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Draftversion January15,2013 PreprinttypesetusingLATEXstyleemulateapjv.5/2/11 SATELLITES IN MW-LIKE HOSTS: ENVIRONMENT DEPENDENCE AND CLOSE PAIRS. Roberto E. Gonza´lez1,2, Andrey V. Kravtsov1,2,3, and Nickolay Y. Gnedin4,1,2 Draft version January 15, 2013 ABSTRACT Previousstudies showedthatanestimate ofthe likelihooddistribution ofthe Milky Wayhalo mass canbe derivedusing the properties ofthe satellites similarto the Largeand SmallMagellanicClouds 3 (LMC and SMC). However, it would be straightforward to interpret such an estimate only if the 1 properties of the Magellanic Clouds (MCs) are fairly typical and are not biased by the environment. 0 Inthis studyweexplorewhethertheenvironmentoftheMilkyWayaffectsthe propertiesofthe SMC 2 and LMC such as their velocities. To test for the effect of the environment, we compare velocity n distributionsforMC-sizedsubhalosaroundMilkyWayhostsinasampleselectedsimply bymassand a in the second sample of such halos selected with additionalrestrictions onthe distance to the nearest J cluster and the local galaxy density, designed to mimic the environment of the Local Group (LG). 1 We find that satellites in halos in the LG-like environments do have somewhat larger velocities, as 1 comparedto the halosofsimilarmassinthe sample withoutenvironmentalconstraints. Forexample, thefractionofsubhalosmatchingthevelocityoftheLMCis23±2%largerintheLG-likeenvironments. ] We derive the host halo likelihood distribution for the samples in the LG-like envirionment and in O the control sample and find that the environment does not significantly affect the derived likelihood. C We use the updated properties of the SMC and LMC to derive the constraint on the MW halo mass h. log(M200/M⊙) = 12.06+−00..3119 (90% confidence interval). We also explore the incidence of close pairs withrelativevelocitiesandseparationssimilartothoseoftheLMCandSMCandfindthatsuchpairs p - are quite rare among ΛCDM halos. Only 2% of halos in the MW mass range have a relatively close o pair (∆r <40kpc and ∆s<160 km s−1) of subhalos with circular velocities v >50 km s−1. Pairs circ r with masses and separations similar to those of the LMC and SMC (∆r = 23.4±10 kpc, and t MC s ∆s = 128±32 km s−1) are found only in one out of ≈ 30000 MW-sized halos. Interestingly, the MC a halo mass likelihood distribution for host halos constrained to have MC-like close pairs of subhalos is [ quitedifferentfromthegloballikelihoodfromwhichtheMWhalomassconstraintdiscussedabovewas 1 derived. Taking into accountthe close separationof the MCs in the Busha et al.2011method results v in the shift of the MW halo mass estimate to smaller masses, with the peak shifting approximately 5 by a factor of two. 0 Subject headings: Galaxy: fundamental parameters, halo — galaxies: Magellanic Clouds — dark 6 matter 2 . 1 1. INTRODUCTION Kallivayalilet al. 2006b,a). 0 It is still debated how typical is the satellite popula- 3 In the CDM scenario the Milky Way (MW) halo tionoftheMW,butboththeoreticalmodelsandobserva- 1 formed by accretion and disruption of smaller ha- tionsindicatethattheincidenceoftheMagellanicClouds : los, and some of them survived this process as self- v (MCs) satellites is rare for MW-sized galaxies. Semi- bound substructures or subhalos orbiting around the i analytic galaxy formation models predict that only ≃ X host halo (e.g., Klypin et al. 1999b; Moore et al. 1999, 10%oftheMW-sizedgalaxieshavesatellitesasbrightas see Kravtsov 2010 for a recent review). The major- r the LMC (e.g., Kauffmann et al. 1993b; Koposov et al. a ity of these subhalos are likely devoid of stars, but 2009). Boylan-Kolchinet al.(2011)usedlargesampleof some of them are massive enough to host dwarf galax- MW-sizedhalosextractedfromthe Millenium-II simula- ies (e.g., Kauffmann et al. 1993a; Klypin et al. 1999b; tion and found that 20% MW-mass halos host an LMC Bullock et al. 2000; Kravtsov et al. 2004; Font et al. orSMC,andonly ∼2.5%hostboth MCs. Asimilarfre- 2011). The MW and its satellites offer a unique labo- quencywasfoundbyBusha et al.(2011b)usingtheBol- ratory for testing CDM predictions for halo formation shoisimulationof the concordancecosmologyandabun- andassociatedsubstructure,because propertiesofmany dance matching ansatz to assign stellar masses to ha- of the satellites have been studied in details in observa- losand subhalos. Inobservations,James & Ivory(2011) tions,includingpropermotionsandrotationcurves(e.g., searchedfor star-forming satellites around 143 luminous 1Department of Astronomy & Astrophysics, The spiralgalaxiesandfoundthattwo-thirdsofcentralgalax- University of Chicago, Chicago, IL 60637 USA ieshavenosatellitesdowntoluminosity andstarforma- [email protected] tion rates well below those of the MCs. Using the Sloan 2Kavli Institute for Cosmological Physics, The University of Digital Sky Survey (SDSS), Liu et al. (2011a) computed Chicago, Chicago,IL60637USA 3EnricoFermiInstitute,TheUniversityofChicago,Chicago, the occurrence of the satellites similar to the MCs in lu- IL60637USA minosity aroundMW-sizedgalaxiesand found that 11% 4Particle Astrophysics Center, Fermi National Accelerator have one, and only 3.5% have two MCs within a radius Laboratory, Batavia,IL60510USA 2 González, Kravtsov & Gnedin of 150kpc. Similar values for the frequency of MCs are To carry out our analysis we use halos extracted from found in the SDSS in a recent study by Tollerud et al. the Bolshoi simulation (Klypin et al. 2011), which fol- (2011), and in the GAMA survey by Robotham et al. lowed evolution of 20483 particles in 250h−1Mpc cu- (2012). WhatmakesMagellanicCloudsevenmorepecu- bicvolumeassumingconcordanceflatΛCDMcosmology liar is the fact that they are likely to be an interacting with parameters: Ω = 1−Ω = 0.27, Ω = 0.0469, m Λ b pair(see§4.3below)andhaveratherhighvelocitieswith h = H /(100)= 0.7, σ = 0.82 and n = 0.95, compati- 0 8 s respect to the Milky Way. ble with combined constraints from WMAP, BAO, SNe, One caveat in this debate is that some satellite prop- and cluster abundance (Komatsu et al. 2011). The high erties depend sensitively on the MW halo mass (e.g., spatial and mass resolution and relatively large volume Wang et al. 2012). Although there are several methods make the Bolshoi simulation well suited for providing a to constraint the MW halo mass (see e.g., Busha et al. base halo sample for our study. 