AstronomischeNachrichten,7January2016 Milky Way chemo-dynamics in the era of Gaia I.Minchev1,⋆,C.Chiappini1,andM.Martig2 1 Leibniz-Institutfu¨rAstrophysikPotsdam(AIP),AnderSternwarte16,D-14482,Potsdam,Germany 2 Max-Planck-Institutfu¨rAstronomie,Ko¨nigstuhl17,D-69117Heidelberg,Germany 6 ReceivedXXXX,acceptedXXXX 1 PublishedonlineXXXX 0 2 Key words Galaxy: abundances – Galaxy: disc – Galaxy: evolution – Galaxy: formation – Galaxy: kinematics and n dynamics a J ThemaingoalofGalacticArchaeologyisunderstandingtheformationandevolutionofthebasicGalacticcomponents. Thisrequiressophisticatedchemo-dynamicalmodeling,wherediscasymmetries(e.g.,perturbationsfromthecentralbar, 6 spirals arms, and infalling satellites) and non-equilibrium processes are taken into account self-consistently. Here we ] discuss thecurrent statusof Galacticchemo-dynamical modeling and focus on a recent hybrid technique, which helps A circumventtraditionalproblemswithchemicalenrichmentandstarformationencounteredinfullyself-consistentcosmo- G logicalsimulations.Weshowthatthismodelcanaccountforanumberofchemo-kinematicrelationsintheMilkyWay.In addition,wedemonstratethat(1)ourmodelmatcheswelltheobservedage-[α/Fe]andage-[Fe/H]relationsand(2)that . h thescatterintheage-[Fe/H] relationcannot besimplyexplained byblurring(starsonapo- and pericentersvisitingthe p solarvicinity)butsignificantradialmigration(starsbornelsewherebutendingupatthesolarvicinitytodaybecauseofa - o changeinguidingradius)isneeded.Weemphasizetheimportanceofaccuratestellarages,suchasthoseobtainedthrough r asteroseismology by the CoRoT and Kepler missions, for breaking the degeneracy among different Galactic evolution t scenarios. s a [ Copyrightlinewillbeprovidedbythepublisher 1 v 1 Introduction (e.g.,Tisseraetal.2012),itisstillachallengeforcosmolog- 3 icalsimulationstomatchthepropertiesoftheMW(e.g.,the 1 3 Important information concerning the dominant mecha- typicalmetallicitiesofthedifferentcomponents–Tisseraet 1 nismsresponsiblefortheformationoftheMilkyWay(MW) al.2012).Additionally,thefractionoflow-metallicitystars 0 is encoded in the chemistry and kinematics of its stars. A areoftenoverestimated(Caluraetal.2012)andreproducing 1. number of Galactic surveys are currently being conducted thepositionofthin-andthick-discstarsinthe[α/Fe]-[Fe/H] 0 with the aim of obtaining chemical and kinematical infor- plane has proved challenging (Brook et al. 2012; Gibson 6 mation for a vast number of stars, e.g., RAVE (Steinmetz etal. 2013).While such issues couldbe dueto unresolved 1 eta.2006),SEGUE(Yannyeta.2009),APOGEE(Majew- metal mixing (Wiersma et al. 2009), none of the above- : v skietal.2010),HERMES(Freemanetal.2010),Gaia-ESO mentionedsimulationsreproducessimultaneouslythemass, Xi (Gilmore et al. 2012),Gaia (Perrymanet al. 2001),LAM- themorphology,andthestarformationhistory(SFH)ofthe OST(Zhaoetal.2006)and4MOST(deJongetal.2012). MW. r a Tobeabletointerpretthelargeamountsofforthcoming dataweneedgalaxyformationmodelstailoredtotheMW. 1.1 SummaryofMWchemo-dynamicalevolution Producingdisc-dominatedgalaxieshastraditionallybeena modelingtechniques challengeforcosmologicalsimulations(e.g.,Navarroetal. 