Astron. Astrophys. 348, 768–782 (1999) ASTRONOMYAND

ASTROPHYSICS

The nuclear bulge

I. K band observations of the central 30 pc

S. Philipp1,2, R. Zylka2, P.G. Mezger1, W.J. Duschl2,1, T. Herbst3, and R.J. Tuffs4

1 Max-Planck-Institut fur Radioastronomie, Auf dem Hugel 69, D-53121 Bonn, Germany2 Institut fur Theoretische Astrophysik, Tiergartenstrasse 15, D-69121 Heidelberg, Germany3 Max-Planck-Institut fur Astronomie, Konigstuhl 17, D-69117 Heidelberg, Germany4 Max-Planck-Institut fur Kernphysik, Saupfercheckweg, D-69117 Heidelberg, Germany

Received 8 May 1998 / Accepted 22 January 1999

Abstract. Out of ∼ 500 individual source images we haveconstructed a mosaic map1 of the K band surface brightnessin an area∆α × ∆δ ∼ 650′′ × 710′′ (Requiv ∼ 15.8 pc forR0 = 8.5 kpc) centered approximately on Sgr A*. An observ-ing technique was used which allows us to recover an extendedbackground emission. To separate sources from an unresolvedbackground continuum we fitted Lorentzian distributions to thesources and find that about one half of an integrated, not dered-dened K band flux density of752 Jy is contributed by∼ 6×104

stars with flux densities2 S′K

>∼ 100 µJy and the remainder iscontributed by an extended continuum provided by about6×108

stars too weak to be observed as individual sources. We estimatethat>∼ 80% of the integrated flux density of the mosaic is con-tributed by stars in the Nuclear Bulge (NB;R <∼ 300 pc); theremaining<∼ 20% come from stars located along the line of sightin the Galactic Bulge (GB;0.3 <∼ R/kpc<∼ 3) and Galactic Disk(GD; R > 3 kpc).

We determine the K band luminosity functions (KLF) of themosaic and of subareas dominated by Nuclear Bulge, Galac-tic Bulge and Disk stars, respectively, and constructdifferenceKLFs which relate to the specific stellar populations of theseregions. The detection limit isS′

K ∼ 100 µJy, for the com-pleteness limit we estimateS′

K ∼ 2 000µJy. We find that thestellar population of the Nuclear Bulge contains considerablymore bright stars (i.e. with reddened K band flux densitiesS′

K>∼ 5 × 103 µJy), most of which are probably early O stars,

Giants and Supergiants. The stellar population of the GalacticBulge on the other hand is dominated by stars which appear tobe lower mass (<∼ 6M) Main Sequence (MS) stars.

A modelKLF constructed with a Salpeter Initial Mass Func-tion (IMF) for stars of spectral type O9 or later (S′

K<∼ 2 000µJy)

explains the observations satisfactorily and connects well with

Send offprint requests to: P.G. Mezger, BonnCorrespondence to: wjd@ita.uni-heidelberg.de

1 Based on observations collected at the European Southern Obser-vatory, La Silla, Chile, using the IRAC2B camera with the ESO-MPG2.2m telescope.

2 In the following we refer toS′ν as observed andSν as dereddened

flux density.

theobservedKLF of more luminous stars. About6 × 108 starswith masses ranging from 0.06 to 6M account for the unre-solved continuum. Combining observed and model KLF we ob-tain a mosaic KLF which increases∝ S′−1

K for 106 >∼ S′K/µJy>∼

103 and∝ S′−0.6K for 103 >∼ S′

K/µJy>∼ 3 × 10−3.For radii R < 15′′ nearly 90% of the spatially integrated

K band flux density comes from resolved sources which repre-sent a relatively young generation of luminous stars. Farther outthe contribution of the the unresolved continuum (and hence oflow and medium mass MS stars) to the integrated K band fluxdensity increases and attains∼ 40% at a distanceR ∼ 300′′.This indicates a deficiency of low-mass stars within the cen-tral 30′′ (∼ 1.25 pc) and a high star formation activity duringthe past∼ 107–108 yr. Fitting King profiles to the observedsurface brightnesses we derive core radii of∼ 7′′ and∼ 30′′

respectively for resolved and unresolved stars. The mass-to-luminosity ratio of low mass stars in the central 30 pc is foundto be∼ 1M/L.

We present and discuss the radio/IR spectrum of the central30′′ (∼ 1.25 pc) and derive dust and Lyman continuum (Lyc)luminosities of7.5 × 107 L and1.2 × 1050 s−1, respectively.

Key words: stars: luminosity function, mass function – ISM:dust, extinction – Galaxy: center – Galaxy: evolution – Galaxy:stellar content – infrared: stars

1. The central region of the Galaxy: an overview

Our present knowledge of the Galactic Center Region has beenreviewed by Mezger et al. (1996; in the following referred toas MDZ96). To keep this introduction as concise as possiblewe quote here only the most relevant or recent papers and referotherwise to the corresponding sections of this review.

The Central Region extends out to a distance ofR ∼3 kpc where the Galactic Disk with its spiral structure begins.Throughout this paper a distanceR0 = 8.5 kpc to the GalacticCenter is adopted. The Central Region consists of the Galac-tic Bulge (3 ≥ R/kpc ≥ 0.3) and the Nuclear Bulge (R≤ 0.3 kpc). Subunits of the Nuclear Bulge which in the follow-

S. Philipp et al.: The nuclear bulge. I 769

ing will be referred to are: the Central Cavity (R ≤ 1.7 pc) whichis located inside the Circum-Nuclear Disk and specifically thecentral30′′ (linear size∼ 1.25 pc) surrounding the compactsynchrotron source Sgr A* which is associated with a massive(∼ 2.6 × 106M) Black Hole. Contained within the NuclearBulge is the K band mosaic, an area of∆α×∆δ ∼ 650′′×710′′

with an equivalent radiusRequiv ∼ 15.8 pc approximately cen-tered on Sgr A* which has been covered to date by our NIRsurvey. This mosaic includes the subareas Sgr A East and M-0.13-0.08 GMC indicated in Fig. 1b.

The integrated physical characteristics of both the GalacticBulge, Nuclear Bulge and – for comparison – of the GalacticDisk are given in MDZ96, Table 5. Referred to the total massesof stars or Interstellar Matter (ISM) these integral characteris-tics are rather similar in the Nuclear Bulge and Galactic Disk,but in the Nuclear Bulge the volume densities of matter and ofradiation are about two magnitudes higher. This is the reasonwhy practically all interstellar gas in the Nuclear Bulge exists inmolecular form and why there the dust temperatures are consid-erably higher. The Galactic Bulge, on the other hand, containslittle ISM and shows little signs of recent star formation. Ev-idence for a bar structure in the Galactic Bulge and the outerregions of the Nuclear Bulge are reviewed in MDZ96, Sect. 2.3.

The Circum-Nuclear Disk extends fromR ∼ 1.7 to 7 pcand contains∼ 104 M of ISM mainly in form of clumps ofhydrogen massMH ∼ 30M with a central visual extinctionof AV > 30 mag. The inner edge of the Circum-Nuclear Diskrotates once in 1.5×105 yr around the dynamical center. Partof the gas inside the Central Cavity is ionized and forms theHII region Sgr A West. In recent years the inner30′′ of theCentral Cavity has become one of the best investigated areasin the Galaxy. Observational results related to Circum-NuclearDisk and central30′′ are summarized in MDZ96, Sects. 4 and5.

In a series of papers with the general title “Anatomy ofthe Sgr A complex I – V” (Zylka et al. 1990; 1992; Gordonet al. 1993; Zylka et al. 1995; Beckert et al. 1996) our grouphas investigated the physical state of the ISM in the central partof the Nuclear Bulge and specifically the nature of the enig-matic source Sgr A*. Most of the physical characteristics ob-served in Active Galactic Nuclei (AGN) are also found in theCentral Region of our Galaxy: A massive (∼ 2.6 × 106M)Black Hole, a central mass flow ofM ∼ 10−2M yr−1 for radiiR ∼ 10–150 pc (MDZ96, Sect. 3.5) and indications of mild starbursts∼ 107–108 yrs ago. But the energy produced at presentby this Black Hole is negligible compared to the luminosity ofa cluster of evolved early-type stars in the immediate vicinityof Sgr A*.

