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Astronomy&Astrophysicsmanuscriptno.ms-sabha-new c ESO2010 (cid:13) January8,2010 The extreme luminosity states of Sagittarius A* N.Sabha1,G.Witzel1,A.Eckart1,2,R.M.Buchholz1,M.Bremer1,R.Gießu¨bel2,1,M.Garc´ıa-Mar´ın1,D.Kunneriath1,2, K.Muzic1,R.Scho¨del3,C.Straubmeier1,M.Zamaninasab2,1,andA.Zernickel1 1 I.PhysikalischesInstitut,Universita¨tzuKo¨ln,Zu¨lpicherStr.77,50937Ko¨ln,Germany e-mail:sabha, witzel, [email protected] 2 Max-Planck-Institutfu¨rRadioastronomie,AufdemHu¨gel69,53121Bonn,Germany 3 InstitutodeAstrof´ısicadeAndaluc´ıa(CSIC),CaminoBajodeHue´tor50,18008Granada,Spain e-mail:[email protected] 0 Received/Accepted 1 0 ABSTRACT 2 Wediscussmm-wavelengthradio,2.2-11.8µmNIRand2-10keVX-raylightcurvesofthesupermassiveblackhole(SMBH)coun- n terpartofSagittariusA*(SgrA*)nearitslowestandhighestobservedluminositystates.Weinvestigatethestructureandbrightness a J ofthecentralS-starclusterharboringtheSMBHtoobtainreliablefluxdensityestimatesofSgrA*duringitslowluminosityphases. Wethen discuss the physical processes responsible for the brightest flareaswell as thefaintest flareor quiescent emission inthe 8 NIR and X-ray domain. To investigate the low state of SgrA* we use three independent methods to remove or strongly suppress thefluxdensitycontributionsofstarsinthecentral2”diameterregionaroundSgrA*.Thethreemethodsare:a)low-passfiltering ] A theimage; b)iterativeidentificationandremoval ofindividual stars;c)automaticpointspread function(PSF)subtraction. Forthe lowestobservedfluxdensitystateall3imagereductionmethodsresultinthedetectionoffaintextendedemissionwithadiameter G of0.5”-1.0”andcenteredonthepositionofSgrA*.WeanalyzedtwodatasetsthatcoverthelowestluminositystatesofSgrA*we h. observedtodate.InonecasewedetectafaintK-band(2.2µm)sourceof∼4mJybrightness(de-reddenedwithAK=2.8)whichwe identifyasSgrA*initslowstate.Intheothercasenosourcebrighterorequaltoade-reddenedK-bandfluxdensityof 2mJywas p ∼ detectedatthatposition.AsphysicalemissionmechanismsforSgrA*wediscussbremsstrahlung,thermalemissionofahypothetical - o opticallythickdisk,synchrotronandsynchrotronself-Compton(SSC)emission,andinthecaseofabrightflaretheassociatedradio r responseduetoadiabaticexpansionofthesynchrotronradiationemittingsourcecomponent.Theluminosityduringthelowstatecan t beinterpretedassynchrotronemissionfromacontinuousorevenspottedaccretiondisk.ForthehighluminositystateSSCemission s a fromTHzpeaked sourcecomponentscanfullyaccount forthefluxdensityvariationsobserved intheNIRandX-raydomain. We [ concludethatatnear-infraredwavelengthstheSSCmechanismisresponsibleforallemissionfromthelowesttothebrightestflare fromSgrA*.Forthebrightflareeventof4April2007thatwascoveredfromtheradiototheX-raydomain,theSSCmodelcombined 1 withadiabaticexpansioncanexplaintherelatedpeakluminositiesanddifferentwidthsoftheflareprofilesobtainedintheNIRand v X-rayregimeaswellasthenondetectionintheradiodomain. 1 5 Keywords.blackholephysics,X-rays:general,infrared:general,accretion,accretiondisks,Galaxy:center,Galaxy:nucleus 3 1 1. 1. Introduction the EddingtonluminosityLEdd andmanyordersof magnitudes 0 belowthatofSMBHsinactivegalacticnuclei(AGN)withcom- 0 At the center of the Milky Way stellar motions and variable parablemasses(ofabout4 106M ).Thesurprisinglylowlumi- 1 emission allow us to firmly associate Sagittarius A* (SgrA*) nosityhasmotivatedmany×theore⊙ticalandobservationalefforts : with a 4 106 M super-massive black hole (Eckart & Genzel toexplaintheprocessesthatareatworkinSgrA*.Forarecent v 1996, Ge×nzel et⊙al. 1997, 2000, Ghez et al. 1998, 2000, 2003, summary of accretion models and variable accretion of stellar i X 2005a,2008,Eckartetal.2002,Scho¨deletal.2002,2003,2009, winds onto Sgr A* see Yuan (2006) and Cuadra & Nayakshin Eisenhauer2003,2005,Gillessenetal.2009). r (2006,2009). a Recentradio,near-infraredandX-rayobservationshavede- tectedvariableandpolarizedemissionandgivedetailedinsight intothephysicalemissionmechanismsatworkinSgrA*,which Sgr A* is - in terms of Eddington luminosity - the faintest mayincludeanyorallofsynchrotron,SSC,andbremsstrahlung super-massiveblackholeknown.However,duetoitsproximity emission (e.g. Baganoff et al. 2001, 2002, 2003, Eckart et al. itisbrightenoughtobestudiedingreatdetail.Withthepossible 2003, 2004, 2006ab, 2008ab, 2009, Porquet et al. 2003, 2008, exceptionoftheclosestgalaxies,noextragalacticsuper-massive Goldwurmet al. 2003, Genzelet al. 2003, Ghez et al. 2004ab, blackholewithasimilarfeebleEddingtonratewouldbeobserv- Eisenhauer et al. 2005, Belanger et al. 2006, Hornstein et al. able.Motivatedbytheneedtoexplainthevariableluminosityof 2007,Yusef-Zadehetal.2006ab,2007,2008,2009,Marroneet SgrA*wehaveanalyzeddatafromithighestandloweststates. al.2009,Dodds-Edenetal.2009).Multiwavelengthdetections InordertoseparatetheweakNIRemissionofSgrA*fromthe of the radio pointsource at sub-millimeter,X-ray,and infrared surroundingstars,theuseoflargetelescopesandadaptiveoptics wavelengthshave also been made,showingthat the luminosity (AO)isrequired.Herewepresentthefirstattempttodothiswith associated with SgrA* is on the orderof 10 9... 10 times below near-infrareddataobtainedwiththeVLT.Likewise,highresolu- − − tionisneededin theX-rayregimetoseparateSgrA* fromthe Sendoffprintrequeststo:N.Sabha([email protected]) surroundingdiffuseX-raybackground. 2 Sabha,Witzel,Eckartetal.:TheExtremeLuminosityStatesofSgrA* Table1.ThebrightestX-rayflaresfromSgrA*.Forreferencesseetext. label date Observatory α=Γ 1 X-rayflux NIRL-band 11.8µm − density fluxdensity fluxdensity (µJy) (mJy) (mJy) α Oct.26/27,2000 Chandra 0.0 0.8 0.65 0.07 - - ± ± β Oct.3,2002 XMM 1.2 0.3 2.7 0.4 - - γ Apr.4,2007 XMM 1.3±0.3 1.7±0.3 20 2 <3σ=57 ± ± ± Table2.DetailsonobservingrunsduringwhichSgrA*wasinaverylowNIRluminositystate. Telescope Instrument λ UTandJD UTandJD ObservingID StartTime StopTime VLTUT4 NACO 2.2µm 200423Sept.23:20:45 200424Sept.01:45:11 JD2453272.47969 JD2453272.57304 VLTUT4 NACO 2.2µm 200430Aug.23:49:36 200431Aug.01:28:19 JD2453248.48375 JD2454466.50000 Thetemporalcorrelationbetweentherapidvariabilityofthe with subsection 4.4we use Γ andγ as the bulk boostingfactor near-infrared(NIR)andX-rayemissionsuggeststhattheemis- andtherelativisticelectronLorentzfactor. sion showing 1033 35 erg/sflares arises from a compactsource − within a few tens of Schwarzschild radii of the SMBH. For SgrA* we assume R =2R =2GM/c2 1010 m for a 4 106M blackhole.HereR issoneSgchwarzsch∼ildradiusandR∼ t×hegrav⊙- 2. Observationsanddatareduction s g itational radius of the SMBH. One Rs then corresponds to an Near-infrared (NIR) observations of the Galactic center (GC) angular diameter of 8 µas at a distance to the Galactic cen- were carried out with the NIR camera CONICA and the adap- ∼ ter of d = 8 kpc (Reid 1993, Eisenhauer et al. 2003, Ghez et tive optics (AO) module NAOS (briefly “NACO”) at the ESO al. 2005ab). These observations can be explained in a model VLTunittelescope4(YEPUN)onParanal,Chile.Thedatawere ofanintrinsicallyfaintaccretiondiskthatisdominatedbyred- taken on the night of 30 August and 23 September, 2004. The noiseandtemporarilyharborsabrightorbitingspotpossiblyin dataset taken on 23 September 2004 turned out to be the best conjunction with a short jet (Eckart et al. 2006b, Meyer et al. available set in which SgrA* is in a quiet state. During the 30 2006ab, 2007). The phenomenon can best be studied through Augustobservationssomeweak activityat2.2µmcouldbede- the brightest flares that allow us to derive high signal to noise tected,makingthisdatasetwell-suitedtodeterminetheposition light curves and multi wavelength observations throughoutthe ofSgrA*withrespecttoneighboringstars.Thecombinationof electromagneticspectrum. bothdatasetsisideallysuitedtoobtainafluxdensityestimateor In its lowest luminosity states SgrA* is difficult to detect limitofSgrA*initsquietstate. thoughduetothepresenceofastrongdiffusebackgroundatX- ForallobservationstheinfraredwavefrontsensorofNAOS ray wavelengths and the confusion with nearby stellar sources wasusedtolocktheAOloopontheNIRbright(Ks-bandmagni- inthenear-infrared.Herewediscusstherelativeimportanceof tude 6.5)supergiantIRS7,locatedabout5.6 northofSgrA*. ′′ thebremsstrahlungandSSCprocessforthelowstateofSgrA* Thep∼ixelscalewas13.27mas. andinvestigateifthebrightestflaresofSgrA*canbeexplained The atmosphericconditions(and consequentlythe AO cor- viaaSSCmodelinvolvingup-scatteredsub-millimeterphotons rection) were stable during the observations. The seeing at the fromcompactsourcecomponents.InSects.2and3wedescribe telescope measured in the optical was 0.6”. We used an inte- theobservations,thedatareductionandthealgorithmsweused grationtime ofDIT=2secondsandan∼umberofintegratedim- toextractSgrA*inits lowstate fromthebackgroundemission ages of NDIT=15. Details on start and stop times are listed in ofthedenseclusterofhighvelocitystarsatangularseparations Table2. oflessthanabout1”fromthepositionofSgrA*.Belowwewill All observations in the Ks-band (2.2 µm) were dithered to refertothisassociationofstarsasthe’S-starcluster’.InSect.4 coveralargerareaoftheGCbymosaicimaging.Theskyback- wepresentanddiscussresults.Westartbysummarizingthere- groundfortheKs-bandobservationswasextractedfromtheme- sults ofourdeepKs imagingin subsections4.1and 4.2. In the dian of stacksof ditheredexposuresofa darkcloud – a region followingsubsectionswethendiscussvariousemissionmecha- practicallyemptyofstars – about400”northand713”westof nismsforthelowandhighluminositystatesofSgrA*.Weshow the target. All exposures were sky-subtracted, flat-fielded, and thattheSSCprocesscansuccessfullydiscribeboththelowand corrected for dead or bad pixels. The images were shifted and highluminositystatesandthat-inparticularforthehighstates stacked in a cube with a mean average to get a mosaic image - no extra mechanisms need to be involved (discussion in e.g. oftheGC.AllofthesestepswereperformedwiththeDPUSER Dodds-Eden et al. 2009, Eckart et al. 2009). A brief summary softwareforastronomicalimageanalysis(T.Ott,MPE;seealso andconclusionsarepresentedinSect.5. Eckart & Duhoux 1990). Subsequently, PSFs were extracted Throughout the paper we quote de-reddened infrared flux from these images with StarFinder (Diolaiti et al. 2000) both densitiesusingaKs-band(2.2µm)extinctioncorrectionofA = fordeconvolutionwiththeLucy-Richardson(LRLucy1974)al- Ks 2.8(Scovilleetal.2003,Scho¨deletal.2007,Scho¨deletal.2010 gorithmandforPSFsubtraction. inprep.,Buchholz,Schoedel,Eckart2009).InSect.4.1weuse The flux densities of the sources were measured by aper- Γandγtodescribetheprojectedandthreedimensionalstructure ture photometry with circular apertures of 40 mas radius and ofthecentralstellarclusterrespectively.InTable1andstarting corrected for extinction, using A = 2.8 (Scoville et al. 2003, K Sabha,Witzel,Eckartetal.:TheExtremeLuminosityStatesofSgrA* 3 position 0.5’’ Fig.1.IdentificationofindividualsourcesthatwereusedfortheiterativesubtractionoftheKs-banddatasets(Table2).Hereweshowtheimage derivedfromthe23September 2004data.Thenomenclature wastakenfromthedeconvolved H-bandimagegiveninFig.1byGillessenetal. (2006).Sourcesthatarenotcontainedintherehavelabelsstartingwith’N’.Relativepositionsandfluxdensitiesofthelabeledsourcesaregiven inTable3. Scho¨del et al. 2007, Scho¨del et al. 2010 in prep., Buchholz, and suffer most likely from the proper motion of faint sources Schoedel,Eckart2009).Possibleuncertaintiesintheextinction betweenthepresentdateandthedateusedforidentificationby by a few tenths of a magnitude alter the infrared flux densities Gillessenetal.