New Signatures of the Milky Way Formation in the Local Halo and Inner Halo Streamers in the Era of Gaia
Paola Re Fiorentin, Mario G. Lattanzi, Alessandro Spagna, Anna Curir
DDraft version November 6, 2018
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NEW SIGNATURES OF THE MILKY WAY FORMATION IN THE LOCAL HALO AND INNER HALOSTREAMERS IN THE ERA OF GAIA
Paola Re Fiorentin , Mario G. Lattanzi , , Alessandro Spagna , and Anna Curir INAF - Osservatorio Astrofisico di Torino, Strada Osservatorio 20, 10025 Pino Torinese, TO, Italy Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, 200030 Shanghai, China
Draft version November 6, 2018
ABSTRACTWe explore the vicinity of the Milky Way through the use of spectro-photometric data from the SloanDigital Sky Survey and high-quality proper motions derived from multi-epoch positions extracted fromthe Guide Star Catalogue II database. In order to identify and characterise streams as relics of theMilky Way formation, we start with classifying, select, and study 2417 subdwarfs with [Fe / H] < − . ◦ ÷ ◦ .Finally, we use our simulations to investigate the impact of observational errors and compare thecurrent picture to the promising prospect of highly improved data expected from the Gaia mission. Subject headings:
Galaxy: formation — Galaxy: halo — Galaxy: kinematics and dynamics INTRODUCTIONThe formation and evolution of galaxies is one of theoutstanding problems in astrophysics, one which can beprofitably engaged directly through detailed study of ourown Galaxy, the Milky Way (e.g., Freeman & Bland-Hawthorn 2002; Helmi 2008).In the context of hierarchical structure formation,galaxies such as the Milky Way grow by mergers and ac-cretion of smaller systems, perhaps similar to what arenow observed as dwarf galaxies. These satellite galaxies– torn apart by the tidal gravitational field of the parentgalaxy – are progressively disrupted, giving rise to trailsof stellar debris streams along their orbits, spatial signa-tures that eventually disappear due to dynamical mixing.After the accretion era ends, a spheroidal halo-like com-ponent is left from their collective assembly (e.g., Searle& Zinn 1978; Bullock & Johnston 2005; Abadi et al.2006; Moore et al. 2006; Sales et al. 2007; De Lucia2012).Of all the Galactic components, it is indeed the stellarhalo that offers the best opportunity for probing detailsof the merging history of the Milky Way (see, e.g., Helmi2008). Past explorations have demonstrated that thereis a concrete possibility to identify groups of halo starsthat originate from common progenitor satellites (Eggen1977; Ibata et al. 1994; Majewski et al. 1996; Helmiet al. 1999; Chiba & Beers 2000; Dinescu 2002; Ibataet al. 2003; Kepley et al. 2007; Klement et al. 2009;Morrison et al. 2009; Schlaufman et al. 2009; Smith re fi[email protected] et al. 2009; Duffau et al. 2014).Simulations show that a Milky-Way mass galaxywithin a ΛCDM universe will have halo stars associatedwith substructures and streams (e.g., Johnston 1998;Harding et al. 2001; Starkenburg et al. 2009; Helmiet al. 2011; Gomez et al. 2013). These substructures,much like those seen in the halo system of the Milky Way,are sensitive to recent (within the last 8 Gyr) mergingevents, and are more prominent in the outer region of thehalo (galactocentric radii beyond 15 −
20 kpc), whereasthe inner-halo region appears significantly smoother.Based on data from the SEGUE spectroscopic sur-vey, Schlaufman et al. (2009) found that metal-poormain-sequence turnoff stars in the inner-halo region ofthe Milky Way (within ∼
20 kpc from the Sun) exhibitclear evidence for radial velocity clustering on small spa-tial scales (they refer to these as ECHOS, for Elementsof Cold HalO Substructure). They estimated that about10% of the inner-halo turnoff stars belong to ECHOS,and inferred the existence of about 1000 ECHOS in theentire inner halo volume. Schlaufman et al. (2011) sug-gest that the most likely progenitors of ECHOS are dwarfspheroidal galaxies with masses on the order of 10 M (cid:12) .In the Solar Neighbourhood, up to 1 − a r X i v : . [ a s t r o - ph . GA ] A ug Re Fiorentin et al.based observations. Formed via destruction of a satellitewhose debris now occupy the inner halo region with noapparent spatial structure, these streamers retain verysimilar velocities and are seen as clumps in angular mo-mentum space where stars from a common progenitorappear rather confined (Helmi & de Zeeuw 2000).Besides the Helmi stream, ω Centauri (Dinescu 2002;Majewski et al. 2012), the Kapteyn and Arcturus(e.g., Eggen 1971) streams, Klement (2010) lists a fewother halo substructures found in the solar neighborhood:these are still small numbers compared to the few hun-dred streams expected (i.e. 300-500, Helmi & White1999; Gould 2003). Actually, recovering fossil struc-tures in the inner halo is considerably more difficult, asstrong phase-mixing takes place. This degeneracy canonly be broken with 6D (phase-space) or 7D (includ-ing abundances) information achievable by integratingastrometry, photometry, and spectroscopy.The SDSS - GSC II Kinematic Survey (from now onSGKS) we exploit here was produced to serve this task(see Spagna et al. 2010b). In the future, new ground-and space-based surveys such as Gaia (e.g., Perrymanet al. 2001; Turon et al. 2005), Gaia ESO Survey(GES; Gilmore et al. 2012), and LAMOST (Zhao et al.2012) will provide high-precision data that will usher usin a new era of Milky Way studies.In Sect. 2, we introduce the data used to isolate a sam-ple of nearby halo subdwarfs from the SGKS catalogue.The kinematic and orbital properties of the local halosubdwarf population are discussed in Sect. 3, where wepresent algorithms to search for kinematic substructures,recovering known streams (Helmi et al. 1999; Dinescu2002; Kepley et al. 2007), as well as new kinematicoverdensities. In Sect. 4, we present the high-resolutionN-body numerical simulations of four minor mergers usedto study galaxy interactions and the properties of accre-tion events in the vicinity of the Sun. In Sect. 5 weinvestigate the impact of observational errors resultingfrom current ground-based data and from high accuratedata expected from the Gaia satellite. Finally, in Sect. 6,we compare observations to these numerical simulationsand infer the nature of the detected fast moving groups. THE SDSS - GSC II KINEMATIC SURVEY(SGKS)This study is based on a new kinematic catalogue,derived by assembling spectro-photometric stellar datafrom the Seventh Data Release of the Sloan Digital SkySurvey (SDSS DR7; Abazajian et al. 2009), whichincluded data from the Sloan Extension for GalacticUnderstanding and Exploration (SEGUE; Yanny et al.2009), supplemented by astrometric parameters ex-tracted from the database used for the construction ofthe Second Guide Star Catalogue (GSC II; Lasker et al.2008). This SDSS - GSC II catalogue contains positions,proper motions, classification, and ugriz photometry for77 million sources down to r ∼
20, over 9000 square de-grees.Proper motions are computed by combining multi-epoch positions from SDSS DR7 and the GSC IIdatabase; typically, 5 −
10 observations are availablefor each source, spanning up to 50 years. The typicalformal errors on those proper motions are in the range2 − − per coordinate for 16 < r < .
