Kinematics and Chemistry of Stars Along the Sagittarius Trailing Tidal Tail and Constraints on the Milky Way Mass Distribution
Jeffrey L. Carlin, Steven R. Majewski, Dana I. Casetti-Dinescu, David R. Law, Terrence M. Girard, Richard J. Patterson
aa r X i v : . [ a s t r o - ph . GA ] N ov A CCEPTED FOR PUBLICATION IN T HE A STROPHYSICAL J OURNAL
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KINEMATICS AND CHEMISTRY OF STARS ALONG THE SAGITTARIUS TRAILING TIDAL TAIL ANDCONSTRAINTS ON THE MILKY WAY MASS DISTRIBUTION J EFFREY
L. C
ARLIN , S
TEVEN
R. M
AJEWSKI , D ANA
I. C
ASETTI -D INESCU , D AVID
R. L AW , T ERRENCE
M. G
IRARD , AND R ICHARD
J. P
ATTERSON Draft version August 29, 2018
ABSTRACTWe present three-dimensional kinematics of Sagittarius (Sgr) trailing tidal debris in six fields located 70-130 ◦ along the stream from the Sgr dwarf galaxy core. The data are from our proper-motion (PM) survey ofKapteyn’s Selected Areas, in which we have measured accurate PMs to faint magnitudes in ∼ ′ × ′ fieldsevenly spaced across the sky. The radial velocity (RV) signature of Sgr has been identified among our follow-up spectroscopic data in four of the six fields and combined with mean PMs of spectroscopically-confirmedmembers to derive space motions of Sgr debris based on ∼ Θ LSR ) from its standard 220 km s - to at least 232 ± - (and possibly as high as 264 ±
23 km s - ) is necessary to bring 3-D model debris kinematics and ourmeasurements into agreement. Satisfactory model fits that simultaneously reproduce known position, distance,and radial velocity trends of the Sgr tidal streams, while significantly increasing Θ LSR , could only be achievedby increasing the Galactic bulge and disk mass while leaving the dark matter halo fixed to the best-fit valuesfrom Law & Majewski (2010a). We derive low-resolution spectroscopic abundances along this stretch of theSgr stream and find a constant [Fe/H] ∼ -1.15 (with ∼ . ∼ ◦ span of this study was all stripped from Sgr on the same orbital passage. Subject headings:
Galaxies: individual: (Sagittarius dwarf spheroidal) — Galaxy: fundamental parameters —Galaxy: kinematics and dynamics — Galaxy: structure INTRODUCTION
With the profusion of data provided in recent years bydeep, large-area photometric surveys such as the Two Mi-cron All Sky Survey (2MASS) and Sloan Digital Sky Sur-vey (SDSS), a wealth of stellar substructure has been uncov-ered in the Milky Way (MW) halo. The finding and subse-quent mapping of numerous stellar tidal streams and overden-sities (e.g., Sagittarius — Ibata et al. 2001; Majewski et al.2003; Belokurov et al. 2006; Monoceros — Newberg et al.2002; Ibata et al. 2003; Yanny et al. 2003; other SDSSstreams — Grillmair 2009; Belokurov et al. 2007; Grillmair2006a,b; Grillmair & Dionatos 2006) has borne out the idea(Searle & Zinn 1978; Majewski 1993; Majewski et al. 1996)that remnants of accreted dwarf galaxies make up much ofthe stellar halo of the Milky Way. The direct confirma-tion of the accretion of late-infalling subhalos via discov-ery of ubiquitous long-lived, coherent tidal debris streamshas provided strong constraints on models of small-scale hi-erarchical structure formation under the prevailing Λ -Cold Department of Astronomy, University of Virginia, P.O. Box 400325,Charlottesville, VA 22904-4325, USA ([email protected]) Department of Physics, Applied Physics, and Astronomy, Rensse-laer Polytechnic Institute, 110 8th Street, Troy, NY 12180, USA ([email protected]) Astronomy Department, Yale University, P.O. Box 208101, NewHaven, CT 06520-8101, USA Department of Physics and Astronomy, University of California, LosAngeles, CA 90095, USA ; Hubble Fellow Visiting Astronomer, Kitt Peak National Observatory, National OpticalAstronomy Observatory, which is operated by the Association of Universi-ties for Research in Astronomy (AURA) under cooperative agreement withthe National Science Foundation.
Dark Matter ( Λ CDM) cosmology (e.g., Abadi et al. 2003;Bullock & Johnston 2005; Font et al. 2006). Furthermore,because the tidal streams retain the kinematical signaturesof the orbits of their progenitors (i.e., angular momentumand energy), stellar debris in the streams can be used assensitive probes of the underlying Galactic gravitational po-tential (e.g., Johnston et al. 1999; Ibata et al. 2001; Helmi2004; Martínez-Delgado et al. 2004; Johnston et al. 2005;Law et al. 2005; Majewski et al. 2006).The best-known and only widely agreed-upon case ofa presently visible dwarf galaxy undergoing tidal disrup-tion in the Milky Way halo is the Sagittarius (Sgr) dwarfspheroidal (dSph) . The core of this galaxy was first dis-covered by Ibata et al. (1994) in a kinematical study of theouter Galactic bulge, with the first large-scale mapping of theSgr leading and trailing tidal arms done by Majewski et al.(2003) using 2MASS M-giant stars. Various studieshave reported the discovery of stars (e.g., Majewski et al.2003; Martínez-Delgado et al. 2004; Belokurov et al. 2006;Yanny et al. 2009b; Correnti et al. 2010; a comprehensivesummary of the earlier detections appears in Majewski et al.2003) or star clusters (e.g., Pal 12: Dinescu et al. 2000; Whit-ing 1: Carraro et al. 2007; many clusters: Bellazzini et al.2003; a summary of Sgr clusters appears in Law & Majewski2010b) plausibly associated with debris from Sgr, eithertrailing or leading it along its orbit. Line-of-sight ve- Though we note that there is now evidence for extended tidal debris pop-ulations around the Carina (Muñoz et al. 2006b, 2008) and Leo I (Sohn et al.2007) dSphs. Also, some debate still exists over whether the HI MagellanicStream derives from tidal stripping of Small or Large Magellanic Cloud gasversus from ram pressure stripping.
Carlin et al.
Figure 1.
Left panel:
Distribution of Kapteyn’s Selected Areas (in equatorial coordinates) for which we have derived proper motions, shown in an Aitoffprojection. Solid points are those fields for which we have additional deep, 4-meter plates (see text). The current orbital plane of Sagittarius is overlaid as a solidblue line, and the shaded (light green) areas represent the sky coverage of SDSS (as of DR5). Regions containing stellar overdensities suggested in the literatureto be part of the "Monoceros ring" are denoted by the blue hatched areas on either side of the disk.
Right panel:
Spatial distribution of the Kapteyn SelectedAreas used in this study overlaid on the predicted distribution of Sagittarius tidal debris from the best-fit triaxial halo model of Law & Majewski (2010a). Goldcolored points represent debris stripped from the Sgr progenitor on the past two perigalactic passages (0-1.3 Gyr ago), and magenta points the previous twopassages (1.3-3.2 Gyr ago). Note that all of the fields are sampling predominantly debris stripped on the same orbital passage (i.e., the gold points), with only SA71 slightly sampling earlier-stripped (magenta) debris. locities (i.e., radial velocities , or RVs) of Sgr mem-bers have been determined at a few positions along thestream (e.g., Dohm-Palmer et al. 2001; Majewski et al. 2004;Monaco et al. 2007), and, along with the spatial distributionof these stars, provide constraints on models of the Sgr-MilkyWay interaction (e.g., Johnston et al. 1995; Helmi & White2001; Ibata et al. 2001; Helmi 2004; Martínez-Delgado et al.2004). A comprehensive effort at modeling the Sgr disruptionconstrained by all observations available after about a decadeof study was done by Law et al. (2005), who were able to re-produce most extant data, but were unable to completely rec-oncile the apparent need for a prolate MW halo potential toproduce the leading arm radial velocities on the one hand,and an oblate halo to match the positions of leading debrison the other. This contradiction has apparently been recentlyresolved by Law et al. (2009), who propose that the MilkyWay might have a triaxial halo; a comprehensive N -bodymodel based on the best-fitting triaxial halo (Law & Majewski2010a, hereafter LM10) reasonably matches nearly all exist-ing constraints (spatial and kinematical) of Sgr tidal debris. The Sagittarius dwarf and its tidal debris are thus proving tobe an excellent laboratory for studying both the dynamics oftidally disrupting dwarf galaxies and star stream formation,as well as the shape and strength of the Galactic gravitationalpotential that is the cause of this disruption. It is this modelof LM10 to which we shall compare our data throughout thiswork.
Our Proper Motion Survey Further complications have arisen due to an apparent bifurcation of theleading stream (Belokurov et al. 2006); the LM10 model was not designed toaddress this issue. Several attempts to explain this detail invoke overlappingdebris from multiple orbital wraps (Fellhauer et al. 2006; though Yanny et al.2009b find similar stellar populations in both arms, likely ruling out thisscenario) or a disk-galaxy progenitor for Sgr (Peñarrubia et al. 2010; but cf.Łokas et al. 2010). The highly-elliptical shape of the Sgr dwarf has recentlybeen reproduced by (Łokas et al. 2010), who model Sgr as a disk galaxy em-bedded in an extended dark halo. Tidal stirring transforms the initially diskdwarf into an extended elliptical shape over two pericentric passages; the ro-tation of the progenitor may also explain the bifurcation of the Sgr leadingarm.
