ThenucleardiscoftheMilkyWay:Earlyformation,longquiescence,andstarburstactivityonebillionyearsagoF.Nogueras-Lara1,R.Schödel1,A.T.Gallego-Calvente1,E.Gallego-Cano1,B.Shahzamanian1,H.Dong1,N.Neumayer2,M.Hilker3,F.Najarro4,S.Nishiyama5,A.Feldmeier-Krause6,J.H.V.Girard7andS.Cassisi81InstitutodeAstrofísicadeAndalucía(CSIC),GlorietadelaAstronomías/n,18008Granada,Spainemail:fnoguer@iaa.es2Max-PlanckInstituteforAstronomy,Königstuhl17,69117Heidelberg,Germany3EuropeanSouthernObservatory(ESO),Karl-Schwazschild-Strasse2,85748Garching,Germany4DepartamentodeAstrofísica,CentrodeAstrobiología(CSIC-INTA),Crta.TorrejónaAjalvirkm4,28850,TorrejóndeArdoz,Spain5MiyagiUniversityofEducation,Aoba-ku,980-0845Sendai,Japan6TheUniversityofChicago,TheDepartmentofAstronomyandAstrophysics,5640S.EllisAve,Chicago,IL60637,USA7SpaceTelescopeScienceInstitute,Baltimore,MD21218,USA8INAF-AstronomicalObservatoryofAbruzzo,ViaM.Maggini,sn.64100Teramo,ItalyThenucleardiscisadensestellarstructureatthecentreoftheMilkyWay,witharadiusof~150pc1.Ithasbeenaplaceofintensestarformationinthepastseveraltensofmillionsofyears1,2,3butitsoverallformationhistoryhasremainedunknownuptonow2.Herewereportthefirstdetailedstarformationhistoryof thisregion.Thebulkof itsstars formedat leasteightbillionyearsago.This initialactivitywasfollowedbyalongperiodofquiescencethatwasendedbyanoutstandingeventabout1Gyrago,duringwhichroughly5%ofitsmassformedinatimewindow~100Myr,inwhatmayarguablyhavebeen one of the most energetic events in the history of theMilkyWay. Star formation continuedsubsequentlyonalowerlevel,creatingafewpercentofthestellarmassinthepast~500Myr,withanincreasedrateupto~30Myrago.Ourfindingscontradictthepreviouslyacceptedparadigmofquasi-continuousstarformationatthecentreoftheMilkyWay4.ThelongquiescentphaseagreeswiththeoverallquiescenthistoryoftheMilkyWay2,5andsuggeststhatourGalaxy’sbarmaynothaveexisteduntilrecently,orthatgastransportthroughthebarwasextremelyinefficientduringalongstretchoftheMilkyWay'slife,andthatthecentralblackholemayhaveacquiredmostofitsmassalreadyintheearlydaysoftheMilkyWay. The GALACTICNUCLEUS survey6 has been specifically designed to study the structure andformationhistoryof theGalactic centre (GC)with sensitive,highangular resolution (0.2” fullwidthathalfmaximum),near-infraredimages.Hereweanalysearectangularregionof∼37.5ʹ×8.3ʹ(about1600pc2atthedistanceoftheGC)centredonSagittariusA*(SgrA*,17h45m40.05s, -29◦00’27.9”,Fig.1,bottom),theMilkyWay’scentralblackhole7,8,9.AregionclosetoSgrA*wasexcludedfromtheanalysisbecause of the extreme stellar crowding, sowere regions dominated by dark foreground clouds. Thefinalcatalogueincludesaccuratephotometryformorethan700,000stars,supersedingothersurveysoftheGCbyordersofmagnitude6,10.

TheHKscolourmagnitudediagram(CMD,Fig.1,topleft)showsaprominentverticalfeatureatH-Ks>1.3,whichcorrespondstogiantstarslocatedattheGC.Starswithbluercolourslieinspiralarmsintheforeground6,10.Thediagonalhigh-densityfeaturethatextendsfromroughly(Ks=14.5,H-Ks=1.3)to(Ks =16.5,H-Ks =3) is causedbydifferentialextinctionand reddeningof theso-called redclump (RC),whichmarksthelocationofheliumcoreburninggiantsinmetal-rich,oldpopulations.StarsintheRCcanbeusedasstandardcandlesbecauseoftheirhighlysimilarluminositiesandtemperaturesacrossabroadrange of ages,metallicities, andmasses11.We used these stars to correct our data for the effects ofinterstellar extinction and reddening, and finally created a so-calledKs-band luminosity function (KLF,correctedforcompleteness,Fig.1,topright),whichreflectsthenumberofstarsingivenbrightnessbins.

Fig.1:Lowerpanel:Ks-bandimageoftheGALACTICNUCLEUSsurveyregionexaminedforthisstudy.Thepositions of Sgr A*, the Arches and the Quintuplet clusters are indicated. The cross-shaped regionoutlinedbyawhitedashed linewasexcludedbecauseof toohighsourcecrowding.Thedarkrectangleright next to the Arches cluster is a field with incomplete data. Upper left: Observed H-Ks CMD. Theverticaldashedlinesshowthetwocolourcutsusedtoexcludeforegroundstars(seeMethods).ThetwoarrowsindicatethedirectionofreddeningandpointtowardthetwoparallelfeaturesthatwedetectedintheRC,correspondingtoold(brighter)andyounger(fainter)stars.TheinsetshowsthedoubleRCintheJ-KsCMD.Thebluerectangleindicatesthestarsusedtocreatetheextinctionmap.Theerrorbars,inblue,show the uncertainties for differentmagnitude bins. Upper right: KLF (grey), obtained after extinctioncorrectionof theobservedstars,andbest-fitmodelof thestar formationhistory (reddashed line).Forsimplicitywe combined the theoretical LFs used into old, intermediate and youngages (orange, greenandblue,respectively).Thezoomshowsthequalityofthedataindetail,includingerrorbarsandmodelfit. The luminosity function of a stellar population changes depending on its age. Therefore, theobservedKLFcanbeinterpretedasthesuperpositionoftheLFsfromstarformationeventsatdifferenttimes. It thus contains the imprint of the formation history of the nuclear disc. We fitted linearcombinations of theoretical single age LFs to our measurements. To deal with the systematicuncertainties related to the models, we used stellar evolutionary models from two different groups(BaSTI12andMIST13,14,15,16,17),whichresulted inverysimilarhistories,butwithsomewhatdifferentagesforspecificevents.Ourmodel fits requireameanmetallicityof thenuclearbulgestarsofabouttwicesolar,inagreementwithwhathasbeenfoundfortheinnermostGalacticbulge10.