2011a; Deason et al. 2012, and references therein), it is The halo catalog we used was constructed using the still quite uncertain. In this study we focus on the BoundDensityMaximahalofinder(Klypin & Holtzman methods that use satellite properties to constrain the 1997; Klypin et al. 1999a), which identified 2285977 ha- MW halo mass. In particular, as shown by Busha et al. losdowntotheresolutioncompletenesslimitofv ≈50 circ (2011a, B11 hereafter), the MW host halo mass likeli- kms−1(correspondingto≈110particlesorM ≈1.7× 200 hood can be computed using the observed MCs prop- 1010 M⊙). The circular velocity vcirc is the maximum erties and a statistically representative sample of CDM of the circular velocity profile v (r) = pGM(<r)/r. halos to evaluate the likelihood that a given halo would circ The parameters of the halo finder were set such that haveeachorallMCsproperties,suchascircularvelocity, the density maxima are not allowed to be closer than hosthalodistance,andvelocitywithinthehost. Suchap- 10h−1kpc, and the finder keeps only the most massive proachprovidesanew interesting constraintonthe MW density maximumif that happens. Halo center is identi- virial mass, but there are certain questions that need to fiedwiththeparticlelocationwhichhasthelargestlocal be addressed to assess its reliability and interpretation. density, and bulk halo velocity is computed as the av- One of such questions is whether the environmentof the erage velocity of the 30 closest neighbors of the central LocalGroupbiasespropertiesofthe MWsatellitepopu- particle. Thealgorithmcomputesanumberofhaloprop- lation,andMCsinparticular. Weexplorethisandother erties after an iterative procedure to remove unbound related questions in more detail in this paper. particles. Another important question is the origin and dynam- Throughoutthis paper wedefined halomass, M , as ics of the MCs. The accretion history of the MCs is 200 the mass enclosed in a sphere of radius R with the still not clear, the presence of the Magellanic Stream 200 density 200 times the critical density of the universe at (MS hereafter), a filament of gas extending 150◦ across theredshiftofanalysis. Anothercommonmassdefinition the sky, with an apparent spatial and chemical associ- is M , the mass within the radius enclosing the mean ation with the MCs, is interpreted as a tidal tail (see vir overdensityof358withrespecttothemeandensityofthe Besla et al. 2012a, and references therein). There are universe (or overdensity of 358×0.27≈97 with respect several clues which indicate that the MCs are bound, to the critical density) (Bryan & Norman 1998). In the and have been interacting recently (Diaz & Bekki 2012; Bolshoi simulation, we find a relation of M /M = Besla et al. 2012b), and there is also some evidence of vir 200 1.21 for host halos of v ≈220 km s−1. the SMC stars accreted onto the LMC (Olsen et al. circ We use MW-sized host halos in the Bolshoi catalogs 2011; Casetti-Dinescu et al. 2012). Close satellite pairs to search for subhalos with velocities and positions sim- are rare in nearby MW-sized galaxies (Robotham et al. ilar to those of the MCs. However,positions of satellites 2012; James & Ivory 2011). Proper motion measure- change on short timescales due to their motion along ments for the MCs (Kallivayalilet al. 2006b,a) indicate their orbits. Therefore, to increase statistics, we stack that they havehigh velocities not alignedwith the Mag- thehalocatalogsofseveralsimulationsnapshotscloseto ellanic Stream, and suggest that the MCs could be z = 0 separated by ∆a = 0.003 (∼42Myrs at z =0). bound and on their first or second pericenter passage During the time interval between snapshots a typical into the MW (Besla et al. 2007, 2010, 2012b). Other MC should move ∼ 15kpc along its trajectory. We studies also suggest that the MCs were accreted in stack satellites of the last 30 snapshots, and the total the same system (D’Onghia & Lake 2008; Nichols et al. time difference between the first and last snapshot is 2011). B11 estimated from the Bolshoi simulation that, ∼ 1.3Gyrs (or ∆z < 0.1), so we can neglect any evo- for a typical MW-sized host, there is a ≃ 72% proba- lution effect in MW mass halos (Munõz-Cuartas et al. bility that the MCs were accreted within the last Gyr. 2011; Diemer et al. 2012; Cuesta et al. 2008). Boylan-Kolchinet al. (2011) and Besla et al. (2012a) For a given MW-sized halo at z = 0 we should, in also favor the late accretion scenario for the MCs. principle,considerthelastN simulationoutputstotrace The paper is organized as follows. We describe the trajectoriesofallsatellites andcheck ifthey matchMCs simulation and halo catalogs used in our study in § 2, contraintsatsometimeintherecentpast. However,this while in § 3 we describe the data samples for our MW-, iscomputationallyexpensive. Instead,inouranalysiswe MCs-, and LG-analogues. We presents the MW halo consider each snapshot as an independent realization of mass likelihood in different environments and under dif- halo properties, which effectively increases the simula- ferentassumptionsonwhether MCs areindependent ve- tion sample by a factor of N. In this approximation we locity samples in § 4 and § 4.3. We present discussion neglect any correlation in the positions and velocities of and our conclusions