A dark matter disc in the Milky Way 9 0 0 2 n a J. I. Read∗1, V.Debattista3, O.Agertz1, L.Mayer1, A.M.Brooks4,F.Governato3 and J G. Lake1 9 1InstituteforTheoreticalPhysics,UniversityofZurich,Winterthurerstrasse1908047 1 2RCUKFellow;CentreForAstrophysics,UniversityofCentralLancashire,Preston,PR12HE ] 3AstronomyDept.,UniversityofWashington,Box351580,SeattleWA98195-1580 A 4CaliforniaInstituteofTechnology,M/C130-33,Pasadena,CA91125 G E-mail: [email protected] . h p Predictingthe localflux of darkmatter particlesis vital fordarkmatter directdetectionexperi- - o ments.Todate,suchpredictionshavebeenbasedonsimulationsthatmodelthedarkmatteralone. r t Hereweincludetheinfluenceofthebaryonicmatterforthefirsttime. Weusetwodifferentap- s a proaches. Firstly, we use dark matter only simulationsto estimate the expectedmerger history [ foraMilkyWaymassgalaxy,andthenaddathinstellardisctomeasureitseffect. Secondly,we 1 v use three cosmologicalhydrodynamicsimulations of Milky Way mass galaxies. In both cases, 8 we find that a stellar/gas disc at high redshift (z∼1) causes merging satellites to be preferen- 3 9 tiallydraggedtowardsthediscplane. Thisresultsinanaccreteddarkmatterdiscthatcontributes 2 ∼0.25−1times the non-rotatinghalo density at the solar position. An associated thick stellar . 1 disc forms with the dark disc and shares a similar velocity distribution. If these accreted stars 0 9 canbeseparatedfromthosethatformedinsitu,futureastronomicalsurveyswillbeabletoinfer 0 thepropertiesofthedarkdiscfromthesestars. Thedarkdisc,unlikedarkmatterstreams,isan : v equilibriumstructurethat must exist in disc galaxiesthat form in a hierarchicalcosmology. Its i X lowrotationlagwithrespecttotheEarthsignificantlyboostsWIMPcaptureintheEarthandSun, r increasesthelikelihoodofdirectdetectionatlowrecoilenergy,booststheannualmodulationsig- a nal,andleadstodistinctvariationsinthefluxasafunctionofrecoilenergythatallowtheWIMP masstobedetermined(seecontributionfromT.Bruchthisvolume). Identificationofdarkmatter2008 August18-22,2008 Stockholm,Sweden ∗Speaker. (cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommonsAttribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/ AdarkmatterdiscintheMilkyWay J.I.Read 1. Introduction The case for dark matter in the Universe is based on a wide range of observational data, from galaxy rotation curves and gravitational lensing, tothe CosmicMicrowave Background Radiation [7];[3]. OfthemanyplausibledarkmattercandidatesinextensionstotheStandardModel,Weakly InteractingMassiveParticles(WIMPs)standoutaswell-motivatedanddetectable[7],givingriseto manyexperimentsdesignedtodetectWIMPsinthelab. Predictingthefluxofdarkmatterparticles through the Earth iskey to the success of such experiments, both tomotivate detector design, and fortheinterpretation ofanyfuturesignal[7]. Previousworkhasmodelledthephasespacedensitydistribution ofdarkmatteratsolarneigh- bourhood using cosmological simulations that model the dark matter alone (see e.g. [13], [12]). Herewemakethe firstattempt toinclude thebaryonic matter –thestars and gasthat makeupthe Milky Way. The Milky Way stellar disc presently dominates the mass interior to the solar radius andlikelydidsoalsointheearlyUniverseatredshiftz=1,whenthemeanmergerrateinaL CDM cosmologypeaks[10]. Thestellarandgasdiscisimportantbecauseitbiasestheaccretionofsatel- lites, causing them to be dragged towards the disc plane where they are torn apart by tides. The material fromtheseaccreted satellites settlesintoathickdiscofstarsanddarkmatter[17]. Inthis work, we quantify the expected properties of this dark disc. Its implications for direct detection experimentsandthecaptureofWIMPsintheSunandEartharepresentedinthecontribution from T.Bruch,thisvolumeandin[2]. Weuse two different approaches. In the first approach (§2), weuse dark matter only simula- tions to estimate the expected merger history of a Milky Way mass galaxy, and then add a stellar disc tomeasure itseffect. Thisworkispresented indetail already in[10]. Inthe second approach (§3),weusecosmologicalhydrodynamicsimulationsoftheMilkyWaytohuntfordarkdiscs. Both approaches arecomplementaryinquantifying theexpectedpropertiesofthedarkdisc. Theformer allows us to specify precisely the properties of the Milky Way disc at high redshift; the latter is fullyself-consistent. 