The distribution of stars around the Milky Way's central black hole II: Diffuse light from sub-giants and dwarfs

5.3 MB·

by  R. Schödel

Astronomy&Astrophysicsmanuscriptno.GC_diffuse (cid:13)cESO2017
January17,2017
The distribution of stars around the Milky Way’s central black hole:
II. Diffuse light from sub-giants and dwarfs
R.Schödel1,E.Gallego-Cano1,H.Dong1,F.Nogueras-Lara1,A.T.Gallego-Calvente1,P.Amaro-Seoane2,andH.
Baumgardt3
1 InstitutodeAstrofísicadeAndalucía(CSIC),GlorietadelaAstronomías/n,18008Granada,Spaine-mail:[email protected]
2 InstitutdeCiènciesdel’Espai(CSIC-IEEC)atCampusUAB,CarrerdeCanMagranss/n08193Barcelona,Spain
InstituteofAppliedMathematics,AcademyofMathematicsandSystemsScience,ChineseAcademyofSciences,Beijing100190,
China
KavliInstituteforAstronomyandAstrophysics,Beijing100871,China
7
ZentrumfürAstronomieundAstrophysik,TUBerlin,Hardenbergstraße36,10623Berlin,Germany
1
3 SchoolofMathematicsandPhysics,UniversityofQueenslandSt.Lucia,QLD4068,Australia
0
2
Received;accepted

n
a
ABSTRACT
J

3 Context. This is the second of three papers that search for the predicted stellar cusp around the Milky Way’s central black hole,
1 SagittariusA*,withnewdataandmethods.
Aims.WeaimtoinferthedistributionofthefainteststellarpopulationcurrentlyaccessiblethroughobservationsaroundSagittariusA*.

] Methods. We use adaptive optics assisted high angular resolution images obtained with the NACO instrument at the ESO VLT.
A
ThroughoptimisedPSFfittingweremovethelightfromalldetectedstarsaboveagivenmagnitudelimit.Subsequentlyweanalyse
G theremaining,diffuselightdensity.Systematicuncertaintiesareconstrainedbytheuseofdatafromdifferentobservingepochsand
obtainedwithdifferentfilters.Weshowthatitisnecessarytocorrectforthelineemissionfromionisedgas,whichwouldotherwise
.
h lead to a systematically biased light density profile. We use a Paschen α map obtained with the Hubble Space Telescope for this
p purpose.
- Results.TheazimuthallyaveragedsurfacelightdensityprofilewithinaprojecteddistanceofR(cid:46)0.5pcfromSagittariusA*canbe
o describedconsistentlybyasinglepowerlawwithanexponentofΓ = 0.28±0.03,similartowhathasbeenfoundforthesurface
r
t numberdensityoffaintstarsinPaperI.
as Conclusions.Theanalyseddiffuselightarisesfromsub-giantandmain-sequencestarswithKS ≈19−20withmassesof1−2M(cid:12).
Thesestarscanbeoldenoughtobedynamicallyrelaxed.Theobservedpower-lawprofileanditsslopeareconsistentwiththeexistence
[
ofarelaxedstellarcusparoundtheMilkyWay’scentralblackhole.WefindthataNukerlawprovidesanadequatedescriptionof
1 thenuclearcluster’sintrinsicshape(assumingsphericalsymmetry).The3Dpower-lawslopenearSgrA*isγ = 1.23±0.05.The
v stellardensitydecreasesmoresteeplybeyondabreakradiusofabout3pc,whichcorrespondsroughlytotheradiusofinfluenceof
7 themassiveblackhole.Atadistanceof0.01pcfromtheblackhole,weestimateastellarmassdensityof2.3±0.3×107M(cid:12)pc−3and
1 atotalenclosedstellarmassof180±20 M(cid:12).Theseestimatesassumeaconstantmass-to-lightratioanddonottakestellarremnants
8 intoaccount.Thefactthatnocuspisobservedforbright(Ks(cid:46)16)giantstarsatprojecteddistancesofroughly0.1-0.3pcimpliesthat
3 somemechanismhasalteredtheirappearanceordistribution.
0
Keywords. Galaxy:center–Galaxy:kinematicsanddynamics–Galaxy:nucleus
.
1
0
7
1. Introduction star cluster around the massive black hole at the centre of the
1
MilkyWay(e.g.,Genzeletal.2010;Schödeletal.2014b).Un-
:
vTheexistenceofpower-lawstellardensitycuspsindynamically fortunately,theobservationshavebeenlimitedtotheredclump
irelaxed clusters around massive black holes (BHs) is a funda- (RC)starsandbrightergiantssofar.Thedensityprofileofthese
X
mental prediction of theoretical stellar dynamics. The problem starsappearstosuggesttheabsenceofastellarcusp(Buchholz
rof a stationary stellar density profile around a massive, star- etal.2009;Doetal.2009;Bartkoetal.2010).However,these
a
accretingBHwasfirstanalysedbyPeebles(1972),followedby stars only represent a small fraction of the old stars in the nu-
Frank & Rees (1976), Lightman & Shapiro (1977), and Bah- clearcluster.Ithasbeenproposedthatstellarcollisionsremoved
call&Wolf(1976).EightyearsbeforePeebles(1972),Gurevich their envelopes in the innermost, densest regions of the cusp,
(1964)hadobtainedananalogoussolutionforthedistributionof which would render them invisible (see, e.g., Alexander 1999;
electronsinthevicinityofapositivelychargedCoulombcentre. Daleetal.2009),butthiscannotfullyexplaintheobservations.
Since then, many authors have worked on this problem with a Another possibility, that has been recently put forward, is that
broadvarietyofmethodsandhavecometosimilarconclusions theyinteractedinthepastwith(a)fragmentinggaseousdisc(s),
(see, e.g., Amaro-Seoane et al. 2004; Alexander 2005; Merritt which is an efficient way to get rid of their envelopes (Amaro-
2006,andreferencestherein). Seoane&Chen2014).TheanalyticalsolutionofAmaro-Seoane
The best-suited (and currently probably also only) environ- &Chen(2014)wasconfirmedbyKieffer&Bogdanovic´ (2016)
mentwherewecantestthepresenceofsuchacuspisthenuclear withelaboratenumericalsimulations.