2. Investigating the nuclear bulge:research program and scientific objectives

Observations of AGNs show that theircentral engine, i.e. aBlack Hole of mass∼ 108–1010M surrounded by an accre-tion disk, is embedded in a Nuclear Bulge of size of a few102 pc, which appears to play an important role in stabilizing

the Disk and initiating the mass flow which feeds the BlackHole. This motivated us to investigate the physical state of theNuclear Bulge in our Galaxy. Here we present the first in aseries of papers which combine ground-based and space-born(ISO3) NIR/MIR observations with submm and radio observa-tions of the central∆l×∆b ∼ 2×3. An average extinction of〈AV〉 ∼ 31 mag prevents any direct observations of the centralfew tens of parsecs atλ <∼ 1 µm. The transition from dust-dominated to star-dominated radiation of the Nuclear Bulge oc-curs atλ ∼ 5–7 µm. Hence stars in the Galactic and NuclearBulge – specifically medium and low mass stars – are pref-erentially observed in the NIR. High mass stars – in additionto being strong NIR sources – interact with the ISM by heat-ing the dust and ionizing the gas. Dust emission at MIR/FIRwavelengths together with free-free radio emission trace thesemassive stars and give information about both their total (L∗)and Lyc luminosity (L

λ<912A ), respectively.The K band (λ2.2 µm) is a good compromise between

a dust absorption increasing withe−τν , whereτν ∝ λ−1.7

for λ <∼ 7 µm, and the stellar flux density increasing withSν ∝ λ−2. Since the seminal papers by Becklin & Neugebauer(1968, 1975 and 1978) who mapped the central 100 pc, the Kband has extensively been used to investigate the stellar contentof the Central Region (MDZ96, Sects. 2.2.1 and 5.3). These ob-servations yielded a surface brightness variation∝ R−0.8 which– after having been calibrated with the observed rotation curve– translates for an assumedM/L ∼ 3 M/L into a massenclosed within the radius R of

M(R)/M = 4.25 × 106R1.2pc (1)

which can be used as a first approximation of the true massdistribution within R <∼ 500 pc (Sanders & Lowinger 1972,corrected forR0 = 8.5 kpc). However, ten years after their firstK band map was published Becklin & Neugebauer (1978) cau-tioned that due to their beam-switching observing techniquesan extended continuum background may have been suppressed.The K band observations presented in this paper not only have ahigh sensitivity for the detection of point sources. The observingmethod in addition is very effective in recovering an extendedbackground continuum which accounts for low-luminosity starswith S′

K<∼ 100 µJy. We find that the K band emission from the

central∼ 30 pc consists of∼ 6.1 × 104 individual sourceswith S′

K>∼ 100 µJy or4 mK <∼ 17 mag with an average sur-

face density of∼ 80 sources pc−2 which are superimposed onan unresolved background. This detection limit corresponds toreddened (for a visual extinction of∼ 31 mag) Main Sequence(MS) stars earlier than B5 or Giants more luminous than spectraltype A1 to G0 (luminosity class III; see Appendix D).

The detection limit is determined by the angular resolutionand sensitivity of the NIR array. The completeness limit, in ad-dition, also depends on the source crowding, i.e. the number of

3 ISO is an ESA project with instruments funded by ESA MemberStates (especially the PI countries: France, Germany, The Netherlandsand the United Kingdom) with the participation of ISAS and NASA.

4 We use the relation between flux density and K band magnitudeSK/Jy = 102.8–0.4mK .

770 S. Philipp et al.: The nuclear bulge. I

stars per pc2 and their intensity. In the central pc2 the crowdingof stars attains a maximum. Eckart et al. (1993) using speckletechniques were able to resolve∼ 350 stars pc−2 with a detec-tion limit of S′

K>∼ 260 µJy, corresponding tomK <∼ 16 mag. It

is found that in the central30′′ a very limited number of highand intermediate mass stars, most of which must have formedduring the past 108 yr, account for∼ 2/3 of the K band in-tegrated flux density,>∼ 99% of the total luminosity and allof the Lyc-photon production rate ofL∗ ∼ 7.5 × 107L andNLyc ∼ 1.2×1050s−1. Low-luminosity stars, on the other hand,which together form the unresolved continuum background, ac-count for>∼ 99% of the stellar mass5. Preliminary observationalresults suggest that beyond the central30′′ the relative contri-bution of luminous stars to the K band flux density decreaseswith increasing distance from Sgr A* (MDZ96, Sects. 4.3 and5.3).

The scientific objective of this paper is to learn more aboutthe stellar population in the central∼ 30 pc of the Nuclear Bulge.This information can only be obtained at wavelengthsλ >∼1 µm. We present and discuss the following observational re-sults:i) A K band mosaic image of size∆α×∆δ = 650′′×710′′

surrounding Sgr A* which covers∼ 0.6% of the total area of theNuclear Bulge.ii) A λ1.2 mm mosaic map of the dust emissionfrom a more extended region of the Nuclear Bulge obtainedwith the IRAM 30m-MRT. iii) The K band luminosity func-tion (KLF) of the sources contained in the mosaic image andin three subareas.iv) The radio through NIR spectrum spatiallyintegrated over the central30′′ and its decomposition into con-tributions by dust, stellar, free-free and free-bound emission.

3. Observations and data reduction of the K band mosaic

We are in the process of mapping the central 2% of the Nu-clear Bulge and selected areas further out in the H and K band(λ = 1.65 and 2.2µm) using the IRAC 2B camera with theESO-MPG 2.2m telescope on La Silla, Chile. The IRAC 2B ca-mera uses a NICMOS3 chip with 2562 pixels. The pixel scalecan be changed between0.151′′ and1.061′′ using lenses A toE, respectively (Lidman et al. 1996). For the chosen lens Bwe have a pixel scale of0.′′278. This produces images of size71.′′2 × 71.′′2. The image shown here in Fig. 1a and b is part ofa K band mosaic which – when finished – will cover an area ofsize∆α × ∆δ = 15′ × 25′. An observing technique has beenselected which allows us to recover an extended backgroundemission using a nearby dark cloud as reference point (see alsoTable 2). 494 images were used to construct the K band mosaicimage of the central650′′×710′′ shown in Fig. 1a and discussedin this paper (see Appendix A and B for a more detailed discus-sion of observing and data processing techniques. Appendix Cdeals specifically with problems associated with K band sourcecounts). Since IRS 7, one of the strongest individual sourcesin all of our NIR images, is variable on time-scales of months(we measured∼ 1.4 Jy in 1995 and∼ 1.2 Jy in 1996) we used

5 The central30′′, according to Genzel et al. (1997), encloses a totalmass of3.3 × 106M, of which2.6 × 106M are associated with acentral Black Hole, leaving a total mass of∼ 0.7 × 106M of stars.

the IR star SA 109–71 as flux density calibrator. In theUKIRTFaint Standard Star Listthis star is designated FS 28 with fluxdensitiesS′

K = 36.41 mJy andS′H = 66.44 mJy.

Theλ 1.2 mm bolometer observations were made using the7- through 37-channel bolometer arrays developed by E. Kreysaand coworkers of the MPIfR (Kreysa et al., 1996) with the IRAM30m-MRT. Uranus and Mars were used as flux density calibra-tors. Extinction caused by the atmosphere was measured usingSKYDIPS. The observing and reduction procedures will be de-tailed in a forthcoming paper. In Fig. 1b the surface brightnessof the dust emission is overlaid as a contour map on the K bandmosaic shown in Fig. 1a.

4. K band sources in the central 30 pc

4.1. Radial dependence of the surface brightnessIK ∝ Rα

The K band surface brightness of the mosaic shown in Fig. 1ais due to stellar emission. Possible sources of contamination ofthe stellar emission from the Nuclear Bulge will be discussedin Sect. 4.3. Down to a certain flux density limit (or alterna-tively an upper limit of K magnitude mK) the stars are seenas individual sources; below this limit the stars form an unre-solved background. This limit is not very well-defined since itdepends on seeing and source-crowding which both vary fromimage to image out of which the mosaic is constructed6. Inchopped observations such an extended unresolved backgroundwill be suppressed. In ON-OFF observations the measured sur-face brightness will depend on the surface brightness of the OFFposition.

In addition to an average visual extinction of〈AV〉∼ 31 magbetween Sun and Central Region observations suffer from ex-tinction due to dust clouds in or in front of the Nuclear Bulge.In those cases where Fig. 1b shows a close correlation betweenstrong dust emission and K-light extinction, the compact GiantMolecular Clouds (GMCs) seen inλ 1.2 mm dust emission mustbe located in the Nuclear Bulge. Note, however, the presenceof ionized gas, e.g. the spiral-shapedλ 1.2 mm emission featuresurrounding the point source Sgr A* which is due to free-freeemission from the HII region Sgr A West.