(2009).ThenwelistinTable3theskyprojected of SgrA* by a few 10%. These variations are easily compen- relativeoffsets∆α,∆δandradialdistanceRfromSgrA*inarc- satedforbyinsignificantvariationsinthespectralindicesorthe seconds. The uncertainties in the offsets are better than a third boostingwhich donotinfluencethe generalresults obtainedin of a pixel i.e. 0.004” We then list in Table 3 the observed Ks thispaper. magnitudederivedinthispaperandtheobservedK’magnitude listed by Do et al. (2009b)correctedby an offset value of -0.2 Thefluxdensitycalibrationwascarriedoutwiththeknown magnitudes.Thescatterbetweenbothvaluesaftercorrectionfor Ks-band flux densities of IRS16C, IRS16NE, and IRS21 by this offset is 0.2 magnitudes, so that the offset corresponds to Blum,Sellgren&Depoy(1996).Subsequentlytherelativepho- 1σinmagnitudes(20%influx)andiswellwithintheexpected tometry for Sgr A* was done using 10 sources within 1′.′6 of calibrationuncertaintiesforfaintstarsinthecrowdedfield.The Sgr A* as secondary calibrators (S67, S92, S35, S8, S76, S1, difference between both mangitude values is listed in the last S2, S87, S65, S30; Gillessen et al. 2006).This results in a Ks- column.For sourcesS0-8,S0-18andS0-38no magnitudesare band flux density of the high velocity star S2 of 22 1 mJy, given by Do et al. (2009b). The large magnitude difference in ± whichcompareswellwiththemagnitudeandfluxforS2quoted thecaseofS0-12ismostlikelyduetotheblendofS59andS60. by Ghez et al. (2005b)and Genzel et al. (2003).The measure- ThetwoNIRfilters K andK’(Doetal. 2009b)areverysimi- s mentuncertaintiesforSgrA*wereobtainedonthenearbyref- larwithKs(NACO):λ =2.18µmandwidth∆λ=0.35µmand center erence star S2. The backgroundflux in the immediate vicinity K‘(NIRC):λ =2.124µmandwidth∆λ=0.351µm.Notrans- center of Sgr A* was obtained by averaging the measurements at six formationbetweenmagnitudesderivedwiththesefilterswasap- random locations in a field located about 0′.′6 west of Sgr A* plied. The 0.2 mag scatter relates to stars of different bright- that is free of obviousstellar sources. A Ks-band image of the nesses at different epochs between which they are moving at central 4.3” 2.5”is shown in Fig. 1. This field is at the center different locations in the cluster with respect to different local × of the stellar cluster of which we show a 15” 15”overviewin backgrounds.TherelativefluxdensityuncertaintyforthestarS2 × Fig.2a).Thesourcepositionsandrelativeastrometrywasestab- -whichweuseasanestimateforSgrA*-isdeterminedwithin lishedviaStarFinder.ThepositionsinTable3aregivenrelative asingleepochatfixedposition. to the position of SgrA* as determinedfrom the 23 September 2004data.Welistthenamefollowingthenomenclatureusedby Gillessenetal.(2009)andinthesecondcolumnthenameused byDoetal.(2009b).SourceslabeledwithN hadnotbeeniden- tified before. Identifications with question marks are tentative 4 Sabha,Witzel,Eckartetal.:TheExtremeLuminosityStatesofSgrA* Table3.Sourcesusedforiterativesourcesubtractionforthe23September2004data. name other ∆α ∆δ R flux Ks K’-0.2 ∆mag name arcsec acrsec arcsec mJy S62 0.01 -0.02 0.03 1.52 17.0 S17 S0-17 0.02 -0.09 0.09 8.06 15.2 15.5 -0.3 S38? -0.08 0.05 0.10 1.27 17.2 S55 0.07 -0.09 0.11 0.71 17.9 S40 0.12 0.00 0.12 1.88 16.8 S2 S0-2 0.02 0.13 0.13 22.00 14.1 13.9 0.2 S13? S0-8 -0.11 0.09 0.14 7.04 15.4 ? S19 0.06 -0.15 0.16 1.79 16.9 S14 0.16 0.12 0.20 7.41 15.3 S18 S0-38 -0.20 -0.06 0.21 2.19 16.7 ? S44 -0.08 -0.23 0.24 1.13 17.4 S20 0.21 0.12 0.24 8.80 15.1 S39 -0.10 0.23 0.25 1.37 17.2 S1 S0-1 0.00 -0.25 0.25 14.00 14.6 14.5 0.1 S63 0.24 -0.13 0.28 1.20 17.3 S4 S0-3 0.29 0.12 0.31 14.02 14.6 14.3 0.3 S22 0.17 -0.27 0.32 2.39 16.6 S12 -0.06 0.31 0.32 8.04 15.2 S23 0.32 -0.08 0.33 1.01 17.5 S52 0.19 0.27 0.33 0.98 17.5 NS2 0.18 0.32 0.36 1.06 17.4 S21 -0.33 -0.14 0.36 2.03 16.7 S36 0.27 0.25 0.36 3.66 16.1 S60/59 S0-12 -0.29 0.24 0.37 6.70 15.4 14.2 1.2 S41 -0.23 -0.31 0.38 1.10 17.4 S10 S0-6 0.04 -0.38 0.38 21.99 14.1 14.0 0.1 S5 0.34 0.19 0.39 9.47 15.1 S42 -0.17 -0.37 0.40 1.62 17.0 S9 S0-5 0.18 -0.36 0.40 12.66 14.7 14.9 -0.2 S57 0.42 -0.14 0.44 0.89 17.6 S25 S0-18 -0.11 -0.43 0.44 10.71 14.9 ? S47 0.38 0.23 0.45 2.73 16.4 S28 -0.01 0.46 0.46 1.56 17.0 S6 0.47 0.09 0.48 8.02 15.2 S8 S0-4 0.39 -0.28 0.48 17.72 14.4 14.3 0.1 S32 0.33 -0.36 0.49 2.85 16.4 NS1 0.27 0.42 0.50 1.81 16.9 S37 0.33 0.38 0.50 2.74 16.4 S7 S0-11 0.51 -0.05 0.51 10.38 15.0 15.1 -0.1 S43 -0.51 -0.15 0.53 1.30 17.2 S29 -0.21 0.49 0.54 2.33 16.6 S27 S0-27 0.14 0.53 0.55 7.34 15.3 15.5 -0.2 S49 0.56 0.04 0.56 1.60 17.0 S45 0.19 -0.52 0.56 7.59 15.3 S24 S0-28 -0.16 -0.54 0.56 6.26 15.5 15.6 -0.1 S53 0.29 0.49 0.57 1.30 17.2 S34 0.32 -0.47 0.57 8.55 15.2 S11 S0-9 0.17 -0.58 0.60 23.79 14.1 14.2 -0.1 S46 0.24 -0.56 0.61 6.92 15.4 S48 0.44 0.45 0.63 3.21 16.2 S35 S0-13 0.54 -0.43 0.69 45.90 13.3 13.3 0.0 3. Subtractingstars 2009)showthatonscalesofafewarcescondsthisisareasonable assumptionandthatPSFvariationshavetobetakenintoaccount To investigate the low luminosity state of SgrA* we use three onlyforfields 10”.Whethertheresidualextendedemissionwe independent methods to remove or strongly suppress the flux find close to S≥grA* is due to rsiduals from the subtracting al- density contributions of stars in the central 2” diameter region gorithmsorassociatedwithadditionalstellaremissionfromthe around SgrA*. All three methods give comparable results and S-starclusterisdiscussedinSect.4.1. allowustoclearlydeterminethestellarlightbackgroundatthe centeroftheMilkyWayagainstwhichSgrA*hastobedetected. WeassumethatthePSFasdeterminedfromstarsinthecen- tralfewarcsecondsoftheimageisuniformacrossthecentralS- starcluster.Investigationsoflargerimages(e.g.Buchholzetal. Sabha,Witzel,Eckartetal.:TheExtremeLuminosityStatesofSgrA* 5 3.1.Linearextractionofextendedfluxdensity 100:1weshowinFig.2b)alow-passfilteredversionoftheKs- band image that was obtained by following the algorithm out- With the point spread function P and the object distribution O linedabove.Theprominentsourceshavebeenlabeledwiththeir wecanwritetheformationofanimageI as names.InFigs.2c),d)ande)weshowtheextendedfluxdensity distributionofthefollowingsources:IRS1W,IRS21,IRS10W. I =O P=(∆+E) P=∆ P+E P. (1) ∗ ∗ ∗ ∗ Thesebow-shockstructuresareshownattheangularresolution ofabout0.1”asdeliveredbytheAOsystem.Theycomparevery Here the symbol denotes the convolution operator. The ∗ wellwiththesourcestructurespublishedbyTanneretal.2005. variable ∆ denotes the distribution of stellar sources and E the Here the algorithm detects very bright sources like IRS 7 also distributionofextendedemission.Bothtypesofsourcesareas- asanextendedobjectsincethestarisoverexposedandnotwell sumed to be ideally unresolved or resolved with respect to the describedbytheusedPSF.InFig.3weshowresultsofthealgo- pointspreadfunction.Toproduceahigh-passfilteredimagewe rithmonthecentral2” 2”.Inadditiontoresidualsofthefilter cancalculateasmooth-subtractedimageΣas × processaroundthepositionofbrightstars,weseeanincreased fluxdensitylevelwithinthedashed0.5”diametercirclecentered Σ= I G I =(∆+E) P G (∆+E) P. (2) ∗ − ∗ ∗ − ∗ onthepositionofSgrA*.Thedisadvantageofthisalgorithmis that any point-like emission from SgrA* is also strongly sup- HereweuseanarrowGaussianGnormalizedtoanintegral pressed. The residuals (ringing) still evident around the bright powerofunity.Thiscanberewrittenas stars are a consequence of the choice of the apodization filter thatneedstobedefinedinthecaseoflineardeconvolution.This Σ=∆ (P G P)+(E P G E P). (3) ∗ ∗ − ∗ ∗ − ∗ filter is used to suppressthe usual highspatial frequencynoise that arises due to small number division problems. We used a Since the width of the extendedemission is expected to be cosine-bellshapedfilter thatpreservesthe highangularresolu- muchlargerthanthefullwidthathalfmaximumofthePSF,and tionbutresultsinsomeresidualringing.However,theresulton in particular since the GaussianG is narrow with respect to P, thebackgroundemissionisnotstronglyinfluencedbythis,since wecaninferthatE P G E P.Thenthedifferentialpoint ∗ ∗ ∼ ∗ the bright stars are sufficiently far away from the central posi- spread function P G P is the PSF of the high-pass filtered ∗ − tion.The comparisonto theresults ofthe othertwo algorithms differentialimage usedtoremovethecontributionsofstarsnearSgrA*showsthat theresultisalsolittleaffectedbythemuchfainterstarscloseto Σ ∆ (P G P). (4) ∼ ∗ ∗ − SgrA*.Theircontributionhasbeenefficientlysuppressedbythe algorithm. Since Σ is fully dominated by the contribution of the dis- tributionofunresolvedstellarsources,thisdistribution∆canbe retrievedviaalineardeconvolutionofthedifferentialimagewith 3.2.IterativePSFsubtraction thedifferentialPSF TheiterativePSFsubtractionwascarriedoutwithinthecentral 2”to3”aroundthepositionofSgrA*.Thiswasperformedbyre- ∆ Σ%(P G P). (5) ∼ ∗ − sizing,shiftingandscalingthePSFtothepositionandthevalue ofeach star andthen subtractit. The sourcesused forthispro- Here the symbol % denotes the deconvolution operation. cessarelistedinTable3andareshowninFig.1.Atotalnumber Consequentlythedistributionofextendedflux(i.e.alow-passed of51starsweresubtractedsothattheresultingbackgroundwas filteredversionoftheimage)E Pcannowbeisolatedvia ∗ assmoothaspossible.InFig.4weshowtheresultingsubtracted image of the area of interest around SgrA*. All stars brighter E P=I ∆ P (6) ∗ − ∗ thanabout17.5m (seeKLFinFig.6)havebeensubtractedwith ascaledversionofthePSF.ThethinlinesinFigs.4a)andb)are or usedtotriangulatethepositionofSgrA*.Fig.4a)showstheim- I Σ P%(P G P)=∆ P+E P ∆ P= E P. (7) ageobtainedfromasectionofthe30AugustdatasetwithSgrA* − ∗ ∗ − ∗ ∗ − ∗ ∗ flaring.ComparedtoS2with 22mJySgrA*hasabrightnessof ∼ The advantage of this new method is that it is independent about4mJy.Fig.4b)showstheimageobtainedfromasectionof of inputmodels,i.e. it doesnotdependon the identificationof the23SeptemberdatasetwithSgrA*inaquiescentphase.Here individual stars or on assumptions on the existence or proper- SgrA* is clearly not detected and is fainter than about 2 mJy ties of a diffuse backgroundflux density distribution. Also the (de-reddened). method only uses linear operations, i.e. image subtraction and Figure4alsorevealsthepresenceoffaintresidualextended linear convolution and deconvolution (Fourier multiplications emission-centeredonthepositionofSgrA*.Thisresidualemis- and divisions). Therefore it is not dependent on the flux den- sionismostlikelyfromthecentralS-starclusterofhighvelocity sityofsourcesandnumbersofiterations,asisthecaseformany stars. We determinedthe position of SgrA* from the data with non-linear algorithms (e.g. the Lucy-Richardson or maximum SgrA*inaflarestatetakenon30August,2004.Takinganupper entropy algorithm). In order to demonstrate the validity of the limitoftheobservedtwodimensionalprojectedstellarvelocity approachwe show the results we obtained on the central 15” dispersionof 1000km/sandthefactthatfortheGalacticcen- × ∼ 15” of the 23 September data in Fig. 2. For all the prominent terpropermotionof1mas/yrcorrespondstoabout39km/s,the extendedKs-bandsources(Fig.2)the extendedKs-bandemis- relative positional uncertainty for stars observed between both sioncanberetrievedanditsstructurecomparesverywelltothe epochsisexpectedtobewellbelow2mas.ThinlinesinFigs.4a) previously published results (e.g. Ott, Eckart & Genzel 1999, and b) are used to triangulate the position of SgrA*. Figure 4 Tanneretal.2002,2005).