in § 5. satellites between snapshots. For example, in the ex- 2. SIMULATIONANDHALOCATALOGUES treme case of a purely circular orbit, a single LMC or Satellites in MW-like hosts 3 SMC analogue would be counted N times. However, for 3.3. The Local Group analogues realistic eccentric orbits such double counting is quite TheMilkyWayisnotanisolatedgalaxy,butislocated rare, especially for satellites with relatively small radial in a pair with M31 (≈770 kpc awayMcConnachie et al. distances to host centers similar to those of the SMC 2005; Ribas et al. 2005) and is surrounded by a num- andLMC.Ontheotherhand,wehavealargenumberof ber of smaller galaxies, collectively known as the Local hostsandsatellitesineachsnapshot,andtherandomness Group of galaxies. On larger scales the environment of of their orbital configuration produces consistent distri- the Local Group is rather low-density: in a sphere of butions and average fraction of satellites matching any 50 Mpc radius around the LG, the estimated density is given set of constraints, for any number of snapshot se- ∼3timeslowerthanaverage(Karachenstev2012),while lected. Wehavetestedforthedoublecountingeffectsus- inasphereof5MpcthedensityaroundtheLocalGroup ingdifferentnumberofsnapshots,N,computingthedis- isclosetothemeandensityoftheuniverse(Klypin et al. tributionofsatellitesmatchingseveralsetofconstraints, 2003; Karachentsev2005). In addition, the nearest clus- andwe havefound no significantdifferences inthe prop- ter to the Local Group is the Virgo Cluster ∼16.5 Mpc erties of satellites for N .30. away (Mei et al. 2007). ToexplorewhetherenvironmentoftheLocalGroupon 3. HALOSAMPLESANDOBSERVATIONALCONSTRAINTS differentscalesaffectsstatisticsoftheMC analogues,we In our analysis we use the following three main obser- derive several MW analogue samples that mimic differ- vational measurements. ent aspects of the real MW environment: the host halos in the P sample have an M31-sized companion in relative isolation with no other large neighbor; host halos 3.1. The Milky Way halo mass in the LGP sample are a subset of halo pairs from the ToselectMWanaloguesfromtheBolshoi-derivedhalo Psample,butwithadditionalenvironmentalconstraints catalogues, we select halos within the broad mass range designed to more closely mimic the LG environment; fi- M200c = 0.8−2.9×1012 M⊙, which covers the range nally, host halos in the S sample include all host halos of current observational constraints: e.g., using HI gas that are not in included in the LGP- and P- samples. distribution (Kalberla et al. 2007), kinematics of stars These sample definitions and naming convention will be (Sofue et al. 2009; Xue et al. 2008; Gnedin et al. 2010; used for both host halos in the MW halo mass range Wilkinson & Evans 1999; Deason et al. 2012), satel- (Section3.3)andhalosamplesina widerangeofmasses lite dynamics (Watkins et al. 2010), escape velocity (Section 4). Note that for the P and LGP samples the (Smith et al. 2007), and timing argument (Li & White mass of the M31-like companion is always fixed to the 2008). There are (∼ 57000) host halos in this mass same mass range, even as its MW analogue halo mass is range in the Bolshoi simulation at z = 0, which contain varied within a wider range. ∼115000 subhalos with vcirc >50 km s−1. Belowthesampledefinitionsaredescribedinmorede- tail. 3.2. Magellanic Cloud analogues The P sample: the host halos are required to have a companion similar to M31, which we define using the We follow Busha et al. (2011a) and use the following observedpropertiesoftheMagellanicCloudstoselectap- same mass range of M200c = 0.8−2.9×1012 M⊙(e.g., Watkins et al.2010;Evans et al.2000). Thepairsarere- propriateMCanaloguesamongsubhalosintheMWhalo quiredtoberelativelyisolatedandnotbepartofatriplet analogues and to constrain the halo mass of the Milky or a larger group. As a quantitative isolation criterion Way: the distance to the host center r , the total speed 0 for the pair we use the force constraint F < κF , relativetothe hostcenters,andthesubhalocircularve- i,com 12 where F is the gravitational force between the pair locityv . ForthesequantitiesweuserecentHST mea- i,com circ and any neighbor halo i within a 5h−1Mpc radius of the surementsby Kallivayalilet al.(2013): v =76.1±7.6 kms−1,r =50±5kpc,s=321±24kmsc−ir1cfortheLMC, pair center-of-mass, and F12 is the force between halos andv =0 60±5kms−1,r =60±5kpc,s=217±26km inthe pair,andκis aconstantparameter. The isolation s−1forcirtche SMC. The halo0s hosting the MCs analogues criterion becomes increasingly strict for decreasing values of κ. The Milky Way and M31 do not have massive arerequiredtohaveatleasttwosubhaloswithv >50 km s−1and we will consider only the two subhacliorcs with neighbors within 5 Mpc, and should thus have κ < 0.1. The actual value of κ is, however, uncertain, and we ex- the largest circular velocities5. plore a range of values in the further analysis. We use Note that r errors are inflated from their actual ob- 0 κ = 0.1, 0.15, 0.2, 0.25 which results in 205, 378, 598, servational values to improve statistics of the sample of 810 LG-like halo pairs, respectively. From the a poste- the MC analogues. The range of r we use corresponds 0 riori analysis of satellite properties, results are largely to typicalradialdisplacementof subhalos along its orbit consistent for different κ values and we thus use κ=0.2 between consecutive snapshots. These parameters are inthispapertomaximizethestatisticsoftheMWhosts. used everywherein this paper, except in § 4.2, where we The598LG-likehalopairswefoundusingκ=0.2repre- use a different definition for the MCs analogues assum- sent∼2%ofallhalosintheMWmassrange,and∼80% ing a single bound system, and in § 5, where we include of these pairs are bound under the two-body point mass two additional constraints: the relative separation and energy approximation. velocity of the clouds. The LGP sample of halos is a subset of halos in the P sample with additional constraints on the local 5 In B11, the MCs analogues are selected in hosts that have and global environment to more closely mimic the envi- exactly two subhalos with vcirc >50 km s−1, we will explore the ronment of the Local Group. Namely, we require that effects ofthisdifferenceintheResultssection. 