1991;Abadietal.2003).Althoughanincreaseinresolution Amajorconsiderationinadiscchemo-dynamicalmodelis andimprovedmodelingofstarformationandfeedbackhave taking into account the effect of radial migration, i.e., the resultedinMW-massgalaxieswithreducedbulgefractions factthatstarsendupawayfromtheirbirthplaces(see,e.g., (Guedesetal.2011;Martigetal.2012),typicallythesesim- Sellwood and Binney 2002; Roskar et al. 2008, Minchev ulationsdo notinclude chemicalevolution.Galaxy forma- and Famaey 2010). Below we quickly summarize models tionsimulationsincludingsometreatmentofchemicalevo- whichincluderadialmigration. lutionhavebeenperformedbyseveralgroups(e.g.,Scanna- 1. Semi-analytical models tuned to fit the local metal- piecoetal.2005;Fewetal.2012). licity distribution,velocitydispersion,and chemicalgradi- However,while the results are encouragingand global ents,etc.,today(e.g.,SchoenrichandBinney2009;Kubryk, observed relations are reproduced, such as the metal- Prantzos, and Athanssoula 2014) or Extended distribution licity trends between the different galactic components functions(SandersandBinney2015): ⋆ Correspondingauthor:[email protected] −Easytovaryparameters Copyrightlinewillbeprovidedbythepublisher 2 Minchevetal.:MilkyWaychemo-dynamics − Provide good description of the disc chemo-kinematic To match the MW in terms of dynamics, at the end of statetoday the simulation we downscale the disc radius by a factor −TypicallynotconcernedwiththeMilkyWaypasthistory of 1.67 and adjust the rotational velocity at the solar ra- −Timeandspatialvariationsofmigrationefficiencydueto dius to be 220 km/s, which affects the mass of each par- dynamicsresultingfromnon-axisymmetricdiscstructureis ticle according to the relation GM ∼ v2r, where G is the hardtotakeintoaccount. gravitationalconstant.Thisplacesthe bar’scorotationres- 2. Fully self-consistent cosmologicalsimulations (e.g., onance (CR) and 2:1 outer Lindblad resonance (OLR) at Kawata and Gibson 2003; Scannapieco et al. 2005; ∼ 4.7 and ∼ 7.5 kpc, respectively, consistent with a num- KobayashiandNakasato2011;Brooketal.2012): berofstudies(e.g.,Dehnen2000,Minchev,Nordhaus,and −Dynamicsself-consistentinacosmologicalcontext Quillen 2007, Minchev et al. 2010). At the same time the −Canlearnaboutdiscformationandevolution discscale-length,measuredfromparticlesofallagesinthe −Notmuchcontroloverfinalchemo-kinematicstate range3<r<15kpc,becomes∼3kpc,incloseagreement −ProblemswithSFHandchemicalenrichmentduetoun- withexpectationsintheMW. knownsubgridphysics The chemical evolution model we use here is for the −Muchlargercomputationaltimesneededifchemicalen- thin disc only. The idea behind this is to test, once radial richmentincluded. mixingand mergerperturbationsare taken into account,if 3.Hybridtechniqueusingsimulationinacosmological wecanexplaintheobservationsofboththinandthickdiscs context + a classical (semi-analytical) chemical evolution without the need of invoking a discrete thick-disc compo- model(Minchev,Chiappini,andMartig2013,2014): nent.Adetaileddescriptionofthechemicalmodelisgiven − Avoids problems with SFH and chemical enrichmentin inMCM13. fullyself-consistentmodels −Canlearnaboutdiscformationandevolution −NoteasytogetMilkyWay-likefinalstates. 