Thederivedstar formationhistory(SFH) issummarized inFig.2.Over80%ofthestars formedbetween8–13.5Gyrago.Thisinitialformationwasfollowedbyaquiescentperiodofmorethan6Gyrduration, which was ended by a remarkable event 600Myr or 1 Gyr ago (depending on themodelsused), during which ~5% of the stellar mass formed (in the following we refer to this as the “1 Gyr

event”).Star formationcontinued intherecentpast,butona lower level.Thepast30Myrhavebeenrelativelyactivewithastarformationrate0.2-0.8M⊙/yr(usingBaSTIandMISTmodelstoestimatetheuncertainties).This is ingoodagreementwithconstraints fromclassicalCepheids3,andrequiresthatafew106M⊙ starsformedintherecentpastintheGC.Thisimpliesthat,inadditiontotheknownyoung,massiveclusters(theArches,Quintuplet,andCentralclusters),theremustbealargenumberofclustersthathaveeludeddetectionsofarbecauseoftheirpartialdissolutioninaheavilycrowdedfield18. The1GyreventhasleftavisibleimprintintheCMD(Fig.1,upperleftpanel).TheRCsequenceisdouble(seeMethodssection),withaweakerone,correspondingtostarscreatedinthe1Gyrevent,runningparalleltotheprimaryone,about0.5magnitudesfainter,thatcorrespondstotheoldeststars.

Thenucleardiscregionwithin120pcofSgrA*contains(8±2)×108 M⊙basedonnear-infraredflux densities1, which we confirm here using independent, mid-infrared measurements (Methodssection). Ifwescalethe~1600pc2studiedhere(Fig.1)tothe~17000pc2correspondingtothe120pcradius, thenouranalysisof theKLFresults ina fullyconsistentmassof (9.8±0.6)×108M⊙. If the1Gyrevent comprised the same area, then it created stars with a total mass of (4.2±0.7)×107 M⊙. Ourmodelingshowsthatthedurationofthiseventwasprobablyshorterthan100Myr.Thestarformationratewas thus 0.4-0.5M⊙/yr, notmuch lower than the ~1-2M⊙/yr assumed for the entire Galaxy atpresenttime2,butlimitedtolessthan1%ofitsvolume.Hence,scaledtothesizeoftheMilkyWay,theconditionsintheGCduringthe1Gyreventmusthaveresembledthoseinstarburstgalaxies,thatformstars at rates ≳ 100 M⊙/yr. As a consequence, the 1 Gyr event must have resulted in ≳2×105 corecollapsesupernovaeandthushavedrivenapowerfuloutflowfromtheGCregion.

Fig. 2: Star formationhistoryof thenuclear stellar discasderived from themodel fits to theKLFwithBaSTIandMISTisochrones.TherewasnocontributionforanyoftheBaSTImodelsintherange1.5-8Gyr.

OurresultsshowthatthenucleardiscformedveryearlyintheGalaxy’shistory,andmayhaveasimilar age than the much larger Galactic bulge19, in which it is embedded. The following quiescentperiodsuggeststhatgastransporttowardtheGCwassuppressedorgaswasexpulsedefficiently.Evenintheabsenceofdirectgasinflow,gasfromstellarwindsisexpectedtoaccumulateatthebottomofthepotentialwelloftheMilkyWay.OccasionalactivityofSgrA*,mayhaveplayedaroleindrivingoutlargequantitiesofgasviaanaccretion-poweredcentralwind20.However,thebaroftheMilkyWayisthoughtto be very efficient at transporting gas toward the GC, at a rate of 0.1-1M⊙/yr21 and it is thereforequestionablewhetherblackholeactivityalonecouldhavesuppressedstarformationinthenucleardiscduringbillionsofyears.OurfindingsthereforesuggestthatgastransportthroughtheGalacticbartotheGCwasinefficientduringbillionsofyears,whichmayhaveavarietyofreasons,whichrangefromstallingofgas transport followedbystar formationnear resonances to thenon-existenceof thebar.A recentanalysis of Gaia DR2 data indicates that the Galactic bar may be currently still forming or has beenstronglydisturbedrecently,possiblybytheSgrdwarfsatellitegalaxyorasimilarperturber22,23.

TheMilkyWayhasnotsufferedanymajormerger(20%ofitsmassormore)overthepast~10Gyr5,24, but minor interactions may have been more frequent. In this context it is relevant thatsimulationsoftheorbitoftheSgrdwarfgalaxyindicatethat itmayhavereachedminimumseparationfromtheGCroughly1Gyrago25.Thisevent,orasimilarone,mayhavetriggeredgasinfallintotheGC,followedbystarformation.

Radio, X-ray, and γ-ray observations have found the signatures of strong outflows from theGalacticCentreregion26.Theso-calledFermiBubbles,forexample,arefeaturestracedinmicrowaves,X-rays,andγ-raysthatextendtoabout10kpconbothsidesoftheGalaxyandemanatefromitscentre27,28.AttheirbasestheyappeartoconnecttoX-raystructures,whichhavesizescorrespondingtothescaleofthenucleardiscandmaytraceexhaustchannelsofhotplasma26.Ourresultscanputtheseobservationsintocontext.OneexplanationfortheoriginoftheFermiBubbleswasbasedonthepreviousparadigmofquasi-continuousstarformationattheGC,whichwouldcreatetheFermiBubblesthroughacontinuousinjectionofcosmicrayprotons29.However,thishypothesisrequiresaquasi-continuousstarformationattheGC sustained overmore than 5Gyr and can therefore be ruled out because its basic assumptioncontradictstheSFHderivedhere.Ontheotherhand,weestimatethat~3×104supernovaeexplodedintheGC inthepast30Myr,withanenergy inputof~1051ergeach,onaverage.Asmall fractionofthisenergy will be sufficient to account for the energy in the X-ray outflows. Therefore, recent starformation,possiblycombinedwithsomeactivityofSgrA*,canprovideaplausibleexplanationfortheobservedoutflows30.