To date, no systematic survey has addressed the tangen-tial velocities (derived from proper motions) of the iden-tified major Galactic tidal streams. Only a few studies(e.g., Dinescu et al. 2002; Casetti-Dinescu et al. 2008, 2009;Carlin et al. 2010; Koposov et al. 2010) have published any proper motion results for major Galactic substructures, andtypically not at a level of precision that is useful for constrain-ing dynamical models of tidal stream production and evolu-tion. In an effort to detect and characterize halo substruc-tures, we have been working on a project to obtain full phase-space information (positions and full 3-D space motions)for individual stars in Kapteyn’s Selected Areas (SAs; seeCasetti-Dinescu et al. 2006 for an overview of this project).The sky positions of the Selected Areas were chosen by Ja-cobus Kapteyn (1906) to provide evenly spaced coverage fora systematic exploration of Milky Way structure. We have at-tempted to carry on at least part of this legacy by taking advan-tage of Mt. Wilson 60-inch telescope photographic plate ma-terial taken by Kapteyn and collaborators (Seares et al. 1930)for their survey to make up the first-epoch data of our survey(in particular, near-equatorial fields at δ = 0 ◦ , + ◦ , and - ◦ ).The distribution on the sky of those SAs that make up our sur-vey is shown in an Aitoff projection in Figure 1. Some of theequatorial SA fields lie along the orbit of the Sagittarius dwarfgalaxy (which is approximated by the blue, solid curve in Fig-ure 1) – it is a subset of these fields (in particular, six fieldsalong the trailing tidal tail; see the right panel of Figure 1) thatare the focus of the present work. Constraints on the Local Standard of Rest Velocity
The positions of tidal debris that have been found over alarge stretch of the Sagittarius orbit place fairly strong con-straints on the three-dimensional motions of the Sgr dwarf.It is, however, important to confirm and refine the models bymeasuring space velocities of stream stars (especially propermotions, which are difficult to measure for stars in distantGalactic substructures). In the case of the Sgr trailing tail,however, proper motions measured for debris stars are alsorather sensitive to the Sun’s motion through the Galaxy. Thisarises because much of the Sagittarius trailing tidal tail isinematics of Sgr Tidal Debris in Kapteyn’s Selected Areas 3positioned at a roughly constant distance below the Galacticplane, with the Sgr orbital plane nearly coincidental with theGalactic X GC - Z GC plane. Majewski et al. (2006, hereafter“MLPP”) noted that because of this orientation, longitudinalproper motions of Sgr trailing debris located sufficiently faraway from the South Galactic Pole contain virtually no con-tribution from Sagittarius motions, and almost entirely reflectthe solar motion.Efforts to measure fundamental dynamical properties of theMilky Way, such as its rotation curve, Θ ( R ), are compli-cated by our Sun’s own (poorly known) motion within theGalaxy. Measurements of Θ LSR , the Galactic rotation speedat the solar circle (the
Local Standard of Rest , “LSR”), varyby 25%, despite many efforts at its determination. The valueadopted by the IAU in 1985 of Θ LSR = 220 km s - (seeKerr & Lynden-Bell 1986) has long represented a reasonableapproximation to existing measurements (note, however, thatprior to the 1985 IAU adoption of Θ LSR = 220 km s - , the1964 IAU general assembly adopted 250 km s - ; see a listingof pre-1985 measurements of Θ LSR in Kerr & Lynden-Bell1986). Constraints taking into account the ellipticity of thedisk have suggested the LSR velocity could be as low as ∼ - (Kuijken & Tremaine 1994). A similarly low valueof 184 ± - was found by Olling & Merrifield (1998),who modified previous methods of determining the Oort con-stants by including radial variations of gas density in theirmass modeling of the Galactic rotation curve. Proper motionsof Galactic Cepheids from Hipparcos (Feast & Whitelock1997) yield a result of Θ LSR = (217 . ± . R /
8) km s - (where R is the distance from the Sun to the Galactic center;the IAU adopted value is R = 8 . Hipparcos data (van Leeuwen2007) with improved systematic errors, Yuan et al. (2008)found Θ LSR = (243 ± R /
8) km s - based on thin-disk O-B5 stars. Estimates based on absolute PMs of Galactic bulgestars in the field of view of globular cluster M4 using the Hubble Space Telescope (HST) yield (202 . ± . R / - (Kalirai et al. 2004) and (220 . ± . R /
8) km s - (Bedin et al. 2003) (with both studies using data from thesame HST observations). Long-term
V LBA monitoring of SgrA*, the radio source at the Galactic center, led to a propermotion of Sgr A* from which Reid & Brunthaler (2004) re-vised the LSR velocity upward to (235 . ± . R /
8) kms - . Ghez et al. (2008) combined stellar kinematics near theGalactic center with the proper motion of Sgr A* to derive(229 ± R / .
4) km s - . More recently, Θ LSR has beensuggested to be even higher, (254 ± R / .
4) km s - , basedon trigonometric parallaxes of Galactic star-forming regions(Reid et al. 2009). Reanalysis of these same data, includ-ing the Sgr A* proper motion, by Bovy et al. (2009) founda similar (244 ±
13) km s - . Koposov et al. (2010) providedconstraints on the MW halo potential by analysing the GD-1(Grillmair & Dionatos 2006) stellar stream, combining SDSSphotometry, USNO-B+SDSS proper motions (see Munn et al.2004, 2008), and spectroscopy to obtain 6-D phase-space data Throughout this paper, when we refer to Galactic Cartesian ( X , Y , Z ) GC coordinates, we are specifically referring to a right-handed Cartesian framecentered on the Galactic center, with X GC positive in the direction from theSun to the Galactic center, Y GC in the direction of the Sun’s motion throughthe Galaxy, and Z GC upward out of the plane. Assuming the Sun is at R = 8 . X , Y , Z ) GC =(-8.0,0,0) kpc.The corresponding velocity components will be denoted ( U , V , W ) GC , wherethe “GC” denotes velocities relative to the Galactic rest frame. over a large stretch of the stream, which they used to estimate Θ LSR = (224 ± R / .
4) km s - (though this result is madesomewhat more uncertain due to a systematic dependence onthe flattening of the disk+halo potential). Finally, a combinedestimate including many of the above results as priors finds avalue of (236 ± R / .
2) km s - (Bovy et al. 2009). Mostof the estimates discussed here rely on the Oort constants, andthus are dependent on our incomplete knowledge of R . De-spite numerous attempts at determining the circular velocityat the solar circle, this constant remains poorly constrained. Itis clear that independent methods would be valuable to obtainalternative estimates of Θ LSR .Here we use a new, independent method for ascertaining Θ LSR that has the advantage over most of the previously men-tioned methods in that the results have virtually completedecoupling from an assumed value of R . As discussed inMLPP, the trailing arm of the Sagittarius tidal stellar streamis ideally placed to serve as an absolute velocity reference forthe LSR. With an orbital pole of ( l p , b p ) = (274 , - ◦ , Sgris almost on a polar orbit, and the line of nodes of the inter-section of the Galactic midplane and the Sgr debris plane isalmost coincident with the Galactic X GC axis (the axis con-taining the Sun and Galactic center). This is illustrated inFigure 2, which shows the projection of Sgr debris from theLM10 model onto the Galactic X GC - Z GC , Y GC - Z GC , and X GC - Y GC planes. In the upper left panel (the X GC - Z GC plane),the Sgr orbital plane is nearly face-on, while in the other twopanels, few Sgr debris points are seen more than ∼ X GC - Z GC plane (i.e., | Y GC | . within its (vir-tually non-precessing; Johnston et al. 2005) debris plane, asobserved from the LSR, are therefore almost entirely in theGalactic U and W velocity components (i.e., in the X GC - Z GC plane), whereas V motions of Sgr tidal tail stars almost en-tirely reflect solar motion — i.e., Θ LSR (plus the Sun’s pecu-liar motion in V , established to be in the range ∼ +5 to +12km s - ; e.g., Dehnen & Binney 1998). The Sgr trailing tailis positioned fairly equidistantly from the Galactic disk fora substantial fraction of its stretch across the Southern MWhemisphere (Majewski et al. 2003). This band of stars arcingalmost directly “beneath” us within the X GC - Z GC plane (seethe upper panel of Figure 2) provides a remarkable, stationaryzero-point reference against which to make direct measure-ment of the solar motion almost completely independent ofthe Sun’s distance from the GC. Because of the fortuitous orientation of the Sgr debris, themajority of Θ LSR motion (i.e., V ) is seen in the proper motionsof these stars, with the reflex solar motion almost entirely con-tained in the µ l cos(b) component for Sgr trailing arm stars (atleast for those stream stars away from the South Galactic Pole(SGP) coordinate “discontinuity", where the µ l cos(b) of Sgrstream stars switches sign). Fig. 4 of MLPP shows the essenceof the proposed experiment via measurement of µ l cos(b) forSgr trailing arm stars, which shows a trend with debris longi-tude, Λ ⊙ , that reflects the solar motion. In the region from100 ◦ . Λ ⊙ . ◦ , µ l cos(b) is nearly constant, because themotion of Sgr debris contributes little to the V -component ofvelocity. Thus accurate measurement of µ l cos(b) for Sgr trail-ing tail stars along this stretch of the stream will provide ameans of estimating Θ LSR with almost no dependence on R . Λ ⊙ was defined by Majewski et al. 2003 as longitude in the Sgr debrisplane as seen from the Sun; Λ ⊙ = 0 ◦ at the present Sgr position, and increasesalong the trailing tail. Carlin et al.Five of the Kapteyn fields for which we have precise ( ∼ - ) proper motions lie squarely on the Sgr trailing armin this Λ ⊙ range, and one other (SA 92) is on the peripheryof the stream. In Section 4.2, we will use the mean Sgr debrisproper motions derived in four of these six fields to deriveconstraints on Θ LSR . Metallicities and Detailed Abundances of the SagittariusSystem
Chou et al. (2007) presented one of the first studies ofhigh-resolution spectroscopic metallicities derived for Sgr de-bris. Their work showed that M-giants along the Sagittar-ius leading stream exhibit a significant metallicity gradient(which had previously been suggested to be present oversmaller separations from the Sgr core based on photometrictechniques; e.g., Alard 2001; Martínez-Delgado et al. 2004;Bellazzini et al. 2006), decreasing from a mean [Fe/H] = -0.4 in the core to ∼ - . ∼ - ◦ from the core(i.e., between 300 > Λ ⊙ > ◦ ) , and to ∼ - . & ◦ from the main Sgr body. Such a population gradient alongthe stream likely arose due a strong metallicity gradient be-ing present in the dSph before its tidal disruption; thus theouter, more metal-poor populations were preferentially lost astidal stripping progressed at earlier times relative to the moreintermediate-age (and higher metallicity) populations remain-ing in the core (a mechanism for this process has been demon-strated in the context of an N - body model by LM10). Inaddition, apparently some younger populations were formedeven after Sgr began disrupting. The existence of a popula-tion gradient has also been seen by Bellazzini et al. (2006),who found that the relative numbers of blue horizontal branch(BHB) stars to red clump (RC, or red horizontal branch) starsare much higher in a leading stream field than in the Sgr core.Since BHB stars arise in older, more metal-poor populationsthan the RC stars, this must indicate that the stripped popula-tion was made up of predominantly older, less-enriched starsthan remain in the core today. Keller et al. (2010) extendedthe search for chemical evolutionary signatures to the trail-ing tail of Sgr, observing a handful of stars selected from the2MASS M-giant catalogs of Majewski et al. (2003) at highresolution in each of two fields at distances of 66 ◦ and 132 ◦ from the core. Keller et al. combined the mean metallicities inthese two fields with the [Fe/H] = -0.4 result for the Sgr corefrom Monaco et al. (2005), and derived a metallicity fit as afunction of Λ ⊙ of ∆ [Fe/H] = (-2.4 ± × - dex degree - .This trend (seen in their Figure 4) also passes through themean metallicity of [Fe/H] ≈ -0.6 derived by Monaco et al.