The nuclear bulge I. K band observations of the central 30 pc

Out of similar to 500 individual source images we have constructed a mosaic map(1) of the K band surface brightness in an area Delta alpha x Delta del ta similar to 650 " x 710 " (R-equiv similar to 15.8 pc for R-0 = 8.5 kpc) centered approximately on Sgr A*. An observing technique was used which all ows us to recover an extended background emission. To separate sources from an unresolved background continuum we fitted Lorentzian distributions to t he sources and find that about one half of an integrated, not dereddened K band flux density of 752 Jy is contributed by similar to 6 x 10(4) stars wi th flux densities' S-K' greater than or similar to 100 mu Jy and the remain der is contributed by an extended continuum provided by about 6 x 10(8); st ars too weak to be observed as individual sources. We estimate that greater than or similar to 80% of the integrated flux density of the mosaic is con tributed by stars in the Nuclear Bulge (NB; R less than or similar to 300 p c); the remaining less than or similar to 20% come from stars located along the line of sight in the Galactic Bulge (GB; 0.3 less than or similar to R /kpc less than or similar to 3) and Galactic Disk (GD: R > 3 kpc). We determine the K band luminosity functions (KLF) of the mosaic and of sub areas dominated by Nuclear Bulge, Galactic Bulge and Disk stars, respective ly, and construct difference KLFs which relate to the specific stellar popu lations of these regions. The detection limit is S-K' similar to 100 mu Jy, for the completeness limit we estimate S-K' similar to 2 000 mu Jy. We fin d that the stellar population of the Nuclear Bulge contains considerably mo re bright stars (i.e. with reddened K band Aux densities S-K' greater than or similar to 5 x 10(3) mu Jy), most of which are probably early O stars, G iants and Supergiants. The stellar population of the Galactic Bulge on the other hand is dominated by stars which appear to be lower mass (less than o r similar to 6M.) Main Sequence (MS) stars. A model KLF constructed with a Salpeter Initial Mass Function (IMF) for sta rs of spectral type O9 or later (S-K' less than or similar to 2 000 mu Jy) explains the observations satisfactorily and connects well with the observe d KLF of more luminous stars. About 6 x 10(8) stars with masses ranging fro m 0.06 to 6 M. account for the unresolved continuum. Combining observed and model KLF we obtain a mosaic KLF which increases proportional to S-K'(-1) for 10(6) greater than or similar to S-K'/mu Jy 10(3) and x S-K'(-0.6) for 10(3) greater than or similar to S-K'/mu Jy greater than or similar to 3 x 10(-3) For radii R < 15 " nearly 90% of the spatially integrated K band Aux densit y comes from resolved sources which represent sent a relatively young gener ation 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 Aux density increases and attains similar to 40% at a distance R simil ar to 300 ". This indicates a deficiency of low-mass stars within the centr al 30 " (similar to 1.25 pc) and a high star formation activity during the past similar to 10(7)-10(8) yr. Fitting King profiles to the observed surfa ce brightnesses we derive core radii of similar to 7 " and similar to 30 " respectively for resolved and unresolved stars. The mass-to-luminosity rati o of low mass stars in the central 30 pc is found to be similar to 1M./L.. We present and discuss the radio/IR spectrum of the central 30 " (similar t o 1.25 pc) and derive dust and Lyman continuum (Lyc) luminosities of 7.5 x 10(7) L. and 1.2 x 10(50) s(-1), respectively.