Wefindthat≳90%ofthestellarmassoftheGCwereinplace8Gyrago.Sinceblackholesgrowmostly through the accretion of gas and star formation requires the presence of gas, the low starformationrateoverthefollowingGyrmayimplythatthecentralblackhole,SgrA*,hadalreadyacquiredmostofitspresentdaymassintheearlydaysofourGalaxy.

ThisisthefirsttimethatwehavegainedsomedetailedinsightintotheformationhistoryofthenucleardiscintheGC.Futurespectroscopicandhighangularresolutionimagingfollow-upobservationswillbeabletoconstrainthedifferenteventsfurtherandteachusabouttheformationhistoryoftheGCanditsimplicationsontheevolutionoftheMilkyWayanditssupermassiveblackhole.

DataAvailability

All the raw data used in this study are available at the ESO Science Archive Facility(http://archive.eso.org/eso/eso_archive_main.html)underprogrammesIDs195.B-0283and091.B-0418.ThefinalversionoftheGALACTICNUCLEUSsurvey(imagesandpointsourcecatalogues)willbereleasedtothepublicviatheESOPhase3platformwithinthenextyear.Authorcontributions

F. N.L. Reduced the data and produced the catalogue, carried out themain part of the analysis, andwrotethedraftversionof themanuscript.R.S.plannedtheresearchproject,collaborated in thedataanalysisandinterpretation,andorganisedthewritingofthemanuscript.A.T.G.-C.collaboratedinthedatareduction.S.C.ComputedthetheoreticalLFs.E.G-C.,B.S.,H.D.,N.N.,M.H.,F.N.,S.N.,A.F.-K.andJ.H.V.G.participatedactivelyinthescientificdiscussionandinterpretationandcontributedtotheproductionofthefinalversionofthemanuscript.

AcknowledgementsThisworkhasmadeuseofBaSTIwebtools.Theresearchleadingtotheseresultshasreceivedfundingfrom the European Research Council under the European Union’s Seventh Framework Programme(FP7/2007-2013)/ERCgrantagreementnº[614922].ThisworkisbasedonobservationsmadewithESOTelescopesat theLaSillaParanalObservatoryunderprogrammes IDs195.B-0283and091.B-0418.Wethank the staff of ESO for their great efforts and helpfulness. F. N.-L. acknowledges financial supportfromaMECDpre-doctoralcontract,codeFPU14/01700.WeacknowledgesupportbytheStateAgencyfor Research of the Spanish MCIU through the “Center of Excellence Severo Ochoa” award for theInstitutodeAstrofísicadeAndalucía(CSIC)(SEV-2017-0709).

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METHODSIDataFor this work we have used the J-, H- and Ks-band photometry of 14 different fields from theGALACTICNUCLEUSsurvey6.Thisisanearinfrared,highangularresolution(~0.2’’)surveyoftheGalacticCentrecarriedoutwith theHighAcuityWide-fieldK-band Imager locatedat theVeryLargeTelescope(HAWK-I/VLT).Thespeckleholographyalgorithmiskeyforthissurveytoovercomeatmosphericseeing.The high angular resolution of the GALACTICNUCLEUS data reduces crowding by a factor of ≳ 10comparedtoseeinglimitedsurveys.Asaconsequence,GALACTICNUCLEUSreachesseveralmagnitudesdeeper than other surveys of the same region6,10. All the data will be publicly available via the ESOscience archive facilitywithin the next year. The photometric uncertainties are less than 0.05mag atJ~20,H~17andKs~16,withazeropointuncertaintyof0.036maginallthreebands.Wehaveproducedthe final photometric catalogue by combining all fields, correcting for possible photometric offsetsbetweenthem.

IIRemovingdarkclouds

Weexcludedregionswithdarkcloudsbecausetheyarelargelyopaqueandlimittheobservationofstarsbelongingtothenuclearstellardisc(NSD).Giventhattheextinctionislargerforshorterwavelengths,weuseda J-banddensitymapto identifydarkclouds6.Wedefinedapixelsizeof~6’’andcomputetheJ-banddensityforeachpixel.Wemaskedregionswithlessthan5%ofthemaximumdensitydetected(Fig.3).Varyingthispercentagebetween3%and7%didnotresultinanysignificantchangetoourresults.

Fig.3:J-banddensitymap.Thedarkpatchesarecloudsofmoleculargasanddust.TheyimpedetheviewintotheGCandwerethereforeexcludedfromthisstudy(whitedashedlinecontours).Thecentralcross-shapedregioncorrespondstoalowcompletenessregion.IIIExtinctionmap

Asdescribed inourpreviouswork,weusedRC stars to compute anextinctionmap tode-redden thephotometry and to correct for differential extinction6,10. We selected a pixel scale of 2.5”pixel-1 andcomputed the colour excess H-Ks using only stars within 5’’ from a given pixel. Since the differentialextinction and the extinction in the line of sight can vary significantly on arc second scales, weconsidered only stars whose H-Ks value lies within 0.25 mag of the value corresponding to the starclosesttoanygivenpixel.Weimposedaminimumoffivestarsfulfillingtheseconditionsperpixelontheextinctionmap.Weweighted thedistances to the centreof thepixelwithan inverse-distanceweight(IDW)method6,10.Weused theRC stars shown in the rectangle in Fig. 1 (upper left) andassumedan

extinctionindexof2.30±0.086.ThisregionismainlypopulatedbyRCstarsorRGBBstarswhoseintrinsiccoloursaresimilar10.Wecomputedtheintrinsiccolour(H-Ks)0=0.07±0.03takingintoaccountdifferentmetallicitiesandstellaragesofRCandRGBBstars,BaSTImodelsandthecorrespondingfiltersofHAWK-I.Fig.4showstheobtainedextinctionmap.Thestatisticaluncertaintiesofthepixelsare~3%andwerecalculatedtakingintoaccountthedispersionofthestarsusedtocomputetheextinctionvalueofeachpixeland the standarddeviationof the intrinsic colour computedpreviously.The systematicsare~6%and considers the systematic uncertainty of the zero point forH and Ks, and the uncertainties of theextinction index and the effective wavelength. These uncertainties do not influence the differentialextinctioninanysignificantway.