Fig. 2a shows the K band surface brightness integrated incircular aperturesS′

integr as observed here (heavy solid curve)and earlier by Becklin & Neugebauer (1968). K and H bandflux densities contained withinR = 15′′ are given in Table 1a.The flux density ofS′

K ∼ 11 Jy obtained here compares reason-ably well with the flux density of∼ 9 Jy derived by Becklin &Neugebauer (including IRS 7) if one allows for a contribution ofS′

K ∼ 2 Jy due to both the sum of calibrational uncertainties anda suppressed unresolved background in the Becklin and Neuge-bauer survey. Note that the Becklin and Neugebauer integratedflux densities are centered on IRS 7, whose flux density has beensubtracted for the integration. For comparison purposes we alsosubtracted the IRS 7 flux density and centered the integration onIRS 7. If the integrated flux density increases asS′

K ∝ R2+α,

6 We estimate a detection limit ofS′K ∼ 100 µJy and a completeness

limit of our source counts forS′K >∼ 2 000 µJy.

S. Philipp et al.: The nuclear bulge. I 771

Fig. 1. aK band mosaic of the central∆α×∆δ ∼ 650′′ ×710′′ centered approximately on Sgr A*. The black square indicates “no usable data”.White framed contours indicate subareas of the mosaic each of size5400′′, which are referred to in the text. The upper rectangle is centeredon the synchrotron source Sgr A East, the lower irregularly shaped area is centered on the compact cloud core M-0.13–0.08.b Overlaid on theK band mosaic is a contour map representing the dust emission observed atλ 1.2 mm with MPIfR bolometer arrays in the IRAM 30-m MRT(Θb = 11′′). Contour levels are: 90, 240, 390, 540, 690, 840, 990, 1180, 1680, 2180, 2680, 3180 and 3680 mJy/11′′ beam. 100 mJy/11′′ beamcorresponds to aτ1.2mm = 4 × 10−4 for Z/Z ∼ 2 andTdust ∼ 40 K. The correspondingλ2.2 µm opacity isτ2.2 µm = 0.98.

the surface brightness must increase asIK(R) ∝ Rα. Linear fitsto our observations yield exponents decreasing fromα ∼ 0.27for R < 10′′ to α ∼ −0.56 atR > 100′′. For10′′ < R < 100′′

we obtainα ∼ −0.65, i.e. an exponent which is not too farfrom but still significantly smaller than the exponentα ∼ −0.8which is generally adopted for the radial variation of the K bandsurface 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 segments centered along l andb shows clear effects of extinction by foreground cloud coresespecially for the segments centered on positive longitudes andnegative latitudes, respectively.

The K band mosaic shown as Fig. 1a consists of sourcesoverlaid on a continuum background, which we hypothesizeto consist of a very large number of stars too weak to be ob-served as individual sources. The K band surface brightnessof the mosaic integrated in concentric circles of radiusR butcentered on Sgr A* and including IRS 7is shown in Fig. 2b asheavy solid curve. The K band surface brightness integratedover all of the mosaic yields a flux density ofS′

integr ∼ 752 Jy(Table 2b). We tried to separate sources and unresolved back-ground in two different ways: In a first attempt we fitted modified

Lorentzian distributions (Diego, 1985) to the individual sourcesand obtained for the K-mosaic Fig. 1a∼ 6.1×104 sources withS′

K>∼ 100 µJy or mK <∼ 17 mag (see Appendix C). The flux

density of all separated sources is referred to in the following asS′

∗fit7. This quantity, integrated in concentric circles is shown

in Fig. 2b as heavy dotted curve. Integrated over the mosaicS∗fit ∼ 370 Jy (Table 2c).

In a second attempt we determined the surface brightnessin areas away from strong sources and refer to it as background(bcg). The corresponding flux density integrated in concentriccircles is shown in Fig. 2b as light solid curve. Integration overthe mosaic yieldsS′

bcg ∼ 283 Jy (Table 2c).The differenceS′

Star = S′integr − S′

bcg offers another wayto estimate the flux density of the ensemble of resolved stars.This quantity integrated in concentric circles is shown as dashedcurve in Fig. 2b. If the KLF were complete down to our detec-tion limit of S′

K ∼ 100 µJy one would expectS′∗fit ∼ S′

Star.This is actually the case for radiiR <∼ 60′′. For larger radiiS′

Star > S′∗fit and substitution of the integrated flux densi-

7 Note for the following discussion of the KLF thatS′∗fit =

S′cum(S′

K >∼ 100 µJy), withS′cum defined by Eq. (4) if both flux den-

sities refer to the same area andS′K = 100 µJy is the detection limit.

772 S. Philipp et al.: The nuclear bulge. I

Fig. 2. aObserved K band surface brightness integrated in concentriccircles of radiusR centered on IRS 7 but with its flux density subtracted.Heavy solid curve: Data from this paper. The heavy solid line hasbeen approximated by power laws of the formS′

K(R) ∝ R2+α (seetext). Black dots and dotted line: Earlier results obtained by Becklin &Neugebauer (1968) presented in the same form and their approximationby a power lawS′

K(R) ∝ R1.2 (see text).b K band surface brightnessesof resolved stars and unresolved continuum based on our observationsand integrated in concentric circles of radiiR centered on Sgr A* andincluding the flux density of IRS 7. Heavy solid line: Total integratedflux densityS′

integr; light solid curve: Flux densityS′bcg contributed by

the unresolved background emission. Dotted and dash-dotted curves:Flux densityS′

∗fit andS′Star = S′

integr − S′bcg, respectively, which

both relate to resolved stars withS′K > 100µJy ormK < 17 mag (see

text).c K band surface brightnessesIK(R) derived for the mosaic andits point source and continuum components and averaged in circles ofradii R centered on Sgr A*. Here the flux density of IRS 7 has beensubtracted.

ties from Table 2 yields for the mosaicS′∗fit/S′

Star ∼ 0.83,indicating that our first method to separate resolved sourcesand unresolved background ignores a number of sources inthe flux density range100 <∼ S′

K/µJy<∼ 2 000 which are nei-ther counted as separated sources (and therefore are not in-cluded in the KLF) nor are counted as contribution to thesmooth background continuum. Thislost flux densityamountsto(S′

Star−S′∗fit)/S′

integr<∼ 10% of the total K band flux density

of the mosaic. The difference is small enough to allow for thefurther discussions to useS′

∗fit as the K band flux density of theensemble of separated stars. Note that forR <∼ 15′′ the contri-bution of the high-luminosity (and hence relatively young) starsto S′

integr is >∼ 80%, while atR ∼ 300′′ their contribution hasdecreased to∼ 50%.

The K band surface brightnesses of the mosaic and its pointsource and continuum components have been computed with

the relationIK(R) = S′K(R)πR2

2+α2 which is valid for a power law

radial dependenceIK(R) ∝ Rα. The result is shown in Fig. 2c.R = 0′′ refers to the position of Sgr A*, the flux density of IRS 7has been subtracted. The surface brightness of the luminous starsdetected as point sources decreases much more rapidly (actually

∝ R−0.8) than the unresolved continuum due to MS stars withM∗ <∼ 20M. The relative deficiency of these low and mediummass stars or – perhaps more correctly – the overabundance ofhigh-mass, high-luminosity stars in the central15′′ (∼ 1.25 pc)stands out clearly in this diagram. We note that withinR <∼ 30′′

the surface brightness of the resolved stars agrees well withthe surface brightnesses derived by Allen (1994; see Fig. 35 inMDZ96).

4.2. K band luminosity functions (KLF)

The logarithmic KLF, i.e. the number of sourcesdN(S′K) per

logarithmic bindlogS′K normalized to the unit solid angle of

1′′ (in the following referred to either as KLF or asobservedKLF) is shown in Fig. 3a for the mosaic and for two selectedareas within the mosaic indicated in Fig. 1a by white contours.The rectangle of area5400′′ referred to as “East” is centered onthe synchrotron source Sgr A East thought to be the remnantof a gigantic explosion which occurred∼ 5 × 104 yr ago (seeMDZ96, Sect. 3.6) and appears to have cleared the foregroundfrom dust thus allowing a deep view into the Nuclear Bulge. A

S. Philipp et al.: The nuclear bulge. I 773

Table 1.Characteristics of the central 30′′ (=1.25 pc for R0 = 8.5 kpc)

RadiusR = 15′′ = 0.62 pcAreaΩ = 707′′ = 1.2 pc2

a. NIR flux densities of the central30′′

Band λ/µm ν/Hz S′ν/Jy Aν/AV Sν/Jy

H 1.65 1.82 1014 2.41 0.180 411±30 %K 2.2 1.36 1014 10.9 0.122 355±30 %

b. Fit parameters of a Planck decomposition of the dereddened spec-trum (Fig. 5)