(Acomparisonofdifferentdeconvolu- showsthatforthedatasettakenon23September2004noNIR tionalgorithmsusedinthecrowdedGalacticcenterfieldisgiven counterpartofSgrA*wasdetected.For30August2004wefind in Ott, Eckart & Genzel 1999.) At a dynamic range of about a NIR counterpartof SgrA* with a dereddenedflux density of 6 Sabha,Witzel,Eckartetal.:TheExtremeLuminosityStatesofSgrA* Fig.2. TheKs-bandimageoftheGalacticcenter region(a)takenon 23 September 2004. The central 15” 15” image was taken with the × adaptive optics system NACO at the ESO VLT and the results of the low-passfilteralgorithm.(b,c,d,e).Thecontourlinesareseparatedby 8%ofthepeakbrightnessofIRS10W. Fig.4. Results of the iterative star subtraction obtained for the 30 August(a)23Septemberdata(b)asdescribedinSect.3.2. Fig.3. The inner 2” 2” of the central stellar cluster (23 September × 2004).ThepositionofSgrA*isatthecenteroftheimagesa)andb).In panela)weshowthecorrespondingimagesectiontakenoutoftheKs- bandimageinFig.2a).Inpanelb)weshowthecorrespondingimage sectiontakenoutofthelow-passfilteredversioninFig.2b). about4mJywitha3σuncertaintyofabout2mJy.Estimatesof thefluxdensitylimitsanduncertaintiesaregiveninSect.4.2. 3.3.AutomaticPSFsubtraction Fig.5. Result of the automatic PSF subtraction obtained for the 23 We also analyzed the images with the StarFinder (Diolaiti et September2004data. al. 2000)programpackage.It notonly providesaccurate point source photometry but also a reliable estimation of the diffuse background emission. With a point spread function (PSF) ex- 4. Resultsanddiscussion tractedfrombrightstarsneartheguidestar(inthiscaseIRS7), we performed photometry and astrometry on the deconvolved Firstweanalyzethepropertiesofthecentralclusterofhighve- imageviaPSFfittingwiththeStarFinderpackage.Theresulting locitystarsandcomparethemtotheresultsofpublishedinves- diffuse backgroundemission is shown in Fig. 5. In addition to tigations.Wecanthenconfidentlyderivethefluxdensitylimits some residualemission from unresolvedstars this method also on SgrA* and show that contributions to the lowest luminos- reveals extended emission centered on the position of SrgA* itystatesfrombremsstrahlungareunlikely.Wethendiscussthe within the dashed0.5”diametercircle centeredon the position extremeluminositystates of SgrA*in the frameworkof a syn- of SgrA*. This finding agrees with the low-pass filtered image chrotronself-Comptonmechanism. inFig.3. 4.1.ImagingtheS-starclusterandthedetectionofSgrA*in itslowluminositystate The detected number of 51 stars within a radial distance of about 0.5” from SgrA* results in a surface number density of 68 8arcsec 2,takingthe square-rootasthe uncertaintyofthat − ± value. This result agrees with the central number density of Sabha,Witzel,Eckartetal.:TheExtremeLuminosityStatesofSgrA* 7 30 August 2004 23:49:36 to 01:28:19 1.0 20 1 15 ) mJy] (N flux [10 g 0.5 o 0.5 l 5 0 0 20 40 60 80 100 0.0 0 whm [arcsec]000...243 1122 1144 1166 1818 psf f0.1 0 20 40 60 80 100 time [min] Ks magnitude Fig.8. The 30 August 2004 light curve of the flux density measured Fig.6.KLFhistogramofthestarsdetectedinthecentralfieldderived ina40masradiuscircularaperturecenteredonthepositionofSgrA* from the 23 September 2004 data. The straight full and dashed lines (black).WeshowthelightcurveofthereferencestarS2ingreen.The indicatetheKLFslopeof0.21 0.02foundforradiioflessthan6”by bottompanelshowstheFWHMseeinginarcsecondsmeasuredonthe ± Buchholzetal.(2009). PSFextractedforthefield.Thegreypointsshowthebackgroundcounts nearSgrA*.Thewidthoftheerrorbarsisclosetothesizeofthedata points. y nsit 1.01E0 23 September 2004 nte 23:20:45 to 01:45:11 d i 0.8 20 e g a r e v a 15 y all mJy] uth 0.5 flux [10 m zi e a 5 v ati el 0 r 0 50 100 150 1E−2 0.02radius in arc0s1e.E−1c1onds0.2 0.3 whm [arcsec]000...243 psf f0.1 0 50 100 150 Fig.7. Azimuthal average of the diffuse background emission as de- time [min] rivedfromthethreedifferentmethodsapplied:lowpassfiltering(red), manualPSFsubtraction(green),andautomaticPSFsubtraction(blue). Fig.9.ThesameasFig.8butfor23September2004. Thecurves(meanfluxand1σuncertaintyperpixel)havebeencalcu- latedinanuliof39.8mas(3pixels)widthandnormalizedtothevalue at30masradiuscorrespondingtooneresolutionelementat2.2µm.The blackdashedlinemarksaprofilewithanexponentialdecreaseof0.2. no significant deviation from a straight powerlaw line can be detected- implyingthatthe completenessis highandprobably comparabletothe 70%valuederivedformag =17byScho¨del K 60 10arcsec 2 givenby Do et al. (2009b)in their Figs. 9 and etal.(2007).Inthe∼intervalrangingfromKs=17.50to18.25the − ± 10. stellar countsdrop quicklyto about20%of the value expected Figure6showstheKLFhistogram(K-bandluminosityfunc- fromthestraightpowerlawline. tion)thatcanbederivedforthestarsdetectedinthecentralfield. All three methods we used to correct for the flux density Thebinningof0.75magnitudesallowsforasufficientnumberof contribution of the stars in the central 2” reveal faint extended binsto clearly detectthe linearslope in the doublelogarithmic emission around SgrA* (see Figs. 3b, Fig. 4b and Fig. 5). For plot and to have a sufficiently large number of sources per bin the iterative and automatic PSF subtraction the PSFs were ex- (about10) at the same time. With d log(N)/d log(Ks)=0.3 0.1 tractedwitharadiusof1”,whichisabouttwicetheFWHMof ± the data compare well with the KLF slope of 0.21 0.02found the S-star cluster. In case of a PSF misplacement a significant ± fortheinnerfield(R<6 )byBuchholzetal.(2009). flux density contribution to the central position can only come ′′ Withinthecentral0.5arcsecondradiusregionaroundSgrA* fromtheaboutfivestars thatarelocatedwithin oneFWHM of and in the magnitudeintervalrangingfromKs=16.75 to 17.50 SgrA*. They have a median brightnessof about 2 mJy. To ex- 8 Sabha,Witzel,Eckartetal.:TheExtremeLuminosityStatesofSgrA* plain all of the 2 mJy at the center by this effect, each star sivestarsthataretooyoungtobedynamicallyrelaxed.Thesmall ∼ wouldhavetoprovideabout0.4mJyor20%ofitsfluxdensity. valueoftheprojecteddiffuselightexponentΓ Γ may diffuse inner ∼ Thiscanonlyberealizedbyasystematicpositionalshiftofthese therefore imply the absence of a pronounced, relaxed cusp of starstowardsthecenterbyabout1pixel 13maseach.Still,the stars. ∼ positionalaccuracywhichistypicallyreachedisontheorderof However,there may in fact exist a deficit of late-type stars a fewtenthsofapixel.Largerdisplacementsresultin aclearly near Sgr A* (see also Genzel et al. 2003, Fig. 7). It may well identifiablecharacteristicplus/minuspatternintheresidualflux bethatmostofthespectroscopicallyidentifiedlatetypestarsat distribution along the shift direction. However, allowing for a smallprojecteddistancesareatlargerthreedimensionalradiir maximum positional uncertainty of 1 pixel and approximating RfromSgrA*.InthiscasetheobservedΓ Γ willbea diffuse inner ∼ theindependentshiftsoffivestarsbyfiveshiftsofasinglestar mixturebetweenthemuchsteeperΓ forearlytypestarsand early that follows a random walk pattern, the expected effective dis- thelowervalueΓ forlatetypestars.Adetaileddiscussionis late placement is 1/√5 pixels for a single shift of each star. It will giveninDoetal.(2009b),Buchholzetal.(2009),Scho¨deletal. result in a 5% peak flux contribution of each of the 5 stars - (2007),andGenzeletal.(2003). assumingthatthe displacementsare systematicallytowardsthe The main result for the present analysis of faint lumi- center, i.e. a total maximum contribution of 0.4 mJy. This im- nosity states of SgrA* is that the observed flat background plies that about one 20%-30% of the flux density detected at light and number density distribution described by the expo- thecentermaybeexplainedbyapositionalmisplacementofthe nent Γdiffuse Γinner as well as the high degree of completeness ∼ neighboringstars.Thereforeweassumethatthebulk(morethan reached around Ks=17.5 allows us to clearly distinguish the 2/3)of thisextendedemission towardthe centercanbe associ- emission of SgrA* against the stellar light background at the atedwiththe 0.5”-1”diameterS-starclusteraroundSgrA*and centeroftheMilkyWay.Thisalso showsthatSgrA*isideally isduetofaint∼starsatorbeyondthecompletenesslimitreached suitedto performa case studyto investigatethissuper-massive intheKLF. blackholeinitslowestactivitystate. The extended residual emission is not distributed az- imuthally uniformaboutthe position of SgrA*.This is not ex- 4.2.ObservingSgrA*atlowluminosities pectedeither.Theshapeoftheresidualemissionwillalwaysbe dominated by the randomly distributed few brightest stars that Highangularresolutionimagesin thenear-infraredallowusto contributetoit.Alsothelightofthecentralstellarclusterisnot unambiguouslyattributebrightdereddenedfluxlevelstoSgrA* distributed azimuthally uniform on any scale: On scales larger (e.g.Genzeletal.2003,Eckartetal.2004,Ghezetal.2004ab, than0.5pcitisaffectedbydustabsorption(e.g.extinctionmap Hornstein et al. 2006, Do et al. 2009a). The identification of by Buchholz et al. 2009), on scales less than 0.5 pc the bright fainter emission from SgrA* becomes increasingly difficult, membersoftheIRS16cluster arepredominantlylocatedto the since one can expect confusion from the 1” diameter S-star ∼ east, and during the past decade in the central arcsecond most clusterthatiscenteredonthelocationofSgrA*.Duetothehigh ofthebrighterS-starshavebeenlocatedtothesouthandeastof propermotionsof thestars withintheS-star cluster thisconfu- SgrA*. sionalsochangesonthetimescalesofmonthstoyears.Fromthe The diffuse background emission can be compared to the locationofSgrA*Doetal.(2009a)findobserved0.082 0.017 projecteddistribution of stars Σ(R) R Γ, with R being the pro- mJy(K = 17.2)ordereddened1.75 0.36mJy(assumin±gtheir − ′ ∝ ± jectedradius.Independentoftheappliedmethodwefindthatthe valueof A = 3.3)asthethefaintestobservedK fluxdensity K ′ ′ azimuthallyaveragedresidualdiffusebackgroundemissioncen- (see also Hornstein et al. 2002 and Eckart et al. 2006). Using teredatthepositionofSgrA*decreasesverygentlyasafunction A =2.8thisresultsinafluxdensityof1.1 0.2mJy K ′ ± of radius (Fig. 7). The ratio between the brightness measured ForthelowfluxdensitystateDoetal.(2009a)reportedred withinorattheedgeofthecentralresolutionelement(R 0.03”) colorsand variabilitycomparedto stellar sources.For the very ∼ andataprojectedradiusofe.g.R=0.2”is1.5 0.15,correspond- lowluminositylevelstheyreportwithanaveragepowerlawex- ± ingtoΓ =0.20 0.05.Thisisconsistentwiththedistribution ponentof-0.17 0.32abluerspectrumthanthatreportedearlier diffuse ± ± ofnumberdensitycountsofthestellarpopulationsinthecentral byHornsteinetal. (2002)witha powerlaw slopeof0.6 0.2. ± arcsecondsderivedfromimagingVLTandKeckdata.Buchholz Thecontaminationfromnearby(predominantlyblue)starsises- etal.(2009)andDoetal.