2.1 Comparisontorecentobservationalresults For the rest ofthe paperwe focuson the resultsof the lattermodel. The MCM13 model has been shown in previous works to match simultaneously the following observational 2 Ourchemo-dynamical model constraints,someofwhicharereproducedinFig.1: ToproperlymodeltheMWitiscrucialtobeconsistentwith • The disc morphology, scale-length and rotation curve someobservationalconstraintsatredshiftz = 0,forexam- today(seeMCM13); ple, a flat rotationcurve,a smallbulge, a centralbarof an • The local age-velocitydispersion relation (Sharma et al. intermediate size, gas to total disc mass ratio of ∼ 0.14 at 2014); the solar vicinity, and local disc velocity dispersionsclose • The more centrally concentrated [α/Fe]-enhanced (old) totheobservedones. disc (Bensby et al. 2011; Bovy et al. 2012; see Minchev, It is clear that cosmological simulations would be the Chiappini,andMartig2014b,Fig.11); natural framework for a state-of-the-art chemodynamical • The distribution of scale-heights for mono-abundance study of the MW. Unfortunately, as described above, a subpopulations found in SEGUE G-dwarfs (MCM13, number of star formation and chemical enrichment prob- Fig.13); lemsstillexistinfullyself-consistentsimulations.Wehave, •Thereversaloftheradial[α/Fe]andmetallicitygradients therefore,resortedtothenextbestthing–ahigh-resolution (e.g.,APOGEE-Andersetal.2014),whensampledistance simulation in the cosmological context coupled with a from the disc mid-plane is increased (Minchev et al. purechemicalevolutionmodel(see detaileddescriptionin 2014b). Minchev,Chiappini,andMartig2013,hereafterMCM13). • The MDF for stellar samples at different distance from The simulation we used is part of a suite of numerical thediscmidplane(Fig.1,a,b). experiments first presented by Martig et al. (2012), where • The metallicity variation with vertical distance from the the authors studied the evolution of 33 simulated galax- plane(Fig.1,c); ies from z = 5 to z = 0 using the zoom-in technique de- •TheinversioninvelocitydispersionrelationinRAVEand scribed by Martig et al. (2009).This techniqueconsists of SEGUE (Fig. 1, d, e; Minchev et al. 2014;Guiglion et al. extracting merger and accretion histories (and geometry) 2015); foragivenhaloinaΛ-CDMcosmologicalsimulation,and •The[α/Fe]-[Fe/H]plane(currentFig.1,f;Ramirezetal. thenre-simulatingthesehistoriesatmuchhigherresolution 2013); (150 pc spatial, and 104−5 M⊙ mass resolution).The inter- • The flaring of mono-abundance populations (assuming estedreaderisreferredtoMartigetal.(2012)formorein- similarity to mono-age populations) found by Bovy et al. formationonthesimulationmethod. (2015) and predicted earlier by Minchev et al. (2015), Originally, our galaxy has a rotational velocity at the whereModel1inthelatterpaperpresentsthesamegalaxy solar radius of 210 km/s and a scale-length of ∼ 5 kpc. astheoneusedfortheMCM13chemodynamicalmodel. Copyrightlinewillbeprovidedbythepublisher asnaheaderwillbeprovidedbythepublisher 3 Adibekyan et al. (2012) SEGUE, DR9, Brauer et al. (2015) Schlesinger et al. (2012) 0.1<|z| kpc 0.5<|z|<3 kpc MCM13 Model 7.9<r<8.1 kpc 6<r<10 kpc MCM13 Model = 0 dex = 0.2 dex (a) (b) 6<r<10 kpc (c) RAVE Giants, SN>65 MCM13 model 7<r<9 kpc –1.0[Fe/H] |z|<0.6 kpc –0.8 dex Kinematical selection of simulated data as in –0.45 high-resolution spectroscopic surveys (e.g., –0.3 Bensby et al. 2003) –0.17 –0.04 Ramírez et al. (2013) Thick disk