The nuclear bulge of the Galaxy - II. The K band luminosity function of the central 30 pc

Philipp et al. (1999, Paper I) investigated the K band emission from a mosa ic of size Delta alpha x Delta delta similar to 650 " x 710 " centered appr oximately on Sgr A* (R-equiv similar to 15.8 pc for R-0 = 8.5 kpc). For the similar to 6 x 10(4) stars above the detection limit (S-K' similar to 100 mu Jy(1)) an observed K-band luminosity function (KLF) has been obtained. B elow the completeness limit (S-K' similar to 2 000 mu Jy). an ever increasi ng 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 th e flux density range 3 x 10(-3) greater than or similar to S-K'/mu Jy great er than or similar to 2 x 10(6). The overall KLF consists of four sectors o beying power laws of the form dN (S-K')/dlogS(K)' proportional to S-K'(gamm a 1+1), where gamma(1) + 1 decreases from -0.6 to -1.75. Sector I correspon ds to a Salpeter Initial Mass Function (IMF) and represents Main Sequence ( MS) stars with M-* less than or similar to 1 M., which account for similar to 90% of the dynamical mass but only similar to 6% of the K band flux dens ity. Sector II represents MS stars with M-* greater than or similar to 1 M. and red giants. These stars account for only similar to 6% of the dynamica l mass and a similar percentage of the integrated K-band surface brightness but represent similar to 80% of the bolometric stellar luminosity in the m osaic. The Mass Function (MF) of MS stars is dN/dM(*) proportional to M-*(- 2.35) (i.e., the Salpeter IMF) for M-* less than or similar to 1 M. and dN/ dM(*) proportional to 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 I I I and IV, represent giants and supergiants which, thou gh they account for only a small fraction of the mass, dominate the integra ted K-band surface brightness. The slope of sector II of the KLF, gamma(1) + 1 similar to -0.8 has been in ferred from the KLF in the NGC 6522 Baade's Window (BW). To make this secto r join smoothly to the neighboring KLF section. we have to set the surface density of low-mass (similar to 1 M.) MS stars at similar to 56 times that in BW. Paper I shows. in agreement with earlier observations, that massive stars a re preferentially formed in the central parsec. A preliminary discussion of star formation rates suggests that bimodal star formation (introduced by G listen & Mezger [1983] for thr: spiral arm region of the Galactic Disk) may also apply to the central 30 pc. Preferential formation of stars with mass es M-* greater than or similar to M-c similar to 1-5 M. would make conversi on 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 forma tion rate similar to 10(8)-10(9) yrs ago.