4 González, Kravtsov & Gnedin Fig.1.— Distribution of the local galaxy overdensity (left panel), distance to the nearest cluster-sized (M200 > 1.5×1014 M⊙) halo (center panel), and distance from the pair companion for halos in the P sample (solid black line), LGP sample (short-dashed line), and S-sample (red long-dashed line). The maximum local overdensity, the minimum distance to the closest cluster, and the minimum pair separation used as additional constraints for the LGP sample of the MW analogues in the LG-like environments are shown by the black arrows. The MW is ∼ 16.5Mpc away from the Virgo cluster(middle panel, red arrow) and separation between the MW and M31 is ∼770kpc(rightpanel,red arrow). halos in this sample do not have a cluster-sized halo are≈1.3%of the total number of hosthalos in the MW moremassivethanM200 =1.5×1014M⊙within12Mpc. halomassrange. ThisindicatesthattheLGenvironment This mass limit is close to the mass of the Virgo Cluster oftheMilkyWayisratherrareforhalosofthismass,the M⊙(e.g., Fouqué et al. 2001; Nulsen & Bohringer 1995, factalsoindicatedbythe“coldness”ofthelocalvelocity and references therein). For the local environment we field of galaxies (e.g., Klypin et al. 2003). compute the galaxy density field using Voronoi tessella- The figure shows that the P sample halos are located tion (VT hereafter) on halo positions and masses (sim- in environments with similar overdensity distribution to ilar to the method of Schaap & van de Weygaert 2000; theS-samplehalos,buthaveanarrowerdistributiondue González & Padilla 2010). The VT partitions the vol- to the force constraint and the chosen κ = 0.2 value, ume intocells,whereeachcellisassociatedwithasingle which eliminates responsible pairs close to other larger hosthalo. Theshapeandvolumeofeachcellisdefinedby halos and single isolated halos. distribution of halo neighbors. The adaptive local density canbe computed using the localcell volume around 4. THEMWHALOMASSESTIMATE eachhaloandtheenclosedhalomass,butinsteadweuse Inthe contextofthe B11method, inordertoestimate also neighbors cell volumes and masses to compute the the halo mass of the Milky Way from the properties of average, in this way we generate a smooth density field the MCs, such as circular velocity, velocity and position where the typical number of direct neighbors around a relative to the center, we explore two aspects which can halo is ≈ 14. We use only the host halos with mass affectthemassestimate: 1)theenvironment,inparticu- higher than M200 = 1.5×1010 M⊙for density computa- larwhetherdifferencesinthe environmentcorrespondto tion,anddefinethelocaloverdensityasδ =(ρ−hρi)/hρi, the differences in the subhalo populations of halos, and where hρi is the mean of the density distribution. The 2)whetheritmattersifMCsaretreatedastwoindepen- local density of the LG is not well constrained, but the dent dynamical samples or a single tracer (a bound pair abundanceofluminousgalaxieswithin3−6Mpcisclose sharingacommontranslationalmotionoftheircenterof to the average density of galaxies in the local universe mass). (Karachentsev 2005). Another local environment con- 4.1. Effect of the environment straint we include is the distance to the M31-like pair companion. To test for possible effects of the MW environment on Figure1showsthedistributionofthelocaldensity,dis- subhalostatistics,weextractallsubhaloswithv >50 circ tancetothe closestVirgo-sizedhalo,anddistancetothe km s−1, and compute their distance to the host center M31-sizedpaircompanionfortheMWanaloguehalosin r and the total speed relative to host s. Subhalos very 0 the Psample,andthe cuts weimpose todefine the LGP close to the host center (r <20h−1kpc) are removed to 0 sample. Specifically, we select only halos with the local avoidartefactsorresolution-relatedproblemsinthehalo overdensity smaller δ =1.04 to avoid systems located in identification procedure. the highest density decile. The mean overdensityfor the Figure 2 shows abundance of subhalos with v > circ S-sample is located at log(δ+1) ∼ 0, and for the LGP 50,60,70kms−1infourmassrangesaround1012M⊙. As sample it is located 0.5 dex lower. expect, the average number of subhalos increases with We exclude halos with Virgo-sized neighbors closer increasing host halo mass and decreases for increasing than 12 Mpc and require that distance to the pair com- subhalo circular velocities. The figure shows that there panionisintherange0.4<∆r <1.2Mpctoavoidclose, isno significantdifference inthe abundancesofsubhalos possibly merging pairs, but to include pairs with sepa- in hosts of the S and LGP samples, which means that rations similar to the actual distance between the Milky the Local Group environment does not appreciably af- WayandM31. Theseconstraintseliminateaboutathird fectabundanceofthe massivesubhalosinthe MW-sized ofhalosfromthePsample;thehalosintheLGPsample hosts. Satellites in MW-like hosts 5 nificant change in the distribution at the SMC speed). Therefore, the fraction of satellites matching the velocity of the LMC is somewhat enhanced in the LG-like environments. This can affect the MW mass estimate because LMC velocity is the mainconstraintdriving the mass likelihood distribution to larger masses (see B11 and Fig. 5 below). Wehavetestedwhetherthechoiceofκparameterused in the isolation criterion (see § 3.3) influences the velocity distribution and have found that the result velocity distribution is almost the same for values of κ in the range 0.1< κ<0.25, with a weak trend towards higher fractionofsubhalosinthe LGPsamplematchingthe velocities of the LMC and SMC for lower κ values. The magnitude of the trend, however, is comparable to the uncertainties in the velocity distribution. Fig. 2.