the young stellar cluster around the supermassive black hole at the Galactic
center. The observations show a break in the surface-density profile of young
stars at approximately 13 arcsec (0.52 pc). These observations
spectroscopically confirm previous suggestions of a break based on photometry.
Using Gemini North's Near-Infrared Integral Field Spectrometer (NIFS) we are
able to detect and separate early- and late-type stars with a 75% completeness
at Ks = 15.5. We sample a region with radii between 7" to 23" (0.28 pc to 0.92
pc) from Sgr A*, and present new spectral classifications of 144 stars brighter
than Ks = 15.5, where 140 stars are late-type (> 1 Gyr) and only four stars are
early-type (young, 4-6 Myr). A broken power-law fit of the early-type
surface-density matches well with our data and previously published values. The
projected surface-density of late-type stars is also measured and found to be
consistent with previous results. We find that the observed early-type
surface-density profile is inconsistent with the theory of the young stars
originating from a tightly bound infalling cluster, as no significant trail of
young stars is found at radii above 13". We also note that either a simple disk
instability criterion or a cloud-cloud collision could explain the location of
the outer edge, though we lack information to make conclusive remarks on either
alternative. If this break in surface-density represents an edge to the young
stellar cluster it would set an important scale for the most recent episode of
star formation at the Galactic center.
