------------------------------------------------------------------------ From: Sabine Philipp sphilipp@mpifr-bonn.mpg.de X-Accept-Language: en MIME-Version: 1.0 To: gcnews@aoc.nrao.edu Subject: Abstracts ... %http://www.aoc.nrao.edu/staff/sphilipp/ \documentclass{aa} \usepackage{epsf,times} \setlength{\emergencystretch}{10.0pt} \begin{document} \thesaurus{4(08.12.3; 09.04.1; 10.03.1; 10.05.1; 10.19.2; 13.09.6)} \authorrunning{S.\ Philipp, R.\ Zylka, P.G.\ Mezger, W.J.\ Duschl, T.\ Herbst, R.J.\ Tuffs} \titlerunning{The Nuclear Bulge I: The Stellar Population} \title{The Nuclear Bulge I: K Band Observations of the Central 30\,pc} \author{S.\ Philipp\inst{1,2}, R.\ Zylka\inst{2}, P.G.\ Mezger\inst{1}, W.J.\ Duschl\inst{2,1}, T.\ Herbst\inst{3}, R.J.\ Tuffs\inst{4}} \offprints{P.G.\ Mezger, Bonn} \mail{wjd@ita.uni-heidelberg.de} \institute{Max-Planck-Institut f\"ur Radioastronomie, Auf dem H\"ugel 69, D-53121 Bonn, Germany \and Institut f\"ur Theoretische Astrophysik, Tiergartenstra{\ss}e 15, D-69121 Heidelberg, Germany \and Max-Planck-Institut f\"ur Astronomie, K\"onigstuhl 17, D-69117 Heidelberg, Germany \and Max-Planck-Institut f\"ur Kernphysik, Saupfercheckweg, D-69117 Heidelberg, Germany } \date{Received \dots ; accepted \dots} \maketitle \begin{abstract} Out of $\sim 500$ individual source images we have constructed a mosaic map of the K band surface brightness in an area $\Delta\alpha\times\Delta\delta \sim 650''\times710''$ ($R_{\rm equiv} \sim 15.8$\,pc for $R_0 = 8.5$\,kpc) 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 $752$\,Jy is contributed by $\sim 6\times10^4$ stars with flux densities $S_{\rm K}^\prime \ga 100\,\mu$Jy and the remainder is contributed by an extended continuum provided by about $6\times10^8$ stars too weak to be observed as individual sources. We estimate that $\ga 80\%$ of the integrated flux density of the mosaic is contributed by stars in the Nuclear Bulge (NB; $R \la 300$\,pc); the remaining $\la 20\%$ come from stars located along the line of sight in the Galactic Bulge (GB; $0.3 \la R/$kpc$ \la 3$) and Galactic Disk (GD; $R > 3$\,kpc). 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 {\it difference} KLFs which relate to the specific stellar populations of these regions. The detection limit is $S_{\rm K}^\prime \sim 100\,\mu$Jy, for the completeness limit we estimate $S_{\rm K}^\prime \sim 2\,000\,\mu$Jy. We find that the stellar population of the Nuclear Bulge contains considerably more bright stars (i.e. with reddened K band flux densities $S_{\rm K}^\prime \ga 5\times10^3\,\mu$Jy), 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 ($\la 6 {\rm M}_\odot$) Main Sequence (MS) stars. A {\it model} KLF constructed with a Salpeter Initial Mass Function (IMF) for stars of spectral type O9 or later ($S_{\rm K}^\prime \la 2\,000\,\mu$Jy) explains the observations sa\-tisfactorily and connects well with the {\it observed} KLF of more luminous stars. About $6\times10^8$ stars with masses ranging from 0.06 to 6 ${\rm M}_\odot$ account for the unresolved continuum. Combining observed and model KLF we obtain a mosaic KLF which increases $\propto S_{\rm K}^{\prime - 1}$ for $10^6 \ga S_{\rm K}^\prime/\mu$Jy$ \ga 10^3$ and $\propto S_{\rm K}^{\prime - 0.6}$ for $10^3 \ga S_{\rm K}^\prime/\mu$Jy$ \ga 3\times10^{-3}$. ... shortened ... We present and discuss the radio/IR spectrum of the central 30$''$ ($\sim$ 1.25\,pc) and derive dust and Lyman continuum (Lyc) luminosities of $7.5 \times 10^7$\,{\rm L}$_\odot$ and $1.2 \times 10^{50}$\,s$^{-1}$, respectively. \end{abstract} \keywords{Stars: luminosity function, mass function -- ({\it ISM:\/}) dust, extinction -- Galaxy: center -- evolution -- stellar content -- Infrared: stars} \section{The central region of the Galaxy: \newline an overview} Our present knowledge of the Galactic Center Region has been reviewed by Mezger et al.\ (1996; in the following referred to MDZ96). To keep this introduction as concise as possible we quote here only the most relevant or recent papers and refer otherwise to the corresponding sections of this review. The Central Region extends out to a distance of $R \sim 3\,$kpc where the Galactic Disk with its spiral structure begins. Throughout this paper a distance $R_0 = 8.5\,$kpc to the Galactic Center is adopted. The Central Region consists of the Galactic Bulge ($3 \ge R/{\rm kpc} \ge 0.3$) and the Nuclear Bulge (R $\le 0.3\,$kpc). Subunits of the Nuclear Bulge which in the following will be referred to are: the Central Cavity ($R \le 1.7\,$pc) which is located inside the Circum-Nuclear Disk and speci\-fi\-cally the central $30''$ (linear size $\sim 1.25$\,pc) surrounding the compact synchrotron source Sgr~A* which is associated with a massive ($\sim 2.6\times10^6 {\rm M}_\odot$) Black Hole. Contained within the Nuclear Bulge is the K band mosaic, an area of $\Delta\alpha\times \Delta\delta \sim 650''\times710''$ with an equivalent radius $R_{\rm equiv} \sim 15.8$\,pc approximately centered on Sgr~A* which has been covered to date by our NIR survey. This mosaic includes the subareas Sgr A East and M-0.13-0.08 GMC indicated in Fig.\,\ref{figk_band}b. The integrated physical characteristics of both the Galactic Bulge, Nuclear Bulge and - for comparison - of the Galactic Disk are given in MDZ96, Table\,5. Referred to the total masses of stars or Interstellar Matter (ISM) these integral characteristics are rather similar in the Nuclear Bulge and Galactic Disk, but in the Nuclear Bulge the volume densities of matter and of radiation are about two magnitudes higher. This is the reason why practically all interstellar gas in the Nuclear Bulge exists in molecular form and why there the dust temperatures are considerably higher. The Galactic Bulge, on the other hand, contains little ISM and shows little signs of recent star formation. Evidence for a bar structure in the Galactic Bulge and the outer regions of the Nuclear Bulge are reviewed in MDZ96, Sect. 2.3. The Circum-Nuclear Disk extends from $R \sim$ 1.7 to 7\,pc and contains $\sim$ 10$^4$\,${\rm M}_\odot$ of ISM mainly in form of clumps of hydrogen mass $M_{\rm H}$ $\sim$ 30\,${\rm M}_\odot$ with a central visual extinction of $A_{\rm V} > 30$\,mag. The inner edge of the Circum-Nuclear Disk rotates once in 1.5$\times$10$^5$\,yr around the dynamical center. Part of the gas inside the Central Cavity is ionized and forms the H{\sc II} region Sgr A West. In recent years the inner $30''$ of the Central Cavity has become one of the best investigated areas in the Galaxy. Observational results related to Circum-Nuclear Disk and central $30''$ are summarized in MDZ96, Sects. 4 and 5. In a series of papers with the general title ``Anatomy of the Sgr A complex I -- V'' (Zylka et al.\, 1990; 1992; Gordon et al.\,1993; Zylka et al.\, 1995; Beckert et al.\,1996) our group has investigated the physical state of the ISM in the central part of the Nuclear Bulge and specifically the nature of the enigmatic source Sgr~A*. Most of the physical characteristics observed in Active Galactic Nuc\-lei (AGN) are also found in the Central Region of our Galaxy: A massive ($\sim 2.6\times10^6{\rm M}_\odot$) Black Hole, a central mass flow of {\it \.M} $\sim 10^{-2} {\rm M}_\odot$yr$^{-1}$ for radii $R \sim 10 - 150$\,pc (MDZ96, sect.\,3.5) and indications of mild star bursts $\sim 10^7-10^8$\,yrs ago. But the energy produced at present by this Black Hole is negligible compared to the luminosity of a cluster of evolved early-type stars in the immediate vicinity of Sgr~A*. \section{Investigating the Nuclear Bulge: \newline Research program and scientific objectives} Observations of AGNs show that their {\it central engine}, i.e. a Black Hole of mass $\sim 10^8 - 10^{10} {\rm M}_\odot$ surrounded by an accretion disk, is embedded in a Nuclear Bulge of size of a few 10$^2$pc, which appears to play an important role in stabilizing the Disk and initiating the mass flow which feeds the Black Hole. This motivated us to investigate the physical state of the Nuclear Bulge in our Galaxy. Here we present the first in a series of papers which combine ground-based and space-born (ISO\footnote{ISO is an ESA project with instruments funded by ESA Member States (especially the PI countries: France, Germany, The Netherlands and the United Kingdom) with the participation of ISAS and NASA.}) NIR/MIR observations with submm and radio observations of the central $\Delta l \times\Delta b \sim 2^\circ \times 3^\circ$. An average extinction of $<$$A_{\rm V}$$>$ $\sim 31$\,mag prevents any direct observations of the central few tens of parsecs at $\lambda\la1\mu$m. The transition from dust-dominated to star-dominated radiation of the Nuclear Bulge occurs at $\lambda\sim 5 - 7\mu$m. Hence stars in the Galactic and Nuclear Bulge - specifically medium and low mass stars - are preferentially observed in the NIR. High mass stars - in addition to being strong NIR sources - interact with the ISM by heating the dust and ionizing the gas. Dust emission at MIR/FIR wavelengths together with free-free radio emission trace these massive stars and give information about both their total ($L_*$) and Lyc luminosity ($L_{\lambda<912{\rm \AA}}$), respectively. The K band ($\lambda 2.2\,\mu$m) is a good compromise between a dust absorption increasing with $e^{-\tau_\nu}$, where $\tau_\nu\propto\lambda^{-1.7}$ for $\lambda\la7\mu$m, and the stellar flux density increasing with $S_\nu\propto\lambda^{-2}$. Since the seminal papers by Becklin \& Neugebauer (1968, 1975 and 1978) who mapped the central 100\,pc, the K band has extensively been used to investigate the stellar content of the Central Region (MDZ96, sects. 