(2009b)findaΓ 1.5 0.2fortheyoung timatedtocontributeamaximumofabout35%ofthefluxtoac- ∼ ± stars, butamuchflatterdistributionforthelate-type(old)stars countforthisdifferenceinthespectralslope.Doetal.(2009a) withΓ 0.17 0.09orevenΓ -0.12 0.09,respectively.Forpure concludethatevenwhentheemissionisfaintalargefractionof ∼ ± ∼ ± imagingDoetal.(2009b)quoteΓ =0.19 0.06insidearadius the fluxarisingfromthelocationofSgrA*is likelynon-stellar inner ± ofR=3”. and can be attributed to physical processes associated with the In case of a relaxed stellar cluster around a supermassive blackhole. black hole, stellar dynamics predicts to observe a cusp, i.e. a Ourdataallowustoprovideanewindependentestimateon density increasetoward the black holewith Γ = γ 1 = 0.5 to the flux density ofSgrA* in some of its loweststates basedon − 0.75(Bahcall&Wolf1976,Murphy1991;Lightman&Shapiro VLTdata. 1977;Alexander&Hopman2009).Hereγdenotestheexponent In a circular aperture of a diameter of 66 mas diameter (5 ofthethreedimensionaldistributionwhichdoesnotsufferfrom pixelsoraboutoneresolutionelement)wemeasuredereddened projection effects but is harder to deduce from observed data. fluxdensities(using A = 2.8)1.5 0.4mJy,1.3 0.3mJy,and K ± ± Onlyinthecaseofveryextremestellardensitiescollisionscan 1.3 0.2mJy for the low-pass filtering, iterative, and automatic ± leadtoaΓaslowas0.5.Buttherequiredhighdensitiesarenot PSFsubtractionmethod,respectively. reachedintheGalacticcenter. The uncertainties have been derived from the flux density The observedvalues of Γ are significantly lower than what measurements in the central 5 5 pixel aperture and the up- × is predicted by theory. The principal reason is probably to be per limits of the measurement uncertainties per pixel as plot- soughtinthestellarpopulationinthecentralarcseconds,which ted in Fig. 7. These upper limits are 0.33 mJy, 0.24 mJy and towardsSgrA*becomesincreasinglydominatedbyyoungmas- 0.17 mJy for the three methods, respectively. Based on these Sabha,Witzel,Eckartetal.:TheExtremeLuminosityStatesofSgrA* 9 data we derived an upper limit on the formal uncertainties in anyrandom5 5pixelapertureinthecentral0.6”diameterfield × of0.066mJy,0.048mJy and0.034mJyforthe threemethods, respectively.Weadoptedthesevaluesforthecentralaperture.In order to obtain a conservative estimate we added in each case these valuesfive times, so thatthe finaluncertaintyamountsto sixtimesthevalueexpectedforanapertureofthissize-based on the radial averages. There is no clear detection of a source at that position. If the observed flux density limit is fully at- tributed to SgrA* this corresponds to a clear non-detection of any point source at that position with a flux density limit of 2.4 mJy for SgrA* (K 16.3; observed reddened magnitude). s If all of it is stellar, th∼e upper limit is defined by the uncer- 10 0 10 1 10 2 10 3 10 4 10 5 taintyof the measurementandthe limitfora flux densityfrom a non-stellar source at the position of SgrA* is 0.9 mJy (3σ, de-reddenedandK 17.3asanobservedreddenedmagnitude). s ∼ Whileourdatadonotallowustoconfirmtheexistanceofacon- stantquiescentstate,ourfluxdensitylimitisconsistentwiththe flux given by Do et al. (2009a). This flux density limit is also consistent with the light curves of SgrA* shown in Figs.8 and 9. They were obtained in a 40 mas radius aperture centered at the position of SgrA*. The light curveswere taken withoutre- movingany stars from the sourroundingsand the aperturesize ofonly40maswaschosentominimizethecontaminationfrom Fig.10.SketchoftheSgrA*surroundingswithina105Schwarzschild neighboring stars. The bottom parts of Figs.8 and 9 show the radius.TheSMBHenclosesthecentral1Rs volumesurroundedbyan edgeonseendiskwithindicatedspots.Thecirclesarelogarithmically FWHMofthePSFextractedonanearbystar.Thesegraphsshow scaledandlabeledwiththeirradiiinunitsofR .Duringandafterflares thattheseeingandAOperformancewereverystableandsimilar s thespotsexpand tomeettheaccretionflowdensityof about 107cm 3 duringthemeasurementsonbothdates.Especiallyinthesecond − atanapproximateradiusof1000R .Theedgeofthe1.4”FWHMsize halfofthe30AugustlightcurveinFig.8SgrA*wassufficiently Bondisphereislocatedataradiusosfabout 8 104R fora4 106M brightto bedetected,whileitwas ina low state duringtheen- (Baganoffetal.2001,2003). ∼ × S × ⊙ tiretimeduringwhichthe23SeptemberlightcurveinFig.9was taken. Our flux density limit for the 23 Septemberdata is con- sistentwiththecompletenesslimitwereachedinthecentralstar factor is g(ν,T) 0.54 ln(4.7 1010 T/ν). For the X-ray lumi- ∼ × × counts(seeSect. 4.1). nosity in the 2-10 keV range of a H/He plasma this results in L(erg) 1033n2T1/2R3 withthesourceradiusRgivenin pc,the s ≈ e 8 electrondensityn givenincm 3,andthetemperatureT given e − 8 inunityof108K. TheGauntfactorimpliesthatforachangein 4.3.BremsstrahlungemissionfromSgrA* theobservingfrequencyfrom 1018HzintheX-raysto 1014Hz ∼ ∼ 4.3.1. ThequiescentstateX-rayemissionfromSgrA* in theNIRforconstantT>>hν/ktheGauntfactorchangessig- nificantlybyafactorofln(104) 10.SointotaltheKs-bandlu- Baganoff et al. (2001, 2003) reported an extended (R>103 Rs) minosityexpectedoverthisfreq∼uencyrangeisabout1000times thermalbremsstrahlungsourceco-spatialwiththepositionofthe lowerthantheX-rayluminosity.However,alreadyfora 1mJy stronglyvariablepointsourceatthelocationofSgrA*(seealso Ks-bandfluxdensitycontributionandhightemperature∼sabove Quataert2003).Theauthorsderive1.4” 0.14”fortheintrinsic 108KthepredictedX-rayfluxwouldwellexceedthemeasured FWHMsizeofthesource.Thiscorrespo±ndsto 8 104RS fora values. 4 106 M blackhole. Thescale of the extende∼ds×tructurecen- Substantialfluxdensitycontributionsduetobremsstrahlung te×redonS⊙grA*isconsistentwiththeexpectedBondiaccretion can only occur if a sufficient amount of ’cooler’ gas (i.e. radius(1”-2”;Bondi1952)for matteraccretinghydrodynami- <<108 K)ismixedintothecentralaccretionflowordisk.Such callyontotheSMBH.ForthebrightflareemissionoftheX-ray a two phase medium has alreadybeen discussed in the context point source bremsstrahlung is not a likely mechanism to pro- offlaresfromSgrA*(Yuanetal.2003,seealsoPageetal.2004, duce the observed NIR flux density excursions (Genzel et al. Nayakshin&Sunyaev2003).Apossiblequiescentphaseatlow 2003, Yuan et al. 2003, Quataert, 2002). In part motivated by infrared Ks-band flux density could in principle be provided thebluespectrumreportedbyDoetal.(2009a)-assumingthat through bremsstrahlung emission from a cooler denser phase notallofthebluecharacterisduetostellarcontamination-we embedded in the hot accretion flow or in the outer parts of a investigatehereifthelowestNIRfluxdensityvaluescanbeex- potentialaccretiondisk.InluminousAGNacoolopticallythick plainedbyabremsstrahlungcontributionfromahotdisk. diskwithT 105Kisbelievedtocoexistwithahotopticallythin coronawith∼T 109K.AtthelowerSMBHmassandluminosity ∼ of SgrA* such materialcould have an even lower temperature. 4.3.2. PossiblelowstatebremsstrahlungNIRluminosity? However,alowerlimittothetemperatureofsuchcoolinclosure We now estimate the possible contribution of the X-ray emit- isgivenbythefactthatnostrongrecombinationlineemissionis ting gas that is associated with the compact disk or jet foot- observedtowardsSgrA*.Onlyfortemperaturesabove106Kthe point of SgrA* to its Ks-band luminosity. The frequency contributiontothetotalluminosityfromthermalbremsstrahlung and temperature dependency of the volume emissivity for the is greater than that from recombinationradiation. This implies bremsstrahlung is E dν g(ν,T) exp(-hν)dν. Here the Gaunt for106Ka Ks-bandluminosityof L(erg) 1029n2R3. Ata dis- ν ∼ × kT s ∼ e 10 Sabha,Witzel,Eckartetal.:TheExtremeLuminosityStatesofSgrA* Table4.SourcecomponentparametersforSSCmodelsofthebrightestX-rayflaresfromSgrA*. model γ γ S α R ν B S S S S S 1 2 max, synch 0 max MIR, NIR, NIR, NIR, X ray, obs obs synch synch synch SSC −SSC label [Jy] [GHz] [G] [mJy] [mJy] [mJy] [mJy] [µJy] @11.8µm @3.8µm @2.2µm @2.2µm @2-10keV 1σ 0.1 0.1 0.1 250 10 1.0 1.0 1.0 1.0 20 → ± ± ± ± ± ± ± ± ± ± Aα 360 2900 1.9 1.19 0.3 1850 18 59 15 8.0 0 0.65 Aβ 360 2900 3.2 1.25 0.3 1850 12 82 20 10 0 2.6 Aγ 360 2900 1.3 1.05 0.2 1850 11 58 18 10 0 1.8 Bα 6 1300 2.8 1.10 0.3 2190 26 133 20 0.0 11 0.65 Bβ 6 1300 4.3 0.98 0.3 2190 18 226 26 0.0 15 2.6 Bγ 6 1300 3.3 1.01 0.3 2190 20 219 17 0 10 1.8 ξ 360 2900 11.5 1.40 20.5 480 6 0 0 0 0 <0.04 A 360 2900 0.5 1.10 0.1 2360 51 23 6.7 3.7 0 0.038 low B 6 1300 0.8 1.30 0.2 1230 15 15 3.6 0 3.7 0.037 low Q 70 2050 0.08 1.30 0.1 1080 44 0.58 0.18 0.1 <0.01 <0.010 spot Table5.Modeldensities,lowerSSCcutofffrequenciesandlowerlimitsonthesourcecomponentmasses model N c(γ2ν ) 1 ρ mass 0 1 max,obs − erg 1cm 3 nm cm 3 M − − − Aα 0.25 1.3 3 107 3 ⊙10 16 − Aβ 0.22 1.3 6×107 5×10 16 − Aγ 14 1.3 2×108 5×10 16 − × × Bα 0.74 4100 2 1011 2 10 12 − Bβ 13 4100 3×1011 3×10 12 − Bγ 7 4100 2×1011 2×10 12 − × × ξ 4 10 4 4.8 1 106 3 10 12 − − × × × A 0.39 1.0 1 107 3 10 18 Blow 0.013 7300 3×1011 8×10−13 Qlow 7 10 4 56 3×107 9×10−18 spot × − × × − tance of 8 kpc and a wavelength of 2.2µm 1 mJy of dered- 4.4.SynchrotronSelf-ComptonemissionfromSgrA* denedflux∼densitycorrespondstoaluminostityofνL =1.2 1034 ν × Rapidvariabilityontimescalesofafewminutesandthestrong ergs/s=3.1L . ⊙ indicationofsynchronous(polarized)NIRand X-rayflux den- sity variations linked with time delayed sub-mm/mm flux ex- cursionsclearlysuggeststhatanonthermalemissionmechanism In order to obtain 1 mJy Ks-band flux density the prod- isatwork.Synchrotronemissionfromcompactsourcecompo- uct n2eR3 needs to be on the order of 8×104. This allows us to nentsthatunavoidablyscatterelectromagneticpowerintotheX- estimate the required densities: The Ks-band diffraction limit raydomainappeartobea primechoiceforsuchamechanism. of the VLT UT4 corresponds to a projected linear size of Belowweinvestigatethehighestandlowestluminositystatesto 2.4 10−3pc 8000RS atthedistanceofSgrA*.Similarly,1RS validatetheapplicabilityoftheSSCmechanism. cor×responds∼to3 10 7pc. − × 4.4.1. EssentialsofcurrentSgrA*SEDmodeling For such an unresolved or even more compact source with Generallytheelectronenergydistribution N(E)responsiblefor sizes ranging from 1 to 8000 R we find electron densities theoverallSED ofSgrA*isdescribedbya power-law N(E) = S from 2 1012cm 3 to 2 106cm 3 and Thompson scattering op- N E p = N (mc2γ) p with a Lorentz factor γ and an electron − − 0 − 0 − × × ticaldepthsontheorderof1to0.01,respectively.Thisimplies power-lawindex p.Thispower-lawexhibitsseveralbreaksat thatforan’unresolved’bremsstrahlungemittingKs-bandsource the electron density is several orders of magnitude higher than γ <γ <γ , (8) min cool max the estimated density of 107cm 3 of hotter gasin the accretion − flow(Yuanetal.2003).Combinedwiththehighopticaldepths where γ , γ and γ are the minimum, maximum, and min max cool this shows that a substantial bremsstrahlung contribution of a the ’cooling break’ Lorentz factors, respectively (Yuan et al. compact source to the Ks-band flux density even in the quies- 2003,Quataert2002,Mahadevan& Quataert1997).Here γ cool cent phase can therefore be regarded to be very unlikely (see marksthedifferencebetweentheemissionofathermaldistribu- alsoYuanetal.2003). tionofelectronswithγ =γ andγ γ and min,thermal min max,thermal cool ∼