(2007) in a narrow region centered at Λ ⊙ = 100 ◦ .For consistency, all of the data included in the Keller et al.(2010) study (including those from Monaco et al. 2005, 2007and Chou et al. 2010) were derived from M giants, whichare, however, biased toward metal-rich, and therefore rela-tively younger, stars. In the current study, we explore themetallicity in fields between 75 < Λ ⊙ < ◦ from the Sgrcore along the trailing tail using predominantly main sequencestars. Such stars near the main sequence turnoff are muchless prone to metallicity biases than M giants, because MSTOstars are present in all stellar populations. An additional ad-vantage of focusing on MSTO stars is that the number densityof turnoff stars is much higher than both young, M giant trac-ers and older horizontal-branch stars; this provides us a muchlarger sample with which to characterize the Sgr trailing tailmetallicity. Older trailing debris populations have recently been studied by Sesar et al. (2010), who used SDSS Stripe82 data to develop a new technique for estimating metallic-ity from photometric data where both RR Lyrae variables andmain-sequence stars from the same structure can be identified.Their work found a constant [Fe/H] = -1.20 ± α -element abundance; the α elements (e.g.,Mg, Ca, Ti) are produced mainly in Type II supernovae (SNe),which are the evolutionary endpoints of massive stars thatdominate the chemical evolution at early times. Once TypeIa SNe begin to occur, the [ α /Fe] ratio will decrease, be-cause α -elements are less effectively produced by these su-pernova progenitors, while the overall metallicity, [Fe/H], willcontinue to increase. This produces a “knee” in the [ α /Fe]vs. [Fe/H] diagram, which acts essentially as a chronome-ter for a given system, since the [Fe/H] of the knee indi-cates the transition from SNII-dominated evolution to SNIacontributions. This phenomenon has been seen in a num-ber of dSph systems, which typically show lower [ α /Fe] ata given [Fe/H] than Galactic populations because of a slowerenrichment (e.g., Shetrone et al. 2001, 2003; Venn et al. 2004;Tolstoy et al. 2003; Geisler et al. 2005; see also a recent re-view by Tolstoy et al. 2009). However, at the lowest metal-licities, the [ α /Fe] of dSphs more closely resemble thoseof the MW halo. Studies by Sbordone et al. (2007) andMonaco et al. (2005) found the same underabundance of α -elements relative to the Milky Way for the core of the Sagittar-ius dSph. This finding has been extended into the Sgr trailingstream by Monaco et al. (2007), and into the leading arm byChou et al. (2010), with both studies using M-giants from thecatalog of Majewski et al. (2003). However, M giants are bi-ased to higher metallicity and more recently star-forming pop-ulation(s) of Sgr, so a natural next step in understanding theevolution of the original, pre-disruption Sgr dSph is to derivedetailed abundances (especially for s-process and α -elements)for a significant sample of the more metal-poor, older starspopulating the core or, more accessibly, in Sgr’s more nearbystreams. In Section 5 we present relative Mg abundances de-rived from our spectra. We show that the majority of con-firmed old, metal-poor Sgr stream members appear to havedistinct Mg abundances from those of the Milky Way stellarpopulations along the lines of sight probed. Goals of This Paper
Here, we present data in six of the Kapteyn’s Selected Areasfrom our deep proper-motion survey (Casetti-Dinescu et al.2006). In these six fields intersecting the trailing tidal tailof the Sgr system, we have augmented our proper-motioncatalogs with follow-up spectroscopy. Sgr debris has beenidentified from among the stars with measured radial veloc-ities, and these Sgr candidates are used to derive the meanthree-dimensional kinematics and chemistry of the Sgr trail-ing stream.In Section 2.2, we briefly introduce the proper mo-tion survey (a more detailed discussion of the survey ap-pears in Casetti-Dinescu et al. 2006), and discuss in depththe spectroscopic observations with the WIYN+Hydra andMMT+Hectospec multifiber instruments that yielded a totalof > ∼ - - per star,or ∼ . - . - mean for each field) yet measuredfor Sagittarius debris. These measured kinematics are com-pared to the models of Law & Majewski (2010a), and foundto agree rather well with the predictions for Sgr debris mo-tions. However, we follow in Section 4 with an analysis ofthe residual disagreement between our measurements and themodels, or more accurately, we use the discrepancy to re-assess the magnitude of the solar reflex motion, which is thedominant contributor to the proper motions in the directionof Galactic longitude. We show that our proper motion data(specifically, µ l cosb) are inconsistent with the standard IAUvalue of 220 km s - for the Local Standard of Rest motion atthe ∼ - σ level and favor a significantly higher value, con-sistent with several of the most recent Θ LSR studies using ra-dio techniques. In Section 5 we apply a software pipeline de-signed to derive stellar abundances from low-resolution spec-tra to the numerous spectra we have obtained for this project.While the metallicities show a hint of a gradient among themetal-poor stars in our study consistent with previous work,we cannot rule out a constant [Fe/H] over the range of streamlongitude covered. We also examine the relative magnesiumand iron index strengths for information on α -abundance pat-terns of Sgr debris. We find Mg abundances of Sgr membersare typically lower at a given [Fe/H] than field stars, consistentwith the behavior seen in most MW dSphs. Finally, Section 6concludes with a brief summary of our work, and future av-enues these data can be used to explore. THE DATA
Field Locations
The data discussed here are part of our ongoing deepproper-motion survey in a subset of Kapteyn’s Selected Ar-eas (Majewski 1992; Casetti-Dinescu et al. 2006) at declina-tions of ± ◦ and 0 ◦ . The survey as designed by Kapteyn(1906) consists of ∼ ◦ fields evenly spaced at ∼ ◦ in-tervals along strips of constant declination (see Fig. 1 inCasetti-Dinescu et al. 2006). A handful of our near-equatorialsurvey fields (see the left panel of Figure 1) fall on ornear the location of Sgr trailing tidal debris as mapped byMajewski et al. (2003) using M-giants from 2MASS. The lo-cation of our fields relative to the models (constrained bythe Majewski et al. data, among others) of Law & Majewski(2010a) can be seen in the right panel of Figure 1, which sug-gests that we can expect a significant contribution from Sgrdebris to the stellar populations along these lines of sight.In Casetti-Dinescu et al. (2006) and Casetti-Dinescu et al.(2008) we showed that faint ( V or g & B - V < . g - r < .
6) overdensities (at colors and magnitudes con-sistent with the expected Sgr main sequence turnoff) in thecolor-magnitude diagrams of those SA fields intersecting theSgr orbital path also show clumping in the distributions oftheir proper motions; these excesses and their clumping inproper motion space suggest that a distant, common-motionpopulation, likely to be Sgr tidal debris, is present in thesefields. In this work, we focus on six fields: SAs 116, 117, 92,93, 94, and 71 (listed in order of increasing Λ ⊙ ). Coordinatesfor these fields are given in Table 1, which includes equatorialand Galactic positions as well as the longitude and latitude inthe Sagittarius coordinate system. In this study, we are dis-cussing fields that are ∼ ◦ - ◦ from the core of the Sgr Figure 2.
Sagittarius debris from the best-fit triaxial halo model ofLaw & Majewski (2010a), shown in Galactic ( X , Y , Z ) GC (right-handed) co-ordinates. Colors represent debris stripped on successive orbits, as in Fig-ure 1, with 2 passages of additional (earlier) debris included as cyan points.The three panels represent the projection of Sgr debris onto the Galactic X GC - Z GC , Y GC - Z GC , and X GC - Y GC planes. In the upper left panel (the X GC - Z GC plane) the Sgr orbital plane is nearly face-on; open black squaresin this panel denote the positions of the Kapteyn Selected Areas in thisstudy along the Sgr trailing tail. The Sun is represented by the circle at( X GC , Z GC )=(-8.0,0.0) kpc, with the Sgr core (black dots) beyond the Galacticcenter as viewed from our position, and slightly below the plane. The upperright and lower left panels (i.e., the Y GC - Z GC and X GC - Y GC planes) illustratethe near-coincidence of the Sgr orbital plane with the Galactic X GC - Z GC plane. Note that very few Sgr debris points make excursions of more than ∼ -
10 kpc to either side of the Galactic X GC - Z GC plane (in the Y GC direc-tion). dSph, along its trailing stream.The positions of the SAs in this study in the Galactic Carte-sian X GC - Z GC plane are shown in the upper left panel ofFigure 2, overlaid atop simulated Sgr debris from the LM10model. Of course, to place points on this figure for the SAsrequires an estimate of heliocentric distance. Where neededthroughout this work, we use mean distances to Sgr debris ineach SA field estimated from the LM10 model debris alongcorresponding lines of sight. We have chosen to do this ratherthan measure Sgr debris distances because (a) our data in mostfields don’t reach much fainter than the main sequence turnoffof Sgr, and (b) the expected line-of-sight depth of the Sgrstream in this portion of the trailing tail is ∼
10 kpc, which“smears” the main sequence out by as much as ∼ . Photometry and Proper Motions
For those fields (SAs 92, 93, 94, and most of SA 116)that lie within the Sloan Digital Sky Survey (SDSS) foot-print, we have used photometry (shown in Figure 3) fromSDSS Data Release 7 (DR7; Abazajian et al. 2009) for ouranalyses. The remaining photometric data for this survey(for SAs 71 and 117) are photographic and derived fromthe late epoch (du Pont 2.5-m telescope) plates from whichthe proper motions were measured. Calibration of the pho- Carlin et al.
Table 1
Kapteyn’s Selected Areas in This StudySA RA Dec l b Λ ⊙ a B ⊙ E ( B - V ) b (J2000.0) (J2000.0) (degrees) (degrees) (degrees) (degrees)71 03:17:11.5 15:24:57.6 167.1 -34.7 128.2 -5.6 0.1994 02:55:58.1 00:30:03.6 175.3 -49.3 116.3 4.8 0.0993 01:54:52.1 00:46:40.8 154.2 -58.2 103.2 -3.2 0.0392 00:55:03.8 00:47:13.2 124.9 -62.1 90.1 -10.6 0.03117 01:17:04.1 -14:11:13.2 149.0 -75.7 87.6 5.1 0.02116 00:18:08.4 -14:19:19.2 90.1 -75.0 74.9 -1.4 0.02 a Coordinates in the Sagittarius system as defined by Majewski et al. (2003). Λ ⊙ and B ⊙ are analogous to Galactic longitude and latitude, but rotated such thatthe Sgr core defines the center of the system (i.e., Λ ⊙ , B ⊙ = 0 ◦ , ◦ ), with Λ ⊙ increasing along the trailing tidal tail. The fields in this study sample the trailingtail between 74 - ◦ from the Sgr core. b Interstellar reddening value estimated from the maps of Schlegel et al. (1998).
Figure 3.
Left:
SDSS color-magnitude diagrams (CMDs) of all stars with measured proper motions in the four fields of our survey that overlap the SDSSfootprint. Each of these CMDs shows the blue ( g - r ∼ .
5) swath of stars at the bright end made up of primarily Milky Way thin- and thick-disk MSTO stars.Below this feature at similar blue, ( g - r . .
6) colors, but at fainter ( g & .
5) magnitudes in each field is an apparent overdensity likely made up of Sagittariusmain-sequence stars. Note that the much deeper proper motion catalog of SA 94 samples much more of the Sgr main sequence than those catalogs for the otherfields.
Right:
Proper motion vector point diagrams (VPD) , separated into a blue (0 . < g - r < .
8) sample (middle column) and a red (1 . < g - r < .
7) subset(right). Red stars from the prominent feature visible at red colors ( g - r & .