Fig.4:ExtinctionmapAKs.Whitepatchesandpixelsindicateregionswherethenumberofstarswasnotenough to compute an extinction value. Those regions mainly correspond to dark clouds and werepreviouslyexcludedfromouranalysis.AfterapplyingtheextinctionmaptotheCMD,weobtainedthede-reddenedCMDshowninFig.5.

Fig.5:CMDKsversusH-Ksshowingoriginaldata(reddots)andtheresultafterapplyingtheextinctioncorrection(inblack).Theblackdashedlineshowsthecut inH-Kstoexcludetheforegroundpopulation.

TheredandcyanlinescorrespondtoBaSTIisochronesofanoldandayoungpopulation~10Gyrand~1Gyr,respectivelyaccordingtoourresults.Onlyarandomfractionofthetotalamountofstarsisshownforclarity.

IVLuminosityFunction

Maskingofdarkclouds

ToobtaintheKLF,wemaskedtheregionclosesttoSgrA*(thenuclearstarcluster),wheretheextremesourcecrowdinglimitsthecompletenessofourdatasignificantlyatmagnitudesKs≳15.ForegroundstarsAbout 50% of the interstellar extinction toward the GC is caused by dust in the Galactic Disc. Thebar/bulgeisrelativelydustfreeandroughlytheother50%ofextinctioniscausedbydustintheCentralMolecular Zone,which formsalreadypartof theGC1. TheHKsCMD (Fig. 1) showshow stars in spiralarmsintheforegroundGalacticDiskappearonlyinsignificantnumbersatH-Ks≲1.We have chosen a colour cut ofH-Ks= 1.3 to exclude foreground stars. Themost extreme intrinsiccolours inH-Ks,about0.2-0.3mag,are reachedM-typedwarfsorgiants. Inorder to contaminateoursample,thosestarswouldhavetosufferareddeningofH-Ks>1magandthuslieintheinnermostpartsoftheDiskorouterlayersofthebar.However,M-typemainsequencestarswouldbemanymagnitudesfainterthanourdetectionlimitandcanthusberuledoutascontaminants.M-typegiantsareverybrightandrare.WewouldexpecttoseetheminthetopoftheH-KsCMD.However,thereareonlystarswithH-Ks > 1.5 in this part of the CMD. With our chosen colour cut we can therefore safely excludecontaminationbyforegroundstarsintheGalacticDisk.Whataboutcontaminationbystarsintheforegroundbar/bulge?Wehaveshowninpreviousworkthattheextinction toward the innermostpartsof thebar (at~90pcvertical separation fromSgrA*) isAKs~1.2,almosthalf themeanextinctionasmeasuredfortheGCfieldstudiedhere10.Withthereddeningcurve inferred for this work AKs=1.2 corresponds to H-Ks= 1.0.With the scatter frommeasurementuncertainties, stars from the innermostbulge/barmay therefore contaminateour sample to a certaindegree. We consider that this potential contamination does not pose any serious problem for ouranalysisbecausethosecontaminatingstarswouldbelongtoa~12Gyroldsingleage,metal-richstellarpopulation10andwouldthusonlyaffect theoldestagebin in theSFH. Ifwecouldcleanlysubtract thecontaminant stars, we would at most expect a decrease of the number of or a tendency towardsomewhatyoungagesstarsintheoldestagebin.Wetestedthiseffectbychoosingastrictercolourcutof H-Ks= 1.5 and repeating our analysis of the SFH. Indeed, the age of the oldest stars tend to besomewhatyounger(movingfrom~13Gyrto11Gyr),buttherestoftheSFHisunaffected.Inaddition,toobtainaroughestimateofthepotentialcontaminationbyforegroundstars,wevariedthecolour cut by Δ(H-Ks) = 0.2mag. This corresponds to the standard deviation, ΔAKs = 0.25mag, of themeanextinctiondetermined forour survey region (seeabove). Thenumberof stars that get includedintoorexcludedfromthefinalsamplevariesthenbyabout2%.WegeneratedandanalysedtheKLFsforbothcasesandappliedtheKLFfittingwithMCestimationofuncertaintiesasdescribedabove.Wedidnotfindanysignificantdifferencewithrespecttoourresults.ForcreatingtheKLF,weuseallstarsdetectedatKsanddonotrequirethattheyaredetectedatH,too.Since reddening rises steeply towardshorterwavelengths,highly reddenedstarsmaynothaveanyH-

band counterparts. We can safely assume that stars without anyH-band counterpart are not in theforeground.Finally,itisimportanttopointoutthatwearedealingwithacomplexsituationhere:Thebar/bulgeandthe NSD cannot be spatially separate features and stars from the bar are expected to be presentthroughouttheNSD.Asdescribedabovethiswillnotchangeanyofourconclusionsinasignificantwaybecausethecontaminatingpopulationisold,singleage,andmetalrich.SaturationWe corrected for saturation in the Ks-band by using the SIRIUS/IRSF survey31 to replace the HAWK-Iphotometryforbrightstars(Ks<11.5mag).CompletenessGiven the large size of the images, the great number of stars, the variability of stellar density withposition, and the variation of the data quality for each field and filter, we considered the standardmethod of determining completeness through inserting and recovering of artificial stars as unviablebecauseofitscomplexityandtheenormousamountsofcomputationtimenecessaryforsuchatest(weestimateseveralweeksonourmulticoreserver).Wethereforeusedapreviouslydevelopedalternativeapproach,whichisbasedondeterminingthecriticaldistanceatwhichastarofanygivenmagnitudecanbe detected around a brighter star32. This critical distance can then be translated into completenessmapsforeachmagnitudebinanalysed.Thismethodassumesthattheprobabilityofdetectingasourcewith a givenmagnitude is uniform across the analysed field. Since the stellar density is non-uniformacrossoursurveyareaandthequalityofthedatadependsonthespecificobservingconditionsandfilterforeachofthe14fieldsthatmakeupthefinalmosaic,wedividedtheentirefieldinto108smallersub-regionsof2’x1.4’.Weconsideredthesesub-regionssufficientlysmalltoassurethevalidityofthebasicassumption of constant stellar density and homogeneous stellar population. To estimate the overallcompletenessofour star countsand its relateduncertainty,we thenaveragedover thecompletenesssolutions obtained for each of the sub-regions and used the corresponding standard deviation asuncertainty(Fig.6).To test thereliabilityofourapproach,weperformedtwo independent tests in thecentral fieldof themosaic,wherecrowdingismostsignificant:(1)Weestimatedcompletenessthroughastandardartificialstartestandfoundthatthecompleteness is~80%atKs~16mag, inagreementwiththecompletenessestimationbasedontheabove-describedmethod.(2)WecomparedourKLFwithaKLFobtainedfromdiffraction limited NACO/VLT images (~0.06”angular resolution) of the NSC (Gallego-Cano et al.,submittedtoA&A)ataprojecteddistanceofabout2pcfromSgrA*.Again,wefoundacompletenessof~80%atKs~16mag,inagreementwithourcompletenessestimation.

