4. K band sources in the central 30 pc
4.1. Radial dependence of the surface brightness
The K band surface brightness of the mosaic shown in Fig. 1a 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 ) 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 6. 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.
In addition to an average visual extinction of 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. 1b shows a close correlation between strong dust emission and K-light extinction, the compact Giant Molecular Clouds (GMCs) seen in 1.2 mm dust emission must be located in the Nuclear Bulge. Note, however, the presence of ionized gas, e.g. the spiral-shaped 1.2 mm emission feature surrounding the point source Sgr A* which is due to free-free emission from the HII region Sgr A West.
Fig. 2a shows the K band surface brightness integrated in circular apertures as observed here (heavy solid curve) and earlier by Becklin & Neugebauer (1968). K and H band flux densities contained within are given in Table 1 a. The flux density of Jy obtained here compares reasonably well with the flux density of Jy derived by Becklin & Neugebauer (including IRS 7) if one allows for a contribution of 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 , the surface brightness must increase as . Linear fits to our observations yield exponents decreasing from for to at . For we obtain , i.e. an exponent which is not too far from but still significantly smaller than the exponent 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 90o 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. 1a 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 but centered on Sgr A* and including IRS 7 is shown in Fig. 2b as heavy solid curve. The K band surface brightness integrated over all of the mosaic yields a flux density of Jy (Table 2 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. 1a sources with Jy or mag (see Appendix C). The flux density of all separated sources is referred to in the following as 7. This quantity, integrated in concentric circles is shown in Fig. 2b as heavy dotted curve. Integrated over the mosaic Jy (Table 2 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. 2b as light solid curve. Integration over the mosaic yields Jy (Table 2 c).
The difference 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. 2b. If the KLF were complete down to our detection limit of Jy one would expect . This is actually the case for radii . For larger radii and substitution of the integrated flux densities from Table 2 yields for the mosaic , indicating that our first method to separate resolved sources and unresolved background ignores a number of sources in the flux density range Jy 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 lost flux density amounts to of the total K band flux density of the mosaic. The difference is small enough to allow for the further discussions to use as the K band flux density of the ensemble of separated stars. Note that for the contribution of the high-luminosity (and hence relatively young) stars to is , while at their contribution has decreased to .
The K band surface brightnesses of the mosaic and its point source and continuum components have been computed with the relation which is valid for a power law radial dependence . The result is shown in Fig. 2c. 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 ) than the unresolved continuum due to MS stars with . 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 ( pc) stands out clearly in this diagram. We note that within the surface brightness of the resolved stars agrees well with the surface brightnesses derived by Allen (1994; see Fig. 35 in MDZ96).
4.2. K band luminosity functions (KLF)
The logarithmic KLF, i.e. the number of sources per logarithmic bin normalized to the unit solid angle of (in the following referred to either as KLF or as observed KLF) is shown in Fig. 3a for the mosaic and for two selected areas within the mosaic indicated in Fig. 1a by white contours. The rectangle of area referred to as "East" is centered on the synchrotron source Sgr A East thought to be the remnant of a gigantic explosion which occurred 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. 1b) and outlining a region of high K band extinction is referred to as M-0.13-0.08 This cloud core is located pc in front of Sgr A* (MDZ96, Sect. 3.4), has a visual extinction of mag and therefore blocks all NIR emission from stars located behind the dense core.
Fig. 4a 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 Jy. Most have flux densities of a few hundred µJy but two stars have flux densities as high as Jy and Jy. For comparison purposes the KLF of the M-0.13-0.08 cloud core is also shown in Fig. 4a. Fig. 4b 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 difference KLFs relate to the stellar populations in the Nuclear Bulge and in the Galactic Bulge and Galactic Disk, respectively.
For the numerical handling a linear KLF which samples the number of sources in linear bins dS is more useful. It relates to the logarithmic KLF by
where and . Then the cumulative number of sources with Jy is
and the corresponding cumulative flux density is
4.3. 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 mag for the central pc.
4.3.1. Dust emission
There are no observational indications for the presence of dust in the Central Region much hotter than K (see Fig. 5 and MDZ96, Fig. 25). Emission from small particles is mainly observed at 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.
4.3.2. 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. 5).
4.3.3. Stars in the Galactic Bulge and Disk
To estimate the contribution from stars in Galactic Bulge and Galactic Disk we make use of the m balloon survey by Hayakawa et al.(1981), made with an angular resolution of . This survey shows the Nuclear Bulge (in galactic longitude) as a narrow source of FWHP and peak surface brightness of Jysr-1 superimposed on the much wider brightness distributions of Galactic Bulge and Galactic Disk which have, however, comparable amplitudes. Their surface brightnesses of Jysr-1 and 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 Jy/arcsec2. This means a contribution of Jy or to the integrated flux density of the central , Jy or to the flux density of the mosaic and Jy or 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 . 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 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. 1b, this paper).
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 2 we obtain the ratio , which places the dark cloud very few kpc from the Sun. For M-0.13-0.08 the entries in Table 2 b yield and assuming a similar relation we estimate Jy as an upper limit of the Dark Cloud continuum. The corresponding surface brightness is Jy/arcsec-2.
4.3.5. Deviations from the adopted standard visual extinction of mag
The standard visual extinction as derived by Rieke et al. (1989) is mag. The corresponding K band extinction follows from Mathis et al. (1983). According to these authors mag is due to dust located between galactic radii -3.5 kpc while, according to MDZ96, Sect. 4.2.3, the remaining 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 and more. Direct measurements of the K band extinction within yields an average of mag with individual values as high as mag (Sellgren et al. 1996). Such a spatially variable extinction will certainly increase the scatter in the observed KLF but should not affect our basic conclusions. Catchpole et al. (1990) show that is - to a first order - constant in l with mag but drops off rapidly in b attaining mag at .
© European Southern Observatory (ESO) 1999
Online publication: August 13, 199