2) in each CMD should be primarily nearby Galactic M-dwarfs. The blue starscontain main sequence turnoff stars of MW populations, as well as candidate Sgr MSTO stars. The proper motions of many stars are tightly clumped in the bluesamples, suggesting that a distant, common-motion stellar population (i.e., Sgr debris) may be present among these stars. tographic magnitudes in the blue (IIIa-J+GG385) and vi-sual (IIIa-F+GG495) passbands onto the standard Johnson-Cousins system was achieved using CCD photometry takenin 1997-1998 with the Swope 1-m at Las Campanas Obser-vatory. However, that UBV CCD photometry only covers asmall portion ( ∼ - ∼ . B and V photometry.inematics of Sgr Tidal Debris in Kapteyn’s Selected Areas 7Details of the proper motion reductions appear inCasetti-Dinescu et al. (2006), so here we provide only anoverview. For all of the near-equatorial ( - ◦ ≤ δ ≤ ◦ ) Se-lected Areas in our study, proper motions are derived fromplates taken with the Mt. Wilson 60-inch between 1909-1912,combined with deliberately matched plates (in approximatearea and plate scale) taken by S. Majewski with the 2.5-m LasCampanas du Pont telescope between 1996-1998. All plateswere digitized with the Yale PDS microdensitometer. Mostbackground QSOs and galaxies are near the limiting magni-tude of the proper motion catalogs derived from solely theMt. Wilson and du Pont plates; therefore if we used only thesedata, the correction to an absolute proper motion frame wouldbe determined by only a handful of poorly-measured faint ob-jects. To extend the proper motion limiting magnitude beyondthe limit imposed by the Mt. Wilson plates, we augmentedthe Kapteyn survey data with measurements of plates fromthe first Palomar Observatory Sky Survey (POSS-I), whichwere taken in the early 1950s. These plates, while of muchcoarser plate scale (67 . ′′ - ; compare to 10 . ′′
92 mm - forthe du Pont, and 27 . ′′
12 mm - for the 60”), are deeper thanthe 60” plates, and provide a ∼ and the du Pont plates, allowing us toextend the limiting magnitude of the survey (at least for thePOSS-I/du Pont proper motion baseline) to V & . ∼
50% completenessat SDSS r magnitudes of ∼
22 (compared to ∼
50% complete-ness at r ∼ . . ′′ - ) plate scale at inter-mediate epochs and the increased depth provided by the 4-mplates. Radial Velocities
The survey fields in which we focus this Sgr study fall on ornear the portion of the trailing stream in which Majewski et al.(2004) and Monaco et al. (2007) have identified a clear Sgr ra-dial velocity signature. These fields can be seen relative to theorbital path of the Sgr dSph in the left panel of Figure 1, andwith respect to the expected location of Sgr trailing tidal de-bris according to the best-fitting models of Law & Majewski(2010a) in the right panel of Figure 1. We have already shownevidence (Casetti-Dinescu et al. 2006, 2008) that the overden-sities of faint, blue stars that are tightly clumped in propermotions in a few of these fields are likely made up of Sgrdebris. It was these apparent overdensities that guided ourtarget selection for spectroscopic follow-up. We began withspectroscopy from the Hydra multifiber spectrograph on theWIYN 3.5-m telescope; in most of the shallower fields of thissurvey, moderate-resolution spectra can be obtained with thisinstrument in a reasonable amount of observing time. For thedeep fields (and some of the shallower fields as well), we usedanother multi-object spectrograph, the Hectospec instrumenton the MMT 6.5-m, which allowed us to observe &
200 Sgr stream candidates simultaneously per setup down to faint ( g or V & .
5) magnitudes. We describe the observations anddata reduction for each instrument separately below.
Sample Selection
Targets for spectroscopic follow-up were selected to liewithin the locus of the suspected Sgr main sequence turnoff(MSTO) at faint ( g or V & .
5) magnitudes and blue ( g - r or B - V . .
8) colors. Casetti-Dinescu et al. (2006) showedthat the proper motions of these Sgr MSTO candidates clumpmore tightly than those of the predominantly nearby M-dwarfs at red colors. The tight clumping in the proper motionvector point diagram (VPD) of stars in the MSTO feature wasused to define a selection box in proper motion space whichshould contain any Sgr debris that is present in each field, andeliminate a good fraction of unrelated stars of similar colorand magnitude. Care was taken not to be too stringent witheither the proper motion or photometric criteria, to preserveas many potential Sgr stars in the wings of the distributionsas possible. Because the quality and depth of the photometryand proper motions varies between fields, different candidateselection criteria were adopted for each field.For WIYN+Hydra observations, only stars brighter than20th magnitude (either V or g , depending on whether a givenfield had SDSS photometry) were included in the multifibersetups, because fainter stars than this require rather long ex-posures with a 3.5-meter telescope to achieve adequate signal-to-noise for radial velocity measurement. After all availablefibers were filled with MSTO candidates the remaining fiberswere assigned to targets at relatively bright magnitudes ( . WIYN+Hydra Observations
Spectroscopic data were obtained during a total of eight ob-serving runs with the WIYN 3.5-m telescope between De-cember 2002 and November 2008. We used the Hydra multi-fiber spectrograph in two different setups. The first one (Dec.2002, Nov. 2003 observing runs) used the [email protected] gratingwith the red fiber cables and an order centered in the neigh-borhood of the Mg triplet (5170 Å) and covering about 980Å of the spectrum. This setup delivered a dispersion of 0.478Å pix - and a resolving power R ∼ ∼ λ = 4400–7200 Å at a dispersion of 1.397 Å pix - , for aspectral resolution of 3.35 Å ( R ∼ λ = 5200 Å). Thisspectral region was selected to include the H β , Mg triplet,Na D, and H α spectral features. Typically 60-70 targets wereplaced on Hydra fibers, with the remaining 15-20 fibers placedon blank sky regions to allow for accurate sky subtraction.Each of the 2005-6 datasets was obtained in less than optimalconditions, including substantial scattered moonlight in Dec.2005 and cloudy conditions in both 2006 runs. The major-ity of the 2007 and 2008 data were obtained under favorableconditions. We further note that the Nov. 2008 observing The WIYN Observatory is a joint facility of the University ofWisconsin-Madison, Indiana University, Yale University, and the NationalOptical Astronomy Observatory.
Carlin et al.
Table 2
Summary of Spectroscopic ObservationsSA Date Telescope/Instrument Exposures N stars Mag. limit(seconds) Dec 2002 WIYN+Hydra a c - Nov 2003 WIYN+Hydra a
10 x 1800, 4 x 1800 74 18-19- Dec 2005 WIYN+Hydra b b b b ... TOTAL .................... 50392 Oct 2006 WIYN+Hydra b d - - SDSS - 211 21.5 ... TOTAL .................... 25493 Oct 2006 WIYN+Hydra b d - Oct 2007 WIYN+Hydra b ... TOTAL .................... 29294 Oct 2007 WIYN+Hydra b d - Dec 2007 WIYN+Hydra b ... TOTAL .................... 432116 Oct 2007 WIYN+Hydra b d - Dec 2007 WIYN+Hydra b b ... TOTAL .................... 122117 Oct 2007 WIYN+Hydra b c - Dec 2007 WIYN+Hydra b ... TOTAL .................... 206 a These WIYN+Hydra observations used the [email protected] grating with the red fiber cables, centered at ∼ ∼ . b These WIYN+Hydra observations used the [email protected] grating with the red fiber cables, yielding spectra covering wavelengths from ∼ - ∼ .
35 Å resolution. c “Roughly calibrated” V magnitudes (see Casetti-Dinescu et al. 2006). d SDSS g magnitude. run occurred after the WIYN Bench Spectrograph Upgrade,which included the implementation of a new collimator intothe Bench configuration, as well as a new CCD that deliversgreatly increased throughput.Table 2 summarizes the observations. Each Hydra con-figuration was exposed multiple times (usually in sets of 30min. exposures) to enable cosmic ray removal. Standard pre-processing of the initial two-dimensional spectra used the CC-DRED package in IRAF. Frames were summed, then 1-Dspectra were extracted using the DOHYDRA multifiber datareduction utilities (also in IRAF). Dispersion solutions werefitted using 30–35 emission lines from CuAr arc lamp expo-sures taken at each Hydra configuration. On each observingrun we targeted a few bright radial velocity standards cover-ing spectral types from F through early K (both dwarfs andgiants), each through multiple fibers, to yield multiple in-dividual cross-correlation template spectra. These RV stan- IRAF is distributed by the National Optical Astronomy Observatory,which is operated by the Association of Universities for Research in Astron-omy (AURA) under cooperative agreement with the National Science Foun-dation. dard spectra were cross-correlated against each other usingthe IRAF tool FXCOR to determine the accuracy of the ve-locities and remove any outliers (i.e., those stellar spectra thatyield unreasonable cross-correlation results due to templatemismatch or some defect, such as a poorly-removed cosmicray, bad CCD column, or other unknown culprit). Measuredvelocities of the RV standards typically agreed with publishedIAU standard values to within 1-2 km s - . Radial velocitiesfor program stars were derived by cross-correlating all objectspectra against all of the standards taken on the same observ-ing run. To maximize the S / N in faint, metal-poor stars, only ∼
200 Å-wide regions centered on the H β , Mg triplet, and H α absorption lines were used for cross-correlation.Radial velocity uncertainties were derived using theVogt et al. (1995) method, as described in Muñoz et al.(2006a) and Frinchaboy et al. (2006). The Tonry-Davis ra-tio (TDR; Tonry & Davis 1979) scales with S / N , such thatindividual RV errors can be calculated directly from the TDR,provided you have multiple observations at varying S / N ofsome particular standard star to map the dependence. Wehave used this technique for all datasets except those frominematics of Sgr Tidal Debris in Kapteyn’s Selected Areas 9the Dec. 2006 observing run, when only a total of four RVstandard spectra were taken. For the SA 71 configuration ob-served on this run, the RV uncertainty for each stars is derivedas the standard deviation of the RV results from that star’sspectrum using cross-correlation against each of the four stan-dards. Typical RV uncertainties for individual measurementsfor all fields were σ V ≈ -
10 km s - , with most spectra hav-ing S / N ∼ S / N (essentially magnitude) for all stars from a single Hydrapointing; however, the varying exposure times between Hydrasetups and changing observing conditions mean that σ V is notstrictly a function of magnitude in our final catalogs. MMT+Hectospec Observations
To obtain spectra of fainter Sgr MSTO candidates, we weregranted three nights of queue-scheduled NOAO observingtime on the MMT 6.5-m. A total of six observing config-urations were observed with the 300-fiber Hectospec multi-fiber spectrograph (Fabricant et al. 2005) mounted at the f/5focus of the MMT. Targets were selected from among the ap-parent stellar overdensities of blue MSTO canidates at mag-nitudes too faint ( g &
20) to be reasonably observed withWIYN+Hydra, but using the same proper motion criteria usedto choose Hydra targets. In each of these configurations, a fewtargets previously observed with Hydra were included for aradial velocity consistency check, and any fibers unable to befilled with faint stars were assigned to brighter ( g <
20) SgrRGB candidates.We used the 270 gpm grating, centered at ∼ ∼ - (4.85 Å resolution). This low resolution al-lows us to obtain adequate signal-to-noise ( S / N &
10 per Å)spectra of stars as faint as g = 22 . g <