Component T λτ=1 Ωs L MH

[K] [ µm] (arcsec)2 L M

cold dust 40 10 1020 1.7 105 327warm dust 150 0.2 900 3.3 106 5.8hot dust 350 0.02 8 2.1 105 0.005cool stars (mK

< 16 mag) 4 000 – 6.7 10−6 1.6 106

cool stars (mK

> 16 mag) 4 000 – 6.3 10−6 1.5 106

hot stars 25 000 – 2.6 10−7 9.2 107

c. Other parameters adopted for the discussion in Sect. 6

Parameter Ref.Mass inM Total 3.3 × 106 1

Black Hole 2.6 × 106

Stellar 0.7 × 106

Dust Luminosity(corr.) inL (7.5 ± 3.5) × 107 2

Lyc-photon productionrate (corr.) in s−1 (1.2 ± 0.5) × 1050 2

Teff , hot stars 2.5 × 104 K 3Teff , cool stars 4 × 103 K 4

Ref:1 Genzel et al., 19972 MDZ96, Sect. 4.33 Najarro et al., 1994, 19974 Eckart et al., 1993

irregularly shaped area of the same size centered approximatelyon one of the dense cores of the GMC M-0.13-0.08 (as visiblethrough its dust emission, see Fig. 1b) and outlining a regionof high K band extinction is referred to as M-0.13-0.08 Thiscloud core is located∼ 50–100 pc in front of Sgr A* (MDZ96,Sect. 3.4), has a visual extinction ofAV ∼ 60 mag and thereforeblocks all NIR emission from stars located behind the densecore.

Fig. 4a shows the KLF in the direction of the Dark Cloudwhich is used as “OFF” position in our observations (seeSect. 3). The central region of the Dark Cloud contains about 60stars with flux densities<∼ 3×103 µJy. Most have flux densitiesof a few hundredµJy but two stars have flux densities as highas∼ 9 000µJy and∼ 11 000µJy. For comparison purposes theKLF 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 fromwhich the KLFs of M-0.13-0.08 and the Dark Cloud have been

Table 2. Characteristics of the K band Mosaic∆α × ∆δ = 650′′ ×710′′ approximately centered on Sgr A*

Equiv. radiusR = 383′′ = 15.8 pcEffective Area1) Ω = 4.1 × 105′′ = 782 pc2

1) Only images with reliable surface brightnesses are counted

a. Center positions and solid angles

Component Projection center Ω(1950.0) 103′′

Mosaic 17:42:29.32 -28:59:18.38 410Sgr A East 17:42:32.75 -28:58:23.37 5.4M-0.13-0.08 17:42:32.75 -29:04:53.39 5.4Dark Cloud 17:41:35.05 -28:52:37.92 5.1

b. K band flux densitiesComponent S′

integr S′GB+GD S′

Star

Jy Jy Jy

Mosaic 752 131 469Sgr A East 26.0 3.31 15.7M-0.13-0.08 4.24 3.31 3.36Dark Cloud · · · · · · · · ·

c. Source fit parameters

Component Ntot S′∗fit S′

bcg

Jy Jy

Mosaic 6.06 × 104 370 283Sgr A East 923 13.2 10.3M-0.13-0.08 775 1.57 0.88Dark Cloud 60 6.6 × 10−2 · · ·

d. Other parameters used for the discussion in Sect. 6

Parameter Ref.

Mass inM 1.17 × 108 1Luminosity inL 5 × 107 2,3Lyc-photon productionrate in s−1 ∼ 1051 3

Ref:1 Eq. (1)2 Cox & Mezger, 19893 Mezger & Pauls, 1979

subtracted. ThesedifferenceKLFs relate to the stellar popula-tions in the Nuclear Bulge and in the Galactic Bulge and GalacticDisk, respectively.

For the numerical handling alinear KLF which samples thenumberN(S′) of sources in linear binsdS is more useful. Itrelates to thelogarithmicKLF by

dNs

dS′ = N(S′) = 0.43S′−1 dN(S′)dlogS′ (2)

where logS′ = log(e)lnS′ and dlnS′ = dS′/S′. Then thecumulative number of sources withS′

K ≤ Smax ∼ 2 × 106 µJyis

774 S. Philipp et al.: The nuclear bulge. I

Fig. 3. aKLF of the mosaic image and of the two subareas indicatedin Fig. 1a, all normalized to a source angle of1′′. Sources are countedin logarithmic bins of width0.08. b Cumulative numberNcum(S′

min)of stars with flux densitiesS′

K ≥ S′min computed with Eq. (3) and the

KLFs shown ina. c Cumulative flux density of starsScum(S′min) with

flux densitiesS′K ≥ Smin computed with Eq. (4) and the KLFs shown

in a.

Fig. 4. aKLF of the Dark Cloud; for comparison purposes is also shownthe KLF in the direction of the compact cloud core M-0.13-0.08 fromFig. 3a.b DifferenceKLFs, i.e. KLF(Sgr A East) minus KLF(M-0.13-0.08) and KLF(M-0.13-0.08) minus KLF(Dark Cloud).

Ncum(S′min) =

S′max∫

S′min

N(S′)dS′ (3)

and the corresponding cumulative flux density is

S′cum(S′

min) =

S′max∫

S′min

N(S′)S′dS′ (4)

ThelogarithmicKLFs as derived from our observations togetherwith Ncum andS′

cum defined by Eqs. (3) and (4) are shown inFigs. 3 and 4 and will be discussed in more detail in Sect. 6.

4.3. Contamination of the K band observations

Here we discuss possible contaminations of the surface bright-nesses and derived flux densities in the Nuclear Bulge by ad-ditional sources of emission and by deviations of the (visual)

S. Philipp et al.: The nuclear bulge. I 775

extinction from the adopted mean value〈AV〉 ∼ 31 mag for thecentral pc.

4.3.1. Dust emission

There are no observational indications for the presence of dustin the Central Region much hotter than∼ 400 K (see Fig. 5and MDZ96, Fig. 25). Emission from small particles is mainlyobserved atλ12–25 µm and is weak in the NIR (Castelaz etal., 1987). Hence we conclude that contamination by hot dustemission of the results presented here is negligible.

4.3.2. Recombination radiation

About 10% of all Lyc-photons in the Galaxy originate in theNuclear Bulge. Apart from free-free emission by electrons ac-celerated in the Coulomb field of ions, free-bound emission andline radiation due to recombination of free electrons with ionsmust be considered. The contribution of emission from ionizedgas to the K band surface brightness has been recently reana-lyzed by Beckert et al. (in prep.) and was found to be negligiblefor 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 andGalactic Disk we make use of theλ2.4 µm balloon survey byHayakawa et al.(1981), made with an angular resolution of∼ 1.7. This survey shows the Nuclear Bulge (in galactic longi-tude) as a narrow source of FWHP∼ 3 and peak surface bright-ness of∼ 1.06 × 107 Jysr−1 superimposed on the much widerbrightness distributions of Galactic Bulge and Galactic Diskwhich have, however, comparable amplitudes. Their surfacebrightnesses of9.6×106 Jysr−1 and1.34×107 Jysr−1 derivedfor Galactic Bulge and Galactic Disk, respectively, can be con-sidered constant across the Nuclear Bulge. Together they con-tribute a K band surface brightness of∼ 3.2× 10−4 Jy/arcsec2.This means a contribution of∼ 0.23 Jy or ∼ 2% to the inte-grated flux density of the central30′′, ∼ 131 Jy or∼ 20% to theflux density of the mosaic and∼ 2.5×104 Jy or∼ 250% to theflux density of the Nuclear Bulge. The reason for this dramaticincrease is that the average surface brightness of Galactic Bulgeand Galactic Disk is assumed to stay nearly constant while thatof the Nuclear Bulge decreases∝ R−0.9. It should be noted thatthis estimate of the contribution of Galactic Bulge and GalacticDisk stars to the flux density of stars in the Nuclear Bulge is avery strict upper limit and that a flux densityS′

GB+GD/2 may inmost cases be a more realistic estimate since very dense cloudcores in the Nuclear Bulge will probably absorb most of the stel-lar emission from behind the Nuclear Bulge (see e.g. MDZ96,Fig. 17 and Fig. 1b, this paper).