5, compa- rable with the internal precision of the SDSS proper mo-tions computed by Munn et al. (2008). Although muchof the photographic material (Schmidt plates) used toderive first epoch information is in common with Munnet al. (2008), plate digitisation and measurement pro-cesses, and the calibration methods that led to the firstepoch positions were somewhat different, with the Munnet al.’ data coming from the USNO-B project. Of par-ticular relevance is the minimisation of systematic errorsthat can affect proper motion accuracy, a true driver inanalysis like those conducted in this study. An accuratevalidation of our proper motions was discussed in Spagnaet al. (2010a).Radial velocities and astrophysical parameters areavailable for about 151 000 sources cross-matched withthe SDSS spectroscopic catalogue Typical accuracy areof 5 −
10 km s − in line of sight velocity, 250 K in effec-tive temperature, T eff , 0 .
25 dex in surface gravity, log g ,and 0 .
20 dex in metallicity, [Fe / H], as estimated withinthe SEGUE Spectral Parameter Pipeline (SSPP; i. e.,Re Fiorentin et al. 2007; Lee et al. 2008a,b; AllendePrieto et al. 2008). We specify that the sample includesonly objects with no problems related to the spectrum,and classified without any cautionary flag by the SSPP.In case of multiple spectra, we take the spectrum withthe highest signal-to-noise ratio.From the SDSS - GSC II catalogue, we select as tracerssources with 4500 K < T eff < g > . . (cid:48) resolution COBE/DIRBE dustmap, that we preferred to the more recent, but of inferiorresolution (7 (cid:48) -14 (cid:48) ), reddening maps published by Schlaflyet al. (2014). Then, we transformed the E ( B − V ) tothe SDSS photometric system by adopting the extinctionratio A r /A V = 0 .
875 (from Table 1 of Girardi et al.2004), that is appropriate for our FGK dwarf sample.Photometric distances good to σ d /d ∼
20% are com-puted by means of the photometric parallax relation es-tablished for FGK main-sequence stars by Ivezi´c et al.(2008). Here, the metallicity-dependent absolute mag-nitude relations, M r = f ( g − i, [Fe / H]), use the spec-troscopic [Fe / H] instead of the photometric metallicityadopted by Ivezi´c et al. (2008). We also apply the ad-ditional colour thresholds from Klement et al. (2009) inorder to remove turn-off stars, whose estimated M r maybe affected by residual systematic errors.Galactic space-velocity components are estimated un-der the assumption that the Sun is at a distance of 8 kpcfrom the centre of the Milky Way, the Local Standardof Rest (LSR) rotates at 220 km s − about the Galacticcenter, and the peculiar velocity of the Sun relative to theLSR is ( U, V, W ) (cid:12) = (10 . , . , .
17) km s − (Dehnen& Binney 1998).Finally, in order to minimise the effect of outliers (e.g.mismatches, blends and sources with low S/N) and there-fore obtain a sample with accurate distance and kine-matics suitable for our stellar stream search, we impose Throughout this work, U , V , and W indicate Galactic velocitycomponents relative to the Local Standard of Rest and follow theconvention with U positive toward the Galactic center, V positivein the direction of Galactic rotation, and W > nner Halo Streamers in the Era of Gaia 3
TABLE 1Halo velocity parameters. (cid:104) U (cid:105) (cid:104) V + 220 (cid:105) (cid:104) W (cid:105) σ U σ V σ W ρ UV ρ UW ρ V W (km s − ) (km s − ) (km s − ) (km s − ) (km s − ) (km s − )15 ± ± − ± ± ± ± − . ± . − . ± .