2.2.1 and 5.3). These observations yielded a surface brightness variation $\propto R^{-0.8}$ which -- after having been calibrated with the observed rotation curve -- translates for an assumed $M/L \sim 3\,{\rm M}_\odot/{\rm L}_\odot$ into a mass enclosed within the radius R of \begin{equation} M(R)/{\rm M}_\odot = 4.25\times10^6R_{pc}^{1.2} \end{equation} \noindent which can be used as a first approximation of the true mass distribution within $R\la 500$pc (Sanders \& Lowinger 1972, corrected for $R_0 = 8.5\,$kpc). However, ten years after their first K band map was published Becklin \& Neugebauer (1978) cautioned that due to their beam-switching observing techniques an extended continuum background may have been suppressed. The K band observations presented in this paper not only have a high sensitivity for the detection of point sources. The observing method in addition is very effective in recovering an extended background continuum which accounts for low-luminosity stars with $S_{\rm K}^\prime \la 100\,\mu$Jy. We find that the K~band emission from the central $\sim 30$\,pc consists of $\sim 6.1\times10^4$ individual sources with $S_{\rm K}^\prime\ga 100\,\mu$Jy or \footnote{We use the relation between flux density and K band magnitude $S_{\rm K}/{\rm Jy} = 10^{2.8-0.4m_{\rm K}}$.} $m_{\rm K} \la 17$\,mag with an average surface density of $\sim$ 80 sources pc$^{-2}$ which are superimposed on an unresolved background. This detection limit corresponds to reddened (for a visual extinction of $\sim 31$\,mag) Main Sequence (MS) stars earlier than B5 or Giants more luminous than spectral type A1 to G0 (luminosity class III; see Appendix D). The detection limit is determined by the angular resolution and sensitivity of the NIR array. The completeness limit, in addition, also depends on the source crowding, i.e. the number of stars per pc$^2$ and their intensity. In the central pc$^2$ the crowding of stars attains a maximum. Eckart et al. (1993) using speckle techniques were able to resolve $\sim$ 350 stars\,pc$^{-2}$ with a detection limit of $S_{\rm K}^\prime\ga 260\,\mu$Jy, corresponding to $m_{\rm K} \la 16$\,mag. It is found that in the central $30''$ a very limited number of high and intermediate mass stars, most of which must have formed during the past 10$^8$\,yr, account for $\sim 2/3$ of the K band integrated flux density, $\ga 99\%$ of the total luminosity and all of the Lyc-photon production rate of $L_*\sim7.5\times10^7{\rm L}_\odot$ and $N_{\rm Lyc}\sim1.2\times10^{50}s^{-1}$. Low-luminosity stars, on the other hand, which together form the unresolved conti\-nuum background, account for $\ga 99\%$ of the stellar mass\footnote{The central $30''$, according to Genzel et al. (1997), encloses a total mass of $3.3\times10^6{\rm M}_\odot$, of which $2.6\times10^6{\rm M}_\odot$ are associated with a central Black Hole, leaving a total mass of $\sim0.7\times10^6{\rm M}_\odot$ of stars.}. Preliminary observational results suggest that beyond the central $30''$ the relative contribution of luminous stars to the K band flux density decreases with increasing distance from Sgr~A* (MDZ96, Sects. 4.3 and 5.3). The scientific objective of this paper is to learn more about the stellar population in the central $\sim$ 30\,pc of the Nuclear Bulge. This information can only be obtained at wavelengths $\lambda \ga 1\,\mu$m. We present and discuss the following observational results: {\it i)\/} A K band mosaic image of size $\Delta\alpha\times\Delta\delta = 650''\times710''$ surrounding Sgr~A* which covers $\sim 0.6\%$ of the total area of the Nuclear Bulge. {\it ii)\/} A $\lambda 1.2$\,mm mosaic map of the dust emission from a more extended region of the Nuclear Bulge obtained with the IRAM 30m-MRT. {\it iii)\/} The K band luminosity function (KLF) of the sources contained in the mosaic image and in three subareas. {\it iv)\/} The radio through NIR spectrum spatially integrated over the central $30''$ and its decomposition into contributions by dust, stellar, free-free and free-bound emission. \section{Observations and data reduction of the K band mosaic} \begin{figure*}[htb] \epsfxsize\textwidth \epsffile{h1016f1.eps} \caption{a) K band mosaic of the central $\Delta\alpha\times\Delta\delta \sim 650''\times710''$ centered approximately on Sgr~A*. The black square indicates ``no usable data''. White framed contours indicate subareas of the mosaic each of size $5400^{\widehat{\prime\prime}}$, which are referred to in the text. The upper rectangle is centered on the synchrotron source Sgr A East, the lower irregularly shaped area is centered on the compact cloud core M-0.13-0.08. \newline b) Overlaid on the K band mosaic is a contour map representing the dust emission observed at $\lambda$ 1.2\,mm with MPIfR bolometer arrays in the IRAM 30-m MRT ($\Theta_b = 11''$). Contour levels are: 90, 240, 390, 540, 690, 840, 990, 1180, 1680, 2180, 2680, 3180 and 3680\,mJy/$11''$ beam. 100\,mJy/$11''$ beam corresponds to a $\tau_{1.2{\rm mm}} = 4\times10^{-4}$ for $Z/Z_\odot \sim 2$ and $T_{\rm dust} \sim 40\,$K. The corresponding $\lambda 2.2\,\mu$m opacity is $\tau_{2.2\mu{\rm m}} = 0.98$.} \label{figk_band} \end{figure*} We are in the process of mapping the central 2$\%$ of the Nuclear Bulge and selected areas further out in the H and K band ($\lambda =$ 1.65 and 2.2$\mu$m) using the IRAC\,2B ca\-me\-ra with the ESO-MPG 2.2m telescope on La Silla, Chile. The IRAC\,2B ca\-me\-ra uses a NICMOS3 chip with 256$^2$ pixels. The pixel scale can be changed between $0.151''$ and $1.061''$ using lenses A to E, respectively (Lidman et al. 1996). For the chosen lens B we have a pixel scale of $0\farcs 278$. This produces images of size $71\farcs 2 \times 71\farcs 2$. The image shown here in Fig.\,\ref{figk_band}a and b is part of a K band mosaic which - when finished - will cover an area of size $\Delta\alpha \times \Delta\delta = 15^\prime \times 25^\prime$. An observing technique has been selected which allows us to recover an extended background emission using a nearby dark cloud as reference point (see also Table \ref{tabmosaic}). 494 images were used to construct the K band mosaic image of the central $650''\times710''$ shown in Fig.\,\ref{figk_band}a and discussed in this paper (see Appendix A and B for a more detailed discussion of observing and data processing techniques. Appendix C deals specifically with problems associated with K band source counts). Since IRS\,7, one of the strongest individual sources in all of our NIR images, is variable on time-scales of months (we measured $\sim 1.4$\,Jy in 1995 and $\sim 1.2$\,Jy in 1996) we used the IR star SA 109-71 as flux density calibrator. In the {\it UKIRT Faint Standard Star List\/} this star is designated FS\,28 with flux densities $S_{\rm K}^\prime = 36.41$\,mJy and $S_{\rm H}^\prime = 66.44$\,mJy. The $\lambda$ 1.2\,mm bolometer observations were made using the 7- through 37-channel bolometer arrays developed by E. Kreysa and coworkers of the MPIfR (Kreysa et al., 1996) with the IRAM 30m-MRT. Uranus and Mars were used as flux density calibrators. Extinction caused by the atmosphere was measured using SKYDIPS. The observing and reduction procedures will be detailed in a forthcoming paper. In Fig.\,\ref{figk_band}b the surface brightness of the dust emission is overlaid as a contour map on the K band mosaic shown in Fig.\,\ref{figk_band}a. \section{K band sources in the central 30\,pc} \subsection{Radial dependence of the surface brightness $I_{\rm K} \propto R^\alpha$} The K band surface brightness of the mosaic shown in Fig.\,\ref{figk_band}a is due to stellar emission. Possible sources of contamination of the stellar emission from the Nuclear Bulge will be discussed in Sect.\,4.3. Down to a certain flux density limit (or alternatively an upper limit of K magnitude m$_{\rm K}$) the stars are seen as individual sources; below this limit the stars form an unresolved background. This limit is not very well-defined since it depends on seeing and source-crowding which both vary from image to image out of which the mosaic is constructed\footnote{We estimate a detection limit of $S_{\rm K}^\prime \sim 100\,\mu$Jy and a completeness limit of our source counts for $S_{\rm K}^\prime \ga 2\,000\,\mu$Jy.}. In chopped observations such an extended unresolved background will be suppressed. In ON-OFF observations the measured surface brightness will depend on the surface brightness of the OFF position. \begin{figure*} \epsfxsize=\textwidth \epsffile{h1016f2.eps} \caption{a) Observed K band surface brightness integrated in concentric circles of radius $ R $ centered on IRS\,7 but with its flux density subtracted. Heavy solid curve: Data from this paper. The heavy solid line has been approximated by power laws of the form $S_{\rm K}^\prime(R) \propto R^{2+\alpha}$ (see text). Black dots and dotted line: Earlier results obtained by Becklin \& Neugebauer (1968) presented in the same form and their approximation by a power law $S_{\rm K}^\prime(R) \propto R^{1.2}$ (see text). \newline b) K band surface brightnesses of resolved stars and unresolved continuum based on our observations and integrated in concentric circles of radii $R$ centered on Sgr~A* and including the flux density of IRS\,7. Heavy solid line: Total integrated flux density $S_{\rm integr}^\prime$; light solid curve: Flux density $S_{\rm bcg}^\prime$ contributed by the unresolved background emission. Dotted and dash-dotted curves: Flux density $S_{*\rm fit}^\prime$ and $S_{\rm Star}^\prime = S_{\rm integr}^\prime - S_{\rm bcg}^\prime$, respectively, which both relate to resolved stars with $S_{\rm K}^\prime > $ 100\,$\mu$Jy or $m_{\rm K} < $ 17\,mag (see text). \newline c) K band surface brightnesses $I_{\rm K}(R)$ derived for the mosaic and its point source and continuum components and averaged in circles of radii $R$ centered on Sgr~A*. Here the flux density of IRS\,7 has been subtracted. } \label{figk_radial} \end{figure*} In addition to an average visual extinction of $<$$A_{\rm V}$$>$ $\sim 31$\,mag between Sun and Central Region observations suffer from extinction due to dust clouds in or in front of the Nuclear Bulge. In those cases where Fig.