Composition of the galactic center star cluster Population analysis from adaptive optics narrow band spectral energy distributions

Context. The GC is the closest galactic nucleus, offering the unique possibility of studying the population of a dense stellar cluster surrounding an SMBH. Aims. The goals of this work are to develop a new method of separating early and late type stellar components of a dense stellar cluster based on narrow band filters, applying it to the central parsec of the GC, and conducting a population analysis of this area. Methods. We use AO assisted observations obtained at the ESO VLT in the NIR H-band and 7 intermediate bands covering the NIR K-band. A comparison of the resulting SEDs with a blackbody of variable extinction then allows us to determine the presence and strength of a CO absorption feature to distinguish between early and late type stars. Results. This new method is suitable for classifying K giants (and later), as well as B2 main sequence (and earlier) stars that are brighter than 15.5 mag in the K band in the central parsec. Compared to previous spectroscopic investigations that are limited to 13-14 mag, this represents a major improvement in the depth of the observations and reduces the needed observation time. Extremely red objects and foreground sources can also be reliably removed from the sample. Comparison to sources of known classification indicates that the method has an accuracy of better than similar to 87%. We classify 312 stars as early type candidates out of a sample of 5914 sources. Several results, such as the shape of the KLF and the spatial distribution of both early and late type stars, confirm and extend previous works. The distribution of the early type stars can be fitted with a steep power law (beta(1 '') = -1.49 +/- 0.12), alternatively with a broken power law, beta(1-10 '') = -1.08 +/- 0.12, beta(10-20)'' = -3.46 +/- 0.58, since we find a drop in the early type density at similar to 10 ''. We also detect early type candidates outside of 0.5 pc in significant numbers for the first time. The late type density function shows an inversion in the inner 6 '', with a power-law slope of beta(R<6 '') = 0.17 +/- 0.09. The late type KLF has a power-law slope of 0.30 +/- 0.01, closely resembling the KLF obtained for the bulge of the Milky Way. The early type KLF has a much flatter slope of (0.14 +/- 0.02). Our results agree best with an in-situ star formation scenario.