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Astronomy&Astrophysicsmanuscriptno.ms-sabha-new c ESO2010 (cid:13) January8,2010 The extreme luminosity states of Sagittarius A* N.Sabha1,G.Witzel1,A.Eckart1,2,R.M.Buchholz1,M.Bremer1,R.Gießu¨bel2,1,M.Garc´ıa-Mar´ın1,D.Kunneriath1,2, K.Muzic1,R.Scho¨del3,C.Straubmeier1,M.Zamaninasab2,1,andA.Zernickel1 1 I.PhysikalischesInstitut,Universita¨tzuKo¨ln,Zu¨lpicherStr.77,50937Ko¨ln,Germany e-mail:sabha, witzel, [email protected] 2 Max-Planck-Institutfu¨rRadioastronomie,AufdemHu¨gel69,53121Bonn,Germany 3 InstitutodeAstrof´ısicadeAndaluc´ıa(CSIC),CaminoBajodeHue´tor50,18008Granada,Spain e-mail:[email protected] 0 Received/Accepted 1 0 ABSTRACT 2 Wediscussmm-wavelengthradio,2.2-11.8µmNIRand2-10keVX-raylightcurvesofthesupermassiveblackhole(SMBH)coun- n terpartofSagittariusA*(SgrA*)nearitslowestandhighestobservedluminositystates.Weinvestigatethestructureandbrightness a J ofthecentralS-starclusterharboringtheSMBHtoobtainreliablefluxdensityestimatesofSgrA*duringitslowluminosityphases. Wethen discuss the physical processes responsible for the brightest flareaswell as thefaintest flareor quiescent emission inthe 8 NIR and X-ray domain. To investigate the low state of SgrA* we use three independent methods to remove or strongly suppress thefluxdensitycontributionsofstarsinthecentral2”diameterregionaroundSgrA*.Thethreemethodsare:a)low-passfiltering ] A theimage; b)iterativeidentificationandremoval ofindividual stars;c)automaticpointspread function(PSF)subtraction. Forthe lowestobservedfluxdensitystateall3imagereductionmethodsresultinthedetectionoffaintextendedemissionwithadiameter G of0.5”-1.0”andcenteredonthepositionofSgrA*.WeanalyzedtwodatasetsthatcoverthelowestluminositystatesofSgrA*we h. observedtodate.InonecasewedetectafaintK-band(2.2µm)sourceof∼4mJybrightness(de-reddenedwithAK=2.8)whichwe identifyasSgrA*initslowstate.Intheothercasenosourcebrighterorequaltoade-reddenedK-bandfluxdensityof 2mJywas p ∼ detectedatthatposition.AsphysicalemissionmechanismsforSgrA*wediscussbremsstrahlung,thermalemissionofahypothetical - o opticallythickdisk,synchrotronandsynchrotronself-Compton(SSC)emission,andinthecaseofabrightflaretheassociatedradio r responseduetoadiabaticexpansionofthesynchrotronradiationemittingsourcecomponent.Theluminosityduringthelowstatecan t beinterpretedassynchrotronemissionfromacontinuousorevenspottedaccretiondisk.ForthehighluminositystateSSCemission s a fromTHzpeaked sourcecomponentscanfullyaccount forthefluxdensityvariationsobserved intheNIRandX-raydomain. We [ concludethatatnear-infraredwavelengthstheSSCmechanismisresponsibleforallemissionfromthelowesttothebrightestflare fromSgrA*.Forthebrightflareeventof4April2007thatwascoveredfromtheradiototheX-raydomain,theSSCmodelcombined 1 withadiabaticexpansioncanexplaintherelatedpeakluminositiesanddifferentwidthsoftheflareprofilesobtainedintheNIRand v X-rayregimeaswellasthenondetectionintheradiodomain. 1 5 Keywords.blackholephysics,X-rays:general,infrared:general,accretion,accretiondisks,Galaxy:center,Galaxy:nucleus 3 1 1. 1. Introduction the EddingtonluminosityLEdd andmanyordersof magnitudes 0 belowthatofSMBHsinactivegalacticnuclei(AGN)withcom- 0 At the center of the Milky Way stellar motions and variable parablemasses(ofabout4 106M ).Thesurprisinglylowlumi- 1 emission allow us to firmly associate Sagittarius A* (SgrA*) nosityhasmotivatedmany×theore⊙ticalandobservationalefforts : with a 4 106 M super-massive black hole (Eckart & Genzel toexplaintheprocessesthatareatworkinSgrA*.Forarecent v 1996, Ge×nzel et⊙al. 1997, 2000, Ghez et al. 1998, 2000, 2003, summary of accretion models and variable accretion of stellar i X 2005a,2008,Eckartetal.2002,Scho¨deletal.2002,2003,2009, winds onto Sgr A* see Yuan (2006) and Cuadra & Nayakshin Eisenhauer2003,2005,Gillessenetal.2009). r (2006,2009). a Recentradio,near-infraredandX-rayobservationshavede- tectedvariableandpolarizedemissionandgivedetailedinsight intothephysicalemissionmechanismsatworkinSgrA*,which Sgr A* is - in terms of Eddington luminosity - the faintest mayincludeanyorallofsynchrotron,SSC,andbremsstrahlung super-massiveblackholeknown.However,duetoitsproximity emission (e.g. Baganoff et al. 2001, 2002, 2003, Eckart et al. itisbrightenoughtobestudiedingreatdetail.Withthepossible 2003, 2004, 2006ab, 2008ab, 2009, Porquet et al. 2003, 2008, exceptionoftheclosestgalaxies,noextragalacticsuper-massive Goldwurmet al. 2003, Genzelet al. 2003, Ghez et al. 2004ab, blackholewithasimilarfeebleEddingtonratewouldbeobserv- Eisenhauer et al. 2005, Belanger et al. 2006, Hornstein et al. able.Motivatedbytheneedtoexplainthevariableluminosityof 2007,Yusef-Zadehetal.2006ab,2007,2008,2009,Marroneet SgrA*wehaveanalyzeddatafromithighestandloweststates. al.2009,Dodds-Edenetal.2009).Multiwavelengthdetections InordertoseparatetheweakNIRemissionofSgrA*fromthe of the radio pointsource at sub-millimeter,X-ray,and infrared surroundingstars,theuseoflargetelescopesandadaptiveoptics wavelengthshave also been made,showingthat the luminosity (AO)isrequired.Herewepresentthefirstattempttodothiswith associated with SgrA* is on the orderof 10 9... 10 times below near-infrareddataobtainedwiththeVLT.Likewise,highresolu- − − tionisneededin theX-rayregimetoseparateSgrA* fromthe Sendoffprintrequeststo:N.Sabha([email protected]) surroundingdiffuseX-raybackground. 2 Sabha,Witzel,Eckartetal.:TheExtremeLuminosityStatesofSgrA* Table1.ThebrightestX-rayflaresfromSgrA*.Forreferencesseetext. label date Observatory α=Γ 1 X-rayflux NIRL-band 11.8µm − density fluxdensity fluxdensity (µJy) (mJy) (mJy) α Oct.26/27,2000 Chandra 0.0 0.8 0.65 0.07 - - ± ± β Oct.3,2002 XMM 1.2 0.3 2.7 0.4 - - γ Apr.4,2007 XMM 1.3±0.3 1.7±0.3 20 2 <3σ=57 ± ± ± Table2.DetailsonobservingrunsduringwhichSgrA*wasinaverylowNIRluminositystate. Telescope Instrument λ UTandJD UTandJD ObservingID StartTime StopTime VLTUT4 NACO 2.2µm 200423Sept.23:20:45 200424Sept.01:45:11 JD2453272.47969 JD2453272.57304 VLTUT4 NACO 2.2µm 200430Aug.23:49:36 200431Aug.01:28:19 JD2453248.48375 JD2454466.50000 Thetemporalcorrelationbetweentherapidvariabilityofthe with subsection 4.4we use Γ andγ as the bulk boostingfactor near-infrared(NIR)andX-rayemissionsuggeststhattheemis- andtherelativisticelectronLorentzfactor. sion showing 1033 35 erg/sflares arises from a compactsource − within a few tens of Schwarzschild radii of the SMBH. For SgrA* we assume R =2R =2GM/c2 1010 m for a 4 106M blackhole.HereR issoneSgchwarzsch∼ildradiusandR∼ t×hegrav⊙- 2. Observationsanddatareduction s g itational radius of the SMBH. One Rs then corresponds to an Near-infrared (NIR) observations of the Galactic center (GC) angular diameter of 8 µas at a distance to the Galactic cen- were carried out with the NIR camera CONICA and the adap- ∼ ter of d = 8 kpc (Reid 1993, Eisenhauer et al. 2003, Ghez et tive optics (AO) module NAOS (briefly “NACO”) at the ESO al. 2005ab). These observations can be explained in a model VLTunittelescope4(YEPUN)onParanal,Chile.Thedatawere ofanintrinsicallyfaintaccretiondiskthatisdominatedbyred- taken on the night of 30 August and 23 September, 2004. The noiseandtemporarilyharborsabrightorbitingspotpossiblyin dataset taken on 23 September 2004 turned out to be the best conjunction with a short jet (Eckart et al. 2006b, Meyer et al. available set in which SgrA* is in a quiet state. During the 30 2006ab, 2007). The phenomenon can best be studied through Augustobservationssomeweak activityat2.2µmcouldbede- the brightest flares that allow us to derive high signal to noise tected,makingthisdatasetwell-suitedtodeterminetheposition light curves and multi wavelength observations throughoutthe ofSgrA*withrespecttoneighboringstars.Thecombinationof electromagneticspectrum. bothdatasetsisideallysuitedtoobtainafluxdensityestimateor In its lowest luminosity states SgrA* is difficult to detect limitofSgrA*initsquietstate. thoughduetothepresenceofastrongdiffusebackgroundatX- ForallobservationstheinfraredwavefrontsensorofNAOS ray wavelengths and the confusion with nearby stellar sources wasusedtolocktheAOloopontheNIRbright(Ks-bandmagni- inthenear-infrared.Herewediscusstherelativeimportanceof tude 6.5)supergiantIRS7,locatedabout5.6 northofSgrA*. ′′ thebremsstrahlungandSSCprocessforthelowstateofSgrA* Thep∼ixelscalewas13.27mas. andinvestigateifthebrightestflaresofSgrA*canbeexplained The atmosphericconditions(and consequentlythe AO cor- viaaSSCmodelinvolvingup-scatteredsub-millimeterphotons rection) were stable during the observations. The seeing at the fromcompactsourcecomponents.InSects.2and3wedescribe telescope measured in the optical was 0.6”. We used an inte- theobservations,thedatareductionandthealgorithmsweused grationtime ofDIT=2secondsandan∼umberofintegratedim- toextractSgrA*inits lowstate fromthebackgroundemission ages of NDIT=15. Details on start and stop times are listed in ofthedenseclusterofhighvelocitystarsatangularseparations Table2. oflessthanabout1”fromthepositionofSgrA*.Belowwewill All observations in the Ks-band (2.2 µm) were dithered to refertothisassociationofstarsasthe’S-starcluster’.InSect.4 coveralargerareaoftheGCbymosaicimaging.Theskyback- wepresentanddiscussresults.Westartbysummarizingthere- groundfortheKs-bandobservationswasextractedfromtheme- sults ofourdeepKs imagingin subsections4.1and 4.2. In the dian of stacksof ditheredexposuresofa darkcloud – a region followingsubsectionswethendiscussvariousemissionmecha- practicallyemptyofstars – about400”northand713”westof nismsforthelowandhighluminositystatesofSgrA*.Weshow the target. All exposures were sky-subtracted, flat-fielded, and thattheSSCprocesscansuccessfullydiscribeboththelowand corrected for dead or bad pixels. The images were shifted and highluminositystatesandthat-inparticularforthehighstates stacked in a cube with a mean average to get a mosaic image - no extra mechanisms need to be involved (discussion in e.g. oftheGC.AllofthesestepswereperformedwiththeDPUSER Dodds-Eden et al. 2009, Eckart et al. 2009). A brief summary softwareforastronomicalimageanalysis(T.Ott,MPE;seealso andconclusionsarepresentedinSect.5. Eckart & Duhoux 1990). Subsequently, PSFs were extracted Throughout the paper we quote de-reddened infrared flux from these images with StarFinder (Diolaiti et al. 2000) both densitiesusingaKs-band(2.2µm)extinctioncorrectionofA = fordeconvolutionwiththeLucy-Richardson(LRLucy1974)al- Ks 2.8(Scovilleetal.2003,Scho¨deletal.2007,Scho¨deletal.2010 gorithmandforPSFsubtraction. inprep.,Buchholz,Schoedel,Eckart2009).InSect.4.1weuse The flux densities of the sources were measured by aper- Γandγtodescribetheprojectedandthreedimensionalstructure ture photometry with circular apertures of 40 mas radius and ofthecentralstellarclusterrespectively.InTable1andstarting corrected for extinction, using A = 2.8 (Scoville et al. 2003, K Sabha,Witzel,Eckartetal.:TheExtremeLuminosityStatesofSgrA* 3 position 0.5’’ Fig.1.IdentificationofindividualsourcesthatwereusedfortheiterativesubtractionoftheKs-banddatasets(Table2).Hereweshowtheimage derivedfromthe23September 2004data.Thenomenclature wastakenfromthedeconvolved H-bandimagegiveninFig.1byGillessenetal. (2006).Sourcesthatarenotcontainedintherehavelabelsstartingwith’N’.Relativepositionsandfluxdensitiesofthelabeledsourcesaregiven inTable3. Scho¨del et al. 2007, Scho¨del et al. 2010 in prep., Buchholz, and suffer most likely from the proper motion of faint sources Schoedel,Eckart2009).Possibleuncertaintiesintheextinction betweenthepresentdateandthedateusedforidentificationby by a few tenths of a magnitude alter the infrared flux densities Gillessenetal.