Fig.6:CompletenessatKs.Thereddashedlineshowsthe80%completenesslimit.

Finally,tocreatetheKLFweremovedtheforegroundstars, limitedtheselectiontomagnitudeswherecompletenessis>2/3(Ks~15.3magextinctioncorrected),andappliedtheextinctioncorrectionwithourextinctionmap.VDoubleRedClumpWe fitteda simplemodelof twoGaussiansplus anexponential background10 to thede-reddenedKLF(Fig.7).ThetwoGaussianscorrespondtothedoubleRCfeaturethatappearsintheCMD.TheDoubleRedClumpisalsoclearlydetectedintheregionaroundtheQuintupletclusterbyrecentlypublishedHSTobservations33.

Fig.7:KLFobtainedwiththeKsde-reddeneddataapplyingthecompletenesscorrection.IngreenatwoGaussian plus an exponential background fit. Red and cyan dashed lines show the position of theGaussians.Theinsetshowsthequalityofthedataindetail,includingtheerrorbarsandmodelfit.

VIStarFormationHistoryWe fitted the KLF with linear combinations of theoretical models. Tracers that constrain the SFHsignificantly are the relative changes in magnitude and number of stars between three differentremarkable features in theLFs10: theasymptoticgiantbranchbump, the redclumpbumpand the redgiantbranchbump(RGBB).We assumed a Salpeter initialmass function for themodels. Initially,we explored the age-metallicityspacebyusingbetweentwoandfivesingleagepopulationsandthreedifferentmetallicities (Z=0.02,0.03and0.04).Weusedthesamemetallicityforallpopulationsineachfit.ThebestfitwasdeterminedbyChisquaredminimisation.ThebulkofbestfitsrequiredametallicityofZ=0.04,consistentwiththemetallicityoftheinnermostbulge,adjacenttotheGCregion10.Althoughwefoundthatacombinationoffiveagescanalreadyprovideuswithasatisfactoryfittothemeasuredluminosityfunction(characterisedbya reducedChi squaredvalueclose to1), apriori, amorecomplex starSFHcannotbeexcluded.ToanalysetheSFHmoreindetail,weresortedtoMonteCarlo(MC)simulationstoexploretheparameterspace spanned by the ages and masses of the different star formation events. Additional fittingparameterswereaconstantinterstellarextinctiontowardtheGC(withdifferentialoffsetsinextinctionhavingalreadybeenaccountedforthroughouruseofextinctionmaps),andaparameter forGaussiansmoothing across bins to absorb magnitude variations due to variable distances and measurementuncertainties. From themeasuredKLFandassumingGaussianuncertainties,we created1000 randomKLFsandfittedthemwithlinearcombinationsoftheoreticalsingleageKLFsofages13.5,11,8,5,3,1,0.8, 0.6, 0.4, 0.2, 0.1, 0.08, 0.05, 0.03Gyr (BaSTI12models). The oldest isochronewas assumed to beenhancedinalphaelements10.WeselectedthefitwiththeleastChisquaredvalueforeachofthe1000simulatedmeasurementsandthusobtainedprobabilitydistributionsfortheagesandmasses.Becauseofdegeneraciesbetweenthecontributionsofmodelpopulationswithsimilarages(andthussimilarLFs),whichcanbesignificantforages>8Gyr,wesummedthecontributionsofthedifferentpopulationsintolargerbinsforFig.2.Toobtaintheoptimumbinwidths,wesimulateddifferentSFHwithuncertaintiesequivalenttotheonesinrealdataandapplyourtechnique.Thus,weselectedthebinwidthaccordingtotheminimumuncertaintiesforagivenbin(Sec.XIformoredetails).WeaddressedpotentialsourcesofsystematiceffectsandcheckedthatthederivedSFHdoesnotchangesignificantly:(1)Potentialcontaminationby foregroundstars.Asdiscussedabove,contaminationbystars fromtheGalacticDiskisnegligibleandcontaminationfromtheinnermostbar/bulgemaybeontheorderofafewpercent.Werepeatedouranalysisbyvaryingthecolour-cutusedfortheexclusionofforegroundstarsbetweenH-Ks=1.1andH-Ks=1.5anddidnotfindanysignificanteffects.Asdiscussedabove,therewillbestarsfromtheinnermostbarpresentthroughouttheNSD,butthispopulationis~12Gyrold,metalrich,andsingleage10andwillthusnotaffectourconclusionsinanysignificantway.(2)Dependingontheprecisevalueofthe(H-Ks)colourthatisusedtode-selectforegroundstars,moreor fewer stars from the Galactic bulge may contaminate our nuclear bulge sample. With a strictercriterion(H-Ks>1.5,upperleftpanelinFig.1)wecanminimisethecontributionfrominnerbulgestars.ForthisLF,weproducedanewextinctionmapusingonlyRCstarswithH-Ks>1.5.TheSFHresultingfrommodel fitting to thedatawith this criterion is very similar, but results in a shift of theoldest nuclearbulgestarstowardsomewhat(by~2Gyr)youngerages.Thisisnotsurprisinggiventhattheinnermostbulge (themaincontaminantof thenuclearbulgesample)has recentlybeen foundtohaveanageofabout13Gyr10.