2. Approach #1: adding a stellardiscto cosmologicaldark matter simulations We used a cosmological dark matter only simulation already presented in [4] to estimate the fre- quency of satellite-disc encounters for a typical Milky Way galaxy; further details are given in [10]. Fromthesimulationvolume,weextractedfourMilkyWaysizedhalosatamassresolutionof m =5.7×105M . Thesubhalosinsideeach‘MilkyWay’andateachredshiftoutputwereidenti- p ⊙ fiedusing thealgorithm in [5]and then traced back intimetotheir progenitor halos asdetailed in [10]. From our sample of four Milky Way mass halos and assuming that mergers are isotropic (whichwemustdosincewedonotknowhowthediscshouldalignwiththedarkmatterhalo),we findthatatypicalMilkyWaysizedhalowillhave1(±1)subhalomergewithinq <20o ofthedisc planewithv >80km/s;2(±1)withv >60;and5(±1)withv >40km/s. Awayfromthe max max max disc plane there will be twice as may mergers at the same mass [10]. It is important to stress that thesenumberscomefromthedistributionoffullydisruptedsubhalos,notthesurvivingdistribution thatissignificantly lessdamaging. Wethenestimatedtheeffectofastellardisconthesemergersbyrunningisolateddisc-merger simulations. WesetupourMilkyWay(MW)model(disc+halosystem)byadiabatically growinga 2 AdarkmatterdiscintheMilkyWay J.I.Read (a) (b) (c) (d) Figure 1: (a): The accreted stars (red) and dark matter (blue) at the end of a simulation where the LMC satellite merged at q =10o to the Milky Way stellar disc; the black contoursshow the underlyingMilky Way stellar distribution. (b): The correspondingvelocitydistributionin vf (rotationvelocity)at the solar neighbourhood;the underlyingMilky Way dark matter halo is shown in green. (c): The dark matter disc to darkmatter halodensity ratior /r as a functionof heightabovethe disc plane (also for8< DDISC HALO R<9kpc),forLMCmergingatq =10o,20o,40oandLLMCatq =10ototheMilkyWaydiscplane. (d): Thesatellite-discinclinationangleq asafunctionoftime;thelinesaretruncatedwhenthesatelliteisfully accreted. discinsideasphericalhalo,asdetailedin[10]. Wechosethreemodelsforoursatellite, butpresent just two here: LMC with v =60km/s, and LLMC with v =80km/s; these were set up as max max scaled versions of our MW model. Wechose a wide range of initial inclination angles to the disc fromq =10−60o,oneretrograde orbit, andrangeofpericentres andapocentres. Thesimulations were evolved using the collisionless tree-code, PkdGRAV [14]. The final evolved systems were mass and momentum centred using the ‘shrinking sphere’ method described in [11], and rotated intotheirmomentofinertiaeigenframe withthezaxisperpendicular tothedisc. The results are shown in Figure 1. The left panel shows the accreted stars (red) and dark matter (blue) at the end of a simulation where the LMC satellite merged at q =10o to the disc. Both the stars and the dark matter have settled into accreted discs. The middle panel shows the corresponding velocity distribution in vf (rotation velocity) at the solar neighbourhood (a cylin- der 8<R<9kpc, |z|<0.35kpc). The underlying dark matter halo is shown in green and is not rotating;theaccretedstarsanddarkmatter(redandblue)havekinematicssimilartothatoftheun- derlyingstellardisc(black). Therightpanelshowsthedarkmatterdisctodarkmatterhalodensity ratio r /r as a function of height above the disc plane for selected merger simulations, DDISC HALO as marked. As the satellite impact angle q is increased, the satellite contributes less material to a dark disc. For q =40o, the density at the solar neighbourhood is nearly flat with z and less than a tenth of the underlying halo density; there is correspondingly less rotation in this simulation. Summing over the expected number and mass of mergers, we find that the dark disc contributes ∼0.25−1 times the non-rotating halo density at the solar position [10]. It is important to stress that all satellites regardless of their initial inclination have some accreted material that is focused intothediscplane(seeFigure1),rightpanel. Assuch,weexpectthattheaccreteddarkandstellar