Thin disk MCM13 Model Thick disk (d) (e) (f) Thin disk Fig.1 Comparisonbetween the prediction of the MCM13 modeland observations.Panels (a) and (b): The red his- tograms show data from Adibekyan et al. (2012) and Bauer et al. (in preparation); the black and blue curves show the model with and without convolvederror, respectively. The metallicity peak shifts to lower [Fe/H] for both the data and model,whendistancefromthediscplaneincreases.Panel(c):Metallicityvariationwithdistancefromthediscplanefor SEGUEG-dwarfdata(red).Panels(d)and(e):Variationsofverticalvelocitydispersionwith[Mg/Fe]forRAVEgiants (d)andforthemodel(e).Panel(f):Comparisontothehigh-resolutiondatabyRamirezetal.(2013).Ashiftinthemodel [O/Fe]of0.05dex(withintheuncertainty)hasbeenapplied.Panels(a),(b),(c),(f)arefromMCM13andpanels(d)and (e)arefromMinchevetal.(2014a). 2.2 Theage-[α/Fe]relation majorityofstarsinthesolarvicinityatthefinalsimulation time have been born close to the solar radius. The second We nowcomparetheage-[α/Fe]andAMRrelationsinthe row,leftpanelindicatesthatthescatterinthemodelAMR model to those resulting from the data by Haywood et al. is related to stars born inside and outside the solar radius. (2013). These authors published ages for single stars with Most stars are containedin the three highestlevels(black, known[Fe/H]and[α/Fe]in theimmediatesolarneighbor- blue,andpurple),i.e.,scatter isnotaslargeasitwouldbe hood.TheirsampleisbasedontheHARPSGTOobserva- naivelyinferredfromthisparticularplot. tions of 1111 stars, described by Adibekyan et al. (2012). The top-right panel of Fig. 2 shows a comparison be- Theoriginalsamplehadtobeseverelyreducedto363stars. tweentheage-[α/Fe]relationbyHaywoodetal.(2013)and This down-selection was based on an absolute magnitude theage-[Mg/Fe]relationresultingfromourmodel.Asmall cutatM < 4.75andonasomewhatlessreproduciblese- V volumesamplearoundthesimulatedsolarradiuswasused, lection of stars with ”a well defined probabilityfunction”. asindicated,similarlytothe data.We expandedthemodel Haywood et al. noted that their absolute age scale could agerangeby10%,inordertomatchthedatarange.Wealso be off by 1 to 1.5 Gyr, while relative ages would have un- shifted the model by 0.03 dex to lower [α/Fe] values. Un- certaintiesof1Gyr.Theirdefinitionof[α/Fe]includesthe certainties of δ[Mg/H]= 0.05 and δ[Fe/H]= 0.1 dex were meanofMg,Si,andTiabundances. implementedinthemodel.Thisresultsinanuncertaintyof Thetop-leftpanelofFig.2showsthemodelage-[O/Fe] 0.11 dex in [Mg/Fe]. We also implemented age errors of relation for stars in the solar vicinity at the final time, but ∼ 1 Gyr, similar to the relative age uncertainty quoted by with different birth radii (from MCM13, Fig. 7). It is im- Haywood et al. It can be seen that the modelmean (green portantto realizethat,asseeninthebottom-leftpanel,the curve) provides a very good match to the data, while the Copyrightlinewillbeprovidedbythepublisher 4 Minchevetal.:MilkyWaychemo-dynamics Haywood et al. (2013) MCM13 model ] e Mean model F e] g/ F M / O [ [ ], e F / α [ δ [Fe/H] = 0.1 dex δ [Mg/H] = 0.05 dex S δ age = 1 Gyr H] tella Fe/ r de H] [ n / s e it F y [ Spatial selection in model to match the data: 7.9 < r < 8.1 kpc |z| < 0.05 kpc ] H / e F [ Blurring only Δ r < 1 kpc g,final Fig.2 ComparisonbetweentheHaywoodetal.