22 star at least 15 ′′ away, distributed throughout the fieldso that a number of them would fall within each of the twoCCD chips of the Hectospec system. The number of expo-sures in each field, each exposure time, the number of starswith measured radial velocities, and the limiting magnitudeof each spectroscopic field are given in Table 2.The Hectospec data were reduced using an external versionof the SAO “SPECROAD” reduction pipeline (Mink et al.2007) written by Juan Cabanela and called ESPECROAD. The pipeline automates many reduction steps, including bias-correction, flat-fielding, cosmic-ray rejection, fiber-to-fiberthroughput adjustments, and sky subtraction. Wavelength cal-ibration was performed manually using sets of three combinedHeNeAr calibration lamp exposures from each night of ob-serving.We derived RVs using the IRAF task FXCOR to cross- Observations reported here were obtained at the MMT Observatory,a joint facility of the Smithsonian Institution and the University of Ari-zona. MMT telescope time was granted by NOAO (proposal ID 2008B-0448), through the Telescope System Instrumentation Program (TSIP). TSIPis funded by the NSF. http://iparrizar.mnstate.edu/~juan/research/ESPECROAD/index.php correlate object spectra against fourteen template RV standardspectra of nine different stars ranging in spectral type fromF through K. We first correlated the standard spectra againsteach other, and found that our measurements agree with pub-lished RVs to within 4.9 km s - for all of these stars, withzero mean offset, and σ ∆ V = 3 . - . To minimize the ef-fects of noise for spectra with lower S / N , the cross-correlationwas restricted to the regions around the H α , Mg triplet, andH β lines.Each of the object spectra was cross-correlated against all14 standards, and the mean RV from each of these 14 mea-surements was adopted as the final result. For the queue-scheduled Hectospec observations, we relied on the queue toprovide radial velocity standards. We were thus unable to ob-tain repeated exposures of the same RV standard stars to allowus to use the “Vogt method” (as described in Section 2.3.2) todetermine RV errors. Instead, uncertainties were estimatedas the standard deviation of the 14 independent RV measure-ments thus derived, and vary (essentially as a function of S / N )from σ V helio ∼ - at g =18.0 to ∼
15 km s - at g = 21.5-22.From repeat measures of a handful of stars, including mul-tiple Hydra or Hectospec observations as well as many ob-served with both systems, we found mean systematic offsetsof < - between observing runs (including both Hydraand Hectospec data). These offsets were applied to all RVsfrom a given run to place all measurements on the same sys-tem as the Dec. 2007 WIYN+Hydra velocities.We also note that because we selected most Hectospec tar-gets to be faint, blue objects with miniscule proper motions,a large number of obvious QSOs and AGN spectra appearedin our data. These were added to the samples of QSOs andgalaxies that provided the fixed absolute proper motion framein each field, improving the zero points in these fields. SDSS spectra
We supplemented our database of radial velocities bymatching our proper motion catalogs to the SDSS spectro-scopic database. The number of additional RVs contributedby SDSS in each field is noted in Table 2. The majorityof SDSS stars are red, nearby M-dwarfs, so very few addi-tional Sagittarius candidates were contributed by the additionof these spectroscopic data. However, the handful of Sgr starsthat are present, as well as any other stars in common withour observations, were used for a consistency check. Fromthe stars in common between SDSS and our observations inSAs 94 and 93, we find mean offsets of ≤ - . The ac-curacies of SDSS radial velocities are ∼ - at g < ∼
15 km s - at g ∼
20 (Yanny et al. 2009a), sowe choose not to offset the RVs . SAGITTARIUS TIDAL DEBRIS KINEMATICS
Radial Velocities
Figure 4 shows all measured velocities in each of thesix survey fields (the total number of stellar radial veloci-ties in each field is given in Table 2) in the Galactocentric( V GSR15 ) frame. These consist of all RVs from WIYN+Hydra, From the Geneva Radial-Velocity Standard Stars at V GSR ≡ V helio + . b cos l + . b sin l + . b , where V helio isthe measured heliocentric radial velocity. This calculation assumes a circu-lar velocity of 220 km s - at the solar circle, and solar peculiar motion of( U , V , W ) = (9 . , . , .
0) km s - . Figure 4.
Measured radial velocities (relative to the Galactic Standard ofRest) in each of the six fields, displayed in order (from top to bottom) ofSgr longitude (i.e., angular distance from the Sgr core), Λ ⊙ . The prominentpeak in each field at V GSR ∼ -
100 km s - is made up primarily of Galacticstellar populations. In SAs 117, 93, 94, and 71, an additional peak at lowervelocities is visible. As shown in Section 3, this peak can be attributed to thepresence of Sgr tidal debris in these fields. MMT+Hectospec, and where available, SDSS. Where mul-tiple measurements exist, the final catalog reflects the error-weighted mean radial velocity. In each of these fields, a broadpeak is seen at V GSR ∼ -
100 km s - which is made up pri-marily of Milky Way stellar populations in these high-latitudefields. An additional velocity peak is evident in SAs 71, 94,93, and 117, well separated (in all fields except SA 117) fromthe Galactic distribution in each of these fields; it is this ad-ditional peak we shall show to consist of mainly Sagittariustrailing tidal debris. There is no readily apparent peak atlower V GSR values in SAs 92 and 116 – this arises for differ-ent reasons in the two cases. SA 116 is the field in which wehave the fewest measured radial velocities, and even the starsfor which we do have data are not optimally selected to findSgr debris. Because of limitations on exposure times due toweather, the observed stars were all at relatively bright mag-nitudes ( g < g &
19) magnitudesand blue colors will be necessary to identify Sgr debris amongthe SA 116 data. In SA 92, on the other hand, nearly twice asmany spectra are available than in SA 116, and mostly at rela-tively faint magnitudes. The paucity of obvious Sgr debris inthis field is because of the location of SA 92 on the peripheryof the stream, where Sgr stellar densities are rather low. Thereare a handful of stars at low ( V GSR < - ) velocities, buthardly enough candidates to assert that a clear Sgr presence isindicated in SA 92. To assess whether these apparent velocity overdensities areexpected among Galactic populations in each line of sight, wecompared the radial velocity distributions to those from theBesançon Galaxy model (Robin et al. 2003). In each SAfield, the model query was run five times to smooth out thefinite sampling statistics in each individual model run. Thefive catalogs were concatenated, then for each Kapteyn fieldthe measured velocities were compared to the expected ra-dial velocities of smooth Galactic populations by scaling thesummed Besançon model to match the total number of starsin the broad peak in each RV histogram. This was done sepa-rately for "bright" and "faint" samples in each field, since starsin different magnitude ranges preferentially sample differ-ent Galactic populations with different velocity distributions(e.g., “faint” blue Galactic stars in the region of the CMDwhere Sgr MSTO stars reside will be predominantly halostars, and thus have a much higher velocity dispersion thanstars of similar color, but much brighter magnitude, wherethin/thick disk MSTO stars predominate).The resulting scaled model distributions are shown as greyfilled histograms in Figure 5 for SAs 71 and 94, with the mea-sured heliocentric radial velocities given as solid-lined his-tograms. The broad peak is reproduced well by the modelpopulations, suggesting that (a) there are no large global ve-locity offsets present in our data, and (b) the prominent peaksare indeed due to foreground/background Milky Way stars.The additional peaks at V helio ≈ -
170 km s - (SA 71) and V helio ≈ -
150 km s - (SA 94) are clearly not due to any ex-pected Galactic populations along these lines of sight.Similar histograms are shown for SAs 93 and 117 in Fig-ure 6, which again clearly show that the broad, prominentpeak in each field is made up of Galactic populations, andthe peaks at V helio ≈ -
160 km s - (SA 93) and V helio ≈ - - (SA 117) are inconsistent with expected Milky Wayvelocities. Note that the peak in SA 117 overlaps the wingsof the Galactic distribution, making it slightly more difficultto isolate bona fide Sgr members in this field on the basis ofradial velocities alone.Finally, we performed the same examination in SAs 92 and116, with the results shown in Figure 7. Nearly all of the ve-locities shown in SA 92 are from the SDSS database, and arepredominantly very red M-dwarfs. For this reason, the longtail of the RV distribution at negative velocities, which is dueto thick disk and halo MSTO stars, is not well reproduced byour data set. There are a small number of stars at Sgr-like ve-locities in Figure 7, but these fall within the expected locusof MW stars, so we cannot definitively say that Sgr membersare present among our SA 92 sample. In SA 116, no excesspeak of measured RVs relative to the model predictions is ap-parent. This is not surprising given (a) the caveats in the firstparagraph of this section regarding the data in SA 116, and(b) the fact that the Law & Majewski (2010a) model predictsSgr debris in this field to have RVs of - . V helio . -
50 kms - , overlapping the wings of the Galactic distribution in thisfield. A handful of Sgr members may thus be present amongour velocities, but they are difficult to distinguish from theMilky Way halo stars by their RVs.With RVs in hand, a next culling for Sgr stream candidateswas obtained by simply taking all stars within a generouslydefined range around the evident associated radial velocitypeak. Such a selection will include a few Milky Way inter- Model query available at http://model.obs-besancon.fr/. inematics of Sgr Tidal Debris in Kapteyn’s Selected Areas 11
Figure 5.
Measured heliocentric radial velocities (solid-line histograms) in SAs 71 (left) and 94 (right), divided into a bright (SA 71: V < .
0; SA 94: g < . V > .
0; SA 94: g > .
5) group (lower panels). The filled gray histogram in each panel is made up of Besançonmodel points along the corresponding line of sight in the same magnitude ranges as the data histograms, scaled to contain the same total number of stars between - < V helio <
100 km s - as the observed data. In the lower panels, a Gaussian representing the best-fitting radial velocity and dispersion of Sgr candidates isshown (dotted curve), along with the sum of this Gaussian and the Besançon distribution (dot-dashed histogram). These two fields include 4-meter plates in theproper motion derivation, and thus contain the deepest proper motions (and the most Sgr candidates) of any fields in the survey. Very little, if any, Sgr debris isevident in the bright samples. Figure 6.
Same as Figure 5, but for SAs 93 (left) and 117 (right), and with slightly different definitions of the bright (SA 93: g < .
0; SA 117: V < . g > .
0; SA 117: V > .
0) group (lower panels). In both of these fields, there is a hint of a peak at Sgr-like velocitiesin the bright samples, suggesting that a few Sgr red giants may have been identified in these fields. lopers, so we examined the samples thus selected to removenon-Sgr stars. We first removed all stars with proper motions | µ | >
10 mas yr - in either dimension; such stars, if actuallyat the distance of the Sgr trailing tail in this region of sky( ∼ > - ) tangential velocities ( V tan = 4 . d µ km s - , where d is thedistance in kpc and µ the proper motion in mas yr - ). Faint,blue stars with proper motions of this magnitude must there-fore be nearby (foreground) MW white dwarfs or metal-poorsubdwarfs. After removing these stars, we then examine thepositions of all selected candidates in the color-magnitude di-agram. We reject faint stars that are well redward of the read- ily apparent Sgr main sequence, and at brighter magnitudes,we remove only stars at positions obviously inconsistent withbeing Sgr red giants or horizontal branch stars. In SA 93,a clear offset was visible between mean proper motions ofbright ( g < .