— AveragenumberofsatellitesintheSandLGPsamples for halos indifferent mass ranges around most likely range of the MW halo mass, and satellite circular velocity ranges defined in legend. Theerrorbarsofthemeanvaluesarecomputedusingthe jackknife method. Top-right legend quotes the fractions of halos withNSATmembersforsubhaloswithvcirc>50kms−1,andhost halomassesintherange0.8<M200<2.9×1012 M⊙. Fig.4.— FractionofsubhalosmatchingthevelocityoftheSMC and LMC in the S (black symbols and lines) and LGP (red sym- bolsandlines)samplesforthreedifferenthalomassrangesaround M200=1012M⊙(thefirstthreeconnectedbins)andthetotalmass range used to define the MWhalo analogues (the gray shaded region). In figure 4 we show the fraction of subhalos with total velocities relative to the host center similar to those of theLMCandSMCforhosthalosindifferentmassranges around M200 = 1012M⊙. There is a small enhancement in the frequency at the LMC velocity, but no difference at the SMC velocity. In the LGP sample the fraction of Fig.3.— Distributionsofthetotalsubhalovelocityintheframe host halos with subhalos matching the LMC velocity is oftheirhosthaloforhostsintheSandLGPsamples. Bluearrows indicatethevelocitiesoftheSMCandLMC.Theuncertaintyofthe larger by 29±10%, 16±4%, and 10±2% than in the S distributionfortheLGP sampleisshownbythedashed lines(es- sample for 0.8−1.2, 1.2−1.9, and 1.9−2.9×1012M⊙ timatedusingthejackknifemethod). Theenvironmenthassmall, mass ranges respectively. but statistically significant effect on the distribution of velocities: WepresentthelikelihooddistributionfortheMWhalo thefractionofsubhaloswiththeLMCvelocityintheLGPsample is23±2%higherthanintheSsample. mass from the constraints from the Magellanic Cloud properties in Figure 5. To compute the likelihood we Figure 3 shows the distributions of the total subhalo used the S and LGP sample constructed without any velocity in the frame of their hosts for halos in the S restrictiononthe M mass ofhalos. Inadditionto the 200 and LGP samples. The fraction of satellites with veloc- likelihoodforalloftheconstraintscombinedforS-sample ities comparable to that of the LMC is 23±2% higher only, we also show likelihoods resulting from using only in LGP sample than in the S sample (there is no sig- one of the constraints for both S and LGP samples. In 6 González, Kravtsov & Gnedin Note that there is a key methodological difference in the waythe likelihooddistributionwasevaluatedin B11 and in our analysis. In our mass estimate we use all the constraints together simply as the distribution of halo properties that satisfy the constraints. This way any correlations between properties, such as expected corre- lationbetweenradialdistancetothehostcenterandtotal velocity are taken into account automatically. B11, on theotherhand,assumethattheprobabilitydistributions for each constraint are independent (see their eq. 3). If wemultiplytheprobabilitydistributionsforradial,speed andcircularvelocityconstraintswegetanestimateofthe MWmasswhichshouldbesimilartothemethodofB11. For the S sample this gives log(M200/M⊙) = 12.24+−00..2255 and for the LGP sample log(M200/M⊙) = 12.44+−00..2242. Thus, treating constraints as independent results in a small overestimate of the mass. 4.2. Dependence on the SMC and LMC constraints The secondkey assumptionofthe B11analysisis that the properties of the two Magellanic Clouds are not correlated. However, the MCs are likely a bound pair, and Fig. 5.— Likelihood distribution for the MW halo mass (black theirvelocitiesandradialpositionscanthusbeexpected line), M200, in the S sample based on the properties of the LMC and SMC allowing the full halo mass range instead of the range to be correlated. We have tested whether this assump- M200 =0.8−2.9×1012M⊙. Lines of different colors show likeli- tionaffects the MW mass estimate by comparingresults hoods when only one constraint is used: exactly 2 subhalos with in the following two cases: 1) properties of the MCs are vc >50km/s (blue line), circular velocities of the MCs (red line), radialpositionsoftheLMCandSMC(orangeline),total velocity treated as independent and we compare mass likelihood relativetothehostcenteroftheLMCandSMC(greenline). Dot- usingbothMCs,onlytheLMC,oronlythe SMC;2)the tedlinesarecorrespondingdistributionsfortheLGPsampleusing MCs are considered to be a bound pair and we compute the same color key, but we omit the distribution using all con- thelikelihoodusingaveragepropertiesofthepair,rather straints together in this case due lack of matching systems. The MWmassestimateintheSsampleislog(M200/M⊙)=12.06+−00..3119 than properties of the two MCs independently. We explore the latter scenario in the next subsection. (90%confidence interval). For the case 1 we compute the mass likelihood for the particular, we present the likelihood for the constraint LMCandSMCindependentlyandfindlog(M200/M⊙)= kthmats−h1owstithhalaolslohtahveerecxoancsttlryatinwtoss(ucibrhcuallaorsvweiltohcivtcyi,rcra>di5a0l 1u2si.n1g8+−b00o..32t33huMsinCgstdhiescLuMssCedoanblyo,vceo.nFsiosrtetnhtewciatshetwheherensuwlet distance, and total velocity) applied after this condition use velocity of the SMC only, the mass is not well con- to compare to the results of B11. strained as the likelihood extends to considerably lower We chose not to enforce the two satellite condition in masses. Thus, the MW mass estimate is dominated by our estimate of the likelihood, instead we allow the host thepropertiesoftheLMC,asisexpectedsinceitismore halotohaveanynumberofsatellitestoincreasethesam- massive and has a higher velocity. ple size, but we will