1999A&A...348..457M

Philipp et al. (1999A&A...348..768P, Paper I) investigated the K band emission from a mosaic of size ΔαxΔδ∼650"x710" centered approximately on Sgr A* (R_equiv∼15.8pc for R₀=8.5kpc). For the ∼6x10⁴ stars above the detection limit (S_K'∼100µJy) an observed K-band luminosity function (KLF) has been obtained. Below the completeness limit (S_K'∼2000µJy), an ever increasing fraction of stars merges into the background continuum. In this paper we combine the observed with model KLFs and thus obtain a complete KLF for the flux density range 3x10^–3>S_K'/µJy>2x10⁶. The overall KLF consists of four sectors obeying power laws of the form dN(S_K')/dlogS_K'∝S_K'^γ1_+1^, where γ₁+1 decreases from -0.6 to -1.75. SectorI corresponds to a Salpeter Initial Mass Function (IMF) and represents Main Sequence (MS) stars with M_*≲1M_☉, which account for ∼90% of the dynamical mass but only ∼6% of the K band flux density. SectorII represents MS stars with M_*>1M_☉ and red giants. These stars account for only ∼6% of the dynamical mass and a similar percentage of the integrated K-band surface brightness but represent ∼80% of the bolometric stellar luminosity in the mosaic. The Mass Function (MF) of MS stars is dN/dM_*∝M_*^–2.35 (i.e., the Salpeter IMF) for M_*≲1M_☉ and dN/dM_* ∝M_*^–4.5 for more massive stars, which is similar to the Present Day MF in the solar vicinity. Part of sector II of the KLF, as well as sectors III and IV, represent giants and supergiants which, though they account for only a small fraction of the mass, dominate the integrated K-band surface brightness. The slope of sector II of the KLF, γ₁+1~-0.8 has been inferred from the KLF in the NGC 6522 Baade's Window (BW). To make this sector join smoothly to the neighboring KLF sections we have to set the surface density of low-mass (∼1M_☉) MS stars at ∼56 times that in BW. Paper I shows, in agreement with earlier observations, that massive stars are preferentially formed in the central parsec. A preliminary discussion of star formation rates suggests that bimodal star formation (introduced by Guesten & Mezger [1983VA.....26..159G] for the spiral arm region of the Galactic Disk) may also apply to the central 30pc. Preferential formation of stars with masses M_*>M_c∼1-5M_☉ would make conversion of matter into radiation by star formation much more efficient and could be the process which powers star burst galaxies. There is an overabundance of evolved stars which can be explained by a strongly increased star formation rate ∼10⁸-10⁹yrs ago.