0) Sgr candidates and fainter ones, so we choseto keep only candidates at g > .
0, on the assumption that thedensity of stream stars should be much greater at fainter mag-nitudes near the lower RGB and MSTO than along the upperRGB. This yields fewer total Sgr candidates, but the ones thatremain have much higher probability of being Sgr membersthan do the brighter candidates.2 Carlin et al.
Figure 7.
Same as Figure 5, but for SAs 92 (left) and 116 (right), and with slightly different definitions of the bright (SA 92: g < .
0; SA 116: g < .
5) sample(upper panels) and faint (SA 93: g > .
0; SA 117: g > .
5) group (lower panels). No excess peak is evident (relative to the Besançon predictions) in either ofthese fields, meaning we have likely sampled very few Sgr radial velocity members along these lines of sight.
Figure 8.
SDSS g vs. g - r CMDs of SA 94; the left panel shows all objects inour proper motion catalog that were flagged as stars by the SDSS star/galaxyseparator. The right panel overplots all stars observed spectroscopically aslarger symbols: candidates within the initial RV selection are black squares(filled squares: final Sgr candidates; open squares: in RV selection, but re-moved by other criteria), open diamonds are stars with RVs outside the SgrRV selection, and open circles are stars that only have RVs in SDSS (notethat none of these ended up being selected as Sgr candidates). The final Sgrcandidates that we selected by RV, proper motion, and color-magnitude po-sition (filled squares) are concentrated around a likely MSTO of Sgr debris.The blue curve is a Girardi et al. (2004) isochrone for a 10 Gyr population at[Fe/H] = -1.3 and a distance of 30 kpc.
Selecting Final Sgr Candidates
We now discuss how we pared down the samples of Sgrcandidates from the initial broad RV and proper motion selec-tions in each field to the final, more securely-identified sam-ples used for analysis. For brevity, we will show detailed ex-amples for only two of the six fields in the study. The firstof these is SA 94, which is the "best-case" field in our study,because it has deep proper motions due to the availability of4-meter plates in its data set. For comparison, we follow theSA 94 discussion with details of SA 93, which has a muchshallower proper motion catalog than SA 94, but also hashigh-quality SDSS photometry. These two fields were cho-sen simply to give the reader an idea of the type and quality
Figure 9.
Proper motion vector point diagram of SA 94, with panels andsymbols as in Figure 8.
Figure 10.
Reduced proper motion diagram (RPMD) for SA 94, where H g ≡ g + µ +
5, with µ in arcsec yr - . Panels and symbols are as in Figure 8.The blue curve is a Girardi et al. (2004) isochrone for a 10 Gyr population at[Fe/H] = -1.3 and a distance of 30 kpc, with the measured mean proper motionof Sgr debris in SA 94 ( µ tot =2.34 mas yr - ) used to convert to reduced propermotion. of the data included in this study, and the process we followedto select Sgr candidates.inematics of Sgr Tidal Debris in Kapteyn’s Selected Areas 13 Selecting Sgr Candidates in SA 94
Figure 8 shows the SDSS g - r vs. g color-magnitude di-agram (CMD) for SA 94. The left panel shows all starsfor which we have measured proper motions, with SDSS-classified galaxies removed from the sample. On the right-hand side, open squares depict all stars observed spectro-scopically to illustrate the candidate selection. The major-ity of spectroscopic targets in this deep proper-motion fieldwere selected from the Sgr MSTO feature of faint, blue stars,and observed with the large-aperture MMT 6.5-m telescope.The remaining targets are either (a) bright stars observed withWIYN+Hydra, or (b) targets chosen to fill unused fibers af-ter all possible MSTO candidates had been assigned. Thefinal culled sample of Sgr candidates (based initially on RVselection, with further interactive proper-motion and CMD se-lection performed as discussed below) is shown by the large,filled black squares. As expected, these concentrate at theSgr MSTO locus, with a handful of brighter stars havingproperties consistent with Sgr membership as RGB or redclump stars. We have overlaid an isochrone from Girardi et al.(2004) for an old (10 Gyr), metal-poor ([Fe/H] = -1.3) popula-tion at the expected distance (d = 29.5 kpc; Law & Majewski2010a) of Sgr debris in SA 94; the age and metallicity of thisisochrone is chosen to match the Sgr metal-poor populationidentified by Siegel et al. (2007), which should be the dom-inant contributor to debris in this portion of the trailing tail.The final set of Sgr candidates in this field concentrate nearthis ridgeline; most of the scatter about the isochrone is likelydue to the ± H g ≡ g + µ +
5, where g is the apparent magnitude and µ is the total proper motion in arcsec yr - , compresses starswith common tangential velocity into coherent features in theRPMD. Thus, a common-motion population should form asequence in the RPMD, even if the population has a signifi-cant line-of-sight depth (see Majewski 1999, especially Fig-ure 4). In Figure 10 we show such a diagram for SA 94, withthe same isochrone as in Figure 8, shifted to the measuredtangential velocity of SA 94 Sgr debris (to be discussed inSection 3.3). After an initial calculation of the mean motion,candidates that were obviously inconsistent with a broadly-defined region ( & H g and/or g - r ) about theridgeline were manually removed from the sample. Selecting Sgr Candidates in SA 93
SA 94 is one of only two fields (with SA 71) of the sixin this study that have KPNO 4-m plates, and thus have 1-1.5magnitude deeper proper motions. Furthermore, of those two,SA 94 has higher-quality photometry (from SDSS) than thephotographic magnitudes used for SA 71. Thus SA 94 is ourbest field in terms of overall data quality. To illustrate how amore typical field compares to the highest-quality SA 94 data,we show in Figures 11, 12, and 13 the same type of plots as inFigures 8, 9, and 10, but for SA 93. This field is located in ahigh stellar density region of the stream, as is SA 94, but has
Figure 11.
SDSS g vs. g - r CMDs of SA 93, with panels and symbols thesame as in Figure 8. Because the proper motion catalog in this field doesn’treach nearly as faint stars as in SA 94, far fewer Sgr candidates have beenidentified among our radial velocities. Note also that for reasons discussedin the text, only stars with g > . ∼ Figure 12.
Proper motion vector point diagram of SA 93, with panels andsymbols as in Figure 8.
Figure 13.
Reduced proper motion diagram (RPMD) for SA 93, where H g ≡ g + µ +
5, with µ in arcsec yr - . Panels and symbols are as in Figure 8.The blue curve is a Girardi et al. (2004) isochrone for a 10 Gyr population at[Fe/H] = -1.3 and a distance of 28 kpc, with the measured mean proper motionof Sgr debris in SA 93 ( µ tot =2.69 mas yr - ) used to convert to reduced propermotion. shallower proper motion data (see Fig. 3), providing far fewer4 Carlin et al. Figure 14.
Proper motions of only the final Sgr candidates in SAs 94 (leftpanel) and 93 (right panel), with individual error bars. In SA 93, a propermotion offset was apparent between faint ( g > .
0) candidates and brighterSgr candidates; for this reason, only the faint candidates were retained. Thered asterisks represent the final maximum likelihood estimate of the meanSgr debris motion in each field.
Sgr MSTO candidates for follow-up spectroscopy. Becausethe available proper-motion data do not sample the MSTO asrobustly as in SA 94, this field was given lower priority forspectroscopy, with only one relatively short MMT+Hectospecconfiguration observed (see Table 2). However, in this oneHectospec setup, nearly all available g . . d = 28 kpc) of Sgrdebris in SA 93 (blue curve in Figure 11) is seemingly con-sistent with all but the brightest of the identified candidates.We have also overplotted (dashed gray curve) an older ( ∼ The RPMD (Figure 13) for SA 93 showsthe same ridgeline as in the CMD, shifted by the final mea-sured tangential velocity for the Sgr candidates. Because theuncertainty in the mean proper motion is much larger in thisfield than in SA 94 (on the order of ∼
100 km s - in tangen-tial velocity for SA 93, compared to ∼
50 km s - in SA 94),it is difficult to conclude much from the RPMD. The benefitsof the additional 4-meter plates in SAs 94 and 71 are clearlyillustrated by the relatively fewer identified Sgr stream mem-bers in the shallower SA 93 field compared to the deeper datasets. Zoomed-in versions of the VPDs for SAs 94 and 93 aregiven in Figure 14, with error bars shown on all points to il-lustrate the quality of the proper-motion data (note that theerror bars on individual stars in each of the panels of Fig. 14are of comparable size, in spite of the higher-quality propermotion data in SA 94 than in SA 93, because the majority ofSgr candidates in SA 94 are faint [ g >
21] MSTO candidates,while SA 93 candidates are mostly > g > .
0) stars in SA 93 and brightercandidates; we included only the faint ( g > .