02 0 . ± . Note . — The Milky Way halo velocity parameters as determined from our selected sample of 2417 FGK subd-warfs. The table lists mean velocities, dispersions, and corresponding correlation coefficients in Galactic coordinates.Noticeable is the correlation between U and W (see text). a threshold on proper-motion errors ( <
10 mas yr − percomponent), constrain magnitudes to the range 13 . 5, limit the errors on the derived velocity compo-nents to better than 50 km s − , and remove total spacevelocities above 600 km s − . These are the properties ofthe 24 634 stars listed in the SGKS catalogue. DATA ANALYSISAmong the full sample of FGK dwarfs from the SGKScatalogue, we have selected specific sub-samples of trac-ers of the Galactic halo population in the inner-halo re-gion, and analysed their phase-space distribution.Here, we focus on a sample of 2417 metal-poor stars([Fe / H] < − . 5) outside the Galactic plane ( | z | > U , V , and W of 12, 13, and 9 km s − , respectively; this resultsin errors in the velocity difference between stellar pairsnot exceeding ∼ 20 km s − . Such a value is suited forcareful investigations of substructure, as the kinematicanalysis presented below will show.3.1. Local halo velocity distribution From the selected sample we measure the mean ve-locities ( (cid:104) U (cid:105) , (cid:104) V + 220 (cid:105) , (cid:104) W (cid:105) ), the velocity ellipsoid( σ U , σ V , σ W ), and the correlations among velocity com-ponents ( ρ UV , ρ UW , ρ V W ) as reported in Table 1.The kinematic properties of the selected tracers arerepresentative of the halo population in the vicinity ofthe Sun (e.g., Chiba & Beers 2000).The significant correlation ρ UW = − . ± . 02 be-tween the radial and vertical velocity components indi-cates a tilt of the velocity ellipsoid (Fig. 1, right panel).Using the tilt formula (see, e.g., Binney & Merrifield1998) tan 2 δ UW = 2 σ UW σ U − σ W = 2 ρ UW σ U σ W σ U − σ W , (1)and the values in Table 1 for the correlation coefficientand velocity dispersions along the U and W axes, wederive a tilt angle of δ UW = − . ◦ ± . ◦ , revealingthat the ( U, W ) distribution points toward the Galacticcenter.In fact, for our halo sample of 2417 FGK subdwarfswith (cid:104) z (cid:105) ≈ (cid:104) R (cid:105) ≈ . (cid:104) tan − ( z/R ) (cid:105) ≈ . ◦ . This resultis fairly consistent with the tilting effects on the velocityellipsoids due to the gravitational potential produced bythe stellar disk and dark matter halo (Bond et al. 2010,and references therein). We also measure smaller but stastistically significant correlations in ( U, V ) and ( V, W )velocity-planes.In the following, we look for halo streamers in the highvelocity tail of the ( U, V, W ) velocity distribution, wherekinematic substructures are more easily detected. In or-der to select high velocity stars, we model the velocitydistribution as a tilted Schwarzschild ellipsoid: f ( U, V, W ) = const · e − E ( U,V,W ) (2)where E is the velocity function defined by: E ( U, V, W ) = R UU R (cid:16) U −(cid:104) U (cid:105) σ U (cid:17) + R V V R (cid:16) V −(cid:104) V (cid:105) σ V (cid:17) + R WW R (cid:16) W −(cid:104) W (cid:105) σ W (cid:17) +2 R UV R (cid:16) U −(cid:104) U (cid:105) σ U (cid:17) (cid:16) V −(cid:104) V (cid:105) σ V (cid:17) +2 R V W R (cid:16) V −(cid:104) V (cid:105) σ V (cid:17) (cid:16) W −(cid:104) W (cid:105) σ W (cid:17) +2 R UW R (cid:16) U −(cid:104) U (cid:105) σ U (cid:17) (cid:16) W −(cid:104) W (cid:105) σ W (cid:17) . (3)Here, R represents the determinant of the symmetri-cal matrix R of the correlation coefficients ρ ij = R ij /R (for i, j = U, V + 220 , W ), and R ij designate the cofac-tor of the corresponding correlation element in R (e.g.,Trumpler & Weaver 1953).Figure 1 shows the kinematic distribution for the indi-vidual components, ( U, V +220 , W ), of the space-velocityvector for the full sample of 2417 selected halo stars; the242 objects comprising the sample of the 10% highestvelocity tail are represented with crosses.As expected, the overall velocity distribution is rela-tively smooth, because of the strong phase-mixing thattakes place in the inner-halo region, and slowly prograde(e.g., Helmi 2008).However, as their motions (in direction and speed) arewell separated from those of the other nearby subdwarfs,we intend to study the degree of clumpiness of the 10%fastest-moving objects. The case study is that, of all theobjects passing within a few kiloparsecs of the Sun, someare part of a diffuse local stellar halo, while some could bedebris of accretion events and remnants from the outer-halo population currently in the Solar Neighbourhood.Before starting to look for kinematic substructures, wecheck for thick disk stars that possibly contaminate ourhalo tracers. Here, we applied to kinematic method de-scribed in Spagna et al. (2004) and estimate the fractionof subdwarfs that is consistent with the 3D velocity dis-tribution of the thick disk population. By assuming a Re Fiorentin et al. Fig. 1.— Distribution of nearby halo stars in velocity space for our selected sample of 2417 FGK subdwarfs, with [Fe / H] < − . | z | > velocity ellipsoid, as estimated by Pasetto et al. (2012),and a rotation velocity V φ = 150 km s − , as measuredby Spagna et al. (2010a) for metal-poor thick disk starswith [Fe / H] (cid:39) − σ (i.e. 87%) con-fidence level a ∼ 10% maximum contamination of thickdisk in the whole sample of 2417 halo tracers. Instead,no contaminant is expected among the subsample of the10% fastest objects.We use the samples described above to detect and sub-sequently identify kinematic halo substructures in the So-lar Neighbourhood as groups of stars moving with similarvelocities and directions. Detection is accomplished byperforming a statistical test based on individual kine-matics aimed at quantifying possible deviations from asmooth distribution of the background halo; cluster anal-ysis in velocity space is then applied for final confirmationof the substructures.3.2. The two-point correlation function: finding theclumps The amount of kinematic substructures that cosmol-ogy might leave in the volume is quantified by means ofthe cumulative two-point correlation function, ξ ( v ), onthe paired velocity difference v = | v i − v j | that measuresthe excess in the number of stellar pairs moving withina given velocity difference when compared to a represen-tative random smooth sample (cfr. Re Fiorentin et al.2005, for more details). Here the random points weredrawn from a multivariate distribution obtained from theobserved data set by random permutations of the orderof