4.3.4. The surface brightness of the Dark Cloud

In the K band observations we use a Dark Cloud as ref-erence OFF position (see Sect. 3). Stars between this Dark

Cloud and the sun appear in our survey as negative pointsources and continuum, respectively. We can eliminate thepoint sources and the continuum visible in the direction ofthe Dark Cloud assuming that the regions of lowest bright-ness have zero intensity and re-adding the additional flux den-sity from sources and continuum visible in the OFF-positionto the ON image. To estimate an upper limit of this contin-uum we compare the Dark Cloud with the subarea M-0.13-0.08. Both images contain only stars in the Galactic Bulge andGalactic Disk. From the entries in Table 2 we obtain the ra-tio S′

∗fit(DarkCloud)/S′∗fit(M − 0.13 − 0.08) ∼ 0.04, which

places the dark cloud very few kpc from the Sun. For M-0.13-0.08 the entries in Table 2b yieldS′

∗fit ∼ S′bcg and assuming a

similar relation we estimateS′bcg ∼ S′

∗fit ∼ 6.6×10−2 Jy as anupper limit of the Dark Cloud continuum. The correspondingsurface brightness isIK ∼ 10−5 Jy/arcsec−2.

4.3.5. Deviations from the adopted standard visual extinctionof 〈AV〉 ∼ 31 mag

The standard visual extinction as derived by Rieke et al. (1989)is 〈AV〉 ∼ 31 mag. The corresponding K band extinctionAK/AV = 0.122 follows from Mathis et al. (1983). Accordingto these authorsAV ∼ 20 mag is due to dust located betweengalactic radiiR ∼ 8.5–3.5 kpc while, according to MDZ96,Sect. 4.2.3, the remaining∼ 11 mag of extinction would be con-tributed by dust in the Nuclear Bulge, probably associated withthe High Negative Velocity Gas (HNVG) seen in OH absorptionagainst the background of synchrotron and free-free emission.OH column densities in the HNVG and visual and K band ex-tinction vary on angular scales of arcsec by±10% and more.Direct measurements of the K band extinction withinR <∼ 1′

yields an average of〈AK〉 ∼ 3.3 mag with individual values ashigh asAK ∼ 6 mag (Sellgren et al. 1996). Such a spatially vari-able extinction will certainly increase the scatter in theobservedKLF but should not affect our basic conclusions. Catchpole etal. (1990) show thatAV is – to a first order – constant inl withAV ∼ 30 mag but drops off rapidly inb attainingAV ∼ 15 magat b ∼ 0.6.

5. The spatially averaged continuum spectrumof the central 30′′ (∼1.25 pc)

K band emission relates to stars. Due to the large distance ofthe Nuclear Bulge (R0 ∼ 8.5 kpc) and the high dust opacityin the direction of the Galactic Center (AV ∼ 31 mag) most ofthe sources above our detection limit of∼ 100 µJy are eitherearly-type MS stars or Giants and Supergiants (see Appendix Dand Fig. D1). While the low- and medium mass MS stars canbe traced by their K band continuum emission the distributionand luminosity of more massive MS stars and Giants can beestimated from the emission of dust and ionized gas located inthe Nuclear Bulge. In this section we derive the radio throughNIR spectrum of the central 30′′ and decompose it into the con-tributions from free-free emission, warm and hot dust emissionand stellar emission.

776 S. Philipp et al.: The nuclear bulge. I

Fig. 5.Observed (I ) and fitted continuum spectrum (heavy solid curve)of the central30′′ (1.25 pc). This spectrum has been decomposed intoPlanck components of various temperatures representing dust emission(with Tdust ≤ 350 K) and stellar emission (withTeff ≥ 4 000 K lightsolid curves) together with free-free and free-bound emission from anionized gas withTeff ∼ 8 000 K(dotted curve). Also shown is part ofan ISOPHOT-PHT-S spectrum (see text).

Fig. 5 shows the dereddened spectrum of the central 30′′

(∼ 1.25 pc forR0 = 8.5 kpc). Data withν < 1014 Hz arefrom Zylka et al. (1995); additional data forν > 1014 Hz havebeen obtained from the K band observations discussed here andfrom an H band mosaic obtained in a similar way which will bepresented and discussed in a later paper. Observed and dered-dened flux densities are given in Table 1a. The spectrum hasbeen decomposed into three characteristic dust components andtwo characteristic stellar components as shown in Fig. 5. Cor-responding fit parameters are given in Table 1b (see Mezger1994 and references therein). Forλ <∼ 5–7 µm the spectrumis dominated by stellar emission. The stellar population withinthe 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 stel-lar mass ofΣM∗ ∼ 0.7 × 106M (see footnote 5). Based onwork by Eckart, Genzel and collaborators (see also MDZ96,Sect. 5.3.2) we attribute of the total observed K band flux den-sity of S′

integr ∼ 11 Jy,∼ 2.3 Jy to 24 hot stars,∼ 4.5 Jy to coolbut luminous stars withmK < 16 mag and∼ 4.2 Jy to low-masslow-luminosity stars withmK > 16 mag. For the hot stars weadopt Teff ∼ 25 000 K (Najarro et al., 1994 and 1997) and forthe cool stars Teff ∼ 4 000 K. With these assumptions we obtainthe two Planck spectra attributed to stellar emission. The corre-sponding luminosity of 9.2×107 L (Table 1b) is well abovethe (corrected) dust luminosity of 7.5×107 L given in Ta-ble 1c. The cool Giants and Supergiants whose progenitors weremedium-mass stars together with the low-mass, low-luminositystars account for comparable luminosities of∼ 1.5 × 106 Lbut their contribution to the total stellar luminosity is negligible.

Also shown in Fig. 5 is part of the spectrum extending fromλ ∼2.66 to 11.56µm which we observed with higher resolu-

tion using ISOPHOT-PHT-S (see Lemke et al., 1996). The datawere reduced with the PHT interactive analysis package PIAV7.0.2p(e) (Gabriel et al., 1996) in the standard way using thedrift recognition, the orbital dependent dark current and the de-fault detector responses. Strong absorptions are found in thewavelength range∼ 2.66–4.92 µm and∼ 8–11.56 µm. Thesefeatures are shown in Fig. 5 for the short wavelength range ofISOPHOT-PHT-S but have not been considered in the contin-uum fit.

The first three components in Table 1b relate to dust. Forwavelengthsλ < λτ=1 the dust is opaque.L are the lumi-nosities of the dust components andMH are – for a metallicityZ/Z ∼ 2 – the associated hydrogen masses, both given insolar units.Ω = 1.133Θ2

s = 1020′′ is the solid angle of aGaussian source of FWHPΘs = 30′′. Hence, the 40 K dustappears to fill the central30′′ completely. Fromλτ=1 ∼ 10 µmwe derive an average visual extinction of this dust component ofAV ∼ 30 mag, which is – within the rather large error margins– close toAV ∼ 31 mag estimated for the extinction betweenGalactic Center and Sun. The 40 K dust is, however, not the dustlocated between Sun and Galactic Center which is too extendedto be seen in emission in submm/FIR images of size∼ 30′′.Furthermore, a dust temperature of 40 K is typical for extendedenvelopes of Galactic Center molecular clouds in the NuclearBulge (e.g., Gordon et al. 1993) but much too high for dust lo-cated in the Galactic Disk. We conclude that the 40 K dust mustbe located close to, but not in front of the Galactic Center, oth-erwise the total extinction towards the central cluster would beAV ∼ 65–70 mag, and therefore deny NIR observations of theNuclear Bulge.

The hydrogen mass associated with all dust componentsis MH ∼ 330 M (Table 1b). The mass of ionized hydrogencontained in the HII region Sgr A West isMHII ∼ 260 M(Table 7 of MDZ96). The central30′′ account for 7 Jy of atotal free-free flux density of 27 Jy atλ2 cm of Sgr A Westencircled by the Circum-Nuclear Disk. The scaled mass of HIIcontained in the central30′′ is MHII ∼ 67 M. It thus appearslikely that all of the 150 K dust and∼ 20 % of the 40 K dustare mixed with the ionized gas and hence with the central starcluster. The remaining part of the 40 K dust could be located inthe neutral gas of the Sgr A East core GMC, but at the remoteionization front of Sgr A West (see MDZ96, Figs. 17a,b). The300 K component is probably contributed by circumstellar dust.

6. Discussion

6.1. The radial distribution withinR ≤ 300′′ of starswith high and low K band luminosities

In the preceding section 5 we have dealt with global characteris-tics of the stellar populations in the mosaic, i.e. the central 30 pc.We separated early-type MS stars, Giants and Supergiants fromlow-mass, low-luminosity stars on the basis of their K band fluxdensity. We found that the surface density of hot and luminousstars decreases much more rapidly than the total K band surfacebrightness which relates to all MS stars as well as Giants and

S. Philipp et al.: The nuclear bulge. I 777

Supergiants. Genzel et al. (1996), on the other hand, investigatedwith high angular resolution the distribution of early and latetype stars out to a distance ofR ∼ 20′′. They find that early typestars are concentrated in the central12′′. Red Supergiants andAGB stars seem to avoid the central4′′ and form a ring whichpeaks atR ∼ 7′′ and extends as far asR ∼ 10′′. Intermediateluminosity stars show a central depression which is not seen,however, in the distribution of the faintest stars. For a some-what more extended region ofR ∼ 30′′ Allen (1994) finds forhot stars (no CO features) a considerably narrower distributionthan for cool stars (with CO features).