discs willcomprise severalaccreted satellites; themostmassivelow-inclination mergers beingthe mostimportantcontributors. Theaccretedstellardiscsharessimilarkinematicstothedarkdisc. Dependingonassumptions about the mass to light ratio of accreted satellites, these accreted stars can make up ∼10−50% 3 AdarkmatterdiscintheMilkyWay J.I.Read (a) MW1 (b) H204 (c) H258 (d) H258dark (e) MW1 (f) H204 (g) H258 (h) H258dark Figure 2: (a-c) The distribution of rotational velocities at the solar neighbourhood for three simulated Milky Way mass galaxies MW1, H204 and H258. The lines show the dark matter (black), stars (red), a doubleGaussianfittothedarkmatter(blue;bluedotted),thematerialaccretedfromthefourmostmassive disruptedsatellites (green,blue, magenta,cyan), andthe sum of allmaterialaccretedfromthese satellites (blackdotted). ThebestfitdoubleGaussianparametersaremarkedinthetopleft,alongwiththeredshift, z. (d) As(a-c), butforthe galaxyH258simulatedwith darkmatteralone. (e-h)Thedecayin radiusr as afunctionofredshiftzofthefourmostmassivedisruptingsatellitesinMW1,H204 H258andH258dark. Wherelessthanfourlinesareshown,thesesatellitesaccretedatredshiftz>3. Thedottedsectionsshowthe evolutionofthemostboundsatelliteparticleafterthesatellitehasdisrupted. of the Milky Way stellar thick disc [10]. (The lower end of this range is more likely given the observedpropertiesofsatellitegalaxiesintheUniversetoday.) IffuturesurveysofourGalaxycan disentangle accreted starsintheMilkyWaythickdiscfromthosethatformedin-situ, thenwewill beabletoinferthevelocitydistribution function ofthedarkdiscfromthesestars. 3. Approach #2: cosmologicalhydrodynamicsimulations Weuse three cosmological hydrodynamic simulations ofMilky Way massgalaxies, twoof which (MW1,H258)havealready beenpresented in[9]and[6]. AllthreewererunwiththeGASOLINE code [16] using the "blastwave feedback" described in [15]. MW1 had cosmological parameters (W m,W L ,s 8,h)=(0.3,0.7,0.9,0.7); H204andH258used(W m,W L ,s 8,h)=(0.24,0.76,0.77,0.73). Atredshift z=0thetypicalparticle massesfordarkmatterstarsandgaswere: (M ,M ,M )= dm ∗ gas (7.6,0.2,0.3)×105M , with associated force softening: (e ,e ,e )=(0.3,0.3,0.3)kpc. The ⊙ dm ∗ gas analysis wasperformed asin§2. Figure2showsthedistributionofrotationalvelocitiesatthesolarneighbourhood(toppanels), andtheorbitaldecayofthefourmostmassivesatellites(bottompanels)forMW1,H204andH258. The right most panels (d) and (h) show the results for the galaxy H258 simulated without any gas orstars–H258dark. Notice that, with the exception of H258dark, in all cases the dark matter requires a double Gaussian fitto itslocal vf velocity distribution. Oncethe baryons (the stars and gas)are included in the simulation, there is a local dark matter disc that lags the rotation of the thin stellar disc 4 AdarkmatterdiscintheMilkyWay J.I.Read by ∼ 50−150km/s. The mass and rotation speed of the dark disc increase for the simulations that have more late mergers. MW1 has no significant mergers after redshift z=2 and has a less significant dark disc, withrotation lag ∼150km/sand dark disc to non-rotating dark halo density ratio r /r =0.23 (obtained from the double Gaussian fit). H204 and H258 both have DDISC HALO extreme dark discs with r DDISC/r HALO >1 and rotation lag ∼< 60km/s; they both have massive mergersatredshiftz<1. 4. Conclusions Low inclination massive satellite mergers are expected in a L CDM cosmology. These lead to the formationofthickaccreteddarkandstellardiscs. Weusedtwodifferentapproachestoestimatethe importance ofthedarkdisc. Firstly,weuseddarkmatteronlysimulationstoestimatetheexpected mergerhistoryforaMilkyWaymassgalaxy,andthenaddedathinstellardisctomeasureitseffect. Secondly, weusedthree cosmological hydrodynamic simulations ofMilkyWaymassgalaxies. In both cases, we found that a typical Milky Way mass galaxy will have a dark disc that contributes ∼0.25−1 times the non-rotating halo density at the solar position. The dark disc has important implications for the direct detection of dark matter [2] and for the capture of WIMPs in the Sun andEarth(seecontribution fromT.Bruch,thisvolume). 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