the velocity components V + 220 and W , after fixing U ; finally, the actual random pairs are obtained afteraveraging over ten independent realisations.This function is computed over the full sample of 2417halo stars, and separately for the sub-sample of the 242fastest-moving stars, corresponding to the 10% high-velocity tail.A statistical excess of stars with small pairwise veloc-ity differences indicates the presence of likely streamersmade of objects with coherent kinematics.Figure 2 shows, using bins of 10 km s − width the two-point correlation function ξ ( v ) for the full sample of 2417 We fixed the bin width following the rule that the interval halo stars (dots) and for the subset of the 10% fastest-moving stars (diamonds). While weak for the full sample,there is a statistically significant signal ( SN R > 4) forthe subset of the fastest stars, that peaks at 40 km s − :the excess of pairs of stars with similar velocities is verynoticeable, and is a direct indication of the presence ofkinematical clumps. Fig. 2.— Cumulative velocity correlation function for the fullsample of halo stars (dots), and the 10% fastest-moving subset (di-amonds) shown in Fig. 1. The error bars are derived from Poisson’sstatistics of the counts. In the following, among the sample of the 242 fasteststars, we focus on the objects with paired velocity differ-ences less than 40 km s − , which yield the statisticallysignificant signal seen in Fig. 2. In addition, we exclude isolated pairs, i.e., “groups” with only two objects.This further selection certainly reduces the numberof detected members, however it makes the followinganalysis more robust by decreasing the contaminationof false positives. The final sample is made of 67 stars. sampled is divided into as many bins as the square rooth of thesample size, in our case ∼ 400 km s − / √ ∼ 10 km s − . nner Halo Streamers in the Era of Gaia 5 Fig. 3.— Distribution of the high-velocity tail from our selected sample with [Fe / H] < − . | z | > − ; the stars belonging to isolated pairs have been excluded. Different colours are used to indicate stars associatedwith the five clumps recovered by the clustering analysis. Clustering analysis: assigning membership In order to classify these 67 objects, we perform K − medoids clustering in the 3D velocity space that de-fines the number of kinematic substructures and theirmembers. This unsupervised learning algorithm is ableto group data into a pre-specified number of clusters thatminimises the RMS of the distance (in velocity space) tothe center of each cluster.The original data set is initially partitioned into clus-ters around K data points referred to as the medoids,then an iterative scheme (PAM, for Partitioning AroundMedoids) is applied to locate the medoids that achievethe lowest configuration “cost”. The algorithm employedby PAM, similar to the K -means clustering algorithm, ismore robust to outliers and obtains a unique partitioningof the data without the need for explicit multiple startingpoints for the proposed clusters (see, e.g., Kaufmann &Rousseeuw 1990; Hastie et al. 2001).There is no general theoretical solution for finding theoptimal number of clusters for any given data set. In-creasing K results in the error function values formallymuch smaller, but this increases the risk of overfitting.In order to keep the final identification safe and simple,we compared the results of runs with different K classes,and the best K resulted following visual inspection ofthe generated distribution. The solution adopted hereis with K = 5: for K < K > We used the implementation of the K − medoids clustering de-veloped as part of the R Project for Statistical Computing et al. (2014). On the other hand, the fact that we havethe complete set of 3D kinematical data and that thewhole sample is confined within 3 kpc from the Sun (i.e.,the distance segregation is implicitly implemented in oursample) suggests the direct use of a classical clusteringalgorithm like PAM as the method of choice.3.4. Angular momentum and orbital properties The space of adiabatic invariants allows better identifi-cation of the different possible merging events that mighthave given rise to the observed substructures. Clump-ing should be even stronger, since all stars originatingfrom the same progenitor should have very similar inte-grals of motion, resulting in a superposition of the corre-sponding streams; that is, the initial clumping of satel-lites are present even after the system has completelyphase-mixed (e.g., Helmi & de Zeeuw 2000).In this study we focus on the plane defined by thecomponents of angular momentum in and out the planeof the Galaxy’s disk, i.e. L xy and L z respectively.Since for a local sample ( x, y, z ) ∼ ( r (cid:12) , , L xy ∼ r (cid:12) | v z | is dominated by the velocityperpendicular to the plane and L z ∼ r (cid:12) v y measures theamount of rotation of a given stellar orbit. Essentially,stars with high/low L xy are on high/low-inclination or-bits; stars with L z < L z > L z versus L xy . As in Fig. 3, the 10% fastest-movingobjects are plotted as crosses, and with the star symbolswe mark the group members identified in Sect. 3.2. Dif-ferent colours indicate the stars associated with the dif-ferent lumps recovered by the cluster analysis in velocityspace.The solid lines show the loci of the known kinematicstructures detected by Remind that: L x = yv z − zv y , L y = zv x − xv z , L z = xv y − yv x ,and L xy = (cid:113) L x + L y . Here v x = − U , v y = V +220, and v z = W . Re Fiorentin et al. Fig. 4.— Distribution of the selected sample of 2417 FGK subdwarfs within 3 kpc of the Sun in the space of adiabatic invariants.Cross symbols indicate the 10% fastest-moving objects. Among them, star symbols identify the 67 sources with paired velocity differencesbelow 40 km s − . As in Fig. 3, different colours are used to indicate stars associated with the five clumps recovered by the clusteringanalysis in velocity space. At L z > 0, the solid box shows the locus of the halo stream discovered by Helmi et al. (1999): the kinematicsubstructures, pink and blue stars (i.e., Groups 1 and 2 in Table 2), on prograde orbits indeed cover the same region. At L z < 0, the solidbox at L z ∼ − L z ∼ − 400 identifies the ω Cen substructures remapped from the L z - L region in Dinescu (2002). The area within the dashed line includesthe kinematic Groups 3, 4, and 5 of Table 2, represented by the red, green, and yellow stars, respectively. 