Articlenumber,page1of13
A&Aproofs:manuscriptno.GC_diffuse
Thefactthatwearedealingwithafundamentalproblemof 2.2. Sourcesubtraction
stellar dynamics, the ambiguity of the observational data and
Subtraction of detected stars is a critical step when estimating
their interpretation, as well as the implications of stellar cusps
the diffuse light. A particular challenge in AO observations is
forthefrequencyofExtreme-MassRatioInspirals(EMRIs,see
the presence of the large seeing halo (FWHM on the order 1”)
Amaro-Seoane et al. 2007 and the review Amaro-Seoane 2012
around the near-diffraction limited core of the PSFs. The dy-
andreferencestherein),andthusonthedetectionrateofsources
namic range of the detected stars comprises >10 magnitudes,
of gravitational radiation (Hopman & Alexander 2005), have
from the brightest star, GCIRS7 with K ≈ 7 to the faintest
urgedustorevisitthistopic.Inparticular,theL3missionofthe S
detectablestarswithKs ≈ 19(seePaperI).Manyofthebright-
EuropeanSpaceAgencyhasbeenapprovedtobedevotedtolow
est stars (K = 9−11) are young, massive stars concentrated
frequency gravitational wave astronomy, with EMRIs being an S
intheIRS16,IRS1,IRS33,orIRS13complexesinthecentral
importantclassofpotentialsources.Themissionimplementing
0.5pc (e.g., Genzel et al. 2003; Lu et al. 2005, 2009; Paumard
thissciencewillfollowtheLaserInterferometerSpaceAntenna
etal.2006).Theymustbecarefullysubtractedtoavoidabiasin
(LISA)missionconcept(Amaro-Seoaneetal.2012,2013)ora
thesurfacelightdensity.Inaddition,thePSFchangesacrossthe
similarone,liketheChineseTaijiconcept(Gongetal.2015)..
field due to anisoplanatic effects, and the variable source den-
This is the second one of a series of papers addressing the
sityandextinctionmeanthatthefaintwingsofthePSFscannot
distribution of stars around SagittariusA* (SgrA*). They are
beestimatedwithsimilarsignal-to-noiseinallpartsofthefield
closely related and use the same data, but focus on different
because there is not a homogeneous density of bright, isolated
methodsandstellarpopulations.Inthisworkweusethediffuse
stars.
light density, while in our first paper (Gallego et al., from now
As explained in Paper I, we extracted the PSFs on overlap-
on referred to as Paper I), we analyse the star counts from the
ping sub-fields, smaller than the isoplanatic angle. In each of
brighter,resolvedstellarpopulation.Wealsorefertheinterested
these sub-fields we used about 10 isolated stars – the brightest
readertothemoredetailedintroductionofPaperIformorede-
onespossible–toestimatethePSFcore.WethenfittedthePSF
tailsaboutthehistoryandthestate-of-the-artoftheinvestigation
halo determined from the brightest star in the field, GCIRS7,
ofthestellarcuspatthecentreoftheMilkyWay.
to the cores. Schödel et al. (2010) have shown for NACO AO
Our primary goal is to find the predicted stellar cusp of the
GC data that the variation of the PSF halo is rather negligible,
nuclear stellar cluster (NSC) around SgrA*. To reach this aim,
whichmeansthatwiththechosenapproachwecanreachapho-
we push the boundaries of observational evidence by reaching
tometricaccuracyofafewpercentacrosstheentirefield.Subse-
toward fainter magnitudes and thus accessing a more represen-
quently,pointsourcesaredetectedandsubtracted.Sincethede-
tativesampleofstarsinthenucelarcluster.InPaperI,weshow
tectionofoccasionalspurioussourcesisnosourceofconcernfor
howweusestackingandimprovedanalysismethodstoprovide
thiswork,wechoseamoreaggressiveapproachthaninPaperI,
acceptably complete star counts for stars about one magitude setting the StarFinder parameters min_correlation = 0.70 and
fainter than what has been done up to now. These stars, of ob- deblend =1forallimages(exceptifstatedexplicitlyotherwise).
servedmagnitudesK ≈ 18atthedistanceandextinctionofthe
s Wenotethatevenwiththesesettingsthedetectioncompleteness
GalacticCentre(GC),areprobablymostlysub-giantstars,with fallsbelow50%forsourcesfainterthanaboutK = 18.0inthe
S
massesof1−2M .Theycanthereforebeoldenoughtobedy-
(cid:12) centralmostarcseconds.
namicallyrelaxed.Indeed,theirdistributioninsideofaprojected
Inordertohaveanextinctionmapthatcoverseventhelarge
distance of R (cid:46) 0.5pc can be approximated well by a single
area of the wide field observations from May 2011, we created
power-law with a slope of Γ ≈ 0.36. This finding is consistent
anextinctionmapfromHAWK-IHandK speckleholography-
withtheexistenceofastellarcuspofoldstarsaroundSgrA*,as S
reducedFASTPHOTobservationsofthecentralsquarearcmin-
wediscussinPaperI.Here,wefocusonthediffusestellarlight
utes(Nogueras-Laraetal.,inprep.).Weusedtheextinctionlaw
density around SgrA*, which provides us with information on
ofSchödeletal.(2010)(A ∝λ−2.2),assumedaconstantintrin-
evenfainterstars. siccolourof(H−K ) =0λ.1forallthestars,andusedthemean
S 0
ofthe20neareststarsforeachpixel.Thisresultsinanextinction
mapwithavariableangularresolutionofroughly2”.Theresults
presentedinthispaperarenotsensitiveinanysignificantwayon
2. Datareductionandanalysis
the variation in these assumptions within their uncertainties. In
particular, changing the exponent of the extinction law to other
2.1. Basicreduction
plausiblevalues(e.g.,2.0,seeNishiyamaetal.2009)willhave
We use the same H and K -band data obtained with the S27 an impact on any of the parameters of interest that is a factor
S
camera of NACO/VLT that are used in PaperI and, addition- ofafewsmallerthanothersourcesofuncertaintiesthatwillbe
ally, K -band NACO/VLT S13 camera data from 4 May/12 discussedhere.