(2009).ThenwelistinTable3theskyprojected of SgrA* by a few 10%. These variations are easily compen- relativeoffsets∆α,∆δandradialdistanceRfromSgrA*inarc- satedforbyinsignificantvariationsinthespectralindicesorthe seconds. The uncertainties in the offsets are better than a third boostingwhich donotinfluencethe generalresults obtainedin of a pixel i.e. 0.004” We then list in Table 3 the observed Ks thispaper. magnitudederivedinthispaperandtheobservedK’magnitude listed by Do et al. (2009b)correctedby an offset value of -0.2 Thefluxdensitycalibrationwascarriedoutwiththeknown magnitudes.Thescatterbetweenbothvaluesaftercorrectionfor Ks-band flux densities of IRS16C, IRS16NE, and IRS21 by this offset is 0.2 magnitudes, so that the offset corresponds to Blum,Sellgren&Depoy(1996).Subsequentlytherelativepho- 1σinmagnitudes(20%influx)andiswellwithintheexpected tometry for Sgr A* was done using 10 sources within 1′.′6 of calibrationuncertaintiesforfaintstarsinthecrowdedfield.The Sgr A* as secondary calibrators (S67, S92, S35, S8, S76, S1, difference between both mangitude values is listed in the last S2, S87, S65, S30; Gillessen et al. 2006).This results in a Ks- column.For sourcesS0-8,S0-18andS0-38no magnitudesare band flux density of the high velocity star S2 of 22 1 mJy, given by Do et al. (2009b). The large magnitude difference in ± whichcompareswellwiththemagnitudeandfluxforS2quoted thecaseofS0-12ismostlikelyduetotheblendofS59andS60. by Ghez et al. (2005b)and Genzel et al. (2003).The measure- ThetwoNIRfilters K andK’(Doetal. 2009b)areverysimi- s mentuncertaintiesforSgrA*wereobtainedonthenearbyref- larwithKs(NACO):λ =2.18µmandwidth∆λ=0.35µmand center erence star S2. The backgroundflux in the immediate vicinity K‘(NIRC):λ =2.124µmandwidth∆λ=0.351µm.Notrans- center of Sgr A* was obtained by averaging the measurements at six formationbetweenmagnitudesderivedwiththesefilterswasap- random locations in a field located about 0′.′6 west of Sgr A* plied. The 0.2 mag scatter relates to stars of different bright- that is free of obviousstellar sources. A Ks-band image of the nesses at different epochs between which they are moving at central 4.3” 2.5”is shown in Fig. 1. This field is at the center different locations in the cluster with respect to different local × of the stellar cluster of which we show a 15” 15”overviewin backgrounds.TherelativefluxdensityuncertaintyforthestarS2 × Fig.2a).Thesourcepositionsandrelativeastrometrywasestab- -whichweuseasanestimateforSgrA*-isdeterminedwithin lishedviaStarFinder.ThepositionsinTable3aregivenrelative asingleepochatfixedposition. to the position of SgrA* as determinedfrom the 23 September 2004data.Welistthenamefollowingthenomenclatureusedby Gillessenetal.(2009)andinthesecondcolumnthenameused byDoetal.(2009b).SourceslabeledwithN hadnotbeeniden- tified before. Identifications with question marks are tentative 4 Sabha,Witzel,Eckartetal.:TheExtremeLuminosityStatesofSgrA* Table3.Sourcesusedforiterativesourcesubtractionforthe23September2004data. name other ∆α ∆δ R flux Ks K’-0.2 ∆mag name arcsec acrsec arcsec mJy S62 0.01 -0.02 0.03 1.52 17.0 S17 S0-17 0.02 -0.09 0.09 8.06 15.2 15.5 -0.3 S38? -0.08 0.05 0.10 1.27 17.2 S55 0.07 -0.09 0.11 0.71 17.9 S40 0.12 0.00 0.12 1.88 16.8 S2 S0-2 0.02 0.13 0.13 22.00 14.1 13.9 0.2 S13? S0-8 -0.11 0.09 0.14 7.04 15.4 ? S19 0.06 -0.15 0.16 1.79 16.9 S14 0.16 0.12 0.20 7.41 15.3 S18 S0-38 -0.20 -0.06 0.21 2.19 16.7 ? S44 -0.08 -0.23 0.24 1.13 17.4 S20 0.21 0.12 0.24 8.80 15.1 S39 -0.10 0.23 0.25 1.37 17.2 S1 S0-1 0.00 -0.25 0.25 14.00 14.6 14.5 0.1 S63 0.24 -0.13 0.28 1.20 17.3 S4 S0-3 0.29 0.12 0.31 14.02 14.6 14.3 0.3 S22 0.17 -0.27 0.32 2.39 16.6 S12 -0.06 0.31 0.32 8.04 15.2 S23 0.32 -0.08 0.33 1.01 17.5 S52 0.19 0.27 0.33 0.98 17.5 NS2 0.18 0.32 0.36 1.06 17.4 S21 -0.33 -0.14 0.36 2.03 16.7 S36 0.27 0.25 0.36 3.66 16.1 S60/59 S0-12 -0.29 0.24 0.37 6.70 15.4 14.2 1.2 S41 -0.23 -0.31 0.38 1.10 17.4 S10 S0-6 0.04 -0.38 0.38 21.99 14.1 14.0 0.1 S5 0.34 0.19 0.39 9.47 15.1 S42 -0.17 -0.37 0.40 1.62 17.0 S9 S0-5 0.18 -0.36 0.40 12.66 14.7 14.9 -0.2 S57 0.42 -0.14 0.44 0.89 17.6 S25 S0-18 -0.11 -0.43 0.44 10.71 14.9 ? S47 0.38 0.23 0.45 2.73 16.4 S28 -0.01 0.46 0.46 1.56 17.0 S6 0.47 0.09 0.48 8.02 15.2 S8 S0-4 0.39 -0.28 0.48 17.72 14.4 14.3 0.1 S32 0.33 -0.36 0.49 2.85 16.4 NS1 0.27 0.42 0.50 1.81 16.9 S37 0.33 0.38 0.50 2.74 16.4 S7 S0-11 0.51 -0.05 0.51 10.38 15.0 15.1 -0.1 S43 -0.51 -0.15 0.53 1.30 17.2 S29 -0.21 0.49 0.54 2.33 16.6 S27 S0-27 0.14 0.53 0.55 7.34 15.3 15.5 -0.2 S49 0.56 0.04 0.56 1.60 17.0 S45 0.19 -0.52 0.56 7.59 15.3 S24 S0-28 -0.16 -0.54 0.56 6.26 15.5 15.6 -0.1 S53 0.29 0.49 0.57 1.30 17.2 S34 0.32 -0.47 0.57 8.55 15.2 S11 S0-9 0.17 -0.58 0.60 23.79 14.1 14.2 -0.1 S46 0.24 -0.56 0.61 6.92 15.4 S48 0.44 0.45 0.63 3.21 16.2 S35 S0-13 0.54 -0.43 0.69 45.90 13.3 13.3 0.0 3. Subtractingstars 2009)showthatonscalesofafewarcescondsthisisareasonable assumptionandthatPSFvariationshavetobetakenintoaccount To investigate the low luminosity state of SgrA* we use three onlyforfields 10”.Whethertheresidualextendedemissionwe independent methods to remove or strongly suppress the flux find close to S≥grA* is due to rsiduals from the subtracting al- density contributions of stars in the central 2” diameter region gorithmsorassociatedwithadditionalstellaremissionfromthe around SgrA*. All three methods give comparable results and S-starclusterisdiscussedinSect.4.1. allowustoclearlydeterminethestellarlightbackgroundatthe centeroftheMilkyWayagainstwhichSgrA*hastobedetected. WeassumethatthePSFasdeterminedfromstarsinthecen- tralfewarcsecondsoftheimageisuniformacrossthecentralS- starcluster.Investigationsoflargerimages(e.g.Buchholzetal. Sabha,Witzel,Eckartetal.:TheExtremeLuminosityStatesofSgrA* 5 3.1.Linearextractionofextendedfluxdensity 100:1weshowinFig.2b)alow-passfilteredversionoftheKs- band image that was obtained by following the algorithm out- With the point spread function P and the object distribution O linedabove.Theprominentsourceshavebeenlabeledwiththeir wecanwritetheformationofanimageI as names.InFigs.2c),d)ande)weshowtheextendedfluxdensity distributionofthefollowingsources:IRS1W,IRS21,IRS10W. I =O P=(∆+E) P=∆ P+E P. (1) ∗ ∗ ∗ ∗ Thesebow-shockstructuresareshownattheangularresolution ofabout0.1”asdeliveredbytheAOsystem.Theycomparevery Here the symbol denotes the convolution operator. The ∗ wellwiththesourcestructurespublishedbyTanneretal.2005. variable ∆ denotes the distribution of stellar sources and E the Here the algorithm detects very bright sources like IRS 7 also distributionofextendedemission.Bothtypesofsourcesareas- asanextendedobjectsincethestarisoverexposedandnotwell sumed to be ideally unresolved or resolved with respect to the describedbytheusedPSF.InFig.3weshowresultsofthealgo- pointspreadfunction.Toproduceahigh-passfilteredimagewe rithmonthecentral2” 2”.Inadditiontoresidualsofthefilter cancalculateasmooth-subtractedimageΣas × processaroundthepositionofbrightstars,weseeanincreased fluxdensitylevelwithinthedashed0.5”diametercirclecentered Σ= I G I =(∆+E) P G (∆+E) P. (2) ∗ − ∗ ∗ − ∗ onthepositionofSgrA*.Thedisadvantageofthisalgorithmis that any point-like emission from SgrA* is also strongly sup- HereweuseanarrowGaussianGnormalizedtoanintegral pressed. The residuals (ringing) still evident around the bright powerofunity.Thiscanberewrittenas stars are a consequence of the choice of the apodization filter thatneedstobedefinedinthecaseoflineardeconvolution.This Σ=∆ (P G P)+(E P G E P). (3) ∗ ∗ − ∗ ∗ − ∗ filter is used to suppressthe usual highspatial frequencynoise that arises due to small number division problems. We used a Since the width of the extendedemission is expected to be cosine-bellshapedfilter thatpreservesthe highangularresolu- muchlargerthanthefullwidthathalfmaximumofthePSF,and tionbutresultsinsomeresidualringing.However,theresulton in particular since the GaussianG is narrow with respect to P, thebackgroundemissionisnotstronglyinfluencedbythis,since wecaninferthatE P G E P.Thenthedifferentialpoint ∗ ∗ ∼ ∗ the bright stars are sufficiently far away from the central posi- spread function P G P is the PSF of the high-pass filtered ∗ − tion.The comparisonto theresults ofthe othertwo algorithms differentialimage usedtoremovethecontributionsofstarsnearSgrA*showsthat theresultisalsolittleaffectedbythemuchfainterstarscloseto Σ ∆ (P G P). (4) ∼ ∗ ∗ − SgrA*.Theircontributionhasbeenefficientlysuppressedbythe algorithm. Since Σ is fully dominated by the contribution of the dis- tributionofunresolvedstellarsources,thisdistribution∆canbe retrievedviaalineardeconvolutionofthedifferentialimagewith 3.2.IterativePSFsubtraction thedifferentialPSF TheiterativePSFsubtractionwascarriedoutwithinthecentral 2”to3”aroundthepositionofSgrA*.Thiswasperformedbyre- ∆ Σ%(P G P). (5) ∼ ∗ − sizing,shiftingandscalingthePSFtothepositionandthevalue ofeach star andthen subtractit. The sourcesused forthispro- Here the symbol % denotes the deconvolution operation. cessarelistedinTable3andareshowninFig.1.Atotalnumber Consequentlythedistributionofextendedflux(i.e.alow-passed of51starsweresubtractedsothattheresultingbackgroundwas filteredversionoftheimage)E Pcannowbeisolatedvia ∗ assmoothaspossible.InFig.4weshowtheresultingsubtracted image of the area of interest around SgrA*. All stars brighter E P=I ∆ P (6) ∗ − ∗ thanabout17.5m (seeKLFinFig.6)havebeensubtractedwith ascaledversionofthePSF.ThethinlinesinFigs.4a)andb)are or usedtotriangulatethepositionofSgrA*.Fig.4a)showstheim- I Σ P%(P G P)=∆ P+E P ∆ P= E P. (7) ageobtainedfromasectionofthe30AugustdatasetwithSgrA* − ∗ ∗ − ∗ ∗ − ∗ ∗ flaring.ComparedtoS2with 22mJySgrA*hasabrightnessof ∼ The advantage of this new method is that it is independent about4mJy.Fig.4b)showstheimageobtainedfromasectionof of inputmodels,i.e. it doesnotdependon the identificationof the23SeptemberdatasetwithSgrA*inaquiescentphase.Here individual stars or on assumptions on the existence or proper- SgrA* is clearly not detected and is fainter than about 2 mJy ties of a diffuse backgroundflux density distribution. Also the (de-reddened). method only uses linear operations, i.e. image subtraction and Figure4alsorevealsthepresenceoffaintresidualextended linear convolution and deconvolution (Fourier multiplications emission-centeredonthepositionofSgrA*.Thisresidualemis- and divisions). Therefore it is not dependent on the flux den- sionismostlikelyfromthecentralS-starclusterofhighvelocity sityofsourcesandnumbersofiterations,asisthecaseformany stars. We determinedthe position of SgrA* from the data with non-linear algorithms (e.g. the Lucy-Richardson or maximum SgrA*inaflarestatetakenon30August,2004.Takinganupper entropy algorithm). In order to demonstrate the validity of the limitoftheobservedtwodimensionalprojectedstellarvelocity approachwe show the results we obtained on the central 15” dispersionof 1000km/sandthefactthatfortheGalacticcen- × ∼ 15” of the 23 September data in Fig. 2. For all the prominent terpropermotionof1mas/yrcorrespondstoabout39km/s,the extendedKs-bandsources(Fig.2)the extendedKs-bandemis- relative positional uncertainty for stars observed between both sioncanberetrievedanditsstructurecomparesverywelltothe epochsisexpectedtobewellbelow2mas.ThinlinesinFigs.4a) previously published results (e.g. Ott, Eckart & Genzel 1999, and b) are used to triangulate the position of SgrA*. Figure 4 Tanneretal.2002,2005).