\,\ref{figk_band}b shows a close correlation between strong dust emission and K-light extinction, the compact Giant Molecular Clouds (GMCs) seen in $\lambda$ 1.2\,mm dust emission must be located in the Nuclear Bulge. Note, however, the presence of ionized gas, e.g. the spiral-shaped $\lambda$ 1.2\,mm emission feature surrounding the point source Sgr~A* which is due to free-free emission from the H{\sc II} region Sgr A West. Figure\,\ref{figk_radial}a shows the K band surface brightness integrated in circular apertures $S_{\rm integr}^\prime$ as observed here (heavy solid curve) and earlier by Becklin \& Neugebauer (1968). K and H band flux densities contained within $R = 15''$ are given in Table \ref{tabcentral}a. The flux density of $S_{\rm K}^\prime \sim 11$\,Jy obtained here compares reasonably well with the flux density of $\sim 9$\,Jy derived by Becklin \& Neugebauer (including IRS\,7) if one allows for a contribution of $S_{\rm K}^\prime \sim 2$\,Jy due to both the sum of calibrational uncertainties and a suppressed unresolved background in the Becklin and Neugebauer survey. Note that the Becklin and Neugebauer integrated flux densities are centered on IRS\,7, whose flux density has been subtracted for the integration. For comparison purposes we also subtracted the IRS\,7 flux density and centered the integration on IRS\,7. If the integrated flux density increases as $S_{\rm K}^\prime \propto R^{2+\alpha}$, the surface brightness must increase as $I_{\rm K}(R) \propto R^\alpha$. Linear fits to our observations yield exponents decreasing from $\alpha \sim 0.27$ for $R < 10''$ to $\alpha \sim -0.56$ at $R > 100''$. For $10''< R < 100''$ we obtain $\alpha \sim -0.65$, i.e. an exponent which is not too far from but still significantly smaller than the exponent $\alpha \sim -0.8$ which is generally adopted for the radial variation of the K band surface brightness in the inner part of the Nuclear Bulge (see e.g. Sanders \& Lowinger, 1972; Bailey, 1980). We should mention, however, that integration in 90$^\circ$ segments centered along l and b shows clear effects of extinction by foreground cloud cores especially for the segments centered on positive longitudes and negative latitudes, respectively. The K band mosaic shown as Fig.\,\ref{figk_band}a consists of sources overlaid on a continuum background, which we hypothesize to consist of a very large number of stars too weak to be observed as individual sources. The K band surface brightness of the mosaic integrated in concentric circles of radius $R$ {\it but centered on Sgr~A* and including IRS\,7} is shown in Fig.\,\ref{figk_radial}b as heavy solid curve. The K band surface brightness integrated over all of the mosaic yields a flux density of $S_{integr}^\prime \sim 752$\,Jy (Table \ref{tabmosaic}b). We tried to separate sources and unresolved background in two different ways: In a first attempt we fitted modified Lorentzian distributions (Diego, 1985) to the individual sources and obtained for the K-mosaic Fig.\,\ref{figk_band}a $\sim 6.1\times10^4$ sources with $S_{\rm K}^\prime\ga 100\,\mu$Jy or $m_{\rm K} \la 17$\,mag (see Appendix C). The flux density of all separated sources is referred to in the following as $S_{*\rm fit}^\prime$~~\footnote{Note for the following discussion of the KLF that $S_{*\rm fit}^\prime = S_{\rm cum}^\prime(S_{\rm K}^\prime \ga 100\,\mu$Jy), with $S_{\rm cum}^\prime$ defined by eq.(4) if both flux densities refer to the same area and $S_{\rm K}^\prime = 100\,\mu$Jy is the detection limit.}. This quantity, integrated in concentric circles is shown in Fig.\,\ref{figk_radial}b as heavy dotted curve. Integrated over the mosaic $S_{*\rm fit} \sim 370$\,Jy (Table \ref{tabmosaic}c). In a second attempt we determined the surface brightness in areas away from strong sources and refer to it as background (bcg). The corresponding flux density integrated in concentric circles is shown in Fig.\,\ref{figk_radial}b as light solid curve. Integration over the mosaic yields $S_{\rm bcg}^\prime \sim 283$\,Jy (Table \ref{tabmosaic}c). \begin{table} \caption{{\bf Characteristics of the central 30$''$ \newline (=1.25\,pc for R$_0$ = 8.5\,kpc)}} Radius $R = 15'' = 0.62$\,pc \\ Area $\Omega = 707^{\widehat{\prime\prime}} = 1.2$\,pc$^2$\\ \\ {\bf a.} NIR flux densities of the central $30''$\\ \\ \begin{tabular}{|c|c|c|c|c|c|} \hline Band & $\lambda/\mu$m & $\nu/$Hz & $S_\nu^\prime/$Jy & $A_\nu / A_{\rm V}$ & $S_\nu/$Jy \\ \hline H & 1.65 & 1.82\,10$^{14}$ & 2.41 & 0.180 & 411$\pm$30\,\% \\ K & 2.2 & 1.36\,10$^{14}$ & 10.9 & 0.122 & 355$\pm$30\,\% \\ \hline \end{tabular} \\ \\ \\ {\bf b.} Fit parameters of a Planck decomposition of the dereddened spectrum (Fig.\,\ref{30-spec}) \\ \\ \begin{tabular}{|l|r|c|c|c|c|} \hline Component & $T$ & $\lambda_{\tau = 1}$ & $\Omega_{\rm s}$ & $L$ & $M_{\rm H}$ \\ & [K] & [$\mu$m] & (arcsec)$^2$ & ${\rm L}_\odot$ & ${\rm M}_\odot$ \\ \hline cold dust & 40 & 10 & 1020 & 1.7\,10$^5$ & 327 \\ warm dust & 150 & 0.2 & 900 & 3.3\,10$^6$ & 5.8 \\ hot dust & 350 & 0.02 & 8 & 2.1\,10$^5$ & 0.005 \\ cool stars ($m_{\rm K}$ & & & & & \\ \,\,\,$< 16$\,mag) & $4\,000$ & --- & 6.7\,10$^{-6}$ & 1.6\,10$^6$ & \\ cool stars ($m_{\rm K}$ & & & & & \\ \,\,\,$> 16$\,mag) & $4\,000$ & --- & 6.3\,10$^{-6}$ & 1.5\,10$^6$ & \\ hot stars & $25\,000$ & --- & 2.6\,10$^{-7}$ & 9.2\,10$^7$ & \\ \hline \end{tabular} \\ \\ \\ {\bf c.} Other parameters adopted for the discussion in Sect.\,6 \\ \\ \begin{tabular}{|l|c|c|} \hline Parameter & & Ref.\\ Mass in ${\rm M}_\odot$ \,\,\,\,Total & $3.3\times10^6$ & 1 \\ \qquad \qquad \qquad Black Hole & $2.6\times10^6$ & \\ \qquad \qquad \qquad Stellar & $0.7\times10^6$ & \\ Dust Luminosity & & \\ \,\,\,(corr.) in ${\rm L}_\odot$ & $(7.5\pm3.5)\times10^7$ & 2 \\ Lyc-photon produc- & & \\ \,\,\,tion rate (corr.) in s$^{-1}$ & $(1.2\pm0.5)\times10^{50}$ & 2 \\ $T_{\rm eff}$, hot stars & $2.5\times10^4$ K & 3 \\ $T_{\rm eff}$, cool stars & $4\times10^3$ K & 4 \\ \hline \end{tabular} \\ \\ Ref:\\ $[1]$ Genzel et al., 1997 \\ $[2]$ MDZ96, Sect.\,4.3 \\ $[3]$ Najarro et al., 1994, 1997 \\ $[4]$ Eckart et al., 1993 \label{tabcentral} \end{table} \noindent The difference $S_{\rm Star}^\prime = S_{\rm integr}^\prime - S_{\rm bcg}^\prime$ offers another way to estimate the flux density of the ensemble of resolved stars. This quantity integrated in concentric circles is shown as dashed curve in Fig.\,\ref{figk_radial}b. If the KLF were complete down to our detection limit of $S_{\rm K}^\prime \sim 100\,\mu$Jy one would expect $S_{*\rm fit}^\prime \sim S_{\rm Star}^\prime$. This is actually the case for radii $R\la 60''$. For larger radii $S_{\rm Star}^\prime > S_{*\rm fit}^\prime$ and substitution of the integrated flux densities from Table\,\ref{tabmosaic} yields for the mosaic $S_{*\rm fit}^\prime / S_{\rm Star}^\prime \sim 0.83$, indicating that our first method to separate resolved sources and unresolved background ignores a number of sources in the flux density range $100 \la S_{\rm K}^\prime/\mu$Jy$ \la 2\,000$ which are neither counted as separated sources (and therefore are not included in the KLF) nor are counted as contribution to the smooth background continuum. This {\it lost flux density} amounts to $(S_{\rm Star}^\prime - S_{*\rm fit}^\prime) / S_{\rm integr}^\prime \la 10\%$ of the total K band flux density of the mosaic. The difference is small enough to allow for the further discussions to use $S_{*\rm fit}^\prime$ as the K band flux density of the ensemble of separated stars. Note that for $R \la 15''$ the contribution of the high-luminosity (and hence relatively young) stars to $S_{\rm integr}^\prime$ is $\ga 80\%$, while at $R \sim 300''$ their contribution has decreased to $\sim 50\%$. The K band surface brightnesses of the mosaic and its point source and continuum components have been computed with the relation $I_{\rm K}(R) = \frac{S_{\rm K}^\prime(R)}{\pi R^2} \frac{2+\alpha}{2}$ which is valid for a power law radial dependence $I_{\rm K}(R) \propto R^\alpha$. The result is shown in Fig.\,\ref{figk_radial}c. $R = 0''$ refers to the position of Sgr~A*, the flux density of IRS\,7 has been subtracted. The surface brightness of the luminous stars detected as point sources decreases much more rapidly (actually $\propto R^{-0.8}$) than the unresolved continuum due to MS stars with $M_* \la 20 {\rm M}_\odot$. The relative deficiency of these low and medium mass stars or -- perhaps more correctly -- the overabundance of high-mass, high-luminosity stars in the central $15''$ ($\sim 1.25$\,pc) stands out clearly in this diagram. We note that within $R \la 30''$ the surface brightness of the resolved stars agrees well with the surface brightnesses derived by Allen (1994; see Fig.\,35 in MDZ96). \begin{table} \caption{{\bf Characteristics of the K band Mosaic} \newline $\mathbf {\Delta\alpha \times\Delta\delta}$ {\bf = 650$''\times$710$''$ approximately centered on Sgr~A*}} Equiv. radius $R = 383 '' = 15.8$\, pc \\ Effective Area$^{1)}$ $\Omega = 4.1\times10^{5 \widehat{\prime\prime}} = 782$\, pc$^2$ \newline 1) Only images with reliable surface brightnesses are counted\\ \\ {\bf a.} Center positions and solid angles\\ \\ \begin{tabular}{|l|c c|c|} \hline Component &\multicolumn{2}{|c|}{Projection center}& $\Omega$\\ &\multicolumn{2}{|c|}{(1950.0)} & $10^{3 \widehat{\prime\prime}}$ \\ \hline Mosaic & 17:42:29.32 & -28:59:18.38 & 410 \\ Sgr A East & 17:42:32.75 & -28:58:23.37 & $5.4$ \\ M-0.13-0.08& 17:42:32.75 & -29:04:53.39 & $5.4$ \\ Dark Cloud & 17:41:35.05 & -28:52:37.92 & $5.1$ \\ \hline \end{tabular} \\ \\ \\ {\bf b.} K band flux densities \\ \\ \begin{tabular}{|l|c|c|c|} \hline Component & $S_{\rm integr}^\prime$ & $S_{\rm GB+GD}^\prime$ & $S_{\rm Star}^\prime$ \\ & Jy & Jy & Jy \\ \hline Mosaic & $752$ & $131$ & $469$\\ Sgr A East & $26.0$ & $3.31$ & $15.7$ \\ M-0.13-0.08& $4.24$ & $3.31$ & $3.36$\\ Dark Cloud & $\cdots$ & $\cdots$ & $\cdots$ \\ \hline \end{tabular} \\ \\ \\ {\bf c.} Source fit parameters \\ \\ \begin{tabular}{|l|c|c|c|} \hline Component & $N_{\rm tot}$ & $S_{*\rm fit}^\prime$ & $S_{\rm bcg}^\prime$ \\ & & Jy & Jy \\ \hline Mosaic & $6.06\times10^4$ & $370$ & $283$ \\ Sgr A East & $923$ & $13.2$ & $10.3$ \\ M-0.13-0.08& $775$ & $1.57$ & 0.88 \\ Dark Cloud & $60$ & $6.6\times10^{-2}$ & $\cdots$\\ \hline \end{tabular} \\ \\ \\ {\bf d.