The mosaic presented here gives information about the stel-lar distribution in the intermediate distance range2′′ <∼ R <∼300′′. This seeing limited data allowed to measure∼ 6.1 × 104

individual stars as weak asS′K ∼100µJy or mK ∼ 17.0mag

yielding a surface density of∼ 80 stars pc−2 most of which areMS stars earlier than O9, Giants and Supergiants. We estimate acompleteness limit of ourobservedKLF at∼ 2 000µJy. The un-resolved background should therefore consist of MS stars laterthan spectral type O9 (M∗ <∼ 19M) and Giants less luminousthan spectral type M0 (luminosity class III) whose progenitorstars had masses<∼ 4M. (See Appendix D; Note that a1MMS star located in the Nuclear Bulge has a reddened K fluxdensity of onlyS′

K ∼ 2 µJy.)Fig. 2b shows the contribution of the resolved stars and unre-

solved background to the integrated K band flux density, Fig. 2cshows the surface brightnesses of these components as derivedfrom the data in Fig. 2b. The surface brightness of the resolvedstars actually decreases∝ R−0.8 as derived for the originalBecklin and Neugebauer data. The surface brightness of the un-resolved background representing medium and low mass MSstars and a few Giants, on the other hand, stays nearly constantout toR ∼ 10′′ and decreases only slowly farther out.

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

IK(R) = I0

1(

1 +(

RRc

)2)0.5 − 1(

1 +(

Rt

Rc

)2)0.5

(5)

to the observed radial surface brightness variationsI∗fit andIbcg (Fig. 6). HereRc is the core radius andRt is the ra-dius at which the surface brightness drops to zero. While Kingprofiles with core radiiRc ∼ 7′′ and ∼ 30′′ give good fitsfor IK(R)/I0 >∼ 0.5 the observed surface brightnesses atR > Rc drop much more slowly than even a King profile withRt = ∞. This slow decrease forR > Rc may in part be dueto the contamination by stars in the Galactic Bulge and Galac-tic Disk, which amounts to an average surface brightness ofIGB+GD ∼ 3.2 × 10−4 Jy/arcsec−2. The much smaller coreradius of the luminous and therefore young stars indicates thatrecent (<∼ 107–8 yr) star formation activity – compared to thetotal stellar mass – decreases rapidly from the center outwards.

Fig. 6.The radial distribution of K band surface brightnesses observedfor resolved (I ′

∗fit) and unresolved (I ′bcg) stars together with King pro-

files and fit parametersRc andRt. Also shown is the estimated con-tribution I ′

GB+GD of stars located in the Galactic Bulge and GalacticDisk.

6.2. General characteristics of the observed KLFs

In Sect. 4.2 we discuss the characteristics of theobservedKLFs.TheobservedKLF of the mosaic,dN(S′)/ dlogS′, constructedfrom ∼ 6.1 × 104 individual sources and shown in Fig. 3a,increases∝ S′−1

K in the range4 × 103 <∼ S′K/µJy<∼ 105.

For S′K

>∼ 105 µJy the increase steepens slightly, while forS′

K<∼ 4 × 103 µJy the KLF flattens and eventually begins to

decrease forS′K

<∼ 2 000µJy. Remember thatS′K ∼ 100 µJy is

the detection limit andS′K ∼ 2000 µJy is the estimated com-

pleteness limit of our observations. Contamination of the mosaicKLF by stars in the Galactic Bulge and Galactic Disk amountsto SGB+GD/S′

integr<∼ 17% (see Table 2b,c and the paragraph

Stars in the Galactic Bulge and Diskin Sect. 4.3). An attempt toseparate foreground and Nuclear Bulge stars based on their H/Kcolors has to be postponed to a later paper. The KLFs of the sub-areas Sgr A East (low foreground extinction) and M-0.13-0.08(high foreground extinction) shown in Fig. 3a behave qualita-tively similarly: they all attain a maximum and subsequentlydecrease. But their maxima are shifted fromS′

K ∼ 103 µJyfor the M-0.13-0.08 KLF to∼ 104 µJy for Sgr A East KLF. Inpart this is due to the fact that forS′

K<∼ 2 000µJy the KLF is

determined by the incompleteness of the source counts whichincreases with decreasingS′

K and also depends very much onthe crowding of the area. For the crowded subarea Sgr A Eastwe therefore find fewer sources forS′

K<∼ 2 000µJy than in the

less crowded subarea M-0.13-0.08.For the more luminous K band sourcesS′

K > 2 000µJy onenotices, however, characteristic differences intrinsic to the threeKLFs and hence to the stellar population which they sample.Remember that the KLF of the Sgr A East subarea samples apopulation of stars deep inside the Nuclear Bulge which havean obvious overabundance of luminous stars. In case of thesubarea M-0.13-0.08 a dense cloud core blocks the emission

778 S. Philipp et al.: The nuclear bulge. I

from the (luminous) stars in the center of the Nuclear Bulge. Wetherefore should observe a KLF which relates predominately tothe stellar population of the Galactic Bulge and Galactic Disk.The fact that the integrated surface brightness of this subareais S′

integr ∼ 4.24 Jy and hence is only slightly higher than theestimated contribution from stars located in the Galactic Bulgeand Galactic Disk ofS′

GD+GB ∼ 3.31 Jy (Table 2) supports thisassumption.

The KLF of the mosaic contains contributions from areasof high and low foreground extinction and therefore lies be-tween the two extreme cases. The difference KLF(Sgr A East)– KLF(M-0.13-0.08) (Fig. 4b) shows in an impressive way thecontribution by early MS O stars, Giants and Supergiants withS′

K>∼ 3×103 µJy 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 inthe Galactic Bulge and Galactic Disk. The KLF of M-0.13-0.08samples all stars between the sun and the Nuclear Bulge whilethe KLF of the Dark Cloud contains only stars in the GalacticDisk out to a distance of a few kpc from the sun. A comparisonof the two KLFs (Fig. 4a,b) shows that the Dark Cloud KLF hasa deficiency of sourcesS′

K<∼ 4×103 µJy. This can be explained

by the fact that the Dark Cloud is so close to the sun that evenlow-mass stars appear as relatively luminous K band sources.

6.3. Comparison of the observedwith a model KLF of the mosaic

We hypothesize that the unresolved K band continuum observedin the central 30 pc of the Nuclear Bulge is the continuation ofthe observedKLF towards sources beyond the detection limitof our survey. In this section we try to verify this hypothesisby comparing our observations with amodelKLF computedfor the standard Salpeter IMF8. For numerical computations weterminate the IMF of the Nuclear Bulge atM∗ ∼ 20M, themass of an O9 star with a K band flux densityS′

K ∼ 1000 µJy,normalize it to the stellar massΣM∗ ∼ 1.2×108M containedwithin the mosaic (Table 2d) and thus obtain

dN = 1.81 × 107(

M∗M

)−2.35

dM∗ M∗ <∼ 20M (6)

Integration fromM∗ ∼ 0.06M (corresponding to the lowestmass MS star of spectral type M8) toM∗ ∼ 20M yields a totalnumber of∼ 5.9 × 108 MS stars contained within the mosaic.We also compute the K band flux density of MS stars (see Ap-pendix D) and find that in the mass range0.06 <∼ M∗/M <∼ 20the result is well represented by the power-law approximation(

S′K

µJy

)= 1.6

(M∗M

)2.3

M∗ <∼ 20M (7)

Combination of the two equations yields for thelinear modelKLF as defined by Eq. (3)

KLF(mod) = N(S′K) = 1.03 × 107S′−1.6

K (8)

8 For the sake of simplicity we use here this IMF although beingaware that it overestimates the number of stars at both the high- andlow-mass end (Scalo, 1986)

Remember, however, for a comparison with theobservedKLF’sshown in Fig. 3a that themodelKLF dN(S′)/dlogS′ whichcounts source numbers in logarithmic bins is related to the abovelinear KLF N(S′) = dN(S′)/dS′ which counts sources inlinear bins by Eq. (2) and hence is∝ S′−0.6. The cumulatedsource number is

Ncum(mod) =

S′max∫

S′min

N(S′)dS′

= 1.76 × 107 (S′−0.6

min − S′−0.6max

)(9)

= 5.7 × 108sources

in good agreement with Eq. (6). Here and in the followingEq. (10)Smin = SK(M8 star) ∼ 3 × 10−3 µJy andSmax =SK(O9 star) ∼ 103 µJy have been substituted. The cumulatedflux density is

S′cum(mod) =

S′max∫

S′min

S′N(S′)dS′

= 2.59 × 107 (S′0.4

max − S′0.4min

)µJy (10)

= 408Jy

This latter result can be used to verify that themodelKLFactually is a reasonable extension of theobserved mosaicKLF.If the model KLF describes the distribution of medium and low-mass stars correctly one would expectS′

cum(mod) + S′∗fit =

S′integr. Combination of eq(10) withS′

∗fit = 370 Jy from Ta-ble 2c yields 778 Jy as compared toS′

integr = 752 Jy (Ta-ble 2c). This increase by∼ 4% can be explained by theoverlap ofmodelandobservedKLF in the flux density range100 <∼ S′

K<∼ 2 000µJy.