1. Helmi et al. (1999) at300 < L z < − and1400 < L xy < − ,2. Kepley et al. (2007) at − < L z < − − and0 < L xy < − ,3. Dinescu (2002) at − < L z < − 200 kpc km s − and0 < L xy < L limxy kpc km s − . The most noticeable feature in Fig. 4 is certainly thekinematic group corresponding to the stream found byHelmi et al. (1999). Here, we identify 25 subdwarfs,including 4 stars already detected by Klement et al.(2009), and 21 new members. By inspection of Fig. 3 wenotice that the 10 members belonging to Group 1 (pinkstar symbols) run along near-parallel orbits and cross the For the Dinescu (2002) region, the curve delimiting the L xy upper part was derived by remapping the L z - L region shown inFig. 4 of that paper; therefore 671 < L limxy < Milky Way’s disk at high speed from South to North, andthe 15 objects in Group 2 (blue star symbols) cross theMilky Way’s disk at similar speed and angle, but fromNorth to South.The three remaining lumps of fast-moving stars (redGroup 3, green Group 4, and yellow Group 5) appearon the retrograde side of Fig. 4. The pentagonal boxconfined by the dashed line includes most of the membersof Group 3 (5 stars), Group 4 (21 stars), and Group 5(16 stars).These groups, and in particular the small Group 3, donot appear to be easily associated with known streamsand, in Sect. 5, we discuss the possibility that all thesestars come from a common progenitor or from three dif-ferent merging events.Anyhow, we note that Group 4 might be the par-ent populations of the counter-rotating “outliers”, with V φ < − 250 km s − , found by Kepley et al. (2007),while the slightly retrograde Group 5 ( V φ ≈ − 50 km s − )seems to be related to the kinematic structure found byDinescu (2002), and confirmed by both Meza et al.(2005) and Majewski et al. (2012). These authors havenner Halo Streamers in the Era of Gaia 7 TABLE 2Main individual characteristics of the fastest-moving stars found members of 5 differentkinematics groups. Group ID U V + 220 W L xy L z [Fe / H](km s − ) (km s − ) (km s − ) (kpc km s − ) (kpc km s − ) (dex)1 a / pink 52209-0694-596 143 ± 14 33 ± 12 293 ± − . ± ± ± − . ± 31 54 ± 31 285 ± 16 2232 614 − . ± 23 158 ± 28 169 ± 27 1459 1678 − . ± 13 76 ± 16 246 ± − . ± ± ± − . ± 12 8 ± 12 272 ± − . ± 11 16 ± 11 257 ± 10 2045 405 − . ± 17 84 ± 26 261 ± 23 1820 590 − . ± ± ± − . a / blue 52316-0559-336 189 ± ± − ± − . ± ± − ± − . c ± 14 149 ± − ± − . ± 19 82 ± − ± 17 2215 706 − . c ± ± − ± − . ± 10 102 ± − ± − . ± ± − ± − . c ± ± − ± − . c ± 13 144 ± − ± 13 1663 1011 − . ± ± − ± − . ± 15 170 ± − ± 13 1858 1324 − . ± 14 129 ± − ± 12 2153 1097 − . ± ± − ± − . ± 15 80 ± − ± − . ± 10 115 ± − ± − . b / red 54179-2567-458 − ± − ± 16 214 ± − − . − ± − ± 22 209 ± − − . − ± − ± 14 230 ± − − . − ± − ± 19 232 ± 10 1521 − − . − ± − ± ± − − . b / green 52059-0597-072 125 ± − ± − ± − − . ± − ± − ± − − . ± − ± − ± − − . ± − ± − ± 20 1195 − − . ± − ± − ± 14 916 − − . ± − ± − ± − − . ± − ± − ± − − . ± − ± − ± 12 199 − − . ± − ± − ± 21 1826 − − . ± − ± − ± − − . ± − ± − ± − − . ± − ± − ± − − . ± − ± − ± − − . ± − ± − ± − − . ± − ± − ± 10 507 − − . ± − ± − ± − − . ± − ± − ± − − . ± − ± − ± − − . ± − ± − ± − − . ± − ± − ± 16 977 − − . ± − ± − ± − − . b / yellow 53035-1433-600 322 ± − ± 13 22 ± − − . ± − ± 18 59 ± 18 120 − − . ± − ± 35 68 ± 18 258 − − . ± − ± 12 21 ± − − . ± 13 17 ± 22 121 ± 13 1787 − − . ± − ± − ± − − . ± − ± ± − . ± 23 0 ± 16 115 ± 15 468 420 − . ± − ± − ± − − . ± − ± ± − . ± − ± ± − . ± − ± 19 24 ± 19 332 − − . ± − ± 40 42 ± 11 1155 − − . ± − ± − ± − − . ± − ± 12 25 ± − − . ± − ± ± − − . Note . — Main individual characteristics of the 67 selected fastest-moving stars with paired velocity differencesless than 40 km s − , and belonging to 5 different kinematics groups. These are 25 subdwarfs (21 new) on 2streamers (Group 1 and Group 2) both members of the stream known to Helmi et al. (1999) originally made ofred giants and RR Lyrae. The remaining 42 are subdwarfs members of three newly discovered kinematic groups(Group 3, 4, and 5); see text for their dynamical interpretation. a Subdwarf members associated with the Helmi et al. (1999) stream. b Subdwarf members of the newly discovered kinematic groups. c Subdwarf members classified by Klement et al. (2009). Re Fiorentin et al.also discussed the possibility that such a stream is formedby the tidal debris of ω Cen in the solar neighborhood,even though Navarrete et al. (2015) have recently ruledout this hypothesis after detailed analysis of the chemicalabundance of this group with respect to the well-knownpeculiar properties of ω Cen. SIMULATIONSWe explore a simulated inner halo based on a set of four high-resolution numerical N-body simulations of minormergers. We analyse the kinematics and orbital prop-erties of these simulations in order to investigate andcharacterise detectable signatures.It is useful to point out that these simulations are notan attempt to “fit” the observations, but they representfour merging events that we assume as representative,in terms of inclination and rotation, of the initial orbitsof the satellites. In particular, these choices allow us toanalyse the two cases suffering maximum and minimumdynamical friction.4.1. N-body simulations We use a set of high-resolution numerical N-body sim-ulations which simulate minor mergers of prograde andretrograde orbiting satellite halos within a dark mat-ter main halo (Murante et al. 2010). The main DMhalo, which contains a stellar, rotating exponential disk,has a NFW radial density profile (Navarro, Frenk &White 1997), with a mass ( M = 10 M (cid:12) ), radius( R = 165 kpc), and concentration ( C = 7 . z = 0;the spin parameter is set to λ = 1. The satellite is rep-resented by a secondary DM halo containing a stellarbulge, and a Hernquist radial density profile (Hernquist1993); the spin parameter is set to λ = 0. The mass ratio, M primary /M satellite ∼ 40, is similar to the estimated massratio of the Milky Way relative to the Large MagellanicCloud. The main physical parameters of our simulatedmergers are listed in Table 3.We consider prograde mergers, in which the satelliteco-rotates with the spin of the disk, as well as retrogrademergers, with a counter-rotating satellite. We analysetwo orbits: a low-inclination orbit with a 10 ◦ tilt withrespect to the disk plane, and a high-inclination orbitwith a 60 ◦ tilt.Initially, the particles of the small system (satel-lite galaxy) orbiting around the (otherwise static) diskgalaxy are all strongly concentrated in space, and shareessentially the same motion. The initial conditions (in-clination, position, and velocity) of the main system andthe four impacting satellites, cosmologically motivated(Read et al. 2008; Villalobos & Helmi 2008), are