0) stars in ourproper motion measurement, because these are more likely tobe true Sgr members. The maximum likelihood estimate of Note that we are not suggesting that Sgr has stars 15.8 Gyr old – thisisochrone is simply meant as a guide to show that these stars could plausiblybe BHB stars associated with Sgr. A blue horizontal branch is only seenin the oldest (log(age) > 10.15) of the Girardi et al. 2004 isochrones at thismetallicity. the absolute proper motion of Sgr debris in each field is rep-resented by the large red asterisks, which have 1 σ uncertaintysmaller than the size of the point. Summary of Sgr Candidate Selection
In summary, the basic Sgr candidate selection in each Se-lected Area began with a broad RV selection centered on theapparent Sgr velocity peak (e.g., - < V hel < -
100 km s - inSAs 94 and 93). This was followed by removing high propermotion stars ( | µ | >
10 mas yr - in either dimension), whichwould have tangential velocities much greater than the MilkyWay escape velocity if those stars were at the 25-40 kpc dis-tances of Sgr debris along the SA lines of sight. We then usedour knowledge of the distance and metallicity expected forSgr debris in these fields to remove stars at faint magnitudesthat are more than ∼ . > σ ) in proper motion. Finally, we manually inspected theremaining candidates to remove any stars that were ∼ - σ outliers from the identified Sgr locus in all observables (i.e.,RV, g - r color, magnitude, and proper motion).Once Sgr candidates were selected using color, magnitude,RV, proper motion, and RPMD criteria, the kinematical prop-erties of Sgr debris in each SA field were estimated usinga maximum likelihood method (e.g., Pryor & Meylan 1993;Hargreaves et al. 1994; Kleyna et al. 2002). The final mea-sured radial velocities and velocity dispersions, along withuncertainties in these values, are given in Table 3 in both theheliocentric and Galactocentric (GSR) frames. The estimatesof the mean radial velocity (in the GSR frame) of Sgr de-bris can be seen in the top panels of Figure 15, which over-lays our measurements atop the best-fitting debris model ofLaw & Majewski (2010a). The colors in the figure were cho-sen to match those used by Law & Majewski (2010a), whocolor-coded points along the stream according to the orbitalpassage on which they became unbound. Gold points corre-spond to debris stripped during the two most recent perigalac-tic passages, and magenta during the previous two passages.This portion of the trailing tail has a well-constrained radialvelocity trend, which was measured by Majewski et al. (2004)and Monaco et al. (2007), and was one of the constraints onthe Law & Majewski (2010a) models. Sgr model trailing taildebris within ± . ◦ of the position of each Kapteyn line ofsight is shown in the right-hand panels of Figure 15 as smallopen squares. This illustrates that not only do our measuredradial velocities agree quite well with the model, but that thedispersion in each field appears to match the distribution ofmodel points. However, we caution that the velocity disper-sions we find (see Table 3) are higher than those derived byMajewski et al. (2004) and Monaco et al. (2007) for the trail-ing tail. It is unclear whether the dispersion is truly intrinsi-cally higher for Sgr trailing tail MSTO populations we sam-pled than for the M giants previously studied, or whether ourderived dispersions are inflated by the large measurement un-certainties for our RVs, velocity zero-point offsets betweenthe many data sets we have combined, or Milky Way fore-ground/background contamination in our Sgr candidate sam-ples. While we have endeavored to account for all of thesefactors, a robust conclusion likely requires high-resolutioninematics of Sgr Tidal Debris in Kapteyn’s Selected Areas 15spectra of trailing-tail MSTO stars. Proper Motions
With the sample of Sgr debris candidates identified in eachfield, we used a maximum-likelihood method to estimatethe Sgr absolute proper motions in both spatial directions( µ α cos( δ ), µ δ ). These results are seen in Table 3 with theiruncertainties, which include the uncertainty in the proper mo-tion zero point in each field added in quadrature to the max-imum likelihood error estimate. The uncertainties for eachfield depend on many factors, including the depth and qualityof the plates, the number of available reference objects (i.e.,background QSOs and galaxies) used to convert from relativeto absolute proper motions, the number and depth of spec-troscopic targets obtained (and thus the number of Sgr candi-dates identified), and the position of each field relative to thehighest-density regions of the stream (i.e., the number of Sgrcandidates expected in each field).Mean proper motions along Galactic coordinates (i.e., µ l cos b , µ b ) in each field are compared to the model ofLaw & Majewski (2010a) as a function of Λ ⊙ in the middleand lower panels of Figure 15, with points once again color-coded by the orbital passage in which they became unbound,and model points within ± . ◦ of each SA line of sight high-lighted for guidance. The results for SAs 94, 93, and 117agree nicely with the model predictions within the uncertain-ties in µ b , but show a ∼ - σ offset from the main trendin µ l cos( b ) (left middle panel). The mean proper motionsalong both directions for SA 71 (the leftmost data points inFigure 15) are slightly shifted (by ∼ - . σ ) from the meanof the model prediction for this field. A number of factorscontribute to the difficulty in selecting a "pure" sample of Sgrdebris in SA 71, and there is thus an additional uncertainty(besides the formal errors) in the mean Sgr debris proper mo-tions in this field. First, this field is at somewhat low lati-tude ( b = - . ◦ ), and thus suffers greater contamination fromGalactic populations, as evidenced by the extended tail oflow-velocity stars in the lower panel of Figure 5. This lowerlatitude also means that SA 71 suffers significantly more red-dening than higher-latitude fields – nearly 0.6 magnitudes ofextinction using the Schlegel et al. (1998) maps. Secondly,the distance of Sgr debris increases with Λ ⊙ along the por-tion of the trailing tail in this study, so that stream membersin SA 71 are nearly 40 kpc away, making them fainter than inthe other fields. Finally, the poor-quality photographic pho-tometry we are limited to in this field renders inscrutable thetypical CMD features such as the blue edge of the Galacticdisk MSTO and the Sgr upper main sequence.Assuming distances to Sgr debris in each field as given inTable 3 and values of V circ = 220 km s - and R = 8.0 kpc,we converted the measured Sgr debris motions to Galacto-centric UVW GC velocities (i.e., Cartesian velocities such thatthe Sun is moving at 9.0, 232.0, 7.0 km s - assuming V circ = 220 km s - and ( U , V , W ) = (9.0, 12.0, 7.0) km s - (Mihalas & Binney 1981) for the solar motion relative to theLocal Standard of Rest; to facilitate direct comparison, valuesused for these constants are the same as those in the LM10model), which are shown in Table 3 (note that we placed SAs92 and 116 – the two fields with no securely identified Sgrmembers – in a separate section in Table 3. These data aregiven for completeness, but are not used for subsequent anal-ysis.). The U GC component should dominate the total spacevelocity of Sgr debris in each of these trailing arm fields. This can be surmised from Figure 2, which shows that the mo-tion of the Sgr trailing tail is oriented almost parallel to theGalactic X -axis in the X GC - Z GC plane. This, in addition tothe fact that the Sagittarius orbital plane is only slightly mis-aligned with the Galactic X GC - Z GC plane (Majewski et al.2003, 2006), suggests that most of the motion in this partof the trailing tail is inward toward the Galactic center androughly parallel to the Galactic disk (i.e., the X GC - Y GC plane)at a distance of ∼ UVW GC velocities in our SA fields – the U GC component in the four fields with quality measurementsis by far the largest component of the 3-D motion. This canbe seen even more clearly by considering the proper motionsalong Galactic coordinates, but in a Galactic rest frame (des-ignated as µ ′ l cos(b) and µ ′ b ). These proper motions, givenin Table 4, show µ ′ l cos(b) proper motions of nearly zero ineach field – as expected for streaming motions confined to the X GC - Z GC -plane. As we will show in Section 4, the offsetof these derived longitudinal proper motions (reflected in the V GC Galactic velocity component) from zero can be used toreevaluate the velocity of the Local Standard of Rest (underthe assumption that the longitudinal motions should be zero). CONSTRAINTS ON MILKY WAY STUCTURE
As discussed in Section 1.1, the opportune orientation ofthe Sgr trailing tidal tail means that the observed motion oftidal stream stars in the Galactic Y direction (i.e., towards[ l , b ] = [90 ◦ , ◦ ]) is dominated by the solar reflex motion,which consists of the solar peculiar motion and the Galacticrotational motion at the solar circle (i.e., the Local Standardof Rest Θ LSR ). As shown by Majewski et al. (2006), the in-trinsic motion of Sgr debris along the Y direction ( V GC , con-tained primarily in the µ l cos(b) component of proper motion)varies only slowly across the region of the trailing tail be-tween 70 ◦ ≤ Λ ⊙ ≤ ◦ , making the fields of view in whichwe have deep proper motion data ideal for constraining Θ LSR .It can be seen in Table 3 that V GC for Sgr debris in each ofthe four fields (SAs 71, 94, 93, and 117) with reliable data isnon-zero at the ∼ σ level. Setting aside SA 71, in which itis difficult to securely identify Sgr debris, the remaining threefields exhibit V GC systematically offset to negative values. Ifindeed the expected V GC for Sgr debris in these fields is zero,this suggests that the value of Θ LSR that was subtracted fromthe V -component of these velocities was lower than it shouldbe – i.e., Θ LSR should be greater than the canonical 220 kms - .In this section, we use variations on the LM10 numericalmodel of the Sgr tidal stream to isolate the contribution to µ l cos(b) from the solar reflex motion and identify the valueof Θ LSR favored by our proper motion data.
N-body models
Though the measured Galactic Cartesian V - velocity (i.e.,motion along the Galactic Y -component) of Sgr trailing tidaldebris is dominated by Solar reflex motion, there is some con-tribution of intrinsic Sgr motion to the V - component of debrisvelocities. In particular, we must consider the following ef-fects when trying to back out Θ LSR from measured V GC forSgr debris: (1) the slight inclination of the Sgr debris plane tothe Galactic XZ GC plane means a small fraction of Sgr spacemotion is projected onto the measured motions (i.e., the V velocity is in fact a function of both Θ LSR and intrinsic Sgrmotion); (2) the Galactic Standard of Rest (GSR) frame ra-dial velocities used to constrain the Sgr model were derived6 Carlin et al.
Table 3
Sagittarius Stream Kinematics in Kapteyn Selected AreasSA
N V helio V GSR σ µ α cos( δ ) µ δ µ l cos(b) µ b U GC V GC W GC distancekm s - km s - km s - mas yr - mas yr - mas yr - mas yr - km s - km s - km s - kpc71 33 -172.9 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Note . — All calculations assume V circ = 220 km s - at R = 8.0 kpc. We used the solar peculiar motion of Mihalas & Binney (1981): ( U , V , W ) = (9.0, 12.0, 7.0) km s - (in a right-handed frame). Figure 15.