consider only the two largest ones. The fact that the main mass constraint comes from Themassestimatesobtainedwithandwithoutenforcing the satellite with the largest velocity is generic. If one the twosatellite conditionare presentedin Table 1. The considers distribution of absolute magnitude of satellite final mass estimate using all of the constraints together velocities as a function of the radial distance to the host is only computed for the S sample, in which there are center,atanygivenr the distributionis broadbuthasa 40 MC-like satellite pairs. There are only 3 such satel- sharpcutoffatthevelocityclosetotheescapevelocityof lite pairs in the LGP sample, and therefore we do not thehost. Itisthissharpcutoffthatconstrainsthemass, attempt to derive the total likelihood for this sample. andthe constraintis due to the satellite with the largest However,giventhatthe likelihooddistributions forindi- absolutevelocityatagivenradius. Thisfactwasrecently vidualpropertyconstraintsaresimilarfortheSandLGP used to constrain the halo mass of the Milky Way with samples,weexpectthatthetotallikelihoodissimilarfor Leo I satellite by Boylan-Kolchinet al. (2012). the combined constraints as well. In principle, we can include additional properties of The MW halo mass estimate for the S sample is the LMC and SMC, such as as their separation or rela- log(M200/M⊙) = 12.06+−00..3119 (90% confidence interval), tivevelocity (≈23kpc and128±32kms−1, respectively which is in generalagreementwith the B11 result in the Kallivayalilet al. 2006a, 2013), in the derivation of the central value. We present results for different samples massconstraint. However,this is difficultinpracticebe- and constraints in Table 1, where we also include both causeveryfewhosthalosintheBolshoisimulationmatch the 68% and 90% confidence interval errors. Due to sig- all of the properties of the LMC and SMC. We examine nificant deviations of the likelihood from the log-normal the incidence of the MC-like close pairs of satellites in form in the tails, the 90% errors are significantly larger the next section. than the 68% ones and we therefore chose to quote the Here we adopt a different approach, in which we as- 90% errors. sume that the LMC and SMC are a bound pair and Satellites in MW-like hosts 7 can be considered as a single subhalo. We then con- v = 85 km s−1are highly unlikely in such small host circ sider the pair as a single velocity tracer and use the halos. As noted above, the lower velocity SMC does not velocity of the center-of-mass of the pair as a con- influence the constraint due to the fact that the bulk of straint. We calculate the center-of-mass velocity as- the constraint is due to the LMC that has the largest suming that the MCs move in the same direction and velocity. Theadditionofthe SMC eitherasindependent neglecting peculiar velocity around the center-of-mass: tracer or as a second object in a pair to get the average k~s k = k~s M +~s M k/(M + M ) = 298 ± 52 km center-of-mass values does not influence the constraint cm 1 1 2 2 1 2 s−1. We also treat the pair as a single subhalo with appreciably. the circular velocity of v = 85.4+16 km s−1. The The summary of all the mass constraints is presented circ −10 masses are evaluated numerically from the M −v in Table 1. In the left half of the table we show the con- 200 circ relation for subhalos in the entire Bolshoi simulation. straints obtained using host halos with any number of The asymmetry in the error range is because we include satellites with Vcirc >50 km s−1, while in the right half larger values for the LMC v (Olsen et al. 2011). Fi- weshowresultsobtainedwiththe requirementthathost nally, we adopt the radial disctiracnce of the center-of-mass halos host exactly two satellites with Vcirc >50 km s−1, of r =(r M +r M )/(M +M )=54±5 kpc. as used in the study of B11. The first column lists the cm 1 1 2 2 1 2 constraints for the S sample, for the case where we mul- tiply the different likelihood distributions for each con- straintinsteadofcomputingthe masslikelihooddirectly (S-multi and LGP-multi), the case when only properties oftheLMCareusedintheconstraint,andthecasewhere weassumethattheSMCandLMCareaboundpairand correspond to a single subhalo with properties given by the mass-weighted average of the SMC and LMC properties for the S and LGP samples (S-bound and LGP- bound). Columns 2−4 and 5−7 show the mass constraints and the errors corresponding to the 68% and 90%confidence intervals. M masses can be converted 200 toM usingtheconversionfactorofM /M =1.21, vir vir 200 computeddirectlytheBolshoisimulationforthehalosof this mass range. 4.3. Close satellite pairs Satellitepairsarequiterare: wefindthatonly≈2%of the MW-sized halos have a pair of subhalos with v > circ 50km/s,separation<40kpc, andrelativevelocity <160 kms−1. Thisfractiondropsto∼1/30000forpairsmore closely resembling the SMC–LMC pair. In this section we explore the incidence of the pop- Fig. 6.— LikelihooddistributionoftheMilkyWayhaloresult- ulation of close subhalo pairs and test whether their ing from the SMC and LMC being considered a bound system properties are distinct from the properties of the overall corresponding to asinglesubhalo (with parameters quoted inthe subhalo population. It is important to clarify these is- text). ThedistributionfortheSsampleisshownbytheblacksolid sues,because velocities andother propertiesof the SMC line, and for the LGP sample by the green solid line. The corresponding halo mass constraints are log(M200/M⊙) = 12.13+−00..3265 and LMC may be influenced by their mutual interac- and log(M200/M⊙) = 12.17+−00..3304 (errors correspond to the 90% tBioonyla(ne-.gK.,olDch’iOnnegthaial.