(3)UsingMIST isochrones13,14,15,16,17 (http://waps.cfa.harvard.edu/MIST/)asanalternativetotheBaSTImodels,weexploredtheinfluenceoftheassumedstellarevolutionmodelsonourresults.Whiletherearesomeshifts in thebest-fitages, theoverall result is,again,unchanged (Fig.2).Wenote,howeverthattheageoftheintermediateagestarsshiftsfrom600Myrto1GyrwhenusingMISTisochrones.(4)WealsoselecteddifferentbinwidthsfortheKLFs,0.03,0.06and0.1mag,andconfirmedthattheresultsdonotchangeinanysignificantway.(5)Wecheckedthatchangingthelimittoexcludedarkcloudregionsdoesnotaffecttheresults.(6)Westudiedtheeffectofthecompletenesslimitontheresultsapplyingacompletenesslimitof70%.WerepeatedtheanalysisusingBaSTImodelsandwedidnotfindanysignificantvariationwithrespecttotheresultsthatweobtainedwiththe2/3limitappliedpreviously.(7)Weproduceddifferentextinctionmapsforeachofthetestsinvolvingdifferentselectionsofstars.Inthisway,wecreatedextinctionmapsconsideringdifferentcriteriaforthecolourcutH-Ks(2),differentconstrainsforexcludingthedarkcloudsregions(5)andadifferentradiusforclosestarsof10’’insteadof5’’.Wedidnotfindanysignificantchangeintheresults.(8)Themajorityofstarscoveredbyoursamplebelongtotheredgiantbranch.ThismeansthattheirstellarevolutionissofastthatassumingdifferentIMFsdoesnotchangetheresults(Fuelconsumptiontheorem34).Tocheckit,werepeatedtheanalysisusingBaSTImodelsbutconsideringanIMFwithalpha=1.9.Wedidnotfindanysignificantdifference.VIIComparisonoftheoreticalmodelsWeusedmodelsfromtwoindependentgroupstocheckthepossiblesystematicsintroducedbytheuseof any specific theoretical model. We sampled the age parameter according to the differences thatappearbetweenthemainfeaturespresent intheLF(AGBB,RCandRGBB)andtherelativefractionofstarsbetweenthem.TheLFschangeslowlyforages>5Gyr,butveryrapidlyforages<2Gyrwhichiswhywe sample youngagesmoredensely.We realised that thereare significantdifferencesbetweentheBaSTIandtheMISTLFsofcertainages,whichwillresultinageshiftsintheinferredSFH.Therefore,wecompared themodelsandselectedaslightlydifferent sampleofages foreachof themtoequallycover the age-space parameter. Fig. 8 depicts a comparison between BaSTI and MIST models fordifferentageswith thesamemetallicity.Ascanbeseen,atages<2Gyr, theMISTLFs that resembleBaSTILFscorrespondtoastellarpopulationsaroundtwiceasold.

Fig. 8: ComparisonbetweenMISTmodels (upperpanels) andBaSTImodels (lowerpanels) of differentagesandtwicesolarmetallicity.VIIIMetallicityofthestellarpopulationWe assumed twice solar metallicity for all theoretical LFs used to derive the SFH. This has to beinterpreted as amean metallicity and does not exclude that the underlying population can show arelativelybroadrangeofmetallicities.Spectroscopicstudiessupportthatthemetallicityofstarsofbothvery old and young ages at the GC have a mean (super-) solar metallicity35,36,37,38,39,40. Twice solarmetallicitywasalsofoundinaphotometricstudyoftheinnermostbulge,60-90pctoGalacticnorthofSgrA*10.Ourmethodologycannotdistinguishbetweendifferentmetallicitiesatlevelsmorethantwiceabovesolar.This isduetothefactthattherelativedistancebetweenthemainfeaturesintheKLFforyoung ages (AGBB, RC and RGBB) and their relative stellar fraction do not change much for highmetallicities(Fig.9).

Fig.9:Theoretical~1GyrKLFswithdifferentmetallicities.Upperpanel:MISTmodels.Lowerpanel:BaSTImodels.We have also checked whether a bulk of solar metallicity stars could explain the observed KLF.However,wefoundthattheresidualsaresignificantlylargerthanwhenusingtwicethesolarmetallicityandtheChisquareforeachoftheMCsamplesincreasesitsvalueby~30%.Nevertheless,thecomputedSFH agrees within the uncertainties with the derived assuming twice the solar metallicity. Finally,changing themetallicity of the oldest population in our fits to solar (or sub-solar, Z = 0.01 for BaSTImodels) does not change the inferred SFH in any significantway.We concluded that any reasonablevariations of themetallicity of the stellar populations do not have any significant impact on the SFHderivedbyus.IXAlpha-elementenhancementofthestellarpopulationWehaveassumed theoldest LF inourBaSTImodel tobealphaelementenhanced ([α/Fe]=+0.4) toaccount for the inner bulge population10, 39. On the other hand, we have used non-alpha elementenhanced isochrones to fit the stellar population at the NSD. In this way, we have restricted theparameterspaceandhavedecreasedthecomputingtimetomakeitaffordable.Nevertheless,wehavealsocarriedoutseveralteststochecktheeffectofanalphaelementenhancedstellarpopulationattheNSD. In this way, we performed a fit using 5 models varying their ages to cover the age-spaceparameter,withtwicethesolarmetallicityandwiththepossibilityofbeingalphaelementenhancedornot.We found that the best solution obtained agreeswith the scenario thatwe found using our 14modelsfitting.Namely,wefoundthattheminimumchi-squareisobtainedforabulkofoldstars(alphaelement enhanced in this case), followed by a quiescence period, ended by a intermediate-age starformationburst(non-alphaenhanced)andsomeyoungstarformation(alpha-enhanced).Moreover,we

alsotestedasimplescenariousingallthemodelswithanalphaelementenhancedpopulation([α/Fe]=+0.4).Weobtainedthatthechi-squareincreasesitsvalueinmorethan200%withrespecttothebestfitobtainedusinganon-alphaenrichedpopulationfortheNSD.XComparisonwithpreviousresultsTheSFHthatwefounddisagreeswiththesofaracceptedparadigmofaquasi-continuousstarformationwith a roughly constant rate at theGC4. To cross checkour results andmethodologywe appliedourmethodtothepreviouslyusedNICMOSdataset4.Wecreatedextinctionmapsforeachfieldusingthesameapproachdescribedpreviously.Wecombined the~6000starsdetected inall theNICMOS fieldsand generated an extinction corrected F205W LF, applying a completeness correction and removingforegroundstarsasexplainedbefore.WefoundthattheSFHiscompatiblewithbothaconstantSFHandtheonethatweobtainwithourdata(Fig.10).ThisisduetothelargeuncertaintyassociatedwitheachLFbingiventhelownumberofstarspresentinthesmallregionsused.OurGALACTICNUCLEUSdatasetsincludes~100timesmorestarsandallowedustoreallyconstraintheuncertaintiespointingtowardsanon-constantSFH.