ObservedandmodelKLF are compared in more detail inTable 3 and Fig. 7. In Table 3 we subdivide the observed sourcesinto four different bins according to their reddened K band fluxdensities and compare the corresponding observed differentialcumulated flux densities and source numbers. The main contrib-utors to the K band flux density ofS′

integr ∼ 752 Jy integratedover the mosaic are∼ 14 000 Giants (∼ 38%) and a large num-ber (ourmodelKLF predicts∼ 6× 108) of low-mass stars withM∗ <∼ 6M (∼ 49%). Early-type MS stars which are respon-sible for the ionization of the gas and a good part of the dustheating account for only∼ 13% of the K band flux density.In the spectral range O9 – B5 our source counts are incom-plete; a large fraction of the K band flux densities of these starstherefore should be found in the unresolved continuum. Thisassumption is confirmed by the fact that the sum∆Scum(B5 –O9)+∆Scum(M8 – B5) ∼ 389 Jy (observed) and 408 Jy (mod-eled) differ by only ∼ 5% if the corresponding flux densitiesfrom Table 3 are substituted.

A comparison of the characteristics ofobservedandmod-eledmosaic KLF yields good agreement for the range of MSstarsS′

K<∼ 2 000µJy. There is an obvious overabundance of

stars withS′K

>∼ 6 × 103 µJy which most probably are Giantsand Supergiants. The abundance of these stars relative to MS

S. Philipp et al.: The nuclear bulge. I 779

Table 3.Characteristics of the observed and of a model KLF of the mosaic

Stellar Population Giants O9 – O3 B5 – O9 M8 – B5 All starsRange ofS′

K/µJy 6 × 103 – 2 × 106 103 – 6 × 103 102 – 103 3 × 10−3 – 102 3 × 10−3 – 2 × 106

∆Scum(obs.)/Jy 286 77 8 3811) 752∆Ncum(obs.) 1.4 × 104 2.9 × 104 1.8 × 104 · · · 6.1 × 104

∆Scum(mod.)/Jy2) · · · · · ·4) 247 161 < 752∆Ncum(mod.)3) · · · · · ·4) 8.3 × 105 5.6 × 108 5.7 × 108

∆ΣM∗/M5) 2.3 × 105 2.4 × 106 9 × 106 1.1 × 108 1.2 × 108

Notes:1) S′cum(3 × 10−3 − 102 µJy) = S′

integr − S′cum(102 − 2 × 106 µJy)

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 themodelKLF and hence of Eqs. (9) and (10) overestimatesthe contribution of early O stars toNcum andScum. Therefore, no entries forNcum(mod) andScum(mod) are made.5) Rather than using themodelKLF we use Eq. (6) to compute∆ΣM∗ for M∗ <∼ 20M and estimate〈M∗〉 ∼ 50M and∼ 30M for O3 –O9 MS stars and Supergiants, respectively.

Fig. 7. The observedmosaic KLF (Fig. 3a) combined with themodelKLF Eq. (11)

stars can be used to estimate their lifetimes (see e.g. Genzel etal. 1994, Krabbe et al. 1995).

Fig. 7 shows theobservedmosaic KLF from Fig. 3a togetherwith themodelKLF. We transform thelinear modelKLF Eq. (8)into the correspondinglogarithmicKLF using Eq. (2). Normal-ized to1′′ we obtain the relation

dN(S′)dlogS′ = 58.5S′−0.6

K (11)

which is shown in Fig. 7. Note that Tiede et al. (1995) obtaineda similar power-law approximation∝ S−0.69 for theKLF ob-servedin Baade’s window. ObservedandmodeledKLF fit welltogether if we extrapolate theobservedKLF ∝ S′−1

K beyondS′

K>∼ 4×103 µJy, which is not too far from the estimated com-

pleteness limit of∼ 2 000µJy and may be considered as a moreconservative estimate of this limit.

In summary we find that amodelKLF based on the SalpeterIMF with the total mass of MS stars as the only free param-eter (for which we substitute the dynamical mass ofΣM∗ ∼1.2 × 108M as given by Eq. 1) explains theobservedK band

continuum in a quantitative way. The combined (logarithmic)KLF increases∝ S′−1

K for 106 >∼ S′K/µJy>∼ 103 and∝ S′−0.6

Kfor 103 >∼ S′

K/µJy >∼ 3 × 10−3. It appears – and that is theinterpretation of theobservedKLFs which we favor – that theirflattening and subsequent turnover in the flux density rangeS′

K ∼ 103–104 µJy is not an intrinsic characteristic of the Nu-clear Bulge stellar population but rather an artifact due to theincompleteness of the source counts.

6.4. The mass-to-luminosity ratio

Based on the entries in Table 3 we arrive at the conclusionthat within the mosaic, i.e. the central∼ 30 pc about6 × 108

MS stars of spectral type O9 or later account for more than99% of the stellar mass ofΣM∗ ∼ 1.2 × 108M but only for∼ 50% of the integrated K band flux density. Adopting for thelow-mass MS starsTeff ∼ 4 000 K and a total (reddened) fluxdensity ofS′

K ∼ 361 Jy (Table 3) one obtains a luminosity ofL∗(Teff ) ∼ 1.4×108L and a mass-to-dereddened-luminosityratio of ΣM∗/L∗ ∼ 1M/L in agreement with an estimateby Kent (1992).

7. Conclusions

For an area∆α × ∆δ ∼ 650′′ × 710′′ centered approximatelyon Sgr A* and referred to as “mosaic” we have determined itsKLF containing∼ 6.1 × 104 sources with reddened K bandflux densitiesS′

K>∼ 100 µJy. The completeness limit of this

KLF lies in the rangeS′K ∼ (1–4) × 103 µJy. Half of the K

band surface brightness integrated over the mosaic comes froman unresolved continuum formed by an estimated number of∼ 6×108 low and medium mass (<∼ 6M) MS stars. ForS′

K<∼

1 000µJy (O9 stars and later) the characteristics of theobservedKLF and the unresolved continuum are well represented by amodelKLF combined with theobservedand extrapolated KLF.The modelKLF is based on a Salpeter IMF and a total stellarmass contained withinR <∼ 15 pc of ΣM∗ ∼ 1.2 × 108M.The combined KLF increases∝ S′−1

K for S′K

>∼ 1 000µJy and∝ S′−0.6

K for S′K < 1 000µJy. The flattening and turnover of the

780 S. Philipp et al.: The nuclear bulge. I

KLF observed in the central parts of the Nuclear Bulge appearsto be an artifact caused by incompleteness of the source counts.

From the observation we constructeddifferenceKLFs whichmake it possible to obtain KLFs for different spatial sectionsalong the line of sight. This allowed us to isolate the mosaicKLF related to the stellar population of the Nuclear Bulge (seeFig. 4b and Table 3) and to confirm quantitatively the results byGlass et al. (1987), Catchpole et al. (1990), Blum et al. (1996a)and Narayanan et al. (1996) that this stellar population has anexcess of bright stars compared to the stellar population of theGalactic Bulge (0.3 <∼ R/kpc<∼ 3) and the interarm region ofthe Galactic Disk (R >∼ 3 kpc).

Blum et al. (1996b), based on stellar NIR spectroscopy, con-clude that most of the bright, cool stars in the Nuclear Bulgeare intermediate mass/age AGB stars. Our results support thesefindings. O9 – O3 stars contribute only∼ 10%, Giants∼ 40%to the integrated K band flux density. Some of the most luminousK band stars could be Wolf-Rayet stars and Supergiants.

In agreement with Genzel et al. (1996) we find a deficiencyof low-mass low-luminosity stars in the central20′′. Fitting Kingprofiles to the observed surface brightnesses we obtain core radiiof ∼ 7′′ and∼ 30′′, respectively, for resolved and unresolvedstars.