} Other parameters used for the discussion in sect.\,6 \\ \\ \begin{tabular}{|l|c|c|} \hline Parameter & & Ref.\\ \hline Mass in ${\rm M}_\odot$ & $1.17\times10^8$ & 1 \\ Luminosity in ${\rm L}_\odot$ & $5\times10^7$& 2,3 \\ Lyc-photon production & & \\ rate in s$^{-1}$ & $\sim 10^{51}$ & 3\\ \hline \end{tabular} \\ \\ Ref:\\ $[1]$ Eq.(1) \\ $[2]$ Cox \& Mezger, 1989 \\ $[3]$ Mezger \& Pauls, 1978 \label{tabmosaic} \end{table} \subsection{K band luminosity functions (KLF)} The {\it logarithmic} KLF, i.e. the number of sources $dN(S_{\rm K}^\prime)$ per logarithmic bin $d{\rm log} S_{\rm K}^\prime$ normalized to the unit solid angle of $1^{\widehat {\prime\prime}}$ (in the following referred to either as KLF or as {\it observed} KLF) is shown in Fig.\,\ref{figklf}a for the mosaic and for two selected areas within the mosaic indicated in Fig.\,\ref{figk_band}a by white contours. The rectangle of area $5400^{\widehat{\prime\prime}}$ referred to as "East" is centered on the synchrotron source Sgr A East thought to be the remnant of a gigantic explosion which occurred $\sim 5\times10^4$yr ago (see MDZ96, Sect.\,3.6) and appears to have cleared the foreground from dust thus allowing a deep view into the Nuclear Bulge. A irregularly shaped area of the same size centered approximately on one of the dense cores of the GMC M-0.13-0.08 (as visible through its dust emission, see Fig.\,\ref{figk_band}b) and outlining a region of high K band extinction is referred to as M-0.13-0.08 This cloud core is located $\sim 50 - 100$\,pc in front of Sgr~A* (MDZ96, Sect.\,3.4), has a visual extinction of $A_{\rm V} \sim 60$\,mag and therefore blocks all NIR emission from stars located behind the dense core. Figure \ref{figklfdiff}a shows the KLF in the direction of the Dark Cloud which is used as ``OFF'' position in our observations (see Sect.\,3). The central region of the Dark Cloud contains about 60 stars with flux densities $\la 3\times10^3\,\mu$Jy. Most have flux densities of a few hundred $\mu$Jy but two stars have flux densities as high as $\sim 9\,000\,\mu$Jy and $\sim 11\,000\,\mu$Jy. For comparison purposes the KLF of the M-0.13-0.08 cloud core is also shown in Fig.\,\ref{figklfdiff}a. Figure \ref{figklfdiff}b shows the KLFs of Sgr A East and M-0.13-0.08 from which the KLFs of M-0.13-0.08 and the Dark Cloud have been subtracted. These {\it difference} KLFs relate to the stellar populations in the Nuclear Bulge and in the Galactic Bulge and Galactic Disk, respectively. \begin{figure} \setlength{\unitlength}{1mm} \begin{picture}(54,53) \special{psfile=h1016f3a.ps angle=-90 hoffset=-14 voffset=150 hscale=34 vscale=34} \end{picture} \vspace{30mm} \setlength{\unitlength}{1mm} \begin{picture}(54,54) \special{psfile=h1016f3b.ps angle=-90 hoffset=-14 voffset=192 hscale=34 vscale=34} \end{picture} \vspace{15mm} \setlength{\unitlength}{1mm} \begin{picture}(54,54) \special{psfile=h1016f3c.ps angle=-90 hoffset=-14 voffset=192 hscale=34 vscale=34} \end{picture} \caption{a) KLF of the mosaic image and of the two subareas indicated in Fig.\,\ref{figk_band}a, all normalized to a source angle of $1^{\widehat{\prime\prime}}$. Sources are counted in logarithmic bins of width $0.08$. \newline b) Cumulative number $N_{\rm cum}(S^\prime_{\rm min})$ of stars with flux densities $S_{\rm K}^\prime \ge S_{\rm min}^\prime$ computed with Eq.\ (3) and the KLFs shown in Fig.\,\ref{figklf}a. \newline c) Cumulative flux density of stars $S_{\rm cum}(S^\prime_{\rm min})$ with flux densities $S_{\rm K}^\prime \ge S_{\rm min}$ computed with Eq.\ (4) and the KLFs shown in Fig.\,\ref{figklf}a. } \label{figklf} \end{figure} \begin{figure} \setlength{\unitlength}{1mm} \begin{picture}(54,53) \special{psfile=h1016f4a.ps angle=-90 hoffset=-15 voffset=150 hscale=34 vscale=34} \end{picture} \vspace{30mm} \setlength{\unitlength}{1mm} \begin{picture}(54,54) \special{psfile=h1016f4b.ps angle=-90 hoffset=-15 voffset=192 hscale=34 vscale=34} \end{picture} \caption{a) KLF of the Dark Cloud; for comparison purposes is also shown the KLF in the direction of the compact cloud core M-0.13-0.08 from Fig.\,\ref{figklf}a. \newline b) {\it Difference} KLFs, i.e. KLF(Sgr A East) minus KLF(M-0.13-0.08) and KLF(M-0.13-0.08) minus KLF(Dark Cloud). } \label{figklfdiff} \end{figure} For the numerical handling a {\it linear} KLF which samples the number $N(S^\prime)$ of sources in linear bins $dS$ is more useful. It relates to the {\it logarithmic} KLF by \begin{equation} \frac{dN_s}{dS^\prime} = N(S^\prime) = 0.43 S^{\prime -1} \frac{dN(S^\prime)} {d{\rm log}S^\prime} \end{equation} \noindent where ${\rm log}S^\prime = {\rm log}(e){\rm ln}S^\prime$ and $d{\rm ln} S^\prime = dS^\prime/S^\prime$. Then the cumulative number of sources with $S_{\rm K}^\prime \le S_{\rm max} \sim 2\times10^6\,\mu$Jy is \begin{equation} N_{\rm cum}(S_{\rm min}^\prime) = \int \limits_{S_{\rm min}^\prime}^{S_{\rm max}^\prime} N(S^\prime)dS^\prime \end{equation} \noindent and the corresponding cumulative flux density is \begin{equation} S^\prime_{\rm cum}(S_{\rm min}^\prime) = \int\limits_{S_{\rm min}^\prime}^{S_{\rm max}^\prime} N(S^\prime) S^\prime dS^\prime \end{equation} \noindent The {\it logarithmic} KLFs as derived from our observations together with $N_{\rm cum}$ and $S^\prime_{\rm cum}$ defined by Eqs. (3) and (4) are shown in Figs.\,\ref{figklf} and \ref{figklfdiff} and will be discussed in more detail in Sect.\,6. \subsection{Contamination of the K band observations} Here we discuss possible contaminations of the surface brightnesses and derived flux densities in the Nuclear Bulge by additional sources of emission and by deviations of the (visual) extinction from the adopted mean value $<$$A_{\rm V}$$>$ $\sim 31$\,mag for the central pc. \subsubsection{Dust emission} There are no observational indications for the presence of dust in the Central Region much hotter than $\sim 400$\,K (see Fig.\,\ref{30-spec} and MDZ96, Fig.\,25). Emission from small particles is mainly observed at $\lambda 12 - 25 \mu$m and is weak in the NIR (Castelaz et al., 1987). Hence we conclude that contamination by hot dust emission of the results presented here is negligible. \subsubsection{Recombination radiation} About 10\% of all Lyc-photons in the Galaxy originate in the Nuclear Bulge. Apart from free-free emission by electrons accelerated in the Coulomb field of ions, free-bound emission and line radiation due to recombination of free electrons with ions must be considered. The contribution of emission from ionized gas to the K band surface brightness has been recently reanalyzed by Beckert et al.\ (in prep.) and was found to be negligible for the Nuclear Bulge (see also Fig.\,\ref{30-spec}). \subsubsection{Stars in the Galactic Bulge and Disk} To estimate the contribution from stars in Galactic Bulge and Galactic Disk we make use of the $\lambda 2.4\mu$m balloon survey by Hayakawa et al.(1981), made with an angular resolution of $\sim 1.7^{\circ}$. This survey shows the Nuclear Bulge (in galactic longitude) as a narrow source of FWHP $\sim 3^\circ$ and peak surface brightness of $\sim 1.06\times 10^7$\,Jysr$^{-1}$ superimposed on the much wider brightness distributions of Galactic Bulge and Galactic Disk which have, however, comparable amplitudes. Their surface brightnesses of $9.6\times10^6$\,Jysr$^{-1}$ and $1.34\times10^7$\,Jysr$^{-1}$ derived for Galactic Bulge and Galactic Disk, respectively, can be considered constant across the Nuclear Bulge. Together they contribute a K band surface brightness of $\sim 3.2\times10^{-4}$\,Jy/arcsec$^2$. This means a contribution of $\sim 0.23$\,Jy or $\sim 2\%$ to the integrated flux density of the central $30''$, $\sim 131$\,Jy or $\sim 20\%$ to the flux density of the mosaic and $\sim 2.5\times10^4$\,Jy or $\sim 250\%$ to the flux density of the Nuclear Bulge. The reason for this dramatic increase is that the average surface brightness of Galactic Bulge and Galactic Disk is assumed to stay nearly constant while that of the Nuclear Bulge decreases $\propto R^{-0.9}$. It should be noted that this estimate of the contribution of Galactic Bulge and Galactic Disk stars to the flux density of stars in the Nuclear Bulge is a very strict upper limit and that a flux density $S_{\rm GB+GD}^\prime/2$ may in most cases be a more realistic estimate since very dense cloud cores in the Nuclear Bulge will probably absorb most of the stellar emission from behind the Nuclear Bulge (see e.g. MDZ96, Fig.\,17 and Fig.\,\ref{figk_band}b, this paper). \subsubsection{The surface brightness of the Dark Cloud\label{surfacedark}} In the K band observations we use a Dark Cloud as reference OFF position (see Sect.\,3). Stars between this Dark Cloud and the sun appear in our survey as negative point sources and continuum, respectively. We can eliminate the point sources and the continuum visible in the direction of the Dark Cloud assuming that the regions of lowest brightness have zero intensity and re-adding the additional flux density from sources and continuum visible in the OFF-position to the ON image. To estimate an upper limit of this continuum we compare the Dark Cloud with the subarea M-0.13-0.08. Both images contain only stars in the Galactic Bulge and Galactic Disk. From the entries in Table \ref{tabmosaic} we obtain the ratio $S_{*\rm fit}^\prime({\rm Dark Cloud}) / S_{*\rm fit}^\prime({\rm M-0.13-0.08}) \sim 0.04$, which places the dark cloud very few kpc from the Sun. For M-0.13-0.08 the entries in Table \ref{tabmosaic}b yield $S_{*\rm fit}^\prime \sim S_{\rm bcg}^\prime$ and assuming a similar relation we estimate $S_{\rm bcg}^\prime \sim S_{*\rm fit}^\prime \sim 6.6\times10^{-2}$\,Jy as an upper limit of the Dark Cloud continuum. The corresponding surface brightness is $I_{\rm K} \sim 10^{-5}\,$Jy/arcsec$^{-2}$. \subsubsection{Deviations from the adopted standard visual extinction of $<$$A_{\rm V}$$>$ $ \sim 31$\,mag} The standard visual extinction as derived by Rieke et al. (1989) is $<$$A_{\rm V}$$>$ $\sim 31$\,mag. The corresponding K band extinction $A_{\rm K}/A_{\rm V} = 0.122$ follows from Mathis et al. (1983). According to these authors $A_{\rm V} \sim 20$\,mag is due to dust located between galactic radii $R\sim 8.5$--$3.5$\,kpc while, according to MDZ96, sect.