We present K-band λ/Δλ ~ 2600 spectroscopy of five stars
(K ~ 14 - 16 mag) within 0.''5 of Sgr A*, the radio source associated with the
compact massive object suspected to be a 2.6 x 106 \msun black hole at the
center of our Galaxy. High spatial resolution of ~ 0.''09, and good strehl
ratios of ~ 0.2 achieved with adaptive optics on the 10-meter Keck telescope
make it possible to measure moderate-resolution spectra of these stars
individually for the first time. Two stars (S0-17 and S0-18) are identified as
late-type stars by the detection of CO bandhead absorption in their spectra.
Their absolute K magnitudes and CO bandhead absorption strengths are consistent
with early K giants. Three stars (S0-1, S0-2, and S0-16), with rproj<
0.0075 pc (~ 0.''2) from Sgr A*, lack CO bandhead absorption, confirming the
results of earlier lower spectral and lower spatial resolution observations
that the majority of the stars in the Sgr A* Cluster are early-type stars. The
absolute K magnitudes of the early-type stars suggest that they are late O -
early B main sequence stars of ages < 20 Myr. The presence of young stars in
the Sgr A* Cluster, so close to the central supermassive black hole, poses the
intriguing problem of how these stars could have formed, or could have been
brought, within its strong tidal field.Comment: 19 pages, 8 figures, 2 tables. Accepted for publication in Ap