(2013)dataandMCM13model.Leftcolumn:Themodelage-[O/Fe] relationforstarsarrivingtothesolarvicinityfromdifferentradii(top),theage-[Fe/H]relation(middle),anddistributions of birth and final guidingradii (bottom)of stars endingup in the solar vicinity,indicated by the green strip. The dotted redandsolidblueverticallinesinthebottomleftpanelindicatethebar’scorotationandinnerLindbladresonance.Right column: The age-[α/Fe] relation (top), where [Mg/Fe] from the modelis used; the age-[Fe/H]relation (AMR) shows a smallerscatterinthemodelthaninthedata(middle);andtheAMRbutwithmigratorsremovedfromthemodel(bottom). This figure shows that the MCM13 modelis consistent with the observedrelationsand suggests that blurringonly(i.e., lackofmigration)isinsufficienttoexplaintoobservedAMR. scatter in the model is somewhat larger for this particular Finally,thebottom-rightpanelofFig.2showsagainthe plot. modelAMR,butwithmigratorsremovedbyexcludingstars whichhavechangedguidingradiisincetheirbirthbymore Thesecondrow,rightpanelofFig.2 showsthe AMR, than1kpc.Thisassumptionisveryconservativeinthatthe whereitcanbeseenthatthescatterissmallerinthemodel cutstillleavesstarswhichhavemigratedby1kpc.Ourse- than in the data (contraryto what was stated by Haywood lection preserves stars with hot kinematics in the sample, etal.2013).Notethatthedataselectioncontains625stars, e.g.,blurring(starsonapo-andpericentersvisitingtheso- orabout2timesmorethantheobservations.Theobviously lar vicinity) still contaminates the local metallicity distri- muchsmallerscatterinthemodelAMRisthenclearlyreal bution.Wetestedthisbymakingsurethattheage-velocity and not a product of lower number statistics compared to dispersionrelationresultingfromtheoriginalmodelselec- thedata. Copyrightlinewillbeprovidedbythepublisher asnaheaderwillbeprovidedbythepublisher 5 tion(middlerightpanelofFig.2) andthesamplewiththe References migratorsremoved,wereverysimilar. Adibekyan,V.Z.,Sousa,S.G.,Santos,N.C.,etal.2012,A&A, The very small scatter found in the bottom right panel 545,A32 of Fig. 2 suggests that blurring is insufficient to explain Anders,F.,Chiappini,C.,Santiago,B.X.,etal.2014,A&A,564, theobservedAMR.Infact,asevidentfromthesecond-row 115 left-panelofthesamefigure,eventhesignificantmigration Baueretal.,2015,Inpreparation present in the MCM13 modelis insufficientto explain the Bensby, T., Alves-Brito, A., Oey, M. S., et al. 2011, ApJ, 735, LL46 scatter found in the data. Assuming we can trust the data Bovy,J.,Rix,H.-W.,Liu,C.,etal.2012b,ApJ,753,148 presented here, we require either a model with more mi- Bovy,J.,Rix,H.-W.,Schlafly,E.F.,etal.2015,arXiv:1509.05796 gration, or some other way of increasing the scatter in the Brook,C.Betal.2012,MNRAS,426,690 AMR. Calura,F.,Gibson,B.K.,Michel-Dansac,L.,etal.2012,MNRAS, 427,1401 This above comparison shows that the MCM13 model Chiappini,C.,Anders,F.,Rodrigues,T.S.,etal.2015,A&A,576, is also consistent with the data by Haywood et al. (2013), L12 contrary to the statement made in the latter paper. It also deJong,R.S.,Bellido-Tirado,O.,Chiappini,C.etal.2012,Proc- warnsthatameaningfulcomparisonbetweenobservational spie,8446 dataandmodelsmustincludethesamewayofpresentation, Dehnen,W.2000,AJ,119,800 e.g.,inthiscasescatterplotsofthemodelsample,spatially