\,4.2.3, the remaining $\sim 11$\,mag of extinction would be contributed by dust in the Nuclear Bulge, probably associated with the High Negative Velocity Gas (HNVG) seen in OH absorption against the background of synchrotron and free-free emission. OH column densities in the HNVG and visual and K band extinction vary on angular scales of arcsec by $\pm10\%$ and more. Direct measurements of the K band extinction within $R \la 1'$ yields an average of $<$$A_{\rm K}$$>$ $\sim 3.3$\,mag with individual values as high as $A_{\rm K} \sim 6$\,mag (Sellgren et al.\ 1996). Such a spatially variable extinction will certainly increase the scatter in the {\it observed} KLF but should not affect our basic conclusions. Catchpole et al. (1990) show that $A_{\rm V}$ is -- to a first order -- constant in $l$ with $A_{\rm V}$ $\sim 30$\,mag but drops off rapidly in $b$ attaining $A_{\rm V}$ $\sim 15$\,mag at $b \sim 0.6^\circ$. \section{The spatially averaged continuum spectrum of the \newline central 30$''$ ($\sim$1.25\,pc)} \begin{figure} \setlength{\unitlength}{1mm} \begin{picture}(55,69) \special{psfile=h1016f5.ps angle=-90 hoffset=-15 voffset=192 hscale=34 vscale=34} \end{picture} \caption{Observed ({\tt I}) and fitted continuum spectrum (heavy solid curve) of the central $30''$ (1.25\,pc). This spectrum has been decomposed into Planck components of various temperatures representing dust emission (with $T_{\rm dust} \le 350\,$K) and stellar emission (with $T_{\rm eff} \ge 4\,000\,$K light solid curves) together with free-free and free-bound emission from an ionized gas with $T_{\rm eff} \sim 8\,000$\,K(dotted curve). Also shown is part of an ISOPHOT-PHT-S spectrum (see text).} \label{30-spec} \end{figure} K band emission relates to stars. Due to the large distance of the Nuclear Bulge ($R_0 \sim 8.5$\,kpc) and the high dust opacity in the direction of the Galactic Center ($A_{\rm V} \sim 31$\,mag) most of the sources above our detection limit of $\sim 100\,\mu$Jy are either early-type MS stars or Giants and Supergiants (see Appendix D and Fig.\,\ref{figstars_k_limit}). While the low- and medium mass MS stars can be traced by their K band continuum emission the distribution and luminosity of more massive MS stars and Giants can be estimated from the emission of dust and ionized gas located in the Nuclear Bulge. In this section we derive the radio through NIR spectrum of the central 30$''$ and decompose it into the contributions from free-free emission, warm and hot dust emission and stellar emission. Figure\,\ref{30-spec} shows the dereddened spectrum of the central 30$''$ ($\sim$ 1.25\,pc for $R_0 = 8.5\,$kpc). Data with $\nu < 10^{14}$\,Hz are from Zylka et al. (1995); additional data for $\nu > 10^{14}$\,Hz have been obtained from the K band observations discussed here and from an H band mosaic obtained in a similar way which will be presented and discussed in a later paper. Observed and dereddened flux densities are given in Table \ref{tabcentral}a. The spectrum has been decomposed into three characteristic dust components and two characteristic stellar components as shown in Fig.\,\ref{30-spec}. Corresponding fit parameters are given in Table \ref{tabcentral}b (see Mezger 1994 and references therein). For $\lambda\la 5-7\mu$m the spectrum is dominated by stellar emission. The stellar population within the central 30$''$ consists of a mixture of hot and luminous stars, cool Giants and Supergiants and a large number of low-mass, low-luminosity stars which should account for most of the stellar mass of $\Sigma M_*\sim0.7\times10^6{\rm M}_\odot$ (see footnote 5). Based on work by Eckart, Genzel and colla\-borators (see also MDZ96, Sect. 5.3.2) we attribute of the total observed K band flux density of $S_{\rm integr}^\prime \sim 11$\,Jy, $\sim 2.3$\,Jy to 24 hot stars, $\sim 4.5$\,Jy to cool but luminous stars with $m_{\rm K} < 16$\,mag and $\sim 4.2$\,Jy to low-mass low-luminosity stars with $m_{\rm K} > 16$\,mag. For the hot stars we adopt T$_{\rm eff} \sim $ 25\,000\,K (Najarro et al., 1994 and 1997) and for the cool stars T$_{\rm eff} \sim$ 4\,000\,K. With these assumptions we obtain the two Planck spectra attributed to stellar emission. The corresponding luminosity of 9.2$\times$10$^7$\,${\rm L}_\odot$ (Table \ref{tabcentral}b) is well above the (corrected) dust luminosity of 7.5$\times$10$^7$\,${\rm L}_\odot$ given in Table \ref{tabcentral}c. The cool Giants and Supergiants whose progenitors were medium-mass stars together with the low-mass, low-luminosity stars account for comparable luminosities of $\sim 1.5\times10^6\,{\rm L}_\odot$ but their contribution to the total stellar luminosity is negligible. Also shown in Fig.\,\ref{30-spec} is part of the spectrum extending from $\lambda \sim $2.66 to 11.56\,$\mu$m which we observed with higher resolution using ISOPHOT-PHT-S (see Lemke et al., 1996). The data were reduced with the PHT interactive analysis package PIA V7.0.2p(e) (Gabriel et al., 1997) in the standard way using the drift recognition, the orbital dependent dark current and the default detector responses. Strong absorptions are found in the wavelength range $\sim 2.66 - 4.92 \mu$m and $\sim 8 - 11.56 \mu$m. These features are shown in Fig.\,\ref{30-spec} for the short wavelength range of ISOPHOT-PHT-S but have not been considered in the continuum fit. The first three components in Table \ref{tabcentral}b relate to dust. For wavelengths $\lambda < \lambda_{\tau = 1}$ the dust is opaque. $L$ are the luminosities of the dust components and $M_{\rm H}$ are -- for a metallicity $Z/Z_\odot \sim 2$ -- the associated hydrogen masses, both given in solar units. $\Omega = 1.133 \Theta_{\rm s}^2 = 1020^{\widehat{\prime\prime}}$ is the solid angle of a Gaussian source of FWHP $\Theta_{\rm s} = 30''$. Hence, the 40\,K dust appears to fill the central $30''$ completely. From $\lambda_{\tau = 1} \sim 10\,\mu$m we derive an average visual extinction of this dust component of $A_{\rm V} \sim 30$\,mag, which is -- within the rather large error margins -- close to $A_{\rm V} \sim 31$\,mag estimated for the extinction between Galactic Center and Sun. The 40\,K dust is, however, not the dust located between Sun and Galactic Center which is too extended to be seen in emission in submm/FIR images of size $\sim 30''$. Furthermore, a dust temperature of 40\,K is typical for extended envelopes of Galactic Center molecular clouds in the Nuclear Bulge (e.g., Gordon et al.\,1993) but much too high for dust located in the Galactic Disk. We conclude that the 40\,K dust must be located close to, but not in front of the Galactic Center, otherwise the total extinction towards the central cluster would be $A_{\rm V} \sim 65 - 70$\,mag, and therefore deny NIR observations of the Nuclear Bulge. The hydrogen mass associated with all dust components is $M_{\rm H} \sim 330\,{\rm M}_\odot$ (Table \ref{tabcentral}b). The mass of ionized hydrogen contained in the H{\sc II} region Sgr A West is $M_{\rm H II} \sim 260\,{\rm M}_\odot$ (Table\,7 of MDZ96). The central $30^{\prime\prime}$ account for 7\,Jy of a total free-free flux density of 27\,Jy at $\lambda 2$\,cm of Sgr A West encircled by the Circum-Nuclear Disk. The scaled mass of H{\sc II} contained in the central $30''$ is $M_{\rm H II} \sim 67\,{\rm M}_\odot$. It thus appears likely that all of the 150\,K dust and $\sim 20\,\%$ of the 40\,K dust are mixed with the ionized gas and hence with the central star cluster. The remaining part of the 40\,K dust could be located in the neutral gas of the Sgr A East core GMC, but at the remote ionization front of Sgr A West (see MDZ96, Figs.\,17a,b). The 300\,K component is probably contributed by circumstellar dust. \section{Discussion} \subsection{The radial distribution within $R \le 300''$ of stars with \newline high and low K band luminosities} In the preceding section 5 we have dealt with global characteristics of the stellar populations in the mosaic, i.e. the central 30\,pc. We separated early-type MS stars, Giants and Supergiants from low-mass, low-luminosity stars on the basis of their K band flux density. We found that the surface density of hot and luminous stars decreases much more rapidly than the total K band surface brightness which relates to all MS stars as well as Giants and Supergiants. Genzel et al. (1996), on the other hand, investigated with high angular resolution the distribution of early and late type stars out to a distance of $R \sim 20''$. They find that early type stars are concentrated in the central $12''$. Red Supergiants and AGB stars seem to avoid the central $4''$ and form a ring which peaks at $R \sim 7''$ and extends as far as $R \sim 10''$. Intermediate luminosity stars show a central depression which is not seen, however, in the distribution of the faintest stars. For a somewhat more extended region of $R \sim 30''$ Allen (1994) finds for hot stars (no CO features) a considerably narrower distribution than for cool stars (with CO features). The mosaic presented here gives information about the stellar distribution in the intermediate distance range $2'' \la R \la 300''$. This seeing limited data allowed to measure $\sim 6.1\times10^4$ individual stars as weak as $S_{\rm K}^\prime \sim $100\,$\mu$Jy or $m_{\rm K} \sim 17.0$mag yielding a surface density of $\sim 80$ stars\,pc$^{-2}$ most of which are MS stars earlier than O9, Giants and Supergiants. We estimate a completeness limit of our {\it observed} KLF at $\sim 2\,000\,\mu$Jy. The unresolved background should therefore consist of MS stars later than spectral type O9 ($M_* \la 19 {\rm M}_\odot$) and Giants less luminous than spectral type M0 (luminosity class III) whose progenitor stars had masses $\la 4 {\rm M}_\odot$. (See Appendix D; Note that a $1 {\rm M}_\odot$ MS star located in the Nuclear Bulge has a reddened K flux density of only $S_{\rm K}^\prime \sim 2\,\mu$Jy.) Fig.