Integral field spectroscopy of the central parsec of the Galactic Center was obtained at 2.06 micron using BEAR, an imaging Fourier Transform Spectrometer, at a spectral resolution of 74 km s-1. Sixteen stars were confirmed as `` helium stars'' by detecting the \ionHeI 2.058 micron line in emission, providing a homogeneous set of fully resolved line profiles. These observations allow us to discard some of the earlier detections of such stars in the central cluster and to add three new stars. The sources detected in the BEAR data were compared with adaptive optics images in the K band to determine whether the emission was due to single stars. Two sub-classes of almost equal number are clearly identified from the width of their line profiles, and from the brightness of their continuum. The first class is characterized by very broad line profiles (FWHM 1000 km s-1) and by their relative faintness. The other, brighter in K by an average factor of 9, has a much narrower emission component of width 200 km s-1. Most of the emission lines show a P Cygni profile. From these results, we propose that the latter group is formed of stars in or near the LBV phase, and the other one of stars at the WR stage. The division into two groups is also shown by their spatial distribution, with the narrow-line stars in a compact central cluster (\objectIRS 16) and the other group distributed at the periphery of the central cluster of hot stars. In the same data cube, streamers of interstellar helium gas are also detected. The helium emission traces the densest parts of the SgrA West Mini-Spiral. Several helium stars have a radial velocity comparable to the velocity of the interstellar gas in which they are embedded. In the final discussion, all these findings are examined to present a possible scenario for the formation of very massive stars in the exceptional conditions of the vicinity of the central Black Hole.
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