sum-marised in Table 4.From the grid of simulations by Read et al. (2008),we chose four impactors, all of which having the mass ofthe Large Magellanic Cloud. Larger masses would affectthe stability of the stellar disk, and this is not consis-tent with a Milky Way-like galaxy. Conversely, smallermasses would produce minor signatures in our local halosample. The cases λ = 0 and λ = 1 were both studied at lower reso-lution and the results compared; the differences are such that theyhave no bearing on the results presented in this paper. TABLE 3Physical properties of the Halos: Main system and orbitingSatellite. System M DM M ∗ N DM N ∗ r r disk Main 10 . × . × . × . × Note . — Column 1: Main galaxy/Impacting system. Column2: DM mass, in M (cid:12) . Column 3: stellar mass for disk/bulge in themain/satellite, in M (cid:12) . Column 4: DM particles. Column 5: stellarparticles for disk/bulge in main/satellite. Column 6: disk scale radiusfor the main halo, in kpc; Hernquist scale radius for the satellite, inkpc. Column 7: disk truncation radius, in kpc. The four simulations are compiled using the public par-allel Treecode GADGET2 (Springel 2005) on the clus-ter matrix at the CASPUR ( Consorzio Interuniversitarioper le Applicazioni del Supercalcolo ) consortium, Rome.All systems were left to evolve for 4 . 63 Gyr (about 16dynamical timescales of the main halo). After this time,the four satellites have completed their merging with theprimary halo. The final ( x, z ) distribution of the innersatellite star particles and host disk, in both the retro-grade and prograde cases, as well as for the high and lowinclinations, is shown in Fig. 5.4.2. Dynamical friction and tidal stripping Any satellite can in principal be slowed by dynamicalfriction exerted on it by disk and halo particles. It isknown that an object, such as a satellite, of mass M ,moving through a homogeneous background of individ-ually much lighter particles with an isotropic velocitydistribution suffers a drag force (Chandrasekar 1943): F d = − πG M ρ f ( < v s ) ln Λ v s , where v s is the speed of the satellite with respect to themean velocity of the field, ρ f ( < v s ) is the total densityof the field particles with speeds less than v s , and ln Λ isthe Coulomb logarithm (Binney & Tremaine 1987).We expect that, the higher the v s , the weaker is thedynamical friction force. Retrograde satellites are ex-pected to suffer weaker dynamical friction with respectto prograde ones, since in the first case the velocity ofthe satellite is opposite to that of the disk. As a conse-quence, prograde orbits decay faster. This effect is evenmore evident for low-inclination orbits.Another important effect that occurs during mergers isthe tidal disruption of satellites. While tidal disruption ismost important near the centre of the main halo, wherethe gravitational potential is changing more rapidly, dy-namical friction is exerted both by the main halo DMparticles and by the disk star particles.4.3. Debris in the local halo We analyse the observational signature left by thesatellite stars after selecting particles in a sphere of 3 kpcradius centered at the Sun ( x = 8 kpc from the Galaxycenter), and with | z | > Fig. 5.— Final configurations in the ( x, z ) plane of four minor merger events: depicted are the morphologies of the stellar distribution,i.e. the host disk (black) and the satellite bulge (colour), at the final time T = 4 . 63 Gyr of the simulations. Shown are the cases oflow-inclination (10 ◦ tilt) retrograde (top left) / prograde (top right) orbit, and of high-inclination (60 ◦ tilt) retrograde (bottom left) /prograde (bottom right) orbit. The panels only display a randomly selected 10% subset of the total particles utilised. TABLE 4Initial conditions of the Main system and the four impacting Satellites. System Inclination Rotation x y z v x v y v z v (kpc) (kpc) (kpc) (km s − ) (km s − ) (km s − ) (km s − )Main 0 ◦ − . 00 0 . 00 0 . 00 0 . 00 0 . 00 0 . ◦ retrograde 80 . 00 0 . 27 15 . 20 6 . − . 50 0 . 35 62 . ◦ prograde 80 . 00 0 . 27 15 . 20 6 . 30 62 . 50 0 . 35 62 . ◦ retrograde 15 . 00 0 . 12 26 . 00 1 . 20 80 . 10 2 . 00 80 . ◦ prograde 15 . 00 0 . 12 26 . 00 1 . − . 10 2 . 00 80 . Note . — Inclination and rotation of the orbit, position and velocity components, and total velocity. Figure 6 shows the kinematic distribution (velocityprojections) of our simulated inner halo. The differentcolours indicate the association of the 3902 debris starswith different progenitors: the low/high-inclinationretrograde satellites (761/616 green/red dots), andthe high/low-inclination prograde satellites (966/1559blue/yellow dots).The angular momentum distribution of the satellite de-bris is shown in Fig. 7. Despite the chaotic build up of the parent halo, it appears that objects from accreted satel-lites remain confined in limited portions of the ( L z , L xy )plane.The satellite on a low-inclination prograde orbit (yel-low particles), which suffers more from dynamical fric-tion, quickly loses its orbital energy and proceeds to theinner regions of the main halo (Byrd et al. 1986; Mu-rante et al. 2010). For this reason less particles are leftin the outer-halo, see top-right panel of Fig. 5.It is worth noticing that the high inclination prograde0 Re Fiorentin et al. Fig. 6.— Kinematical (velocity space) distribution of the accreted component of the simulated Milky Way inner halo, i.e., 3902 particlesin a spherical volume of radius 3 kpc centered on the “Sun” with | z | > ◦ retrograde/prograde (red/blue), 10 ◦ retrograde/prograde (green/yellow) colliding satellites. Fig. 7.— Angular momentum distribution of the simulated Milky Way halo within 3 kpc of the “Sun”. As in Fig. 6, shown are the 3902particles accreted from four dwarf galaxies: 60 ◦ retrograde/prograde (red/blue), 10 ◦ retrograde/prograde (green/yellow) satellites afterinteraction with the simulated Milky Way. All of the marked regions have the same meaning as in Fig. 4. nner Halo Streamers in the Era of Gaia 11satellite suffers the effect of dynamical friction as well,as a result of its co-rotation with the disk. This effectacts in producing a consistent mass of debris in the solarregion having L xy ranging between 500 kpc km s − and1500 kpc km s − (blue points in Fig. 7).On the other hand, retrograde satellites experienceweaker dynamical friction and leave more particles in theouter-halo region, since their orbits have a longer decaytime and longer periods. Thus, tidal stripping (see e.g.,Colpi et al. 1999) can act longer and more efficientlywhen the satellite is still orbiting at high velocity, andwe