\,\ref{figk_radial}b shows the contribution of the resolved stars and unresolved background to the integrated K band flux density, Fig.\,\ref{figk_radial}c shows the surface brightnesses of these components as derived from the data in Fig.\,\ref{figk_radial}b. The surface brightness of the resolved stars actually decreases $\propto R^{-0.8}$ as derived for the original Becklin and Neugebauer data. The surface brightness of the unresolved background representing medium and low mass MS stars and a few Giants, on the other hand, stays nearly constant out to $R \sim 10''$ and decreases only slowly farther out. To determine the core radii of resolved and unresolved stars we fitted King (1962) profiles of the form \begin{equation} I_{\rm K}(R) = I_0 \left( \frac{1}{\left(1+\left(\frac{R}{R_c}\right) ^2\right) ^{0.5}} - \frac{1}{\left(1+\left(\frac{R_t}{R_c}\right) ^2\right)^{0.5}} \right) \end{equation} \noindent to the observed radial surface brightness variations $I_{*fit}$ and $I_{bcg}$ (Fig.\,\ref{figcorerad}). Here $R_c$ is the core radius and $R_t$ is the radius at which the surface brightness drops to zero. While King profiles with core radii $R_c \sim 7''$ and $\sim 30''$ give good fits for $I_{\rm K}(R)/I_0 \ga 0.5$ the observed surface brightnesses at $R > R_c$ drop much more slowly than even a King profile with $R_t = \infty$. This slow decrease for $ R > R_c$ may in part be due to the contamination by stars in the Galactic Bulge and Galactic Disk, which amounts to an average surface brightness of $I_{\rm GB+GD} \sim 3.2\times10^{-4}\,$Jy/arcsec$^{-2}$. The much smaller core radius of the luminous and therefore young stars indicates that recent ($\la 10^{7 - 8}$\,yr) star formation activity -- compared to the total stellar mass -- decreases rapidly from the center outwards. \begin{figure} \setlength{\unitlength}{1mm} \begin{picture}(55,68) \special{psfile=h1016f6.ps angle=-90 hoffset=-15 voffset=192 hscale=34 vscale=34} \end{picture} \caption{The radial distribution of K band surface brightnesses observed for resolved ($I^\prime_{*\rm fit}$) and unresolved ($I^\prime_{\rm bcg}$) stars together with King profiles and fit parameters $R_{\rm c}$ and $R_{\rm t}$. Also shown is the estimated contribution $I^\prime_{\rm GB+GD}$ of stars located in the Galactic Bulge and Galactic Disk.} \label{figcorerad} \end{figure} \subsection{General Characteristics of the observed KLFs} In Sect.\ 4.2 we discuss the characteristics of the {\it observed} KLFs. The {\it observed} KLF of the mosaic, $dN(S^\prime) /$ $d{\rm log}S^\prime$, constructed from $\sim 6.1\times 10^4$ individual sources and shown in Fig.\,\ref{figklf}a, increases $\propto S_{\rm K}^{\prime -1}$ in the range $4\times10^3 \la S_{\rm K}^\prime/\mu$Jy$ \la 10^5$. For $S_{\rm K}^\prime \ga 10^5\,\mu$Jy the increase steepens slightly, while for $S_{\rm K}^\prime \la 4\times10^3\,\mu$Jy the KLF flattens and eventually begins to decrease for $S_{\rm K}^\prime \la 2\,000\,\mu$Jy. Remember that $S_{\rm K}^\prime \sim 100\,\mu$Jy is the detection limit and $S_{\rm K}^\prime \sim 2000\,\mu$Jy is the estimated completeness limit of our observations. Contamination of the mosaic KLF by stars in the Galactic Bulge and Galactic Disk amounts to $S_{\rm GB+GD} / S_{\rm integr}^\prime \la 17\%$ (see Table \ref{tabmosaic}b,c and the paragraph {\it Stars in the Galactic Bulge and Disk} in Sect.\,4.3). An attempt to separate foreground and Nuclear Bulge stars based on their H/K colors has to be postponed to a later paper. The KLFs of the subareas Sgr A East (low foreground extinction) and M-0.13-0.08 (high foreground extinction) shown in Fig.\,\ref{figklf}a behave qualitatively similarly: they all attain a maximum and subsequently decrease. But their maxima are shifted from $S_{\rm K}^\prime \sim 10^3\,\mu$Jy for the M-0.13-0.08 KLF to $\sim 10^4\,\mu$Jy for Sgr A East KLF. In part this is due to the fact that for $S_{\rm K}^\prime \la 2\,000\,\mu$Jy the KLF is determined by the incompleteness of the source counts which increases with decreasing $S_{\rm K}^\prime$ and also depends very much on the crowding of the area. For the crowded subarea Sgr A East we therefore find fewer sources for $S_{\rm K}^\prime \la 2\,000\,\mu$Jy than in the less crowded subarea M-0.13-0.08. For the more luminous K band sources $S_{\rm K}^\prime > 2\,000\,\mu$Jy one notices, however, characteristic differences intrinsic to the three KLFs and hence to the stellar population which they sample. Remember that the KLF of the Sgr A East subarea samples a population of stars deep inside the Nuclear Bulge which have an obvious overabundance of luminous stars. In case of the subarea M-0.13-0.08 a dense cloud core blocks the emission from the (luminous) stars in the center of the Nuclear Bulge. We therefore should observe a KLF which relates predominately to the stellar population of the Galactic Bulge and Galactic Disk. The fact that the integrated surface brightness of this subarea is $S_{\rm integr}^\prime \sim 4.24$\,Jy and hence is only slightly higher than the estimated contribution from stars located in the Galactic Bulge and Galactic Disk of $S_{\rm GD+GB}^\prime \sim 3.31$\,Jy (Table \ref{tabmosaic}) supports this assumption. The KLF of the mosaic contains contributions from areas of high and low foreground extinction and therefore lies between the two extreme cases. The difference KLF(Sgr A East) -- KLF(M-0.13-0.08) (Fig.\,\ref{figklfdiff}b) shows in an impressive way the contribution by early MS O stars, Giants and Supergiants with $S_{\rm K}^\prime \ga 3\times10^3\,\mu$Jy to the stellar population of the Nuclear Bulge. As mentioned in the paragraph \ref{surfacedark}\ most of the stars seen in the direction of M-0.13-0.08 and Dark Cloud are located in the Galactic Bulge and Galactic Disk. The KLF of M-0.13-0.08 samples all stars between the sun and the Nuclear Bulge while the KLF of the Dark Cloud contains only stars in the Galactic Disk out to a distance of a few kpc from the sun. A comparison of the two KLFs (Fig.\,\ref{figklfdiff}a,b) shows that the Dark Cloud KLF has a deficiency of sources $S_{\rm K}^\prime \la 4\times10^3\,\mu$Jy. This can be explained by the fact that the Dark Cloud is so close to the sun that even low-mass stars appear as relatively luminous K band sources. \begin{table*} \caption{\bf Characteristics of the observed and of a model KLF of the mosaic} \begin{tabular}{|l|c|c|c|c|c|} \hline Stellar Population & Giants & O9 -- O3 & B5 -- O9 & M8 -- B5 & All stars\\ \hline Range of $S_{\rm K}^\prime/\mu$Jy & $6\times10^3$ -- $2\times10^6$ & $10^3$ -- $6\times10^3$ & $10^2$ -- $10^3$ & $3\times10^{-3}$ -- $10^2$ & $3\times10^{-3}$ -- $2\times10^6$ \\ $\Delta S_{\rm cum}(obs.)/$Jy & $286$& $77$ & $8$ & $381^{1)}$ & $752$ \\ $\Delta N_{\rm cum}(obs.)$ & $1.4\times10^4$ & $2.9\times10^4$ & $1.8\times10^4$ & $\cdots$ & $\gg 6.1\times10^4$ \\ $\Delta S_{\rm cum}(mod.)/$Jy$^{2)}$ & $\cdots$ & $\cdots^{4)}$ & $247$ & $161$ & $< 752$ \\ $\Delta N_{\rm cum}(mod.)^{3)}$ & $\cdots$ & $\cdots^{4)}$ & $8.3\times10^5$ & $5.6\times10^8$ & $5.7\times10^8$ \\ $\Delta \Sigma M_*/{\rm M}_\odot^{5)}$ & $2.3\times10^5$ & $2.4\times10^6$ & $9\times10^6$ & $1.1\times10^8$ & $1.2\times10^8$ \\ \hline \end{tabular} \\ \\ footnotes to the table:\\ 1) $S_{\rm cum}^\prime(3\times10^{-3} - 10^2\,\mu$Jy$) = S_{\rm integr}^\prime - S_{\rm cum}^\prime(10^2 - 2\times10^6\,\mu$Jy)\\ 2) From Eq.(10)\\ 3) From Eq.(9)\\ 4) Note that -- as stated in the text -- the use of the Salpeter IMF in the derivation of the {\it model} KLF and hence of Eqs.(9) and (10) overestimates the contribution of early O stars to $N_{\rm cum}$ and $S_{\rm cum}$. Therefore, no entries for $N_{\rm cum}(\rm mod)$ and $S_{\rm cum}(\rm mod)$ are made.\\ 5) Rather than using the {\it model} KLF we use Eq.(6) to compute $\Delta \Sigma M_*$ for $M_* \la 20 {\rm M}_\odot$ and estimate $<$$M_*$$>$ $\sim 50 {\rm M}_\odot$ and $\sim 30 {\rm M}_\odot$ for O3 -- O9 MS stars and Supergiants, respectively. \label{tabklfmodel} \end {table*} \subsection{Comparison of the observed with a model KLF of \newline the mosaic} We hypothesize that the unresolved K band continuum observed in the central 30\,pc of the Nuclear Bulge is the continuation of the {\it observed} KLF towards sources beyond the detection limit of our survey. In this section we try to verify this hypothesis by comparing our observations with a {\it model} KLF computed for the standard Salpeter IMF\footnote{For the sake of simplicity we use here this IMF although being aware that it overestimates the number of stars at both the high- and low-mass end (Scalo, 1986)}. For numerical computations we terminate the IMF of the Nuclear Bulge at $M_* \sim 20 {\rm M}_\odot$, the mass of an O9 star with a K band flux density $S_{\rm K}^\prime \sim 1000\,\mu$Jy, norma\-lize it to the stellar mass $\Sigma M_* \sim 1.2\times10^8 {\rm M}_\odot$ contained within the mosaic (Table \ref{tabmosaic}d) and thus obtain \begin{equation} dN = 1.81\times10^7 \left( \frac{M_*}{{\rm M}_\odot} \right)^{-2.35} dM_* \qquad M_* \la 20 {\rm M}_\odot \end{equation} \noindent Integration from $M_*\sim 0.06 {\rm M}_\odot$ (corresponding to the lowest mass MS star of spectral type M8) to $M_*\sim 20 {\rm M}_\odot$ yields a total number of $\sim 5.9\times10^8$ MS stars contained within the mosaic. We also compute the K band flux density of MS stars (see Appendix D) and find that in the mass range $0.06 \la M_*/{\rm M}_\odot \la 20$ the result is well represented by the power-law approximation \begin{equation} \left(\frac{S_{\rm K}^\prime}{\rm \mu Jy} \right) = 1.6\left( \frac{M_*}{{\rm M}_\odot} \right)^{2.3} \qquad \qquad \qquad M_* \la 20 {\rm M}_\odot \end{equation} \noindent Combination of the two equations yields for the {\it linear model} KLF as defined by Eq.