S
June/13August2011,4May/9August/12September2012,and We demonstrate the result of this strategy in Fig.1. There,
29 March/14 May 2013. We follow the same data reduction weshowthemosaicofthedeepKS image(seePaper I),andthe
steps.TheS13imageswerestackedtoprovideadeepimage,as samefieldaftersubtractionwithasingle,constantPSF,andafter
donewiththeS27imagesinpaperI.Inaddition,weusethecal- subtractionwithavariablePSF,composedofalocalcoreplusa
ibratedHST/NICMOS3imageoftheemissionfromionisedgas global halo. As can be seen, using a single, constant PSF leads
at1.87µm,thatwaspresentedbyDongetal.(2011).Finally,we to variable artefacts associated with the stellar sources across
alsomakeuseofNACO/VLTS27Brackett-γ(Brγ)narrowband the field (see also Schödel 2010). Also, when the wings of the
(NB) observations, obtained on 5 August 2009, with a detector PSF are not determined with high signal-to-noise, then the dif-
integrationtime(DIT)of15s,3averagedreadoutsperexposure fuseemissionisdominatedbyfluxfromtheseeinghalosaround
(NDIT = 3), and 45 dither positions (N = 45). Data reduction brightstars.
was standard, as described in PaperI, including rebinning to a With the variable core plus halo PSF (determined from the
finerpixelscalebyafactorof2. brighteststarIRS7,rightpanel),theresidualsaroundbrightstars
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Schödeletal.:DistributionofstarsaroundSgrA*
Northern
IRS 7
Arm
mini−cavity
Bar
Fig. 1. Source subtraction. Left: Deep K -band mosaic (see PaperI). Middle: Deep K -band mosaic with all detected stars subtracted, using
S S
asingle,constantPSF,fortheentirefield.Right:Deep K -bandmosaicwithalldetectedstarssubtracted,usingalocallyextractedPSFkernel
S
mergedwithaconstanthalo,thatisestimatedfromIRS7.Typicalfeaturesofthemini-spiralofionisedgasareindicated.Logarithmiccolourscale
inallimages,withthesamescaleusedinthemiddleandrightpanels.Northisupandeastistotheleft.
IRS 10W IRS 7
IRS 5
IRS 13E
IRS 1W
IRS 21
Fig.2. Left:HSTNIC3point-source-subtractedPa-αimageoftheGC.Middle:VLTNACOpoint-source-subtractedBr-γ image.Right:VLT
NACOpoint-source-subtractedK continuumimage.Someprominentnon-line-emissionsources(seetext)arelabeled.
S
arestronglysuppressedandanyremainingresidualsarelargely withinabout0.5pc(∼12”foraGCdistanceof8kpc)ofSgrA*,
constant across the field, as can be seen in the right panel of even in broad band images. We therefore have to correct for it
Fig.1. These remaining residuals are typical for PSF subtrac- before we will be able to estimate the diffuse emission arising
tion with an empirical PSF when the PSF is not fully constant fromunresolvedstellarsources.Atthewavelengthsconsidered,
across the field: Since several stars have to be used to derive a theemissionarisesmostlyfromhydrogenandheliumlines(e.g.,
medianPSF,theirslightlydifferentPSFswillresultinaslightly HI at 2.17, 1.64 or 1.74µm, HeI at 1.70, 2.06, or 2.11µm). In
too broad median PSF. This leads to the typical and inevitable Fig.2weshowthemini-spiralasseeninthePaschenαlinewith
artefactsintheformofcore-excesseswithsurroundingnegativ- NIC3/HSTandintheBrackettγlineaswellasinK continuum
S
ities that can be seen around bright stars. Nevertheless, as can withNACO/VLT,respectively.ThePaαimageisfromthesur-
beseen,theresidualsaroundthebrightstarshavebeenstrongly veybyWangetal.(2010)andDongetal.(2011).
suppressed with our method. The only exception is GCIRS7,
SincewewillusetheHSTimageasareferenceforgasemis-
which is extremely bright (a few magnitudes brighter than any
sion,wealignedallourimagesviaafirstorderpolynomialtrans-
othersourceinthefield).Thefilamentarystructureoftheionised
formwiththeHSTimage.Thepositionsofdetectedstarswere
gasintheso-calledmini-spiral(seeGenzeletal.2010,andrefer-
usedtocalculatethetransformationparameterswithIDLPOLY-
encestherein)becomesapparent,withfeaturessuchasthenorth-
WARPandtheimageswerethenalignedusingIDLPOLY_2D.
ernarm,thebar,orthemini-cavityclearlyvisible.
The pixel scale of the resulting images is set to the one of the
HSTimage(0.101”perpixel).
2.3. Subtractionofionisedgasemission As can be seen in Fig2, the Paα image traces the gas
emission very clearly (with the exception of a few Paα excess
AswecanseeintherightpanelsofFigs.1and2,diffuseemis- sources, see Dong et al. 2012) and the K and Brγ images
S
sionfromionisedgasintheso-calledmini-spiral(see.,e.g.,Gen- of the diffuse emission trace the same structures of the mini-
zel et al. 2010) contributes significantly to the diffuse emission spiral. Some differences are given by residuals around bright
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A&Aproofs:manuscriptno.GC_diffuse
stars, by some residual emission associated with the brightest foundthattheyhad anegligibleinfluenceonthebest-fit factor.
star, GCIRS7, by hot dust emission around the probable bow- Wethensubtractedtheextinction-correctedPaαimagefromthe
shocksourcesIRS21,IRS10W,IRS5,andIRS1W,andbyen- extinction-correcteddiffuseemission.
hanced emission in and around the IRS13E complex, probably We measured the mean diffuse emission in annuli around
fromahighergastemperature.Wemarksomeofthesesources SgrA*, using the IDL ASTROLIB routine ROBUST_MEAN
and areas in Fig.2 and will mask them when deriving scaling and rejecting > 3σ outliers. The corresponding uncertainties
factors for gas subtraction and when computing the brightness weretakenastheuncertaintiesofthemeans.TheresultingSFB
ofdiffusestellarlightinthefollowingsections. profiles,bothrawandaftersubtractionofthescaledPa-αemis-
Figure3showsthepointsource-subtractedBrγandK con- sion, are shown in Fig.5. The error bars are probably under-
S
tinuum images after subtraction of the scaled Paα image. The estimatedbecausetherearesystematiceffectspresentinourcor-
scale factor was assumed constant and estimated by eye. All rected images that are very difficult to assess or correct quan-
images were corrected for differential extinction. We also de- titatively, e.g.: The assumption of a constant emission ratio of
termined the scaling factor in a numerical way by producing Paschen-αtolineemissioninK ,uncertaintiesoftheextinction
S
an unweighted best χ2 fit of the scaled Paα image plus an az- map and assumed extinction law, or systematics related to the
imuthallysymmetricsimplepower-lawdiffuselightdensitycen- subtractionofverybrightstars.
tredonSgrA*totheK image.Thefittingregionwaslimitedto Wefittedasimplebrokenpower-lawtothedata:
S
R < 0.5pcwithinSgrA*toavoidcomplicationsfromachange Σ(R)=n ∗(R/R )−Γin,out, (1)
0 0
of slope in the power-law at larger distances (see below). The
where Σ(R) is the surface flux density at a projected distance
resulting best-fit factor was identical - within the uncertainties
R, n is the normalisation of the SFB, R is the break radius,
- to our by-eye estimate. As can be seen in Fig.3, most of the 0 0
emission from the ionised gas in the mini-spiral can be effec- and Γin,out are the power-law indices inside and outside of R0.