&20L11a)k.eT2o00s8el;ecNticahsoalsmeptlealo.f2c0lo1s1e; confidence level) for the S and LGP samples, respectively. Mass estimate for the S sample from Fig. 1 derived when properties of pairs,weconsidersubhaloswithvcirc >50kms−1within bothMCsareusedseparatelyisshownforcomparisonbythedot- the MW-sized halos that have distance to the host cen- ted redline. ter, mutual separation and absolute velocity similar to those of the MCs: 44 < r < 66 kpc, ∆r < 60 kpc, Figure 6 showsthe likelihooddistribution for the MW 150 < s < 400 km s−1, and0∆s < 300 km s−1. We also halo mass estimated with such constraint for the S and estimate if the pairs are bound by computing the total LGP samples. We also include the mass estimate from energyassuming a two body system of two point masses figure 5 for comparison. The halo mass in this case with masses of the SMC and LMC as derived from the is constrained to be log(M200/M⊙) = 12.13−+00..3265 (90% vcirc −M relation in the simulation. Such approxima- confidence interval) in the S sample and log(M200) = tion should be viewed as a rough approximation for the 12.17+0.30 in the LGP sample. We do not find any sig- fraction of bound systems in a given sample, but can be −0.34 nificant variationwith environmentin this case, and the used as a reference. mass estimate errors are consistent with the case when In figure 7 we show the separation and relative veloc- we constrain the mass using both MCs as independent ities of the identified pairs (left panel) and velocity in tracers. The only difference is that the use of the MCs the frame of the host halo of both pair members (right as a single tracer eliminates the tail of the likelihood to- panel),withthex-axisshowingvelocityofthepairmem- wards small masses (M200 ∼ 1011 M⊙), which is due to ber with the larger circular velocity. Red points indi- the fact that subhalos with circular velocities as high as cate pairs that are bound according to our energy es- 8 González, Kravtsov & Gnedin TABLE 1 Constraints on the halomassof the Milky Way usingdifferenthost samplesandproperties of the LMCandSMC Anynumbersubs vcirc>50kms−1 Exactlytwosubs vcirc>50kms−1 Sample log(M200/M⊙) 68%c.i. 90%c.i. log(M200/M⊙) 68%c.i. 90%c.i S-sample 12.06 +0.08-0.05 +0.31-0.19 12.03 +0.06-0.02 +0.34-0.17 S-multi 12.24 +0.13-0.20 +0.25-0.25 12.15 +0.15-0.05 +0.24-0.30 LGP-multi 12.44 +0.07-0.13 +0.24-0.22 12.26 +0.14-0.06 +0.23-0.19 LMConly 12.18 +0.10-0.10 +0.33-0.23 12.17 +0.10-0.11 +0.31-0.24 S-bound 12.13 +0.13-0.11 +0.36-0.25 12.09 +0.11-0.09 +0.28-0.23 LGP-bound 12.17 +0.16-0.19 +0.30-0.34 11.99 +0.16-0.17 +0.47-0.19 Notes: columns2−4showtheconstraints forthecasewhenhosthalosareallowedtohaveanynumberofsatelliteswithvcirc>50km s−1,whilecolumns5−7showthecorrespondingconstraintsforthecasewhenhosthalosarerestrictedtohaveexactlytwosatelliteswith vcirc>50kms−1. Wepresentthemasserrorscorrespondingtoboththe68%and90%confidence intervalsfromthederivedlikelihood distributions. Fig. 7.— PropertiesofclosesubhalopairsinMWmasshalos. Leftpanel: pairseparationandrelativevelocity;rightpanel: totalspeed relativetothehostcenterforbothpairmembers(horizontalaxisforthememberwithlargercircularvelocity). Redpointsindicatesubhalo pairs which are bound if we assume a two-body system. Blue rectangles show the MCs constraints (∆r < 60 kpc, ∆s < 300 km s−1, 150< s< 400 km s−1, 44< r0 < 66 kpc, and vcirc >50 km s−1). Green box in the left panel indicates very close pairs ∆r < 15 kpc, ∆s<70kms−1whichcontainalargefractionoffakepairs(seetextfordetails). timate. The figure shows that only a small fraction of the resolution limit of the simulation. We have visu- pairs has properties similar to those of the SMC–LMC allyinspectedthedarkmatterdensityandvelocityfields pair ∆r = 23.4±10 kpc, and ∆s = 128±32 km around a representative subset of these very close pairs MC MC s−1(shown by the blue boxes in the two panels). The and found that at separation10−20kpc ≈20% subhalo adopted range of separation of 23.4±10 kpcis consider- pairs do not have corresponding distinct peaks in dark ably larger than the actual observational error, which is matterdensityfieldorcoherentlymovingclumpsofdark of the same order as the error in the galactocentric dis- matter (i.e., subhalos are fake). Some of the pairs ap- tance: ≈2kpc(Kallivayalil et al.2006a),butitallowsus pear to be due to misidentification, in which a subhalo to select MC-like pairs without imposing a prohibitively undergoing a tidal disruption is identified as two subha- restrictive constraint on the subhalo pair configuration. los with circular velocities close to the resolution limit. Only ≈ 60 satellite pairs out of 1140 outside the green Ontheotherhand,wefindthatforpairswithseparation region have separations and relative velocities similar to >20kpc, almost all pairs have two clear distinct density those of the SMC and LMC, ∼90% of which are bound peaksinthe darkmatter distributionandcorresponding according to our criterion. coherent velocity streams in the velocity field. TheleftpanelofFig.7showsaratherlargenumberof If we add the constraints that the pair of subhalos in pairs clustered at separation .15kpc and ∆s.70 kpc. a host halos must have separation ∆r = 23.4±10 MC Most of these pairs appear to be artefacts due to fail- kpc, and ∆s = 128±32 km s−1, the resulting like- MC ures of the halo finder for subhalo candidates close to lihood for the Milky Way host halo mass is shown in Satellites in MW-like hosts 9 around Milky Way hosts selected simply by mass and a sampleofsuchhalosselectedwithadditionalrestrictions on the distance to the nearest cluster and local galaxy density, designed to mimic the environment of the Local Group. Wefindthatthevelocitydistributionofsatellites inthe latter sample is shifted somewhatto largerveloci- ties: inparticular,thefractionofsatelliteswiththeLMC speed in the LGP sample is 23±2% larger than in the S sample. Thus, the Local Groupenvironment enhances the probability of high satellite velocities, although the effect is mild. We compute the likelihood distribution for the Milky Way halo mass using the method similar to that of Busha et al. (2011a), and explore how this distribution depends on different properties of the SMC and LMC used as constraints. We find no significant effect of the environmentonthemassestimate. Wealsofindthatthe treatment of different MC properties as mutually independent does not bias the mass constraint. UsingpropertiesoftheSMCandLMCfromtherecent study by Kallivayalil et al. (2013), we derive constraint on the MW halo mass of log(M200/M⊙) = 12.06+−00..3119 Fig.8.