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Astron. Astrophys. 348, 768-782 (1999)

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6. Discussion

6.1. The radial distribution within [FORMULA] of stars with 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 [FORMULA]. They find that early type stars are concentrated in the central [FORMULA]. Red Supergiants and AGB stars seem to avoid the central [FORMULA] and form a ring which peaks at [FORMULA] and extends as far as [FORMULA]. 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 [FORMULA] 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 [FORMULA]. This seeing limited data allowed to measure [FORMULA] individual stars as weak as [FORMULA]100 µJy or [FORMULA]mag yielding a surface density of [FORMULA] stars pc-2 most of which are MS stars earlier than O9, Giants and Supergiants. We estimate a completeness limit of our observed KLF at [FORMULA]Jy. The unresolved background should therefore consist of MS stars later than spectral type O9 ([FORMULA]) and Giants less luminous than spectral type M0 (luminosity class III) whose progenitor stars had masses [FORMULA]. (See Appendix D; Note that a [FORMULA] MS star located in the Nuclear Bulge has a reddened K flux density of only [FORMULA]Jy.)

Fig. 2b shows the contribution of the resolved stars and unresolved background to the integrated K band flux density, Fig. 2c shows the surface brightnesses of these components as derived from the data in Fig. 2b. The surface brightness of the resolved stars actually decreases [FORMULA] 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 [FORMULA] and decreases only slowly farther out.

To determine the core radii of resolved and unresolved stars we fitted King (1962) profiles of the form


to the observed radial surface brightness variations [FORMULA] and [FORMULA] (Fig. 6). Here [FORMULA] is the core radius and [FORMULA] is the radius at which the surface brightness drops to zero. While King profiles with core radii [FORMULA] and [FORMULA] give good fits for [FORMULA] the observed surface brightnesses at [FORMULA] drop much more slowly than even a King profile with [FORMULA]. This slow decrease for [FORMULA] 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 [FORMULA]Jy/arcsec-2. The much smaller core radius of the luminous and therefore young stars indicates that recent ([FORMULA] yr) star formation activity - compared to the total stellar mass - decreases rapidly from the center outwards.

[FIGURE] Fig. 6. The radial distribution of K band surface brightnesses observed for resolved ([FORMULA]) and unresolved ([FORMULA]) stars together with King profiles and fit parameters [FORMULA] and [FORMULA]. Also shown is the estimated contribution [FORMULA] of stars located in the Galactic Bulge and Galactic Disk.

6.2. General characteristics of the observed KLFs

In Sect. 4.2 we discuss the characteristics of the observed KLFs. The observed KLF of the mosaic, [FORMULA] [FORMULA], constructed from [FORMULA] individual sources and shown in Fig. 3a, increases [FORMULA] in the range [FORMULA]Jy[FORMULA]. For [FORMULA]Jy the increase steepens slightly, while for [FORMULA]Jy the KLF flattens and eventually begins to decrease for [FORMULA]Jy. Remember that [FORMULA]Jy is the detection limit and [FORMULA]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 [FORMULA] (see Table 2 b,c and the paragraph 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. 3a behave qualitatively similarly: they all attain a maximum and subsequently decrease. But their maxima are shifted from [FORMULA]Jy for the M-0.13-0.08 KLF to [FORMULA]Jy for Sgr A East KLF. In part this is due to the fact that for [FORMULA]Jy the KLF is determined by the incompleteness of the source counts which increases with decreasing [FORMULA] and also depends very much on the crowding of the area. For the crowded subarea Sgr A East we therefore find fewer sources for [FORMULA]Jy than in the less crowded subarea M-0.13-0.08.

For the more luminous K band sources [FORMULA]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 [FORMULA] Jy and hence is only slightly higher than the estimated contribution from stars located in the Galactic Bulge and Galactic Disk of [FORMULA] Jy (Table 2) 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. 4b) shows in an impressive way the contribution by early MS O stars, Giants and Supergiants with [FORMULA]Jy to the stellar population of the Nuclear Bulge.

As mentioned in the paragraph 4.3.4 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. 4a,b) shows that the Dark Cloud KLF has a deficiency of sources [FORMULA]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.