(3) \begin{equation} {\rm KLF}({\rm mod}) = N(S_{\rm K}^\prime) = 1.03\times10^7 S_{\rm K}^{\prime - 1.6} \end{equation} \noindent Remember, however, for a comparison with the {\it observed} KLF's shown in Fig.\,\ref{figklf}a that the {\it model} KLF $dN(S^\prime)/d{\rm log}S^\prime$ which counts source numbers in logarithmic bins is related to the above {\it linear} KLF $N(S^\prime) = dN(S^\prime)/dS^\prime$ which counts sources in linear bins by Eq.(2) and hence is $\propto S^{\prime -0.6}$. The cumulated source number is \begin{eqnarray} N_{\rm cum}({\rm mod}) & = & \int \limits_{S_{\rm min}^\prime}^{S_{\rm max}^\prime} N(S^\prime) dS^\prime \nonumber\\ & = & 1.76\times10^7 \left( S_{\rm min}^{\prime - 0.6} - S_{\rm max}^{\prime - 0.6} \right) \\ & = & 5.7\times10^8 {\rm sources } \nonumber \end{eqnarray} \noindent in good agreement with Eq.(6). Here and in the following Eq.(10) $S_{\rm min} = S_{\rm K}($M8 star$) \sim 3\times10^{-3}\,\mu$Jy and $S_{\rm max} = S_{\rm K}($O9 star$) \sim 10^3\,\mu$Jy have been substituted. The cumulated flux density is \begin{eqnarray} S_{\rm cum}^\prime({\rm mod}) & = & \int \limits_{S_{\rm min}^\prime}^{S_{\rm max}^\prime} S^\prime N(S^\prime) dS^\prime \nonumber\\ & = & 2.59\times10^7 \left( S_{\rm max}^{\prime 0.4} - S_{\rm min}^{\prime 0.4} \right) \mu{\rm Jy} \\ & = & 408 {\rm Jy} \nonumber \end{eqnarray} This latter result can be used to verify that the {\it model} KLF actually is a reasonable extension of the {\it observed mosaic} KLF. If the model KLF describes the distribution of medium and low-mass stars correctly one would expect $S_{\rm cum}^\prime({\rm mod}) + S_{*\rm fit}^\prime = S_{\rm integr}^\prime$. Combination of eq(10) with $S_{*\rm fit}^\prime = 370$\,Jy from Table \ref{tabmosaic}c yields 778\,Jy as compared to $S_{\rm integr}^\prime = 752$\,Jy (Table \ref{tabmosaic}c). This increase by $\sim 4\%$ can be explained by the overlap of {\it model} and {\it observed} KLF in the flux density range $100 \la S_{\rm K}^\prime \la 2\,000\,\mu$Jy. {\it Observed} and {\it model} KLF are compared in more detail in Table \ref{tabklfmodel} and Fig.\,\ref{figklfmodel}. In Table \ref{tabklfmodel} we subdivide the observed sources into four different bins according to their reddened K band flux densities and compare the corresponding observed differential cumulated flux densities and source numbers. The main contributors to the K band flux density of $S_{\rm integr}^\prime \sim 752$\,Jy integrated over the mosaic are $\sim 14\,000$ Giants ($\sim 38\%$) and a large number (our {\it model} KLF predicts $\sim 6\times10^8$) of low-mass stars with $M_* \la 6 {\rm M}_\odot$ ($\sim 49\%$). Early-type MS stars which are responsible for the ionization of the gas and a good part of the dust heating account for only $\sim 13\%$ of the K band flux density. In the spectral range O9 -- B5 our source counts are incomplete; a large fraction of the K band flux densities of these stars therefore should be found in the unresolved continuum. This assumption is confirmed by the fact that the sum $\Delta S_{\rm cum}($B5 -- O9$) + \Delta S_{\rm cum}($M8 -- B5$) \sim 389$\,Jy ({\it observed}) and 408\,Jy ({\it modeled}) differ by only $\sim 5\%$ if the corresponding flux densities from Table \ref{tabklfmodel} are substituted. A comparison of the characteristics of {\it observed} and {\it modeled} mosaic KLF yields good agreement for the range of MS stars $S_{\rm K}^\prime \la 2\,000\,\mu$Jy. There is an obvious overabundance of stars with $S_{\rm K}^\prime \ga 6\times10^3\,\mu$Jy which most probably are Giants and Supergiants. The abundance of these stars relative to MS stars can be used to estimate their lifetimes (see e.g. Genzel et al. 1994, Krabbe et al. 1995). Figure \ref{figklfmodel} shows the {\it observed} mosaic KLF from Fig.\,\ref{figklf}a together with the {\it model} KLF. We transform the {\it linear model} KLF Eq.(8) into the corresponding {\it logarithmic} KLF using Eq.(2). Normalized to $1^{\widehat{\prime\prime}}$ we obtain the relation \begin{equation} \frac{dN(S^\prime)}{d{\rm log}S^\prime} = 58.5 S_{\rm K}^{\prime - 0.6} \end{equation} \noindent which is shown in Fig.\,\ref{figklfmodel}. Note that Tiede et al. (1995) obtained a similar power-law approximation $\propto S^{-0.69}$ for the {\it KLF observed} in {\it Baade's window}. {\it Observed} and {\it modeled} KLF fit well together if we extrapolate the {\it observed} KLF $\propto S_{\rm K}^{\prime - 1}$ beyond $S_{\rm K}^\prime \ga 4\times10^3\,\mu$Jy, which is not too far from the estimated completeness limit of $\sim 2\,000\,\mu$Jy and may be considered as a more conservative estimate of this limit. \begin{figure} \setlength{\unitlength}{1mm} \begin{picture}(54,68) \special{psfile=h1016f7.ps angle=-90 hoffset=-10 voffset=192 hscale=34 vscale=34} \end{picture} \caption{The {\it observed} mosaic KLF (Fig.\,\ref{figklf}a) combined with the {\it model} KLF eq.(11)} \label{figklfmodel} \end{figure} In summary we find that a {\it model} KLF based on the Salpeter IMF with the total mass of MS stars as the only free parameter (for which we substitute the dynamical mass of $\Sigma M_* \sim 1.2\times10^8 {\rm M}_\odot$ as given by Eq.\,1) explains the {\it observed} K band continuum in a quantitative way. The combined ({\it logarithmic}) KLF increases $\propto S_{\rm K}^{\prime - 1}$ for $10^6 \ga S_{\rm K}^\prime/\mu$Jy $\ga 10^3$ and $\propto S_{\rm K}^{\prime - 0.6}$ for $10^3 \ga S_{\rm K}^\prime/\mu$Jy $\ga 3\times10^{-3}$. It appears -- and that is the interpretation of the {\it observed} KLFs which we favor -- that their flattening and subsequent turnover in the flux density range $S_{\rm K}^\prime \sim 10^3 - 10^4\,\mu$Jy is not an intrinsic characteristic of the Nuclear Bulge stellar population but rather an artifact due to the incompleteness of the source counts. \subsection{The mass-to-luminosity ratio} Based on the entries in Table \ref{tabklfmodel} we arrive at the conclusion that within the mosaic, i.e. the central $\sim 30$\,pc about $6\times10^8$ MS stars of spectral type O9 or later account for more than $99\%$ of the stellar mass of $\Sigma M_* \sim 1.2\times10^8 {\rm M}_\odot$ but only for $\sim50\%$ of the integrated K band flux density. Adopting for the low-mass MS stars $T_{eff} \sim 4\,000$\,K and a total (reddened) flux density of $S_{\rm K}^\prime \sim 361$\,Jy (Table \ref{tabklfmodel}) one obtains a luminosity of $L_*(T_{eff}) \sim 1.4\times10^8 {\rm L}_\odot$ and a mass-to-dereddened-luminosity ratio of $\Sigma M_* / L_* \sim 1 {\rm M}_\odot / {\rm L}_\odot$ in agreement with an estimate by Kent (1992). \section{Conclusions} For an area $\Delta\alpha\times\Delta\delta \sim 650''\times710''$ centered approximately on Sgr~A* and referred to as ``mosaic'' we have determined its KLF containing $\sim 6.1\times10^4$ sources with reddened K band flux densities $S_{\rm K}^\prime \ga 100\,\mu$Jy. The completeness limit of this KLF lies in the range $S_{\rm K}^\prime \sim (1 - 4)\times10^3\,\mu$Jy. Half of the K band surface brightness integrated over the mosaic comes from an unresolved continuum formed by an estimated number of $\sim 6\times10^8$ low and medium mass ($\la 6 {\rm M}_\odot$) MS stars. For $S_{\rm K}^\prime \la 1\,000\,\mu$Jy (O9 stars and later) the characteristics of the {\it observed} KLF and the unresolved continuum are well represented by a {\it model} KLF combined with the {\it observed} and extrapolated KLF. The {\it model} KLF is based on a Salpeter IMF and a total stellar mass contained within $R \la 15$\,pc of $\Sigma M_* \sim 1.2\times10^8 {\rm M}_\odot$. The combined KLF increases $\propto S_{\rm K}^{\prime - 1}$ for $S_{\rm K}^\prime \ga 1\,000\,\mu$Jy and $\propto S_{\rm K}^{\prime - 0.6}$ for $S_{\rm K}^\prime < 1\,000\,\mu$Jy. The flattening and turnover of the KLF observed in the central parts of the Nuclear Bulge appears to be an artifact caused by incompleteness of the source counts. >From the observation we constructed {\it difference} KLFs which make it possible to obtain KLFs for different spatial sections along the line of sight. This allowed us to isolate the mosaic KLF related to the stellar population of the Nuclear Bulge (see Fig.\,\ref{figklfdiff}b and Table \ref{tabklfmodel}) and to confirm quantitatively the results by Glass et al. (1987), Catchpole et al. (1990), Blum et al. (1996a) and Narayanan et al. (1996) that this stellar population has an excess of bright stars compared to the stellar population of the Galactic Bulge ($0.3 \la R/$kpc$ \la 3$) and the interarm region of the Galactic Disk ($R \ga 3$\,kpc). Blum et al. (1996b), based on stellar NIR spectroscopy, conclude that most of the bright, cool stars in the Nuclear Bulge are intermediate mass/age AGB stars. Our results support these findings. O9 -- O3 stars contribute only $\sim 10\%$, Giants $\sim 40\%$ to the integrated K band flux density. Some of the most luminous K band stars could be Wolf-Rayet stars and Supergiants. In agreement with Genzel et al. (1996) we find a deficiency of low-mass low-luminosity stars in the central $20''$. Fitting King profiles to the observed surface brightnesses we obtain core radii of $\sim 7''$ and $\sim 30''$, respectively, for resolved and unresolved stars. We use the integrated radio/IR spectrum to determine dust- and Lyc-photon luminosities for the central $30''$ ($\sim$ 1.25\,pc). A warm component ($\sim$ 150 K) dominates the dust emission. The luminosity of the cool stellar component ($T_{\rm eff} \sim 4\,000$\,K) is not sufficient to provide the heating which appears to be due to $\sim$ 24 hot ($T_{\rm eff} \sim 25\,000$\,K) and luminous ($\sim 4\times10^6 {\rm L}_\odot$) stars, which also are responsible for the ionization of the gas in the Central Cavity. \vspace{9mm} \noindent {\bf Acknowledgements}\\ \\ The data reductions and analyses were carried out on workstations provided by the {\it Alfried Krupp von Bohlen und Halbach Stiftung\/} through a joint grant to the Max-Planck-Institut f\"ur Radioastronomie and the Institut f\"ur Theoretische Astrophysik. This support is greatfully acknowledged. We thank the director of the Max-Planck-Institut f\"ur Astronomie for the generous allocation of observing time at the ESO-MPG telescope. We benefitted much from discussions with P.L.