Sincewedonotknowthecorrectstatisticsoftheerrorbars,we
tivelyremovedbythissimpleprocedure.Fromourby-eyefitwe
interpretethereducedχ2 valuesasorientative,toinferwhether
estimated an uncertainty of 10% for the best scale factor. This red
uncertainty has a negligible effect on the parameters we are in- afitisbetterorworse,andthenrescaletheerrorsofthebest-fit
parameters to a reduced χ2 = 1. Ìn the following, we explore
terestedin,inparticulartheslopeofthepower-lawsurfaceden-
the influence of some of the possible systematic effects on the
sity. For all images and wavelengths used in the following we
results.
applied the numerical procedure to estimate the scaling factor
forthesubtractionofthediffusegasemission. First, we note that a simple power-law provides a clearly
worsefit(χ2 ≈ 26)tothecorrecteddatathanabrokenpower-
An alternative way of subtracting the ionised gas emission red
maybebyusingtheintrinsiclineratioof Brγ/Paα.However, lawfit(χ2red ≈7).Also,wenotethatthebrokenpower-lawfitto
this is not practical in our case because most of our data are theuncorrecteddata,withaχ2 ≈17,isworsethantheonefor
red
broad-bandobservationsand includeadditionallines,e.g. from thecorrecteddata,withaχ2 ≈ 7.Thebestfitswerecomputed
red
the 2.058µm HeI line in the K -band. Also, in the case of the withtheIDLMPFITpackage(Markwardt2009).Wefoundthat
S
Brγimage,noaccuratecalibrationwaspossiblebecausenozero theformaluncertaintiesofthefits,asprovidedbyMPFIT,were
pointobservationsweretakenatthetimeoftheobservationand significantly smaller than the uncertainties due to systematics
theskyconditionswerenotphotometric. (seebelow),evenafterrescalingtoχ2 =1.Wefoundnosignif-
red
icantdifferencesbetweenweightedandunweightedfits(inthis
caseandallothersinthiswork).
3. ThesurfacedensityoffaintstarsintheGC Ourexperimentswiththedatasuggestthatthestrongestsys-
tematic effect can arise from an unknown additive offset of the
In this section we explore the surface brightness (SFB) profile diffuseemission.Althoughtheimagesweresky-subtracted–the
of the diffuse stellar light in observations taken with different
skybackgroundinthecorrespondingfilterswasmeasuredona
cameras and filters, as well as at different epochs. We will also darkcloudatafewarcminutesoffset–thereissomeuncertainty
performvariouschecksonpotentialsourcesofsystematicbias.
relatedtothisprocedure:Therewasonlyoneskymeasurement
Inthefollowingwewillrefertoapoint-sourcesubtractedimage
donefortheapproximatelyonehour-longobservations.Hence,
thathasbeencorrectedforextinctionandforionisedgasemis-
the sky background may have varied. Also, we are interested
sionasacorrectedimage.
in the SFB profile of the nuclear star cluster, but there may be
diffuse flux contributions from other structures, such as the nu-
clear stellar disk (see Launhardt et al. 2002). Fortunately, there
3.1. WidefieldK continuum
S
are several dark clouds contained in the field-of-view (FOV).
First, we examine a wide-field mosaic that was obtained with Those clouds belong most probably to dense gas and dust in
NACO/VLT S27 in May 2011. In total, 4 × 4 pointings were the so-called circumnuclear ring (CNR) in front of the nucelar
observed in K , centred approximately on SgrA*. The images star cluster (see, e.g., Ekers et al. 1983; Lo & Claussen 1983;
S
are relatively shallow, with a total on-target exposure time of Christopher et al. 2005) and can thus serve to estimate the flux
only72sperpointing(4exposureswithDIT =2s,NDIT =9), offset. We measured the median flux density on four positions
butofexcellentandhomogeneousquality. within these dark clouds (see Fig.3) and thus obtained an esti-
Figure4showsthepoint-sourcesubtractedwide-fieldimage mate for the mean and standard deviation of the constant dif-
before and after correction for extinction and gas emission. As fuse flux offset. The surface flux density measurements were
mentioned above, by assuming that the diffuse light from the thenrepeatedaftersubtractingthemeanoffsetandthetwoval-
stars follows a power law inside of R = 0.5pc and that a con- ues resulting from adding or subtracting its standard deviation.
stantscalingfactorisadequatetoremovetheemissionfromthe Theextinctioncorrectionwasperformedafterthesubtractionof
ionised gas, we can numerically fit both the power-law index this potential background bias. We thus could estimate the un-
and the scaling factor. We varied the fitting region and the po- certaintyofthefitparameters.Weobtained:n =20.8±1.2mJy,
0
tential additive offset of the diffuse emission (see below) and R =0.56±0.01pc,Γ =0.29±0.01,andΓ =0.66±0.08.
0 in out
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Schödeletal.:DistributionofstarsaroundSgrA*
Fig. 3. Left: Point-source-subtracted Br-γ image minus scaled Pa-α image. Right:Point-source-subtracted K continuum image minus scaled
S
Pa−αimage.
Fig.4. Left:Point-source-subtractedK widefieldcontinuumimage.Right:Imagecorrectedforextinctionandionisedgasemission.Contam-
S
inatedregions(residuafrombrightstars,hotdust,andIRS13)anddarkclouds,thatareexcludedfrommeasuringthesurfacelightdensity,are
indicatedbygreenpolygons.Thebluecirclesindicateregionsthatwereusedtoestimatetheoffsetofthediffusefluxdensity.
It is also important to assess the influence of the extinction are somewhat different, but the power-law indices agree within
correction on our results. We therefore repeated the procedure their1σuncertainties:n =26.7±2.1mJy,R =0.44±0.03pc,
0 0
withoutcorrectionfordifferentialextinction,i.e.assumingaspa- Γ =0.29±0.03,andΓ =0.76±0.08.
in out
tiallyconstantextinctionofA =3.0,equivalenttothemedian When studying stellar number densities, as in Paper I, as-
KS
over the field. The corresponding SFB profile is shown in the sessingandcorrectingincompletenessduetosensitivityand,in
middle panel of Fig.5. It is similar to the one with differential particular,crowdingcanhavesignificanteffectsontheresults.In
extinctioncorrection,buttherearesomesmalldifferences,such ourstudyofthediffuselightdensity,biasrelatedtocompleteness
as a flattening at the largest distances. The best-fit parameters could occur as well. The contribution of the occasional bright
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A&Aproofs:manuscriptno.GC_diffuse
All subtracted
No differential Subtracted to Ks = 18
extinction correction Subtracted to Ks = 16
Fig.5. Left:MeandiffuseSFBprofilesintheK wide-fieldimagebefore(blue)andafter(red)subtractionofthescaledPaαemission(green).