6.3. Comparison of the observed with a model KLF of 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 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 model KLF computed for the standard Salpeter IMF 8. For numerical computations we terminate the IMF of the Nuclear Bulge at [FORMULA], the mass of an O9 star with a K band flux density [FORMULA]Jy, normalize it to the stellar mass [FORMULA] contained within the mosaic (Table 2 d) and thus obtain


Integration from [FORMULA] (corresponding to the lowest mass MS star of spectral type M8) to [FORMULA] yields a total number of [FORMULA] 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 [FORMULA] the result is well represented by the power-law approximation


Combination of the two equations yields for the linear model KLF as defined by Eq. (3)


Remember, however, for a comparison with the observed KLF's shown in Fig. 3a that the model KLF [FORMULA] which counts source numbers in logarithmic bins is related to the above linear KLF [FORMULA] which counts sources in linear bins by Eq. (2) and hence is [FORMULA]. The cumulated source number is


in good agreement with Eq. (6). Here and in the following Eq. (10) [FORMULA]M8 star[FORMULA]Jy and [FORMULA]O9 star[FORMULA]Jy have been substituted. The cumulated flux density is


This latter result can be used to verify that the model KLF actually is a reasonable extension of the observed mosaic KLF. If the model KLF describes the distribution of medium and low-mass stars correctly one would expect [FORMULA]. Combination of eq(10) with [FORMULA] Jy from Table 2 c yields 778 Jy as compared to [FORMULA] Jy (Table 2 c). This increase by [FORMULA] can be explained by the overlap of model and observed KLF in the flux density range [FORMULA]Jy.

Observed and model KLF are compared in more detail in Table 3 and Fig. 7. In Table 3 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 [FORMULA] Jy integrated over the mosaic are [FORMULA] Giants ([FORMULA]) and a large number (our model KLF predicts [FORMULA]) of low-mass stars with [FORMULA] ([FORMULA]). Early-type MS stars which are responsible for the ionization of the gas and a good part of the dust heating account for only [FORMULA] 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 [FORMULA]B5 - O9[FORMULA]M8 - B5[FORMULA] Jy (observed ) and 408 Jy (modeled ) differ by only [FORMULA] if the corresponding flux densities from Table 3 are substituted.

[FIGURE] Fig. 7. The observed mosaic KLF (Fig. 3a) combined with the model KLF Eq. (11)


Table 3. Characteristics of the observed and of a model KLF of the mosaic.
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 model KLF and hence of Eqs. (9) and (10) overestimates the contribution of early O stars to [FORMULA] and [FORMULA]. Therefore, no entries for [FORMULA] and [FORMULA] are made.
5) Rather than using the model KLF we use Eq. (6) to compute [FORMULA] for [FORMULA] and estimate [FORMULA] [FORMULA] and [FORMULA] for O3 - O9 MS stars and Supergiants, respectively.

A comparison of the characteristics of observed and modeled mosaic KLF yields good agreement for the range of MS stars [FORMULA]Jy. There is an obvious overabundance of stars with [FORMULA]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).

Fig. 7 shows the observed mosaic KLF from Fig. 3a together with the model KLF. We transform the linear model KLF Eq. (8) into the corresponding logarithmic KLF using Eq. (2). Normalized to [FORMULA] we obtain the relation


which is shown in Fig. 7. Note that Tiede et al. (1995) obtained a similar power-law approximation [FORMULA] for the KLF observed in Baade's window . Observed and modeled KLF fit well together if we extrapolate the observed KLF [FORMULA] beyond [FORMULA]Jy, which is not too far from the estimated completeness limit of [FORMULA]Jy and may be considered as a more conservative estimate of this limit.

In summary we find that a 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 [FORMULA] as given by Eq. 1) explains the observed K band continuum in a quantitative way. The combined (logarithmic ) KLF increases [FORMULA] for [FORMULA]Jy [FORMULA] and [FORMULA] for [FORMULA]Jy [FORMULA]. It appears - and that is the interpretation of the observed KLFs which we favor - that their flattening and subsequent turnover in the flux density range [FORMULA]Jy is not an intrinsic characteristic of the Nuclear Bulge stellar population but rather an artifact due to the incompleteness of the source counts.

6.4. The mass-to-luminosity ratio

Based on the entries in Table 3 we arrive at the conclusion that within the mosaic, i.e. the central [FORMULA] pc about [FORMULA] MS stars of spectral type O9 or later account for more than [FORMULA] of the stellar mass of [FORMULA] but only for [FORMULA] of the integrated K band flux density. Adopting for the low-mass MS stars [FORMULA] K and a total (reddened) flux density of [FORMULA] Jy (Table 3) one obtains a luminosity of [FORMULA] and a mass-to-dereddened-luminosity ratio of [FORMULA] in agreement with an estimate by Kent (1992).

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© European Southern Observatory (ESO) 1999

Online publication: August 13, 199