see that a better populated high-velocity tail results(compare Fig. 7 to Fig. 10).The impact of dynamical friction on the two configu-rations considered for the retrograde satellites indicatesthat the high-inclination case is the one less affected bythis force, which again results in efficient stripping whenthe satellite has high orbital velocity. Therefore, suchstripping takes place over a large spatial region, and forthe conservation of 6D phase-space density, by virtue ofLiouville’s Theorem, we expect a small variance in veloc-ity space and in the plane of angular momenta. This isindeed observed for the red particles with respect to thegreen ones in Figs. 6 and 7.Finally, the effect of both gravitational feedback anddynamical friction on the satellites, which lead to lossof stars at different passages with different energies, isclearly evident for the case of low inclination progradeorbit in Fig. 7 at around L xy = 400 kpc km s − and L z = 1750 kpc km s − . “OBSERVED” SIMULATIONSHere we investigate the effects of observational errorson our simulated data, and show how more accurate kine-matic data to be provided by future surveys can improvedetection and characterisation of halo streams. More-over, we compare actual observations with the distribu-tions of debris resulting from the four simulated satellitespresented in the previous section, and discuss the orbitalproperties of the parent dwarf galaxies, possibly respon-sible for accreting on the Milky Way halo.5.1. Observational errors We perturb the original simulations by convolving the“true” data with two cases of error distributions. First,we adopt the accuracy of our SGKS catalogue as rep-resentative of the quality of current wide-field surveys.Then, we assume the mean accuracy expected from theforthcoming Gaia catalogue combined with complemen-tary deep spectroscopic data from on-going and futuresurveys such as GES (Gilmore et al. 2012).The true positions and velocities of each particle arefirst transformed into their astronomical observables ( α , δ , m − M , or π and µ α , µ δ , V r ); then the expected obser-vational errors are added to distance modulus (or directlyto parallax, in the case of the Gaia-like simulation), ra-dial velocity, and proper motion, according to Table 5.The precision in distance is taken to σ m − M = 0 . σ d /d (cid:39) σ π = 20 µ asfor the final precision on trigonometric parallaxes mea-sured by Gaia. In proper motion, the precision is as-sumed to be 2 mas yr − for ground-based observations, and 20 µ as yr − for Gaia. The precision in the radialvelocity is taken to be 10 km s − for the SDSS measure-ments, and 1 km s − for the GES spectroscopic survey.These quantities are finally transformed back to observedpositions vectors and space velocities.5.2. The inner halo model We explore a simulated inner halo based on the super-position of the four simulations of minor mergers and asmooth local component with the same kinematic prop-erties of the observed sample (Table 1).Consistently with the findings of Helmi et al. (1999)and Kepley et al. (2007), we assumed a debris totalfraction of 10% within 3 kpc from the Sun.In the “true” (simulated) catalogue, of the 28 738 par-ticles with | z | > U, W ) plane occupiedby the 10% high velocity tail of the resulting simulatedMilky Way inner halo (right panels), as superpositionthe accreted component (middle panels) and the smoothspheroid (left panels). The synthetic “observed” cata-logue shown in the top panels represent the current pic-ture, according to the SGKS error model. The bottompanels show the distribution of the high velocity particlesas promised by Gaia.The upper panels indicate that distinguishing in ve-locity space the satellites that gave rise to each of thedifferent moving groups with the extant data is a non-trivial task. On the other hand, as the inspection of thelower panels reveals, much of the substructures shown inthe middle panels becomes visible again thanks to thesuperior precision that Gaia will achieve.5.3. Substructures in the correlation function In order to quantify the amount of kinematic substruc-tures present among the 2874 fastest-moving particles,we compute the cumulative velocity correlation functiondescribed in Sect. 3.2. The analysis is performed overthree synthetic catalogues: the “true” simulation, andtwo lists derived from the true values after perturbingthem with either SGKS-like errors or the errors expectedfor the Gaia/GES surveys.Figure 9 shows, using bins of width 5 km s − up tokinematical separations of 50 km s − , the results for thetwo-point correlation function ξ ( v ) for the “true” case(dots), the SGKS-like (squares) and Gaia/GES-like (di-amonds) catalogues. The clear signal in the first bins,peaking at ∆ v ∼ 15 km s − , evidences an excess of par-ticles moving with similar velocities with respect to whatexpected from a fully random sample. In the case of thepure simulation, the two-point velocity correlation func-tion attains a maximum signature of (cid:104) ξ (cid:105) = 0 . ± . ∼ 80% drop to an “observed” value of (cid:104) ξ (cid:105) = 0 . ± . Fig. 8.— The ( U , W ) velocity distribution of the 10% high velocity tail of the simulated sample is shown in the right panels. Thesample is limited to a spherical volume of radius 3 kpc located on the plane of the simulated Milky Way 8 kpc away from its center andwith | z | > TABLE 5Estimated/Expected errors for the SGKS and Gaiacatalogues. Catalogue distance proper motion radial velocitySGKS σ m − M = 0 . σ π = 20 µ as 20 1 Note . — Estimated errors (precision) in parallax ( σ π , in µ as), distance modulus ( σ m − M , in mag), proper motion ( σ µ , in µ as yr − ), and radial velocity ( σ V r , in km s − ) for the SGKS andGaia catalogues. TABLE 6The composition of the 10% High Velocity Tail of the simulated Milky Way Halo. Catalogue Halo+Debris Debris Satellite 1 Satellite 2 Satellite 3 Satellite 4“True” Simulation 2874 1103 (0 . . . nner Halo Streamers in the Era of Gaia 13 Fig. 9.