S
Thestraightdashedlinesarebrokenpower-lawfitstothedata.Thetwoorangedashedlinesshowthebestbrokenpower-lawfitsaftersubtracting
oraddingastandarddeviationofthepotentialoffsetoftheadditivediffusefluxdensity.Middle:Asleftpanel,butassumingaconstantextinction
fortheentirefield.Right:Correctedsurfacebrightnessfordifferentbrightnesslimitsonsubtractedstars.Subtractionofalldetectedstarsinblack,
subtractionofK <16inblue,andsubtractionofK <18inred.
S S
star on the mean surface brightness at a given R will be neg-
ligible due to our use of the ROBUST_MEAN procedure, that
rejectsoutliersandproducesvaluesverysimilartothemedian.
However,insmall,crowdedareas,suchasthecentralarcseconds
near SgrA*, subtraction of faint stars may be significantly less
completesothat,onaveragebrighterstarsremainintheimage
thaninlesscrowdedareas,whichmaycreateasystematiceffect.
To examine this effect, in the right panel of Fig.5 we plot
the corrected K SFB profile for three cases. In each case, all
S
the stars were subtracted to a different brightness limit: All de-
tected stars, all stars K < 18, or all stars K < 16. The 3σ
S S
detection limit for stars in the K wide field image is about
S
K ≈ 19 (albeit at low completeness). As one can see, apart
S
from an overall ∼10−20% shift between the measured SFBs,
theprofileslookverysimilar.Thebestfitparameters-apartfrom
the SFB normalisation, n , - show only a small range of varia-
0
tion and agree within 1 − 2σ of their formal fit uncertainties:
R =0.54−0.56pc,Γ =0.25−0.29,andΓ =0.62−0.66.
0 in out
3.2. Brγ
ThesurfacebrightnessintheBrγnarrowbandfilterimageisan
interestingtestcasebecauseheretheemissionfromtheionised
gaswillprovidearelativelylargefractionoftheoveralldiffuse
Fig. 6. Mean Brackett-γ diffuse SFB inannuli around SgrA* before
emission.Again,wescaledthePaαemissionandsubtractedit,
(blue)andafter(red)subtractionofthescaledPa-αemission.
afterapplyingtheextinctioncorrectionatthetwobands.Wefit-
ted a simpe power-law to the SFB at R ≤ 0.5pc. The resulting
raw and corrected SFB profiles are shown in Fig.6. The bump negativedeviationsofthecorrectedSFBfromapowerlawatR≈
from the ionised gas at 1” (cid:46) R (cid:46) 8” in the SFB profile disap- 0.1pc is due to imperfect subtraction of the high concentration
pearscleanlyaftersubtractionofthescaledPaαimage.Asimple ofverybrightstarsinthisregion.Mostoftheplotsshowninthis
power-lawprovidesaverygoodfit,withthebest-fitpower-law workshowsystematiceffectsinthisregion.
exponentofΓ =0.25.Wedonotfitanybrokenpower-lawbe-
in
causeoftherestrictedFOVwhichwillprovideapoorconstraint
3.4. H-bandimage
onthepower-lawatlargeR.
Analysing the diffuse flux in an H band image represents,
amongothers,atestinaregime,wheredifferentialextinctionis
3.3. DeepK -bandimage
S stronger, where the sky background behaves in a different way,
Here, we analyse the deep K broad band image that we use andwheretheratiooflineemissionrelativetoPa-αisdifferent.
S
for measuring the stellar number surface density in Paper I. A Hence, the H-band can be very helpful in constraining system-
simplepower-lawfittothecorrectedSFBatR (cid:46) 0.5pcresults aticeffects.Asimplepower-lawfittothecorrectedSFBprofile
inapower-lawindexofΓ = 0.27,seeFig.7.Thepositiveand at R (cid:46) 0.5pc results in a power-law index of Γ = 0.32, see
in in
Articlenumber,page6of13
Schödeletal.:DistributionofstarsaroundSgrA*
Fig.7. Plotof K diffuseSFBindeepimage(PaperI)before(blue) Fig. 8. Plot of H surface brightness in deep image (Paper I) before
S
andafter(red)subtractionofthescaledPa-αemission. (blue)andafter(red)subtractionofthescaledPa-αemission.
Fig.8.ThereappearstobeanexcessatprojectedradiiR<0.5”.
This is the most crowded region, immediately around SgrA*.
Probably,thelowerStrehlratioatHmayhaveledtoalesscom-
pletesourcesubtractionthanatK .Sincethisexcessisnotcon-
s
sistentlyobservedinallthefiltersexaminedhere,wethinkthatit
isaspurious,systematicerror.Itdoesnotalterourconclusions.
Alternatively, instead of an excess at R < 0.5 we may be deal-
ingwithanover-subtractionofstellarfluxduetoourimperfect
PSFsintheregionR ≈ 1”,whichisdominatedbythepresence
ofbrightstars(IRS16NE,IRS16C,IRS16SW).
Fig.9. Left:PlotofK surfacebrightnessindeepimagewithS13cam-
S
erabefore(blue)andafter(red)subtractionofthescaledPa-αemission.
Right:CorrectedK surfacebrightness(equivalenttoredpointsinleft
S
panel)whenlimitingthesubtractionofstarstoK ≤16(blue),K ≤18
3.5. DeepK imagewithS13camera S S
S (red),andK ≤20(black).