(Acomparisonofdifferentdeconvolu- showsthatforthedatasettakenon23September2004noNIR tionalgorithmsusedinthecrowdedGalacticcenterfieldisgiven counterpartofSgrA*wasdetected.For30August2004wefind in Ott, Eckart & Genzel 1999.) At a dynamic range of about a NIR counterpartof SgrA* with a dereddenedflux density of 6 Sabha,Witzel,Eckartetal.:TheExtremeLuminosityStatesofSgrA* Fig.2. TheKs-bandimageoftheGalacticcenter region(a)takenon 23 September 2004. The central 15” 15” image was taken with the × adaptive optics system NACO at the ESO VLT and the results of the low-passfilteralgorithm.(b,c,d,e).Thecontourlinesareseparatedby 8%ofthepeakbrightnessofIRS10W. Fig.4. Results of the iterative star subtraction obtained for the 30 August(a)23Septemberdata(b)asdescribedinSect.3.2. Fig.3. The inner 2” 2” of the central stellar cluster (23 September × 2004).ThepositionofSgrA*isatthecenteroftheimagesa)andb).In panela)weshowthecorrespondingimagesectiontakenoutoftheKs- bandimageinFig.2a).Inpanelb)weshowthecorrespondingimage sectiontakenoutofthelow-passfilteredversioninFig.2b). about4mJywitha3σuncertaintyofabout2mJy.Estimatesof thefluxdensitylimitsanduncertaintiesaregiveninSect.4.2. 3.3.AutomaticPSFsubtraction Fig.5. Result of the automatic PSF subtraction obtained for the 23 We also analyzed the images with the StarFinder (Diolaiti et September2004data. al. 2000)programpackage.It notonly providesaccurate point source photometry but also a reliable estimation of the diffuse background emission. With a point spread function (PSF) ex- 4. Resultsanddiscussion tractedfrombrightstarsneartheguidestar(inthiscaseIRS7), we performed photometry and astrometry on the deconvolved Firstweanalyzethepropertiesofthecentralclusterofhighve- imageviaPSFfittingwiththeStarFinderpackage.Theresulting locitystarsandcomparethemtotheresultsofpublishedinves- diffuse backgroundemission is shown in Fig. 5. In addition to tigations.Wecanthenconfidentlyderivethefluxdensitylimits some residualemission from unresolvedstars this method also on SgrA* and show that contributions to the lowest luminos- reveals extended emission centered on the position of SrgA* itystatesfrombremsstrahlungareunlikely.Wethendiscussthe within the dashed0.5”diametercircle centeredon the position extremeluminositystates of SgrA*in the frameworkof a syn- of SgrA*. This finding agrees with the low-pass filtered image chrotronself-Comptonmechanism. inFig.3. 4.1.ImagingtheS-starclusterandthedetectionofSgrA*in itslowluminositystate The detected number of 51 stars within a radial distance of about 0.5” from SgrA* results in a surface number density of 68 8arcsec 2,takingthe square-rootasthe uncertaintyofthat − ± value. This result agrees with the central number density of Sabha,Witzel,Eckartetal.:TheExtremeLuminosityStatesofSgrA* 7 30 August 2004 23:49:36 to 01:28:19 1.0 20 1 15 ) mJy] (N flux [10 g 0.5 o 0.5 l 5 0 0 20 40 60 80 100 0.0 0 whm [arcsec]000...243 1122 1144 1166 1818 psf f0.1 0 20 40 60 80 100 time [min] Ks magnitude Fig.8. The 30 August 2004 light curve of the flux density measured Fig.6.KLFhistogramofthestarsdetectedinthecentralfieldderived ina40masradiuscircularaperturecenteredonthepositionofSgrA* from the 23 September 2004 data. The straight full and dashed lines (black).WeshowthelightcurveofthereferencestarS2ingreen.The indicatetheKLFslopeof0.21 0.02foundforradiioflessthan6”by bottompanelshowstheFWHMseeinginarcsecondsmeasuredonthe ± Buchholzetal.(2009). PSFextractedforthefield.Thegreypointsshowthebackgroundcounts nearSgrA*.Thewidthoftheerrorbarsisclosetothesizeofthedata points. y nsit 1.01E0 23 September 2004 nte 23:20:45 to 01:45:11 d i 0.8 20 e g a r e v a 15 y all mJy] uth 0.5 flux [10 m zi e a 5 v ati el 0 r 0 50 100 150 1E−2 0.02radius in arc0s1e.E−1c1onds0.2 0.3 whm [arcsec]000...243 psf f0.1 0 50 100 150 Fig.7. Azimuthal average of the diffuse background emission as de- time [min] rivedfromthethreedifferentmethodsapplied:lowpassfiltering(red), manualPSFsubtraction(green),andautomaticPSFsubtraction(blue). Fig.9.ThesameasFig.8butfor23September2004. Thecurves(meanfluxand1σuncertaintyperpixel)havebeencalcu- latedinanuliof39.8mas(3pixels)widthandnormalizedtothevalue at30masradiuscorrespondingtooneresolutionelementat2.2µm.The blackdashedlinemarksaprofilewithanexponentialdecreaseof0.2. no significant deviation from a straight powerlaw line can be detected- implyingthatthe completenessis highandprobably comparabletothe 70%valuederivedformag =17byScho¨del K 60 10arcsec 2 givenby Do et al. (2009b)in their Figs. 9 and etal.(2007).Inthe∼intervalrangingfromKs=17.50to18.25the − ± 10. stellar countsdrop quicklyto about20%of the value expected Figure6showstheKLFhistogram(K-bandluminosityfunc- fromthestraightpowerlawline. tion)thatcanbederivedforthestarsdetectedinthecentralfield. All three methods we used to correct for the flux density Thebinningof0.75magnitudesallowsforasufficientnumberof contribution of the stars in the central 2” reveal faint extended binsto clearly detectthe linearslope in the doublelogarithmic emission around SgrA* (see Figs. 3b, Fig. 4b and Fig. 5). For plot and to have a sufficiently large number of sources per bin the iterative and automatic PSF subtraction the PSFs were ex- (about10) at the same time. With d log(N)/d log(Ks)=0.3 0.1 tractedwitharadiusof1”,whichisabouttwicetheFWHMof ± the data compare well with the KLF slope of 0.21 0.02found the S-star cluster. In case of a PSF misplacement a significant ± fortheinnerfield(R<6 )byBuchholzetal.(2009). flux density contribution to the central position can only come ′′ Withinthecentral0.5arcsecondradiusregionaroundSgrA* fromtheaboutfivestars thatarelocatedwithin oneFWHM of and in the magnitudeintervalrangingfromKs=16.75 to 17.50 SgrA*. They have a median brightnessof about 2 mJy. To ex- 8 Sabha,Witzel,Eckartetal.:TheExtremeLuminosityStatesofSgrA* plain all of the 2 mJy at the center by this effect, each star sivestarsthataretooyoungtobedynamicallyrelaxed.Thesmall ∼ wouldhavetoprovideabout0.4mJyor20%ofitsfluxdensity. valueoftheprojecteddiffuselightexponentΓ Γ may diffuse inner ∼ Thiscanonlyberealizedbyasystematicpositionalshiftofthese therefore imply the absence of a pronounced, relaxed cusp of starstowardsthecenterbyabout1pixel 13maseach.Still,the stars. ∼ positionalaccuracywhichistypicallyreachedisontheorderof However,there may in fact exist a deficit of late-type stars a fewtenthsofapixel.Largerdisplacementsresultin aclearly near Sgr A* (see also Genzel et al. 2003, Fig. 7). It may well identifiablecharacteristicplus/minuspatternintheresidualflux bethatmostofthespectroscopicallyidentifiedlatetypestarsat distribution along the shift direction. However, allowing for a smallprojecteddistancesareatlargerthreedimensionalradiir maximum positional uncertainty of 1 pixel and approximating RfromSgrA*.InthiscasetheobservedΓ Γ willbea diffuse inner ∼ theindependentshiftsoffivestarsbyfiveshiftsofasinglestar mixturebetweenthemuchsteeperΓ forearlytypestarsand early that follows a random walk pattern, the expected effective dis- thelowervalueΓ forlatetypestars.Adetaileddiscussionis late placement is 1/√5 pixels for a single shift of each star. It will giveninDoetal.(2009b),Buchholzetal.(2009),Scho¨deletal. result in a 5% peak flux contribution of each of the 5 stars - (2007),andGenzeletal.(2003). assumingthatthe displacementsare systematicallytowardsthe The main result for the present analysis of faint lumi- center, i.e. a total maximum contribution of 0.4 mJy. This im- nosity states of SgrA* is that the observed flat background plies that about one 20%-30% of the flux density detected at light and number density distribution described by the expo- thecentermaybeexplainedbyapositionalmisplacementofthe nent Γdiffuse Γinner as well as the high degree of completeness ∼ neighboringstars.Thereforeweassumethatthebulk(morethan reached around Ks=17.5 allows us to clearly distinguish the 2/3)of thisextendedemission towardthe centercanbe associ- emission of SgrA* against the stellar light background at the atedwiththe 0.5”-1”diameterS-starclusteraroundSgrA*and centeroftheMilkyWay.Thisalso showsthatSgrA*isideally isduetofaint∼starsatorbeyondthecompletenesslimitreached suitedto performa case studyto investigatethissuper-massive intheKLF. blackholeinitslowestactivitystate. The extended residual emission is not distributed az- imuthally uniformaboutthe position of SgrA*.This is not ex- 4.2.ObservingSgrA*atlowluminosities pectedeither.Theshapeoftheresidualemissionwillalwaysbe dominated by the randomly distributed few brightest stars that Highangularresolutionimagesin thenear-infraredallowusto contributetoit.Alsothelightofthecentralstellarclusterisnot unambiguouslyattributebrightdereddenedfluxlevelstoSgrA* distributed azimuthally uniform on any scale: On scales larger (e.g.Genzeletal.2003,Eckartetal.2004,Ghezetal.2004ab, than0.5pcitisaffectedbydustabsorption(e.g.extinctionmap Hornstein et al. 2006, Do et al. 2009a). The identification of by Buchholz et al. 2009), on scales less than 0.5 pc the bright fainter emission from SgrA* becomes increasingly difficult, membersoftheIRS16cluster arepredominantlylocatedto the since one can expect confusion from the 1” diameter S-star ∼ east, and during the past decade in the central arcsecond most clusterthatiscenteredonthelocationofSgrA*.Duetothehigh ofthebrighterS-starshavebeenlocatedtothesouthandeastof propermotionsof thestars withintheS-star cluster thisconfu- SgrA*. sionalsochangesonthetimescalesofmonthstoyears.Fromthe The diffuse background emission can be compared to the locationofSgrA*Doetal.(2009a)findobserved0.082 0.017 projecteddistribution of stars Σ(R) R Γ, with R being the pro- mJy(K = 17.2)ordereddened1.75 0.36mJy(assumin±gtheir − ′ ∝ ± jectedradius.Independentoftheappliedmethodwefindthatthe valueof A = 3.3)asthethefaintestobservedK fluxdensity K ′ ′ azimuthallyaveragedresidualdiffusebackgroundemissioncen- (see also Hornstein et al. 2002 and Eckart et al. 2006). Using teredatthepositionofSgrA*decreasesverygentlyasafunction A =2.8thisresultsinafluxdensityof1.1 0.2mJy K ′ ± of radius (Fig. 7). The ratio between the brightness measured ForthelowfluxdensitystateDoetal.(2009a)reportedred withinorattheedgeofthecentralresolutionelement(R 0.03”) colorsand variabilitycomparedto stellar sources.For the very ∼ andataprojectedradiusofe.g.R=0.2”is1.5 0.15,correspond- lowluminositylevelstheyreportwithanaveragepowerlawex- ± ingtoΓ =0.20 0.05.Thisisconsistentwiththedistribution ponentof-0.17 0.32abluerspectrumthanthatreportedearlier diffuse ± ± ofnumberdensitycountsofthestellarpopulationsinthecentral byHornsteinetal. (2002)witha powerlaw slopeof0.6 0.2. ± arcsecondsderivedfromimagingVLTandKeckdata.Buchholz Thecontaminationfromnearby(predominantlyblue)starsises- etal.(2009)andDoetal.