\ Biermann, A.\ Eckart, M.\ McCaughrean, I.S.\ Glass and J.\ Najarro. \vspace{4mm} \noindent{\bf Appendix}\\ \\ {\bf NIR Observing and data processing techniques} \\ \\ We are in the process of mapping the inner part of the Nuclear Bulge in the K, H and J bands with the IRAC2B ca\-mera in the ESO/MPG 2.2m-telescope. IRAC2B uses a NICMOS3 256$\times$256 pixel detector array. We use the pixel scale of $0\farcs 278$; the field-of-view covered by a single exposure is thus $71\farcs 17 \times 71\farcs 17$.\\ \\ {\it A. Observing strategy}\\ \\ All data presented in this paper were obtained in June 1996. The ``sky'' reference (OFF position) was chosen in the direction of a local Dark Cloud which is offset from Sgr~A* by $\Delta \alpha = -713^{\prime\prime}$, $\Delta\delta = 400^{\prime\prime}$ corresponding to a projected distance of $R\sim 33.6$\,pc from Sgr~A* (see Table \ref{tabmosaic}). I.S. Glass et al. (1987) estimates for this cloud a visual extinction of A$_{\rm V} > 60$\,mag which means that H and K band emission from all stars located behind this Dark Cloud will be blocked. Stars located between Dark Cloud and Sun would appear as negative sources in the mosaic and therefore were readded to the mosaic (see Sect.\,4.1). We observed in sequences of 12 exposures, with each sequence taking about 10-12 minutes. An observing sequence for the production of four different individual mosaic images consists of: central image (15\,s integration time) - Dark Cloud (30\,s) - $2 \times 2$ mosaic images (60\,s) - Dark Cloud (30\,s) - $2 \times 2$ mosaic images (60\,s) - Dark Cloud (30\,s). Although the usage of a fixed ``sky'' position is quite time-consuming, because the telescope slewing-time is longer than the exposure-time, such a procedure is necessary to relate the intensity scale within the mosaic to the same relative zero-level. The central image is used as calibrator to eliminate atmospheric absorption. No straight-forward measurements of the continuum due to unresolved stars are possible. Hence, all integrated surface brightnesses should be considered as (in most cases rather reliable) lower limits (see Sect.\,4.3 where we estimate an upper limit of $\sim 0.05$\,Jy for the integrated continuum in the direction of the Dark Cloud).\\ \\ {\it B. Data processing}\\ \\ The mosaic presented here was analyzed with the reduction program MOPSI\footnote{{\it M\/}ap {\it O\/}n--Off {\it P\/}ointing {\it S\/}kydip {\it I\/}mage} developed by R. Zylka. The regridding algorithm uses a general 3-dimensional rotation and is based on a method developed by C.G.T. Haslam for the NOD2 software package.\\ \\ {\it B.1. Coordinate calculation and image alignment}\\ \\ Datasets obtained with radio- and (sub)mm-telescopes usually do not need any co\-ordinate\--corrections because the pointing-accuracy of these telescopes is clearly better than the angular resolution (at the IRAM 30-m telescope the pointing accuracy is 1--2$''$ compared to an angular resolution of$\sim 11''$). In the case of infrared and optical telescopes the effective resolution (limited by {\it seeing\/}) can be better than the pointing-accuracy (e.g. 1$''$ compared to 5$''$ at the ESO/MPG 2.2m telescope). Hence, accurate positioning of the individual images is one of the main tasks in the construction of a mosaic image. We used two different methods to adjust the coordinates of overlapping images. In the first approach we calculate the correlation coefficient between the two images. In the second approach we use the positions of individual stars as determined by fitting a Lorentzian distribution to the intensity distribution (see below) and solved the overdetermined set of linear equations for the angular shift between two overlapping images. These two methods give similar accuracy of $\sim 1/10$ pixel size. We started from the image on the central stellar cluster. All coordinates are calculated as angular offsets relative to IRS\,7. The positional errors at the edges of the current mosaic might thus reach $1''$. The mosaic shown here in Fig.\,\ref{figk_band}a consist of less than 500 images. The final H band mosaic contains $\sim$1500 images and thus is roughly 3 times larger. This part of the data reduction is the most computing-time expensive process. \\ \\ {\it B.2. Calibration}\\ \\ The mosaicing was performed under varying atmospheric conditions. We did not use point sources within the central cluster to avoid seeing effects. Rather, we used the integral over all stars in the overlapping region of all central images (about $60''\times55''$) were used as a substandard. The time variation of the flux in this overlapping region is due to different atmospheric extinction and in elevation which were corrected for. During very stable atmospheric conditions we derive from the variation of the flux density with the elevation an atmospheric K band zenith extinction $\tau_K=0.07$. This calibration procedure using the central stellar cluster as subcalibrator allowed us to achieve a relative calibration of the surface brightness within the mosaic of $\sim$ 15\% - almost independent of weather conditions. In addition to the variable extinction of the atmosphere, its variable emission also causes problems. Because the slewing of the telescope between the source and the sky-positions takes more than 1 minute we use the time-weighted average of two sky-exposures to subtract the sky emission. This minimizes the effects of variable atmospheric emission. The remaining much smaller intensity steps are automatically corrected, during construction of the mosaic from the center to the outer regions.\\ %\newpage \noindent {\it C. Source decomposition} \\ \\ To separate sources from the unresolved background we fitted Lorentzian distributions to the sources after having subtracted a background from the mosaic, which was determined in areas away from bright stars. The Lorentzian distributions which we fitted are generalizations of the ones given by Diego (1985). The Intensity I at a point (x,y) is given by: \begin{equation} I = b + h\left( 1+d_1^{\,\,p(1+d_2)} \right) ^{-1} \end{equation} \noindent where \begin{figure} \setlength{\unitlength}{1mm} \begin{picture}(53,40) \special{psfile=h1016f8a.ps angle=-90 hoffset=30 voffset=155 hscale=32 vscale=32} \end{picture} \begin{picture}(53,58) \special{psfile=h1016f8b.ps angle=-90 hoffset=-12 voffset=177 hscale=32 vscale=32} \end{picture} \caption{Comparison between the fitting of Gaussian and Lorentzian distributions. \newline a) A K band image showing two stronger and a few weaker stars well above the detection limit of $\sim 100\,\mu$Jy. \newline b) The residual image after subtraction of Lorentzian fits to the stars. \newline c) The residual image after subtraction of Gaussian fits to the stars. } \label{figfitres} \end{figure} \begin{equation} d_1 = \sqrt{\left( \frac{x}{r_x} \right) ^2 + \left( \frac{y}{r_y} \right) ^2 + \left( \frac{x y}{r_\theta} \right)} \end{equation} \noindent and \begin{equation} d_2 = \sqrt{\left( \frac{x}{p_x} \right) ^2 + \left( \frac{y}{p_y} \right) ^2 + \left( \frac{x y}{r_\theta} \right)} \end{equation} \noindent and \begin{equation} r_\theta = \left( -2 \left( \frac{1}{s_x^2} - \frac{1}{s_y^2}\right) \sin\theta\cos\theta\right)^{-1} \end{equation} \noindent while $s_x$ and $s_y$ are defined through \begin{eqnarray} r_x & = & \left(\frac{\cos\theta^2}{s_x^2} + \frac{\sin\theta^2}{s_y^2} \right)^{-\frac{1}{2}} \nonumber\\ r_y & = & \left(\frac{\sin\theta^2}{s_x^2} + \frac{\cos\theta^2}{s_y^2} \right)^{-\frac{1}{2}} \nonumber \end{eqnarray} \begin{figure} \setlength{\unitlength}{1mm} \begin{picture}(53,70) \special{psfile=h1016f9.ps angle=-90 hoffset=-15 voffset=195 hscale=34 vscale=34} \end{picture} \caption{Reddened flux densities for stars of the luminosity classes MS, Giants and Supergiants with different spectral types as well as for different types of Wolf-Rayet stars. Indicated as light dashed line is the flux density corresponding to our approximate completeness limit and as heavy dashed line the flux density corresponding to our detection limit.} \label{figstars_k_limit} \end{figure} \noindent b is the pedestal and h the maximum height of the distribution, $r_x$ and $r_y$ refer to major and minor axis of the ellipse and $r_\theta$ is linked to the position angle $\theta$ of the ellipse. The values of $p_x$ and $p_y$ determine the width of the peak area, which are modified by the exponent power p. For a circular source $r_x = r_y$ $p_x = p_y$ and $r_\theta = 0$. The result of fits using Lorentzian and Gaussian distributions, respectively, is shown in Fig.\,\ref{figfitres}. Obviously, the Lorentzian distribution fit the seeing-broadened point-spread-function of the stars much better.\\ \\ {\it D. Spectral types and K band flux densities} \\ \\ To estimate the K band flux densities of stars of different spectral types and luminosity classes we use the stellar parameters given in Lang (1992) with Eq(5.4) in MDZ96 valid for $R_0 = 8.5\,kpc$ and calculate the flux density $S_{\nu,*} = B_{\nu}(T_{eff})\Omega_*$ of a single star of effective temperature $T_{eff}$ and $\Omega_* = \pi R_*^2$ with $R_*$ the stellar radius. This flux density is given for $\lambda 2.2\,\mu$m: \begin{equation} \frac{S_{\rm K,*}}{{\rm Jy}} = 1.26\times10^{-8} \left(\frac{R_*} {R_\odot}\right) ^2 \left(\frac{T_{eff}}{{\rm K}} \right) \frac{x}{e^x - 1} \end{equation} \noindent with $x = 6.55 \times 10^3$\,K/$T_{eff}$. The flux densities shown in Fig.\,\ref{figstars_k_limit} have been reddened for a K band extinction of $A_{\rm K}/A_{\rm V}$ = 0.122 (Mathis et al., 1983). \begin{thebibliography}{99} \bibitem{01}Allen D.A., 1994, in ``The Nuclei of Normal Galaxies'' (R. Genzel, A.I. 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