S
As a final test, we examine the diffuse light density in a deep, Table1.Best-fitpowerlawindicesforthediffusestellarlightinsideof
R<0.5pc.
multi-epoch K -band image obtained with data from the S13
S
camera of NACO/VLT (see Paper I). Star subtraction through
Data Γ
PSFfittingisparticularlycleaninthiscaseandwedidnothave in
tomasktheareasaroundbrightstarsIRS/,16C,IRS16NW,and KS,widefield 0.29
IRS16SW near SgrA*. As Fig.9 shows, a simple power law Brγ 0.25
withanindexofΓin = 0.25providesasatisfactoryfittothera- KS deepfield 0.27
dialdependencyofthediffuselightdensity. H 0.32
K S13 0.25
S
Wetestedagainthesystematicsofsubtractingthestarsdown
todifferentlimitingmagnitudes(K =16,18,20).Thepower-
s,lim
4. Discussion
lawindexchangesbetween0.25and0.29andtheplotlookssim-
ilarinallcasesascanbeseenintherightpanelofFig.9.Wesee
4.1. Meanprojectedpower-lawindex
asimilarexcessofdiffusefluxatR (cid:46) 0.5”asinthetheH-band
profile.ComparedtotheNACOS27K datathereappearstobe As the preceding sections have shown, measuring the diffuse,
s
anoffsetoftheSFBtowardbrightervalues.Wecouldnotiden- stellarlightaroundSgrA*isanon-trivialundertakingandsub-
tify the source of this offset, but note that it does not affect our jecttopotentiallysignificantsystematiceffects.Inparticular,we
mainconclusions,inparticulartheexistenceofapower-lawcusp have demonstrated that ionised gas contributes significantly to
anditsindex. themeasureddiffusefluxatprojecteddistancesR<0.5pcfrom
Articlenumber,page7of13
A&Aproofs:manuscriptno.GC_diffuse
Fig.11. Left:K luminosityfunction(KLF)measuredonthedeepK S13NACOimage.Middle:SimplemodelKLFforthecaseofcontinuous
S S
starformation,matchedtothedistanceandmeanextinctionoftheGC.Right:Fluxdensitycontributedbydifferenttypesofstars,i.e.theKLF
multipliedbythefluxdensityofstarsinagivenbin.
and narrow band observations, shorter and longer wavelength
filters.ItissatisfyingtoseethattheresultingSFBprofileiscon-
sistentamongallthedatasets.
All our different measurements of the projected stellar sur-
face brightness can be fit well by the simple model of a single
power-lawatR (cid:46) 0.5pc.Thecorrespondingpower-lawindices
are consistent with each other and also with the power-law in-
dex inferred for the stellar number density of faint stars in this
region,asdeterminedinPaperI.Table1liststheresultingbest-
fit power-law indices for the projected diffuse light in the in-
ner ∼ 0.5pc. From these independent measurements we obtain
a best estimate of Γ = 0.28±0.03. This value agrees, within
in
its uncertainties, with what we observe for the number density
of the stars in the range 16.5 (cid:46) K (cid:46) 18.5 that we present in
S
PaperI. It also agrees with the value of Γ = 0.34±0.04 mea-
sured by Yusef-Zadeh et al. (2012) on NICMOS/HST images
within R ≤ 5”/0.2pc. We conclude that the projected surface
densitydistributionofstarsaroundSgrA*canbedescribedwell
byasinglepowerlawwiththesameexponentfordifferentstellar
populations. The faint stars do not show a flat, core-like distri-
bution as has been observed for the bright (K (cid:46) 15.5) giants
S
in the GC (Buchholz et al. 2009; Do et al. 2009; Bartko et al.
2010). The faint stellar population around SgrA* clearly dis-
playsapower-lawcusp.Givenourmeasurements,assumptions,
Fig.10. MeanSFBprofilesinthecorrectedandcombinedKS S13plus andanalysis,wecanexcludeaflatprojectedcorearoundSgrA*
S27wide-fieldimage.Thestraightdashedlinesarebrokenpower-law
withhighconfidence.
fits to the data. The two orange dashed lines show the best broken
power-law fits after subtracting or adding a standard deviation of the
potentialoffsetoftheadditivediffusefluxdensity.
4.2. OptimisedoverallSFBprofile
Mainlyforillustrativepurposes,weproduceda”best”corrected
SgrA*, even when broad-band filters are used. This will result image by combining the corrected S13 and S27 wide-field im-
inanapparentsteepincreaseofthediffusefluxatR(cid:46)0.4pcand ages. The images were matched via a least-squares minimisa-
thenanalmostflatSFBprofileintheinnermost∼0.2pc.Theex- tionofanadditiveoffsetandamultiplicativescalingfactor.We
actsystematicerrorduetotheionisedgaswilldepend,ofcourse, then measured the SFB profile again as in section3.1, that is
onthefilterused.ItisverystronginBrγ(Fig.6)andweakerin we also estimated the uncertainty from inaccuracies in the sky
KS (Fig.7)andH(Fig.8). backgroundsubtraction.Asimplebrokenpower-lawprovidesa
The subtraction of the flux of both the bright stars and the good fit to the data (see Fig.10). The best-fit parameters are:
ionised gas is prone to systematic errors. Fortunately, these er- n = 16.8±1.3mJy, R = 0.56±0.005pc, Γ = 0.28±0.01,
0 0 in
rorswillchangewiththeobservingconditions,e.g.,seeingand andΓ = 0.60±0.07.Wenotethatthebrokenpower-lawisa
out
adaptive optics correction, camera used, or observing wave- purelyadhocchoice,butdoesnotnecessarilyrepresentthein-
length. For this reason, we have used several completely inde- trinsicstructureofthecluster,whichcanbedescribedwellbya
pendentdatasetsthatwereobtainedatdifferenttimesandwith simple3Dpower-lawwithina3Ddistancer<3pcfromSgrA*,
significantly different setups: Deep and shallow images, broad aswediscussinsection4.4
Articlenumber,page8of13
Schödeletal.:DistributionofstarsaroundSgrA*
4.3. WhatkindofstarscontributetothediffuseSFB? (suchassphericalsymmetry)toprovideanapproximate,general
picture.
The stars that contribute dominantly to the diffuse light in our
point-source subtracted images are fainter than K = 18. Fig-
S
ure11 shows the K luminosity function (KLF) for the deep
S
NACOS13image.TheturnoveratK (cid:38)19iscausedbyincom-
S
pletenessduetocrowdingandsensitivity.ThepeakaroundK ≈
S
15.5arisesfromRedClump(RC)stars.Themiddlepanelshows
asimpletoymodelKLF,basedoncontinuous,constantstarfor-
mation from log(t/yr) = 6.6 to log(t/yr) = 10.13 in steps of
∆(log(t))=0.05,withSolarmetallicity,andassumingaChabrier
lognormal initial mass function (see, http://stev.oapd.inaf.it/cgi-
bin/cmd_2.8and Chabrier2001;Bressanetal.2012;Chenetal.
2014,2015;Tangetal.2014)Wepointoutthatwehavenotmade
anyspecificefforttomatchthemodelKLFtothemeasuredone,
except for applying a scaling factor. Studies of star formation
historyormetallicityarebeyondthescopeofthispaper.