— Likelihood distribution of the Milky Way halo mass (90% confidence interval) for the S sample of halos se- using additional constraints that subhalo pairs have separation lected without any environment restrictions. The mass and velocity difference similar to those of the SMC–LMC pair: ∆rMC =23.4±10kpc,and∆sMC =128±32kms−1(black solid constraintwederiveissimilartothatofB11,eventhough line). Likelihooddistributionsforsubhalopairsmatchingonlythe the updated values of MC properties, such as velocities radial distance (orange line), circular velocity (red line), or rela- and their errors,are quite different from the values used tive velocity with respect to the host halo (green line) are shown by B11. The mass constraint is broadly consistent with by the dotted lines. Less than 21% of close pairs are in halos of M200>1012M⊙. other recent estimates of the Milky Way halo mass. The method of B11 does therefore appear to be a ro- figure8. Due to smallnumber ofclosesubhalopairssat- bustway to measurethe MW halo mass. Asubtle issue, isfying the constraints, the mass likelihood distribution however,is that if some of the properties of the LMC or can be computed using only one of the MCs constraints SMC used for the constraint are rare for the systems of at a time together with the separation and velocity dif- the MW mass, the interpretation of the mass likelihood ference constraints. We find that < 21% of close pairs is not straightforward. The Milky Way in this case may are in halos of M200 > 1012M⊙.6 The addition of the be located in the tail of the distribution and interpre- constraint on the pair separation and relative velocity tation of the peak of the likelihood as most likely mass thuspushestheMWhalomassconstrainttoconsiderably of the MW halo is not correct. It remains to be seen lowermasses,ascomparedtotheconstraintwithonlythe howrareparticularpropertiesoftheLMCandSMCare. properties used by B11. This illustrates that the actual We do know, forexample, that the probability ofhaving constraint depends quite sensitively on which properties two satellites of the SMC and LMC luminosity is by it- of the SMC–LMC system are chosen for the analysis, as self quite rare in the hosts of the MW luminosity (e.g., isalsoclearfromthelargedifferencesbetweenmasslike- Liu et al. 2011b; Robotham et al. 2012). lihood distributions for the individual properties shown LMC and SMC are not just two unrelated luminous in Fig. 5. satellites: they are a close pair. We show in this study thatclosesatellitepairsarequiterare: pairswithmasses 5. DISCUSSIONANDCONCLUSIONS and separations similar to those of the LMC and SMC In this study we have explored whether the environ- are found only in one out of ≈ 30000 MW-sized halos. mentofthe Milky Wayaffects propertiesofits twomost Observations also indicate that such close pairs are very massive satellites, the SMC and LMC. These satellites rare (James & Ivory 2011). We find that satellites in are rather rare around galaxies with the Milky Way lu- most close pairs with properties similar to the MCs are minosity and have rather high velocities. As argued likely to be bound to each other. Interestingly, the halo by Busha et al. (2011a), the properties of the SMC and masslikelihooddistributionforhosthalosconstrainedto LMCcanbeusedforausefulindependentestimateofthe have MC-like close pairs of subhalos (∆r =23.4±10 MC Milky Way virial mass. However, it would be straight- kpc,and∆s =128±32kms−1)isquitedifferentfrom MC forwardtointerpretsuchestimateonly ifthe Magellanic thegloballikelihoodfromwhichtheMWhalomasscon- Cloudsarenotveryunusualandtheir propertiesarenot straint discussed above was derived. In particular, less biased by the environment. than 21% of host halos with M200 > 1012M⊙ host MC- To test for the effects of the environment,we compare likeclose pairs. Takinginto accountthe close separation velocity distributions for a sample of MC-sized subhalos of the MCs in the B11 method results in the shift of the MWhalomassestimatetosmallermasseswiththepeak 6 This fraction is for the host halos restricted to have exactly shifting approximately by a factor of two (see Fig. 8). two satellites withVcirc >50 km s−1. If weallow any number of The reason for this shift is the fact that in smaller ha- satellites,thisfractionincreasesto26%. 10 González, Kravtsov & Gnedin los it is more likely to get a pair with small separation This work was supported by NSF via grant OCI- and relatively small velocity difference by chance (not 0904482. AK was in addition supported in part by NSF necessarilybound),mainlybecausevelocitydispersionis grants AST-0807444and by the Kavli Institute for Cos- smaller in smaller mass halos. mological Physics at the University of Chicago through This example clearly shows that a great care should the NSF grantPHY-0551142and PHY- 1125897and an be takeninchoosingwhichofthe satellite propertiesare endowment from the Kavli Foundation. We have made used for the MW mass constraint. extensive use of the NASA Astrophysics Data System and arXiv.orgpreprint server. REFERENCES Besla,G.,Kallivayalil,N.,Hernquist,L.,Robertson,B.,Cox, —.1993b, MNRAS,264,201 T.J.,vanderMarel,R.P.,&Alcock,C.2007,ApJ,668,949 Klypin,A.,Gottlöber, S.,Kravtsov,A.V.,&Khokhlov,A.M. 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