We use the integrated radio/IR spectrum to determine dust-and Lyc-photon luminosities for the central30′′ (∼ 1.25 pc). Awarm component (∼ 150 K) dominates the dust emission. Theluminosity of the cool stellar component (Teff ∼ 4 000 K) is notsufficient to provide the heating which appears to be due to∼24 hot (Teff ∼ 25 000 K) and luminous (∼ 4 × 106L) stars,which also are responsible for the ionization of the gas in theCentral Cavity.

Acknowledgements.The data reductions and analyses were carriedout on workstations provided by theAlfried Krupp von Bohlen undHalbach Stiftungthrough a joint grant to the Max-Planck-Institut furRadioastronomie and the Institut fur Theoretische Astrophysik. Thissupport is greatfully acknowledged. We thank the director of the Max-Planck-Institut fur Astronomie for the generous allocation of observingtime at the ESO-MPG telescope. We benefitted much from discussionswith P.L. Biermann, A. Eckart, M. McCaughrean, I.S. Glass and J.Najarro.

Appendix: NIR Observing and data processing techniques

We are in the process of mapping the inner part of the Nu-clear Bulge in the K, H and J bands with the IRAC2B ca-mera in the ESO/MPG 2.2m-telescope. IRAC2B uses a NIC-MOS3 256×256 pixel detector array. We use the pixel scale of0.′′278; the field-of-view covered by a single exposure is thus71.′′17 × 71.′′17.

Appendix A: observing strategy

All data presented in this paper were obtained in June 1996.The “sky” reference (OFF position) was chosen in the direc-tion of a local Dark Cloud which is offset from Sgr A* by∆α = −713′′, ∆δ = 400′′ corresponding to a projected

distance ofR ∼ 33.6 pc from Sgr A* (see Table 2). I.S.Glass (1987) estimates for this cloud a visual extinction ofAV > 60 mag which means that H and K band emission fromall stars located behind this Dark Cloud will be blocked. Starslocated between Dark Cloud and Sun would appear as negativesources in the mosaic and therefore were readded to the mosaic(see Sect. 4.1).

We observed in sequences of 12 exposures, with each se-quence taking about 10–12 minutes. An observing sequencefor the production of four different individual mosaic imagesconsists of: central image (15 s integration time) – Dark Cloud(30 s) –2 × 2 mosaic images (60 s) – Dark Cloud (30 s) –2 × 2mosaic images (60 s) – Dark Cloud (30 s). Although the usageof a fixed “sky” position is quite time-consuming, because thetelescope slewing-time is longer than the exposure-time, sucha procedure is necessary to relate the intensity scale within themosaic to the same relative zero-level. The central image is usedas calibrator to eliminate atmospheric absorption.

No straight-forward measurements of the continuum dueto unresolved stars are possible. Hence, all integrated surfacebrightnesses should be considered as (in most cases rather re-liable) lower limits (see Sect. 4.3 where we estimate an upperlimit of ∼ 0.05 Jy for the integrated continuum in the directionof the Dark Cloud).

Appendix B: data processing

The mosaic presented here was analyzed with the reduction pro-gram MOPSI9 developed by R. Zylka. The regridding algorithmuses a general 3-dimensional rotation and is based on a methoddeveloped by C.G.T. Haslam for the NOD2 software package.

B.1. Coordinate calculation and image alignment

Datasets obtained with radio- and (sub)mm-telescopes usuallydo not need any coordinate-corrections because the pointing-accuracy of these telescopes is clearly better than the angularresolution (at the IRAM 30-m telescope the pointing accuracyis 1–2′′ compared to an angular resolution of∼ 11′′). In the caseof infrared and optical telescopes the effective resolution (lim-ited byseeing) can be better than the pointing-accuracy (e.g. 1′′

compared to 5′′ at the ESO/MPG 2.2m telescope). Hence, accu-rate positioning of the individual images is one of the main tasksin the construction of a mosaic image. We used two differentmethods to adjust the coordinates of overlapping images. In thefirst approach we calculate the correlation coefficient betweenthe two images. In the second approach we use the positionsof individual stars as determined by fitting a Lorentzian distri-bution to the intensity distribution (see below) and solved theoverdetermined set of linear equations for the angular shift be-tween two overlapping images. These two methods give similaraccuracy of∼ 1/10 pixel size. We started from the image on thecentral stellar cluster. All coordinates are calculated as angularoffsets relative to IRS 7. The positional errors at the edges of the

9 MapOn–Off Pointing Skydip Image

S. Philipp et al.: The nuclear bulge. I 781

current mosaic might thus reach1′′. The mosaic shown here inFig. 1a consist of less than 500 images. The final H band mosaiccontains∼1500 images and thus is roughly 3 times larger. Thispart of the data reduction is the most computing-time expensiveprocess.

B.2. Calibration

The mosaicing was performed under varying atmospheric con-ditions. We did not use point sources within the central cluster toavoid seeing effects. Rather, we used the integral over all stars inthe overlapping region of all central images (about60′′ × 55′′)were used as a substandard. The time variation of the flux inthis overlapping region is due to different atmospheric extinc-tion and in elevation which were corrected for. During verystable atmospheric conditions we derive from the variation ofthe flux density with the elevation an atmospheric K band zenithextinctionτK = 0.07.

This calibration procedure using the central stellar clusteras subcalibrator allowed us to achieve a relative calibration ofthe surface brightness within the mosaic of∼ 15% – almostindependent of weather conditions. In addition to the variableextinction of the atmosphere, its variable emission also causesproblems. Because the slewing of the telescope between thesource and the sky-positions takes more than 1 minute we usethe time-weighted average of two sky-exposures to subtract thesky emission. This minimizes the effects of variable atmosphericemission. The remaining much smaller intensity steps are auto-matically corrected, during construction of the mosaic from thecenter to the outer regions.

Appendix C: source decomposition

To separate sources from the unresolved background we fittedLorentzian distributions to the sources after having subtracteda background from the mosaic, which was determined in areasaway from bright stars. The Lorentzian distributions which wefitted are generalizations of the ones given by Diego (1985). TheIntensity I at a point (x,y) is given by:

I = b + h(1 + d

p(1+d2)1

)−1(C1)

where

d1 =

√(x

rx

)2

+(

y

ry

)2

+(

xy

rθ

)(C2)

and

d2 =

√(x

px

)2

+(

y

py

)2

+(

xy

rθ

)(C3)

and

rθ =(

−2(

1s2

x

− 1s2

y

)sin θ cos θ

)−1

(C4)

Fig. C1a–c. Comparison between the fitting of Gaussian andLorentzian distributions.a A K band image showing two stronger anda few weaker stars well above the detection limit of∼ 100 µJy.b Theresidual image after subtraction of Lorentzian fits to the stars.c Theresidual image after subtraction of Gaussian fits to the stars.

while sx andsy are defined through

rx =(

cos θ2

s2x

+sin θ2

s2y

)− 12

ry =(

sin θ2

s2x

+cos θ2

s2y

)− 12

b is the pedestal and h the maximum height of the distribution,rx andry refer to major and minor axis of the ellipse andrθ islinked to the position angleθ of the ellipse. The values ofpx andpy determine the width of the peak area, which are modified bythe exponent power p. For a circular sourcerx = ry px = py

andrθ = 0. The result of fits using Lorentzian and Gaussiandistributions, respectively, is shown in Fig. C1. Obviously, theLorentzian distribution fit the seeing-broadened point-spread-function of the stars much better.

Appendix D: spectral types and K band flux densities

To estimate the K band flux densities of stars of different spectraltypes and luminosity classes we use the stellar parameters givenin Lang (1992) with Eq(5.4) in MDZ96 valid forR0 = 8.5 kpcand calculate the flux densitySν,∗ = Bν(Teff )Ω∗ of a singlestar of effective temperatureTeff andΩ∗ = πR2

∗ with R∗ thestellar radius. This flux density is given forλ2.2 µm:

SK,∗Jy

= 1.26 × 10−8(

R∗R

)2 (Teff

K

)x

ex − 1(D1)

782 S. Philipp et al.: The nuclear bulge. I

Fig. D1. Reddened flux densities for stars of the luminosity classesMS, Giants and Supergiants with different spectral types as well as fordifferent types of Wolf-Rayet stars. Indicated as light dashed line is theflux density corresponding to our approximate completeness limit andas heavy dashed line the flux density corresponding to our detectionlimit.

withx = 6.55×103 K/Teff . The flux densities shown in Fig. D1have been reddened for a K band extinction ofAK/AV = 0.122(Mathis et al., 1983).

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