The right panel shows the fraction of the total flux con-
tributed by the stars in the different bins of the model KLF. As
canbeseen,starsintheregimeK =19−20donotdiffersignif-
S
icantlyintheiroverallweight.Starsat K ≈ 21,approximately
S
solar mass MS stars, have a weight that is about 3 to 4 times
lower. We thus expect stars with an apparent K ≈ 19−20 at
S
the GC to dominate our measurements of the diffuse light den-
sity. We expect these stars to be early G or late F type main
sequencestarsorsub-giantstarsofsimilarmass.Theywillhave
masses(cid:46) 1.5M andwillliveforseveralGyrs(seealsoFig.16
(cid:12)
in Schödel et al. 2007). They can thus be old enough to be dy- Fig.12. SFBprofileasshowninFig.refFig:KsS13withabest-fit3D
namicallyrelaxedandserveastracersfortheexistenceofastel- simplepower-lawoverplottedasasolidredline.Thebluelinerepre-
larcusp. sentsaforcedfitwithapower-lawindexofγ=1.5,takingintoaccount
onlydataatR>0.4pc.
InPaperIwediscussandtakeintoaccountthepossiblecon-
tamination of the surface number density of K ≈ 18 stars by
s
Asafirst,illustrativeapproximationtotheproblem,wecan
pre-mainsequence(MS)starsfromthemostrecent,afewMyr
assumeasimplepower-lawfortheintrinsic3Dstructureofthe
oldstarformationeventinthecentralR<0.5pc(see,e.g.,Gen-
innermost parsecs of the cluster. It provides a surprisingly rea-
zel et al. 2010; Lu et al. 2013). Such contamination could, in
principle, also be present in the diffuse light. While we cannot sonablefittothedata,asshownbytheredlineintheleftpanel
of Fig.12. Since we need to project a three-dimensional struc-
ruleoutthispossibilitywithcertainty,wepointoutthatboththe
stellarnumberdensityprofileandtheprofileofthediffusestel- ture onto two dimensions, the result of the fit depends on the
lar light probe different stellar masses and evolutionary stages. boundaries, where we cut off the integration along the line of
Also, the power-law index of the diffuse light density profile is sight.Thebest-fitpower-lawindexisγin =1.28foranouterin-
tegration boundary of 10pc and γ = 1.35 for 20pc. We note
consistent with the one derived for the surface number density in
that, in projection, an intrinsic 3D power-law will not appear
counts of stars in the magnitude bins 16.5 ≤ K ≤ 17.5 and
S
as a straight line on a double-logarithmic plot, but always flat-
17.5 ≤ K ≤ 18.5(thelatteraftercorrectionforpre-MSstars).
S
ten toward small radii. For this reason, broken power-laws can
Hence, while we cannot accurately constrain quantitatively the
work well on the projected data (see Fig.10). From theoretical
contamination of our tracer populations by stars that are too
workonthestructureofarelaxedstellarcuspwewouldexpect
youngtobedynamicallyrelaxed,thiscontaminationmusteither
be small or very similar across the different stellar magnitude apower-lawindexofγin (cid:38)1.5foralow-masstracerpopulation.
Wehaveforcedsuchapower-lawfittothedataatR>0.3pc,as
ranges.Thesimilarityofthepower-lawindicesthatwefindfor
differenttracerssuggeststhattheyareindeedrepresentativefor shownbythebluelineintheplot.Whileitfitsthedatareason-
ably well at R = 0.4−0.5pc, it is clearly too steep inside this
the actual underlying structure of the old stars, which are ex-
range. We note that the distance R = 0.4−0.5pc agrees with
pected to dominate the mass of the NSC (see, e.g., Pfuhl et al.
theprojectedsizeofthepreviouslyreportedcoreorbreakradius
2011).
ofthecluster(see,e.g., Eckartetal.1993;Schödeletal.2007;
Buchholzetal.2009;Bartkoetal.2010).
4.4. The3Dstructureofthecluster Assuming an intrinsic simple power-law structure is, of
course, an oversimplification because a large body of previous
Ourobservationsprovideuswiththesurfacebrightness,butwe studies of the stellar density in the GC indicates that the nu-
would like to know the intrinsic structure of the NSC. This is clearclusterfollowsadensityofapproximatelyn(r) ∝ r−2 out-
not a trivial problem and requires a fairly complete and accu- sideofthecentralparsec,withasteepeningslopeatlargerdis-
rateknowledgeofthestellardistributiononlargescalesbothin tances (see, e.g., references and discussions in Launhardt et al.
andaroundtheNSC.Whilewedonotyetpossessverydetailed 2002; Schödel et al. 2007, 2014a; Fritz et al. 2016). A steep-
knowledgeonthestellarpopulationanditsdistribution,wecan ening density profile is also required to avoid that the cluster
use the results of previous work on the large scale structure of mass diverges. A caveat is that previous work was focussed on
theNSCcombinedwithsomebasicorsimplifyingassumptions significantly brighter stars than what we are examining in the
Articlenumber,page9of13
A&Aproofs:manuscriptno.GC_diffuse
present work. A study of the density of different stellar popu- Table2.Best-fitmodelparametersfortheNukerfitstotheSFBprofiles.
lationsthroughoutthenuclearclusterouttodistancesbeyonda
few parsecs is beyond the scope of this work and will be ad- ID rb γ β ρ(rb)
dressed in a later paper. For simplicity – and because we as- (pc) (mJypc−3)
sume that it is a good approximation on large scales – we will 1a 3.21±0.15 1.15±0.01 3.38±0.17 0.67±0.05
assume that the cluster shape is described well by the data in 2b 3.03±0.20 1.17±0.01 2.74±0.12 0.72±0.08
previouspublications.Nowwewillexploretheconsequencesof 3c 2.97±0.21 1.18±0.01 2.58±0.10 0.73±0.08
steeper density slope at larger distances on the inferred three- 4d 3.31±0.15 1.14±0.01 3.68±0.22 0.65±0.05
dimensionalpower-lawnearSgrA*. 5e 3.09±0.15 1.15±0.01 3.13±0.14 0.72±0.05
To constrain the stellar distribution on scales of approxi- 6f 3.22±0.15 1.15±0.01 3.41±0.18 0.67±0.05
mately 1 to 10pc, we use the data on the flux density of the 7g 3.24±0.20 1.16±0.01 3.17±0.15 0.65±0.07
NSCfromSchödeletal.(2014a)andFritzetal.(2016).Thefor- 8h 3.10±0.19 1.16±0.01 2.97±0.12 0.70±0.07
merusedextinction-correctedSpitzer4.5µmsurfacebrightness 9i 3.39±0.22 1.16±0.01 3.38±0.18 0.61±0.06
maps. The latter used extinction corrected near-infrared data 10j 3.37±0.16 1.18±0.01 3.46±0.19 0.66±0.05
fromNACO/VLT,WFC/HST,andVISTA.Bothdatasetsarenot 11k 3.58±0.24 1.21±0.01 3.29±0.17 0.57±0.07
adequatetosamplethelightdensityprofileinsideR≈1pc.The
Spitzer data of Schödel et al. (2014a) are of low-angular reso- Notes. (a) Data from Schödel et al. (2014a), azimuthally averaged;
lutionandlongwavelengthandcompletelydominatedbyafew 1mJyarcsec−2constantemissionsubtracted.
