1999A&A...348..768P

Out of ∼500 individual source images we have constructed a mosaic map of the K band surface brightness in an area ΔαxΔδ∼650"x710" (R_equiv∼15.8pc for R₀=8.5kpc) centered approximately on Sgr A*. An observing technique was used which allows us to recover an extended background emission. To separate sources from an unresolved background continuum we fitted Lorentzian distributions to the sources and find that about one half of an integrated, not dereddened K band flux density of 752Jy is contributed by ∼6x10⁴ stars with flux densities S_K'>100µJy and the remainder is contributed by an extended continuum provided by about 6x10⁸ stars too weak to be observed as individual sources. We estimate that >80% of the integrated flux density of the mosaic is contributed by stars in the Nuclear Bulge (NB; R≲300pc); the remaining ≲20% come from stars located along the line of sight in the Galactic Bulge (GB; 0.3≲R/kpc≲3) and Galactic Disk (GD; R>3kpc). We determine the K band luminosity functions (KLF) of the mosaic and of subareas dominated by Nuclear Bulge, Galactic Bulge and Disk stars, respectively, and construct difference KLFs which relate to the specific stellar populations of these regions. The detection limit is S_K'∼100µJy, for the completeness limit we estimate S_K'∼2000µJy. We find that the stellar population of the Nuclear Bulge contains considerably more bright stars (i.e. with reddened K band flux densities S_K'>5x10³µJy), most of which are probably early O stars, Giants and Supergiants. The stellar population of the Galactic Bulge on the other hand is dominated by stars which appear to be lower mass (≲6M_☉) Main Sequence (MS) stars. A model KLF constructed with a Salpeter Initial Mass Function (IMF) for stars of spectral type O9 or later (S_K'≲2000µJy) explains the observations satisfactorily and connects well with the observed KLF of more luminous stars. About 6x10⁸ stars with masses ranging from 0.06 to 6M_☉ account for the unresolved continuum. Combining observed and model KLF we obtain a mosaic KLF which increases ∝S_K'^–1 for 10⁶>S_K'/µJy>10³ and ∝S_K'^–0.6 for 10³>S_K'/µJy>3x10^–3. For radii R<15" nearly 90% of the spatially integrated K band flux density comes from resolved sources which represent a relatively young generation of luminous stars. Farther out the contribution of the the unresolved continuum (and hence of low and medium mass MS stars) to the integrated K band flux density increases and attains ∼40% at a distance R∼300". This indicates a deficiency of low-mass stars within the central 30" (∼1.25pc) and a high star formation activity during the past ∼10⁷-10⁸yr. Fitting King profiles to the observed surface brightnesses we derive core radii of ∼7" and ∼30" respectively for resolved and unresolved stars. The mass-to-luminosity ratio of low mass stars in the central 30pc is found to be ∼1M_☉/L_☉. We present and discuss the radio/IR spectrum of the central 30" (∼1.25pc) and derive dust and Lyman continuum (Lyc) luminosities of 7.5x10⁷L_☉ and 1.2x10⁵⁰s^–1, respectively.