Few,C.G.,Courty,S.,Gibson,B.K.,etal.2012,MNRAS,424, constrainedasintheobservations. L11 Freeman, K., Bland-Hawthorn, J., and Barden, S. 2010, AAO Newsletter(Feb) Gibson,B.K.,Pilkington,K.,Brook,C.B.,etal.2013,A&A,554, 3 Conclusions 47 Gilmore,G.,Randich,S.,Asplund,M.etal.2012,TheMessenger 147,25 Despitetherecentadvancesinthefieldofgalaxyformation Guedes,J.,Callegari,S.,Madau,P.,etal.2011,ApJ,742,76 Haywood, M., Di Matteo, P.,Lehnert, M. D.,et al. 2013, A&A, and evolution, currently no self-consistent simulations ex- 560,109 istthathavethelevelofchemicalimplementationrequired Majewski,S.R.etal.2010,Vol.265ofIAUSymposium,pp480– to make detailed predictions for the number of ongoing 481 and planned MW observational campaigns. Even in high- Martig,M.,Bournaud,F.,Croton,D.J.,etal.2012,ApJ,756,26 resolution simulations one particle represents ∼ 104 −105 Martig,M.,Bournaud,F.,Teyssier,R.,etal.2009,ApJ,707,250 solar masses, which requires a number of approximations Martig,M.,Rix,H.-W.,Aguirre,V.S.,etal.2015,MNRAS,451, tocomputethis”sub-grid”physics.Here,instead,wehave 2230 assumed that each particle is one star1 and have imple- Minchev,I.,Nordhaus,J.,andQuillen,A.C.2007,ApJ,664,L31 Minchev, I., Boily, C., Siebert, A., & Bienayme, O. 2010, MN- mentedtheexactSFHandchemicalenrichmentfromatyp- RAS,407,2122 ical chemicalevolution modelinto a state-of-the-artsimu- Minchev,I.,&Famaey,B.2010,ApJ,722,112 lation of the formation of a galactic disc. Note that this is Minchev,I.,Famaey,B.,Quillen,A.C.,etal.2012b,A&A,548, the first time that a chemo-dynamicalmodel has the extra 127 constraintofdefiningarealisticsolarvicinityalsointerms Minchev, I.,Chiappini, C., &Martig, M. 2013 (MCM13), A&A ofdynamics. 558,9 Minchev,I.,Chiappini,C.,&Martig,M.2014,A&A,572,92 Availabilityofaccurateagesisveryimportantto make Minchev,I.,Chiappini,C.,Martig,M.,etal.2014,ApJ,781,LL20 progressin the field of Galactic Archaeology.Thishas re- Minchev,I.,Martig,M.,Streich,D.,etal.2015,ApJ,804,L9 centlybecomeevidentwiththeunexpectedresultsofChiap- Navarro,J.F.andBenz,W.1991,ApJ,380,320 pinietal.(2015)andMartigetal.(2015),whousedCoRoT Perryman,M.A.C.etal.2001,A&A,369,339 andKeplerasteroseismicages,respectively,combinedwith Ram´ırez,I.,AllendePrieto,C.,&Lambert,D.L.2013,ApJ,764, APOGEE chemical information, to show the existence of 78 Scannapieco, C., Tissera, P. B., White, S., et al. 2005, MNRAS, significantlyyounghigh-[α/Fe]stars.Thisisalargelyunex- 364,552 pectedresultforchemicalevolutionmodeling,where[α/Fe] Sharma,S.,Bland-Hawthorn,J.,Binney,J.,etal.2014,ApJ,793, has been thoughtto always be a goodproxy for age. Stel- 51 laragesformuchlargersamplesandbroaderdisccoverage Steinmetz,M.,Zwitter,T.,Siebert,etal.2006,AJ,132,1645 are expectedintheverynearfuturefromKepler-2andthe Tissera, P.B., White,S. D.M., and Scannapieco, C. 2012, MN- Gaiamission.Thesewillhelpbreakdegeneraciesandrefine RAS,420,255 chemo-dynamicalmodels,thusbringingusastepcloserto Wiersma,R.P.C.,Schaye,J.,Theuns,etal.2009,MNRAS,399, understandingtheformationofourGalaxy. 574 Yanny,B.,Rockosi,C.,N.H.J.etal.2009,AJ,137,4377 Zhao,G.,Chen,Y.-Q.,Shi,J.-R.,etal.2006,CJAA,6,265 1 Dynamically,thisisagoodassumption,sincethestellardynamicsis collisionless. Copyrightlinewillbeprovidedbythepublisher