(2009b)findaΓ 1.5 0.2fortheyoung timatedtocontributeamaximumofabout35%ofthefluxtoac- ∼ ± stars, butamuchflatterdistributionforthelate-type(old)stars countforthisdifferenceinthespectralslope.Doetal.(2009a) withΓ 0.17 0.09orevenΓ -0.12 0.09,respectively.Forpure concludethatevenwhentheemissionisfaintalargefractionof ∼ ± ∼ ± imagingDoetal.(2009b)quoteΓ =0.19 0.06insidearadius the fluxarisingfromthelocationofSgrA*is likelynon-stellar inner ± ofR=3”. and can be attributed to physical processes associated with the In case of a relaxed stellar cluster around a supermassive blackhole. black hole, stellar dynamics predicts to observe a cusp, i.e. a Ourdataallowustoprovideanewindependentestimateon density increasetoward the black holewith Γ = γ 1 = 0.5 to the flux density ofSgrA* in some of its loweststates basedon − 0.75(Bahcall&Wolf1976,Murphy1991;Lightman&Shapiro VLTdata. 1977;Alexander&Hopman2009).Hereγdenotestheexponent In a circular aperture of a diameter of 66 mas diameter (5 ofthethreedimensionaldistributionwhichdoesnotsufferfrom pixelsoraboutoneresolutionelement)wemeasuredereddened projection effects but is harder to deduce from observed data. fluxdensities(using A = 2.8)1.5 0.4mJy,1.3 0.3mJy,and K ± ± Onlyinthecaseofveryextremestellardensitiescollisionscan 1.3 0.2mJy for the low-pass filtering, iterative, and automatic ± leadtoaΓaslowas0.5.Buttherequiredhighdensitiesarenot PSFsubtractionmethod,respectively. reachedintheGalacticcenter. The uncertainties have been derived from the flux density The observedvalues of Γ are significantly lower than what measurements in the central 5 5 pixel aperture and the up- × is predicted by theory. The principal reason is probably to be per limits of the measurement uncertainties per pixel as plot- soughtinthestellarpopulationinthecentralarcseconds,which ted in Fig. 7. These upper limits are 0.33 mJy, 0.24 mJy and towardsSgrA*becomesincreasinglydominatedbyyoungmas- 0.17 mJy for the three methods, respectively. Based on these Sabha,Witzel,Eckartetal.:TheExtremeLuminosityStatesofSgrA* 9 data we derived an upper limit on the formal uncertainties in anyrandom5 5pixelapertureinthecentral0.6”diameterfield × of0.066mJy,0.048mJy and0.034mJyforthe threemethods, respectively.Weadoptedthesevaluesforthecentralaperture.In order to obtain a conservative estimate we added in each case these valuesfive times, so thatthe finaluncertaintyamountsto sixtimesthevalueexpectedforanapertureofthissize-based on the radial averages. There is no clear detection of a source at that position. If the observed flux density limit is fully at- tributed to SgrA* this corresponds to a clear non-detection of any point source at that position with a flux density limit of 2.4 mJy for SgrA* (K 16.3; observed reddened magnitude). s If all of it is stellar, th∼e upper limit is defined by the uncer- 10 0 10 1 10 2 10 3 10 4 10 5 taintyof the measurementandthe limitfora flux densityfrom a non-stellar source at the position of SgrA* is 0.9 mJy (3σ, de-reddenedandK 17.3asanobservedreddenedmagnitude). s ∼ Whileourdatadonotallowustoconfirmtheexistanceofacon- stantquiescentstate,ourfluxdensitylimitisconsistentwiththe flux given by Do et al. (2009a). This flux density limit is also consistent with the light curves of SgrA* shown in Figs.8 and 9. They were obtained in a 40 mas radius aperture centered at the position of SgrA*. The light curveswere taken withoutre- movingany stars from the sourroundingsand the aperturesize ofonly40maswaschosentominimizethecontaminationfrom Fig.10.SketchoftheSgrA*surroundingswithina105Schwarzschild neighboring stars. The bottom parts of Figs.8 and 9 show the radius.TheSMBHenclosesthecentral1Rs volumesurroundedbyan edgeonseendiskwithindicatedspots.Thecirclesarelogarithmically FWHMofthePSFextractedonanearbystar.Thesegraphsshow scaledandlabeledwiththeirradiiinunitsofR .Duringandafterflares thattheseeingandAOperformancewereverystableandsimilar s thespotsexpand tomeettheaccretionflowdensityof about 107cm 3 duringthemeasurementsonbothdates.Especiallyinthesecond − atanapproximateradiusof1000R .Theedgeofthe1.4”FWHMsize halfofthe30AugustlightcurveinFig.8SgrA*wassufficiently Bondisphereislocatedataradiusosfabout 8 104R fora4 106M brightto bedetected,whileitwas ina low state duringtheen- (Baganoffetal.2001,2003). ∼ × S × ⊙ tiretimeduringwhichthe23SeptemberlightcurveinFig.9was taken. Our flux density limit for the 23 Septemberdata is con- sistentwiththecompletenesslimitwereachedinthecentralstar factor is g(ν,T) 0.54 ln(4.7 1010 T/ν). For the X-ray lumi- ∼ × × counts(seeSect. 4.1). nosity in the 2-10 keV range of a H/He plasma this results in L(erg) 1033n2T1/2R3 withthesourceradiusRgivenin pc,the s ≈ e 8 electrondensityn givenincm 3,andthetemperatureT given e − 8 inunityof108K. TheGauntfactorimpliesthatforachangein 4.3.BremsstrahlungemissionfromSgrA* theobservingfrequencyfrom 1018HzintheX-raysto 1014Hz ∼ ∼ 4.3.1. ThequiescentstateX-rayemissionfromSgrA* in theNIRforconstantT>>hν/ktheGauntfactorchangessig- nificantlybyafactorofln(104) 10.SointotaltheKs-bandlu- Baganoff et al. (2001, 2003) reported an extended (R>103 Rs) minosityexpectedoverthisfreq∼uencyrangeisabout1000times thermalbremsstrahlungsourceco-spatialwiththepositionofthe lowerthantheX-rayluminosity.However,alreadyfora 1mJy stronglyvariablepointsourceatthelocationofSgrA*(seealso Ks-bandfluxdensitycontributionandhightemperature∼sabove Quataert2003).Theauthorsderive1.4” 0.14”fortheintrinsic 108KthepredictedX-rayfluxwouldwellexceedthemeasured FWHMsizeofthesource.Thiscorrespo±ndsto 8 104RS fora values. 4 106 M blackhole. Thescale of the extende∼ds×tructurecen- Substantialfluxdensitycontributionsduetobremsstrahlung te×redonS⊙grA*isconsistentwiththeexpectedBondiaccretion can only occur if a sufficient amount of ’cooler’ gas (i.e. radius(1”-2”;Bondi1952)for matteraccretinghydrodynami- <<108 K)ismixedintothecentralaccretionflowordisk.Such callyontotheSMBH.ForthebrightflareemissionoftheX-ray a two phase medium has alreadybeen discussed in the context point source bremsstrahlung is not a likely mechanism to pro- offlaresfromSgrA*(Yuanetal.2003,seealsoPageetal.2004, duce the observed NIR flux density excursions (Genzel et al. Nayakshin&Sunyaev2003).Apossiblequiescentphaseatlow 2003, Yuan et al. 2003, Quataert, 2002). In part motivated by infrared Ks-band flux density could in principle be provided thebluespectrumreportedbyDoetal.(2009a)-assumingthat through bremsstrahlung emission from a cooler denser phase notallofthebluecharacterisduetostellarcontamination-we embedded in the hot accretion flow or in the outer parts of a investigatehereifthelowestNIRfluxdensityvaluescanbeex- potentialaccretiondisk.InluminousAGNacoolopticallythick plainedbyabremsstrahlungcontributionfromahotdisk. diskwithT 105Kisbelievedtocoexistwithahotopticallythin coronawith∼T 109K.AtthelowerSMBHmassandluminosity ∼ of SgrA* such materialcould have an even lower temperature. 4.3.2. PossiblelowstatebremsstrahlungNIRluminosity? However,alowerlimittothetemperatureofsuchcoolinclosure We now estimate the possible contribution of the X-ray emit- isgivenbythefactthatnostrongrecombinationlineemissionis ting gas that is associated with the compact disk or jet foot- observedtowardsSgrA*.Onlyfortemperaturesabove106Kthe point of SgrA* to its Ks-band luminosity. The frequency contributiontothetotalluminosityfromthermalbremsstrahlung and temperature dependency of the volume emissivity for the is greater than that from recombinationradiation. This implies bremsstrahlung is E dν g(ν,T) exp(-hν)dν. Here the Gaunt for106Ka Ks-bandluminosityof L(erg) 1029n2R3. Ata dis- ν ∼ × kT s ∼ e 10 Sabha,Witzel,Eckartetal.:TheExtremeLuminosityStatesofSgrA* Table4.SourcecomponentparametersforSSCmodelsofthebrightestX-rayflaresfromSgrA*. model γ γ S α R ν B S S S S S 1 2 max, synch 0 max MIR, NIR, NIR, NIR, X ray, obs obs synch synch synch SSC −SSC label [Jy] [GHz] [G] [mJy] [mJy] [mJy] [mJy] [µJy] @11.8µm @3.8µm @2.2µm @2.2µm @2-10keV 1σ 0.1 0.1 0.1 250 10 1.0 1.0 1.0 1.0 20 → ± ± ± ± ± ± ± ± ± ± Aα 360 2900 1.9 1.19 0.3 1850 18 59 15 8.0 0 0.65 Aβ 360 2900 3.2 1.25 0.3 1850 12 82 20 10 0 2.6 Aγ 360 2900 1.3 1.05 0.2 1850 11 58 18 10 0 1.8 Bα 6 1300 2.8 1.10 0.3 2190 26 133 20 0.0 11 0.65 Bβ 6 1300 4.3 0.98 0.3 2190 18 226 26 0.0 15 2.6 Bγ 6 1300 3.3 1.01 0.3 2190 20 219 17 0 10 1.8 ξ 360 2900 11.5 1.40 20.5 480 6 0 0 0 0 <0.04 A 360 2900 0.5 1.10 0.1 2360 51 23 6.7 3.7 0 0.038 low B 6 1300 0.8 1.30 0.2 1230 15 15 3.6 0 3.7 0.037 low Q 70 2050 0.08 1.30 0.1 1080 44 0.58 0.18 0.1 <0.01 <0.010 spot Table5.Modeldensities,lowerSSCcutofffrequenciesandlowerlimitsonthesourcecomponentmasses model N c(γ2ν ) 1 ρ mass 0 1 max,obs − erg 1cm 3 nm cm 3 M − − − Aα 0.25 1.3 3 107 3 ⊙10 16 − Aβ 0.22 1.3 6×107 5×10 16 − Aγ 14 1.3 2×108 5×10 16 − × × Bα 0.74 4100 2 1011 2 10 12 − Bβ 13 4100 3×1011 3×10 12 − Bγ 7 4100 2×1011 2×10 12 − × × ξ 4 10 4 4.8 1 106 3 10 12 − − × × × A 0.39 1.0 1 107 3 10 18 Blow 0.013 7300 3×1011 8×10−13 Qlow 7 10 4 56 3×107 9×10−18 spot × − × × − tance of 8 kpc and a wavelength of 2.2µm 1 mJy of dered- 4.4.SynchrotronSelf-ComptonemissionfromSgrA* denedflux∼densitycorrespondstoaluminostityofνL =1.2 1034 ν × Rapidvariabilityontimescalesofafewminutesandthestrong ergs/s=3.1L . ⊙ indicationofsynchronous(polarized)NIRand X-rayflux den- sity variations linked with time delayed sub-mm/mm flux ex- cursionsclearlysuggeststhatanonthermalemissionmechanism In order to obtain 1 mJy Ks-band flux density the prod- isatwork.Synchrotronemissionfromcompactsourcecompo- uct n2eR3 needs to be on the order of 8×104. This allows us to nentsthatunavoidablyscatterelectromagneticpowerintotheX- estimate the required densities: The Ks-band diffraction limit raydomainappeartobea primechoiceforsuchamechanism. of the VLT UT4 corresponds to a projected linear size of Belowweinvestigatethehighestandlowestluminositystatesto 2.4 10−3pc 8000RS atthedistanceofSgrA*.Similarly,1RS validatetheapplicabilityoftheSSCmechanism. cor×responds∼to3 10 7pc. − × 4.4.1. EssentialsofcurrentSgrA*SEDmodeling For such an unresolved or even more compact source with Generallytheelectronenergydistribution N(E)responsiblefor sizes ranging from 1 to 8000 R we find electron densities theoverallSED ofSgrA*isdescribedbya power-law N(E) = S from 2 1012cm 3 to 2 106cm 3 and Thompson scattering op- N E p = N (mc2γ) p with a Lorentz factor γ and an electron − − 0 − 0 − × × ticaldepthsontheorderof1to0.01,respectively.Thisimplies power-lawindex p.Thispower-lawexhibitsseveralbreaksat thatforan’unresolved’bremsstrahlungemittingKs-bandsource the electron density is several orders of magnitude higher than γ <γ <γ , (8) min cool max the estimated density of 107cm 3 of hotter gasin the accretion − flow(Yuanetal.2003).Combinedwiththehighopticaldepths where γ , γ and γ are the minimum, maximum, and min max cool this shows that a substantial bremsstrahlung contribution of a the ’cooling break’ Lorentz factors, respectively (Yuan et al. compact source to the Ks-band flux density even in the quies- 2003,Quataert2002,Mahadevan& Quataert1997).Here γ cool cent phase can therefore be regarded to be very unlikely (see marksthedifferencebetweentheemissionofathermaldistribu- alsoYuanetal.2003). tionofelectronswithγ =γ andγ γ and min,thermal min max,thermal cool ∼

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