bright stars and by emission from the mini-spiral in the inner (b) Data from Schödel et al. (2014a) perpendicular to Galactic Plane;
parsec.ThedatafromFritzetal.(2016)are,inprinciple,more 1mJyarcsec−2constantemissionsubtracted.
suitable, but are dominatedby RC stars and brightergiants. As (c)DatafromSchödeletal.(2014a)alongGalacticPlane;1mJyarcsec−2
is well known and as we confirm in PaperI, these stars show a constantemissionsubtracted.
core-likestructurewithinR≤0.3pcfromSgr,A*. (d)Like(a),but1.1mJyarcsec−2constantemissionsubtracted.
(e)Like(a),but0.9mJyarcsec−2constantemissionsubtracted.
Toisolatethenuclearclusterfromtheemissionofthenuclear
(f)Like(a),butusingonlydataatR≥0.05pc.
disk and Galactic Bulge, we subtracted a constant flux offset,
(g) Data from Fritz et al. (2016); 6.4mJyarcsec−2 constant emission
which was taken as the mean of the flux in the range 15pc ≤
subtracted.
R ≤ 20pc(1±0.1and6.4±0.35mJyarcsec−2 forthedatasets (h)Like(g),but6.05mJyarcsec−2constantemissionsubtracted.
of Schoedel et al. and Fritz et al., respectively). We scaled the (i)Like(g),but6.75mJyarcsec−2constantemissionsubtracted.
data from Schödel et al. (2014a) and Fritz et al. (2016) to our (j)Like(a),withlowerintegrationboundaryatr=R+0.01pc.
data in the range 1.5pc ≤ R ≤ 2.0pc. At R < 1.5pc, we only (k)Like(g),withlowerintegrationboundaryatr=R+0.01pc.
use the data from our optimised SFB profile (see section4.2).
We then used a 3D Nuker model and projected it onto the sky
tofitthemeasuredsurfacebrightness.WeusetheNukermodel – Constant flux offset: Fits with the mean of the flux in the
(Laueretal.1995)intheformof‘Equ.1”ofFritzetal.(2016): range 15pc ≤ R ≤ 20pc subtracted as well as with the
1sigmadeviationofthisfluxaddedorsubtracted.
(cid:32) r (cid:33)−γ(cid:34) (cid:32) r (cid:33)α(cid:35)(γ−β)/α – Fits with different settings for the minimum integration
ρ(r)=ρ(rb)2(β−γ)/α r 1+ r (2) boundary(r=0.001,0005,and0.01pc).
b b – Fitsfordifferentvaluesofα=10,20,40.
Here,risthe3DdistancefromSgrA*,r isthebreakradius, – Fits to the entire data and fits limited to R > 0.05pc to ex-
b
ρ is the 3D density, γ is the exponent of the inner and β the aminetheinfluenceoftheinnermostregionaroundSgrA*.
one of the outer power-law, and α defines the sharpness of the
Table2 summaries the best-fit parameters that we obtained for
transition.Thedensitywasthenprojectedalongthelineofsight themodel-fitstodifferentdataandundersomedifferentassump-
viaanintegral:
tions (We did not list all the tests that we ran on the data; the
(cid:90) ∞ rρ(r)dr resultingparameterswillrangewithinthevalueslistedintheta-
Σ(R)=2 √ (3) ble).Theχ2 valuesandtheuncertaintiesofthedifferentmodels
r r2−R2 andparametersareverysimilartoeachother.Wecanobtainan
approximate, mean model for the nuclear cluster by taking the
For numerical reasons, to avoid a singularity, we could not in-
tegrate down to r = R and therefore set the minimum r = mean of each best-fit parameter and its standard deviation (not
R+0.001pc.Thebest-fitwasfoundwiththeIDLMPFITpack- errorofthemean).Weobtainrb =3.2±0.2pc,γ=1.16±0.02,
β=3.2±0.3,andρ(r )=0.67±0.05mJypc−3.
age(Markwardt2009).Uncertaintieswerere-scaledtoareduced b
χ2 = 1. We fixed the parameter α = 10 and used only data at Thebreakradiusshowssomedegeneracywiththevalueofα,
R ≤ 20pc.Thebestfits,usingtheazimuthallyaverageddataof that we keep fixed in our fits. For very soft transitions between
the outer and inner power laws, i.e. α < 10, the break radius
Schödel et al. (2014a) and Fritz et al. (2016), subtracted for a
constantoffset,areshowninFig.13. becomes larger, moving to values around 4pc. Theory predicts
that the cusp follows a power-law well inside the break radius
Thereareanumberofeasilysystematicuncertaintiesrelated
andthatthelatterisontheorderoftheradiusofinfluenceofthe
to this procedure. Our primary test of robustness is, of course,
black hole, which has been found to be ∼3pc (e.g., Alexander
theuseofthecompletelyindependentdatasetsofSchödeletal.
2005; Feldmeier et al. 2014; Fritz et al. 2016), consistent with
(2014a)andFritzetal.(2016).Wethenexploredtheparameter
spacebyrepeatingthefittingprocedurefordifferentcases: TheNukerlawbreakradiusdeterminedhereandinPaperI.
Here,wearemostinterestedinthequestionoftheexistence
– Fit with the azimuthally averaged data of Schödel et al. of a stellar cusp. As we can see, γ can be determined very ro-
(2014a)aswellastheirprofilesalongtheGalacticPlaneand bustly and is > 0. We can exclude a flat core with high confi-
perpendiculartoit,toexaminetheinfluenceoftheflattening dence.Anextensiveanalysisofthestellarnumberandfluxsur-
ofthenuclearcluster. facedensityintheGCwaspresentedinFritzetal.(2016).They
Articlenumber,page10of13