— The cumulative velocity correlation functions for the2874 halo particles shown in Fig. 8. The filled dots trace the corre-lation function of the pure simulation, while squares and diamondsdepict the correlation after convolution with current (i.e., SGKS)or Gaia/GES-like errors, respectively. Error bars are derived fromPoisson’s statistics of the counts. the Gaia-like case: in fact, we measure (cid:104) ξ (cid:105) = 0 . ± . ON THE NATURE OF THE HIGH VELOCITYDEBRISAs the space of adiabatic invariants is importantto gain more insight into the properties of the kine-matic substructures detected (Sect. 3.4), we compare the( L z , L xy ) distributions of the observed groups with theresults of the simulations, taking into account the effectof the observational errors. This is shown in Fig. 10,where the top panel corresponds to the SGKS-error sim-ulation, while the bottom panel reproduces what willhopefully be seen with the final Gaia catalogue.The black star symbols in the upper panel of Fig. 10represent the 67 high velocity objects we found fromour statistical analysis in the same volume and shownin Fig. 4 as colored stars. With current data, differentsatellites mix over some regions so that a discreteclassification is not always straightforward. The bottompanel of Fig. 10 clearly shows that this situation ishighly improved with Gaia-like data.We see that our Groups 1 and 2, corresponding to thestream of Helmi et al. (1999), are consistently asso-ciated with the high inclination prograde satellite (blue dots). Because of dynamical friction (cfr. Sect. 4.3), thissatellite includes a low L xy component shown in the fullsample (Fig. 7) that is not part of the high velocity tail(Fig. 10). Thus, these simulated “observations” suggestthe possible presence in the Helmi et al. (1999) streamof debris with lower L xy yet to be discovered.Of particular interest is the case of the retrograde kine-matic groups. In fact, neither the high-inclination sim-ulated satellite nor the one at low-inclination appear tofairly match the observed Groups 3, 4, and 5, i.e. theblack stars with L z (cid:46) inter-mediate region between the debris of the two simulatedretrograde satellites. Furthermore, in Sect. 3.4 we re-mark that the observed Groups 3, 4, and 5 do not wellmatch the streams detected by Dinescu (2002) and Kep-ley et al. (2007). For this reason, we suggest that thesethree groups may represent the debris of an unique pro-genitor accreted along an initial retrograde orbit havingan intermediate inclination in the range comprised be-tween 10 ◦ and 60 ◦ . In alternative, these groups couldbelong up to three different impacting satellites on ret-rograde orbits with inclinations in that same range.The results presented in this section show that themethodology proposed is certainly capable of detect-ing fossil signatures as kinematic substructures amonghigh-velocity stars. From the data at our disposal,there is clear indication that more debris are found fromdwarf galaxies on high-inclination prograde and retro-grade orbits, as well as on low-inclination retrogradeones. We have not identified any debris coming from low-inclination prograde satellites and this might be a limita-tion intrinsic to the methodology of looking at structuresin the space motions of very high velocity stars. Futurework will have to investigate these issues. CONCLUSIONSWe have explored the Solar neighborhood of the MilkyWay through the use of spectro-photometric data fromthe Sloan Digital Sky Survey and high-quality proper mo-tions derived from multi-epoch positions extracted fromthe Guide Star Catalogue II database. A sample withaccurate distances, space velocities, and metallicities isselected as a tracer of the inner-halo population resultingin 2417 subdwarfs with [Fe / H] < − . | z | > Fig. 10.— The 10% high velocity tail component belonging solely to the 4 satellites; convolved with current ground-based errors (top,835 particles) and with the expected Gaia errors (bottom, 1061 particles). Black star symbols are the 67 fast moving debris stars uncoveredfrom the analysis of the SGKS sample. Solid and dashed contours have the same meaning as in Figs. 4 and 7 . nner Halo Streamers in the Era of Gaia 15the region of the mildly retrograde stream detected byDinescu (2002).Comparison to our high resolution N-body simulationsconfirms that the two groups associated with the Helmistream are likely fossil remnants of a dwarf galaxy whichco-rotates with the disk of the Galaxy and moves on ahigh-inclination orbit.As for the three retrograde groups (3, 4 and 5 in Ta-ble 2), they may be debris of an unique progenitor ac-creted along an initial retrograde orbit having an inter-mediate inclination in the range 10 ◦ ÷ ◦ . However, wecannot exclude that these groups belong to different im-pacting satellites on retrograde orbits with inclinationswithin that same range. A more detailed analysis of thechemical abundances of the three detected groups, as wellas more quantitative comparisons to extended simula-tions, are necessary to resolve this issue.In any event, the fastest objects appear with pos-itive and negative L z values (i.e. prograde and ret-rograde motions, respectively) in the angular momen-tum ( L z , L xy ) regions for high-inclination orbits ( L xy (cid:38) − ). On the other hand, for low-inclination both observations and simulations show thatthe fastest objects appear only on retrograde orbits (e.g.,Fig. 10, top panel). This asymmetric distribution is sug-gestive of the role played by dynamical friction duringaccretion.In anticipation of the much improved data expectedover the coming years, in particular the Gaia catalogueand the new ground-based spectroscopic surveys, we alsoinvestigated the impact of observational errors in our dy-namical simulations. The analysis indicates that (see the relevant panels of Figs. 8 and 10) Gaia will greatly influ-ence these studies: for, velocity and angular momentumdistribution will be almost completely dominated by thephysics we are trying to recover, i.e., the dynamical his-tory of the merging events.At that point, full grids (in, e.g., inclination andamount of rotation) of prograde and retrograde high res-olution satellite simulations will be required to preciselycharacterise the debris detected. Then, we will be ableto number the merging events for direct comparison withthe predictions of the (Λ)CDM theory and its associatedmerging paradigm.In conclusion, the results shown might lead us toclaim that the inner halo might have “seen” only twoevents; however the large uncertainties in the extantdata, mostly observational, do not exclude the possibilitythat the events might be as many as four, and perhapsmore given the intrinsic difficulty of our technique to dealwith low inclination prograde mergers.We are grateful to the referee for his/her commentsthat helped us improve the original manuscript. Thiswork has been partially funded by ASI, under contractto INAF I/058/10/0 “Gaia Mission - The Italian Partic-ipation to DPAC”, and by MIUR, through PRIN 2012grant No 1.05.01.97.02 “Chemical and dynamical evo-lution of our Galaxy and of the galaxies of the LocalGroup”. 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