Fig.10:SFHobtainedforNICMOSdatausingBaSTImodels.Thepreviouswork4alsoassumedatop-heavy initialmass function(IMF).Thus,wehaverepeatedouranalysisusingBaSTImodelswithanIMFofalpha=-1.9(theequivalentKroupa/Salpetervaluewouldbealpha=-2.35).Wefoundnosignificantchangeswithrespecttotheresultsthatwehaveobtained.Ontheotherhand,wecomparedoutresultswiththeSFHinferredfromspectroscopicobservationsoftheNuclearStarCluster41.They foundanon-continuousSFH,with>80%of the stars formed>5Gyrago,aminimumaround1Gyrandincreasedstarformationinthepast100Myr.ThisisapproximatelyconsistentwithourfindingsfortheNSD,whichprovideahighertimeresolutionthanthespectroscopicstudy.DifferencesarethatintheSFHoftheNSDderivedherewefindthatthemajorityofstarsareat

least 8 Gyr old and that a negligible fraction of the stars formed between 1.5 and 8 Gyr ago. Thespectroscopicstudyof theNSCdoesnot find the“1Gyrevent” thathas leftaclearmark in theNSD.ThereappearstobenosecondaryRCfeatureintheNSC.Hence,ourresultssuggestthattherearesomedifferencesintheSFHoftheNSCandNSD,butmoredetailedspectroscopicandphotometricstudiesarenecessarytoconfirmthis.XITestswithartificialSFHsToassessthecorrectperformanceofourmethod,wetestedittryingtorecoverartificiallycreatedSFHs.WegeneratedthreeSFHssimulatingdifferentscenarios: (1)Anon-continuousSFH,similar to theonederivedinthiswork,(2)acontinuousconstantSFH,and(3)acontinuousexponentiallydecreasingSFH,usingBaSTImodels.Then,weproducedmockKLFsintroducingnoiseaccordingtotherealone.Applyingour method, we are able to recover the different SFHs within the uncertainties and to distinguishbetween the different scenarios, in particular between the quasi-continuous and the non-continuousSFHs (Fig. 11). This shows that the small uncertainties of our data allow us to overcome possibledegeneraciesbetweensimilarmodels.

Fig.11:Recoveryofsimulatedstarformationhistories.Reddots:AssumedSFH.Green,blueandorangebars:Recoveredstarformation.XIIPropertiesofthe1GyreventToestimatetheuncertaintyinageofthestarformationeventat600Myr/1Gyr,weusedtheprobabilitydistributions computed for theMC simulations carried out with BaSTImodels (Fig. 12). The bin thatincludesthestarformationeventiscomposedofthreemodels(1Gyr,800Myrand600Myr).WefoundthatforthevastmajorityofMCsamplestheonlycomponentthatcontributestotheSFHisthe600Myr

one.SincetheRCpeakisverysensitivetosmallagechangesforyoungstellarmodels(Sec.VII)andwehaveconsideredforthefullfittingproceduremodelsof800and400Myrbesidesofthemostprobableof600Myr,weestimatethattheuncertaintyinagecannotbelargerthan100Myrforthedetectedstarformationevent.

Fig. 12: Probability distribution for the MC simulations carried out using BaSTI models. The legendindicatesthecontributionofeachagebin.Theinsetshowsallthemodelscontributingtothebinwherewedetectthestarformationeventat~1Gyr.

Fig.13:CMDKsversusH−Ks.Redandorangepointsanduncertaintybarsdepictthepeaksofthebestdouble-GaussianfitfoundforeachbinofH–Ks.A direct confirmation of the detected intermediate age star formation event is the presence of asecondaryfeature intheRCintheCMDthat is indicatedbytheredarrowsinFig.1.Tocheckthatthesecondaryfeatureisreal,wedefinedaregionthatincludesbothfeaturescontainingstarswithH−Ks∈[1.3,2.5]anddivideditintoH−Ksbinsof0.05mag.Foreachofthem,wefittedtheKsdistributionwithasingleandadoubleGaussianmodelapplyingtheexpectationmaximisationalgorithmimplementedinthe SCIKIT-LEARN python object GaussianMixture. Using the Bayesian Information Criterion and theAkaikeInformationCriterion,weconfirmedthatacombinationoftwoGaussiansprovidesabetterfitforthedata.Bothfeaturesrunparalleltothereddeningvectorwithslopesof1.19±0.02±0.01and1.15±0.02±0.01forthefirstandthesecondfeature,respectively,asisshowninFig.13.Theerrorsrefertothestatisticalandthesystematicandwerecomputedusingajackkniferesamplingmethod,differentbinwidthsand lowercuts for theRCregionemployed.Thedistancebetween features isΔKs=0.44±0.01.Wealsoestimatedtheextinctiontoeachfeatureassuminganextinctionindexof2.30±0.08andagridofreddened intrinsiccolour (H-Ks)0 instepsof0.01mag.Weminimisedthedifferencebetweendataandthemodel and obtained very similar extinction values of 1.92±0.14mag and 1.94±0.16mag, for thebright and the faint feature, respectively. These similar values allowed us to exclude the alternativescenarioofastellarpopulationbeyondtheGCtoexplainthesecondaryclump.Finally,wealsotriedtofitasingletheoreticalLFtothedatatoexcludetheRGBB10astheexplanationofthesecondaryfeature.Wedidnotgetanysatisfactoryfit.Thus,althoughRGBBstarsmustnecessarilybepresent(andaretakeninto account in the theoreticalmodels used here), it is necessary to consider a secondary RC to fullyexplainthedetectedfeature.

XIIICMDanalysis

The lower completeness inH band due to the lower sensitivity impedes to perform an analysis of itsluminosity function as we have shown for the K band. Instead, to assess the obtained SFH, we alsosimulatedaCMDKsversusH-KsusingBaSTImodels.WeaddedrandomnoisetothemodelsinHandKs

bandsaccordingtotheuncertaintyofthedata,andtookintoaccountthereddeningusingthecomputedextinction of the RC stars in our sample. We based our analysis exclusively on the relative distancebetweentheRCfeaturestoavoidproblemsrelatedtocompleteness.FromourLFfitwefoundthatthemaincontributionstothedoubleRCfeaturearisefromtheoldeststars(≳80%ofthemassis≳8Gyr)andfromthestarformationeventat~1Gyr.Therefore,wesimulatedseveralsyntheticCMDstocheckthisscenario:

(1) We simulated just an old population of 8 Gyr to study the contamination by the RGBB. WeanalysedtheRCfeaturesusingtheSCIKIT-LEARNpythonobjectGaussianMixtureasexplainedintheprevious section.Wedetected a secondary clump that corresponds to theRGBBatΔKs =0.62±0.02mag. This scenario is not compatible with the real data since the relative distancebetweenRCandRGBBis0.18±0.02maglargerthaninthedata,wheretheuncertaintiesfromreal data and the simulation have been propagated quadratically.We concluded that there issomecontaminationfromtheRGBBbutitisnotenoughtoexplainthedoubleRCdetectedwithouranalysis.

(2) WegeneratedaSFHsimilartotheoneobtainedusingstellarmodelsof8Gyr,600Myrand40Myr. We obtained that there is a secondary RC as the one observed in the real data. WecomputedthedistancebetweenfeaturesandobtainedΔKs=0.46±0.03ingoodagreementwiththeresultobtainedforrealdata(ΔKs=0.44±0.01).

(3) WesimulatedacontinuousSFHwithaconstantstarformationrate.Weused5differentmodelsfrom 0.1 to 10.1 Gyr equally spaced in age and combined them. We repeated the previousanalysis and found a two feature structure withΔKs = 0.61±0.03 mag, where the secondaryclumpisduetotheRGBBasinmodel(1)andincompatiblewiththedata.

(4) Finally,wecreatedanexponentialstarformationhistoryusingBaSTImodelsof10Gyr,8Gyr,5Gyr,3Gyr,1Gyr,600Myr,200Myrand30Myr.Wefoundasecondaryclumpduemainlytothe600Myrmodels.We foundΔKs = 0.36±0.04, which is smaller than what wemeasure in theactualdata.Moreover,theAGBBismuchmoreprominentinthissimulationgiventhefractionofyoungstars(Fig.14d)

Fig.14showstheoriginaldataandthesimulationsobtainedfor(2),(3)and(4).WeconcludethatonlytheSFHsimulatedusingtheparametersobtainedwiththeKLFanalysisisabletoreproducetheobserveddata.

Fig 14. Comparison between CMDs produced using real data (a) and several simulations using BaSTImodels:(b)Best-fitsolutionobtainedfromtheKLF.(c)ContinuousSFH.(d)ExponentialSFH.

XIVLow–extinctionregionsanalysis

Toassesstheobtainedresults,werepeatedtheanalysisoftheluminosityfunctionselectingonlylow-extinctionregions.SincetheJbandismorepronetoextinctiongivenitsshorterwavelength,weusedthe J-band density map approach, described in Sect. II, to select the low-extinction regions. Wemasked regionswith a J-band density below 25% of themaximum density detected. The selectedregioncomprises~10%ofthetotalareacoveredandiswelldistributedacrossthefield.Wecreatedextinctionmapsusing theselectedstarsandthe techniquedescribed inSect. III.WeobtainedaKLFremoving the foreground population, correcting for differential extinction, and applying thecompleteness solution, as explained previously. We also created a HLF using the same technique.ComparingbothLFs,wechecked that theHLFcompleteness is significantlyaffectedbysensitivityatH>14mag.Weestimatedthatourcompletenesscorrection(thatonlyconsidersincompletenessduetocrowding), overestimates the completeness ~5% forH~14mag and ~30% forH~15mag. Thus, thefaint end of the RC and the RGBB are not adequately covered by the HLF. Given the highincompletenessatH>14mag,wedecidedtorestrictthefaintlimitoftheHLFtoH=14.1magandapplyacorrectionof5%onthecompletenesssolutionand itsuncertaintiesaccordinglywiththepreviousestimation. We also repeated the analysis assuming a correction of ~10 % without any significant

differenceontheresults.Weappliedour full-fittingLFmethod(Sect.VI)assumingBaSTImodels forboth, HLF and KLF. Figure 15 shows the obtained results. The results agree with a mainly oldpopulationwithaquiescenceperiod~5Gyrfollowedbyasignificantstarformationburst~1Gyr.WebelievethatthestrongercontributionofyoungstarsfortheSFHinferredfromtheHLFisadegeneracy,because bright stars can be either young stars or old giants, and the old population is less wellconstrainedintheHLFbecauseitisshallowerthantheKLF.

Fig15.StarFormationHistoryofthelow-extinctionregionsoftheNSDusingBaSTImodelsforKsandHbands.

XVMassEstimation

WecalculatedthetotalmassoftheNSDusingtheresultsobtainedwhenfittingthe1000MCsampleswithMISTmodels.Forour region,weobtain (6.5±0.4)×107M⊙.TheNSDwaspreviouslyestimated tocontain(8±2)×108M⊙withinR=120pcofSgrA*,basedonitsnear-infraredemission1.Tocrosscheckthis number,weuse an extinction and PAH-emission corrected Spitzer 4.5 µm imageof theGC42 andintegratethelightinsideanellipsecentredonSgrA*with120pcradiusalongtheGalacticplaneandaminor-to-majoraxisratioof0.3642,afterprevioussubtractionofamodelforthebulgeemission(Gallego-Canoetal., submittedtoA&A).Wethenscalewithamass-to-luminosity ratioof0.6±0.243 toobtainatotal stellar mass of (8±4)× 108 M ⊙ , consistent with the one derived from the near-infraredmeasurements.AfterscalingthemassderivedfromtheKLFfitsoftheregionstudiedheretothenuclearbulgeinsideof120pc,weobtainaconsistentvalueof(9.8±0.6)×108M⊙,whichindicatesthatourbasicmethodandassumptions,inparticularabouttheinitialmassfunction,appeartobeadequate.

We computed the total mass of supernovae assuming a standard Salpeter IMF and propagating theuncertaintiesobtainedwhenconsideringthetotalstellarmassformed~1Gyrago(obtainedbymeansofMISTmodelfitting).

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