Kinematics of Sgr candidate stars measured in four SA fields (SAs 71, 94, 93, and 117, from left to right) as a function of longitude in the Sgrcoordinate system defined by Majewski et al. (2003). From top to bottom, the panels depict GSR-frame radial velocity ( V GSR ), proper motion along Galacticlongitude ( µ l cos b), and proper motion along latitude ( µ b ). Colored points depict trailing tail debris from the best-fit Sagittarius model of Law & Majewski(2010a), with different colors representing debris stripped on successive orbits, as in Law & Majewski (2010a). In each row, the right-hand panels depict starsselected from the model to be within ± ◦ of each of the SA fields as small black squares; these are the points to which we compare the measured kinematicsin each field. In the left panels, large open diamonds with error bars represent the maximum likelihood estimates of the mean kinematics of Sgr debris. Notethat it is important to compare measured kinematics (on the left) to the "clouds" of small black squares in corresponding fields in the right panels, rather thancomparing to the trend defined by all of the colored points. This is necessary because at a given Λ ⊙ , the model debris plotted here can come from a large area onthe sky. We are interested in comparing only what the model predicts "should be" seen in each pencil-beam field of view, and thus we select only model debris incorresponding regions of the sky. The measured V GSR for Sgr debris matches the model very well in all four fields, and the µ b proper motions agree in three ofthe four fields (see the text for discussion of the difficulties in selecting Sgr debris in SA 71, the ∼ σ discrepant point furthest to the left). In µ l cos b, however,the measurements for all but one field (again, SA 71) are systematically offset to higher proper motions than predicted by the model. We show that this offset canbe accounted for by an upward revision of Θ LSR , the rotation speed at the Solar circle. assuming a value of Θ LSR ; (3) changing Θ LSR correspond-ingly changes the Milky Way mass scale, which thus affectsthe space velocity of the Sgr dSph in the models. Therefore,taking into account these dependencies on the assumed valueof Θ LSR , we repeat the LM10 analysis, changing Θ LSR to con-struct self-consistent models for the Sgr tidal stream in eachof four choices for the Local Standard of Rest speed, namely Θ LSR = 190 , , ,
310 km s - (in addition to the originalLM10 value of Θ LSR = 220 km s - used in earlier sections ofthis paper). Our methodology is described in detail by LM10. In brief,we constrain the model Sgr dwarf to lie at the observed loca-tion ( l , b ) = (5 . ◦ , - . ◦ ), distance D Sgr = 28 kpc (Siegel et al.2011, Siegel et al. 2007), and radial velocity v Sgr = 142 . - in the heliocentric frame. The orbital plane is constrainedto be that defined by the trailing arm tidal debris, whichhas experienced minimal angular precession (Johnston et al.2005), and the speed of Sgr tangential to the line of sight ( v tan ;see Section 3.3 of LM10) is constrained by a χ minimizationfit to the radial velocities of trailing arm tidal debris. We fixinematics of Sgr Tidal Debris in Kapteyn’s Selected Areas 17 Table 4
Galactic Frame-of-Rest Proper Motions of Sagittarius Debris in SelectedAreasSA V GSR µ ′ α cos( δ ) µ ′ δ µ ′ l cos(b) µ ′ b (km s - ) (mas yr - ) (mas yr - ) (mas yr - ) (mas yr - )71 -141.4 -0.47 0.39 -0.61 0.0094 -141.3 -0.77 -1.09 0.22 -1.3193 -114.1 -0.71 -1.36 0.00 -1.54117 -69.3 -1.17 -1.57 -0.44 -1.91 a All calculations assume V circ = 220 km s - at R = 8.0 kpc, and solar pe-culiar motion of ( U , V , W ) = (9.0, 12.0, 7.0) km s - (in a right-handedframe). Table 5
Masses of Galactic Bulge and Disk Components in the Sagittarius Models Θ LSR M disk M bulge α (km s - ) ( M ⊙ ) ( M ⊙ ) -190 6 . × . × . × . × . × . × . × . × . × . × . × . × . × . × a The mass of the disk and bulge components in each of the models of theSgr stream. Each model is specified by the value of Θ LSR that constrainedthe fit; the 220 km s - model is that of LM10. The ratio of disk to bulgemass is constant throughout – the constant α is the scaling factor, such that M disk = α ∗ M disk , / s and M bulge = α ∗ M bulge , / s . The total mass, axisratios, and scale length of the Galactic dark matter halo were fixed to thebest-fit values of LM10. the mass and radial scalelength of the Sgr progenitor so thatthe fractional mass loss history of the dwarf is similar in allmodels to that of LM10.The adopted Milky Way Galactic mass model consists ofthree components: a Hernquist spheroid (representing theGalactic bulge), a Miyamoto & Nagai (1975) disk, and a log-arithmic dark matter halo. The Local Standard of Rest in thismodel is given by: Θ LSR = p R ⊙ ( a bulge + a disk + a halo ) (1)where a bulge , a disk , and a halo respectively represent the grav-itational acceleration exerted on a unit-mass at the locationof the Sun due to the Galactic bulge, disk, and halo compo-nents. In the LM10 model (for which Θ LSR = 220 km s - ),the bulge/disk/halo respectively contribute 32%/49%/19% ofthe total centripetal acceleration at the position of the Sun,corresponding to bulge/disk masses M bulge = 3 . × M ⊙ and M disk = 1 . × M ⊙ , and a total mass within 50 kpc of4 . × M ⊙ .Since the baryonic Galactic disk and bulge components arethe dominant factors in determining Θ LSR (together compris-ing >
80% of the total centripetal force), we therefore scalethe total bulge + disk mass as necessary to normalize the rota-tion curve at the solar circle ( R ⊙ = 8 kpc) to the chosen valueof Θ LSR . The masses of the disk and bulge components ineach of the models are given in Table 5. We leave the ra- tio of bulge/disk mass fixed in order to preserve the shape ofthe rotation curve interior to the solar circle. In addition, wefix the Galactic dark matter halo parameters (mass, axis ra-tios, and scalelength) to the best-fit values derived by LM10since these authors found that these values were relatively in-sensitive to factors of ∼ Results
Constraints on Θ LSR were derived in two ways. In the firstof these methods, we assumed (as argued previously in thispaper, as well as in MLPP) that the dominant contribution tothe measured µ l cos(b) component of Sgr motion is due to thesolar rotation, and that the largest component of Θ LSR is along µ l cos(b). We have shown that these are reasonable first-orderassumptions, and thus use only the longitudinal proper mo-tions as constraints on fitting Θ LSR in our first attempt. Afterdoing so, however, we performed a similar analysis, but us-ing all three dimensions of Sgr debris motions as constraintsto determine Θ LSR . In the following, we present both results,which come out somewhat different from each other (thoughconsistent within 1 σ ). Fits using only µ l cos(b) tend to preferrelatively high values of Θ LSR , while those constrained by full3-D kinematics tend toward lower values more in line with theIAU standard of 220 km s - . Θ LSR
Constraints Using Only µ l cos( b) Motions of SgrDebris We quantify the agreement of our proper motions withthose of simulated Sgr tidal debris from each of our grid ofmodels using a χ statistic. The χ fitting was performedusing mean Sgr debris proper motions in only SAs 71, 94,93, and 117 – as discussed in Section 3.1, the results in SAs92 and 116 are unreliable for a variety of reasons. For ourmodel comparison, we first select all LM10 Sgr model pointswithin ± . ◦ in both Λ ⊙ and ( α, δ ) of each SA field. Thelarge area (relative to the 40 ′ × ′ coverage of each SA field)used to select model debris corresponding to each SA positionensures that enough N - body particles are selected for robustmeasurement of model debris motions at each position. Thisalso makes the fitting less sensitive to small-scale differencesin positions and densities of debris stars between the mod-els and the actual stream that arise due to the vagaries of themodeling and our incomplete knowledge of the Sgr trailingtail properties. Figure 16 shows the model debris µ l cos(b) asa function of Λ ⊙ for each of the five Sgr simulations, withpoints corresponding to each SA field shown as small opengray squares. It is clear that µ l cos(b) changes very little overthe 6 ◦ ranges in ( α, δ ) used. Furthermore, the small number ofselected model points, even in such a large selection region,shows that these broad selection criteria are necessary to havesufficient model points for comparison. The maximum like-lihood proper motion results in SAs 71, 94, 93, and 117 areshown in Figure 16 as open black diamonds, with error barsreflecting 1 σ uncertainties. It can be seen in the figure that themodels with Θ LSR >
220 km s - tend to reproduce the longi-tudinal proper motions for most of the fields better than thestandard 220 km s - value of this fundamental constant. Notethat SA 71, at Λ ⊙ = 128 ◦ , is the exception to this trend – asdiscussed in Section 3.3, identifying bona fide Sgr debris inthis field is more difficult than the others and so these data aremore suspect.Each of the Sgr model simulations provides predicted kine-matics of Sgr debris for a Galactic potential constrained by a8 Carlin et al. Figure 16.
Mean longitudinal proper motions, µ l cos(b) (large open diamonds with error bars), in (from left to right) SAs 71, 94, 93, and 117 as a function of Λ ⊙ . Model debris from the Sgr simulations are shown as the colored points; from top to bottom, these represent models with Θ LSR = 310, 280, 250, 220, and190 km s - . The sudden drop in µ l cos(b) for Λ ⊙ . ◦ is due to the inversion in sign that occurs as the debris sweeps past the South Galactic pole. Small opengray squares denote the model debris corresponding (within ± ◦ in RA, Dec, and Λ ⊙ ) to each SA field. It is clear that higher values of Θ LSR provide a bettermatch of the small grey squares to the observed µ l cos(b) values in the Selected Areas (diamonds). given value of Θ LSR . As discussed previously, the Galactic V -component of the Sgr debris space velocity along the trailingtail contains little contribution due to the Sgr motion; nearlyall the V velocity (as measured by the µ l cos(b) componentof the proper motion) is reflected Solar motion. Thus, to firstorder, we can simply compare our mean Sgr proper motionsalong Galactic longitude in the trailing tidal tail to our modelsof Sgr debris for different values of Θ LSR and determine thevalue of Θ LSR that best reproduces the measured PMs. To doso, we defined a χ residual: χ µ = X i µ l , SA [i] - µ l , mod [i] σ µ l , SA [i] (2)where µ l , SA [i] represents the mean µ l cos(b) proper motionin each of the four SA fields, and µ l , mod [i] the mean propermotion of the corresponding model debris for each field. The residuals are weighted by the uncertainty, σ µ l , SA[i] , ineach SA proper motion. This χ statistic was initially cal-culated for the proper motions presented in Table 3 rela-tive to each of the five Sgr debris models (corresponding to Θ LSR = 190 , , , ,
310 km s - ). Rather than runningnew (and laborious) N -body simulations for many interme-diate values of Θ LSR and calculating χ for each of them,we choose to find the minimum χ by fitting a parabola tothe χ results for each of the five modeled values of Θ LSR .The results of the χ calculation and the parabolic fit are seenin Figure 17 for the proper motions of the “best” SA sam-ples given in Table 3. The minimum of the parabola yields Θ LSR , min = 270 . - .To estimate the uncertainty in Θ LSR , we choose a bootstrap(resampling with replacement) method (see Andrae 2010 andreferences therein). This technique uses the entire sample ofinematics of Sgr Tidal Debris in Kapteyn’s Selected Areas 19individual Sgr candidate star proper motions, and thus yieldsan estimate of the errors in Θ LSR including the effects ofproper motion measurement errors and "contamination" ofthe proper-motion samples by Milky Way stars. Our selectedsamples of Sgr candidates in SAs 71, 94, 93, and 117 shouldcontain mostly Sgr debris, plus some amount of contamina-tion by MW stars that will vary depending on the depth ofthe proper-motion and radial-velocity catalogs, the local Sgrstream density, and the Galactic latitude of each field. Fromthe Sgr samples in each field, we performed 100,000 boot-strap resamplings, wherein N random selections were madefrom the N original stars in each field (i.e., the catalogs ofcandidates were resampled with replacement). Iteratively 3 σ -clipped mean proper motions of these resampled Sgr candi-dates were measured, and the mean proper motions used in anidentical χ fitting routine to that described above. Assum-ing that the contaminants in each sample are somewhat uni-formly distributed in their kinematical quantities, this methodshould yield a statistically robust result for Θ LSR and its un-certainty (due to both the intrinsic measurement errors and theMW contamination). The best-fitting values of Θ LSR for these100,000 samples are given as a histogram in the left panel ofFigure 18, along with a Gaussian fit (red curve) to the results.From this Gaussian, we derive a final value of Θ LSR = 264 ± - . Θ LSR
Constraints Using Three-Dimensional Motions of SgrDebris
The constraints we derived on Θ LSR using only the longi-tudinal proper motions assume that the contributions of Θ LSR to µ b and V GSR are negligible. If the Sgr orbital plane wasexactly coincident with the Galactic XZ GC plane, then indeedthe rotation velocity at the solar circle would only be reflectedin the µ l cos(b) motions. In reality, the Sgr orbital plane is not perfectly aligned with the Milky Way XZ -plane, so there issome projection of V circ onto µ b and V GSR . In fact, for Sgr de-bris in the four fields of view comprising this study (SAs 71,94, 93, and 117), only (75%, 87%, 61%, 58%, respectively) ofthe total value of Θ LSR is projected onto µ l cos(b). We ran the χ fitting again, but this time including all three dimensionsof the motion as constraints. The bootstrap analysis gave a re-sult of Θ LSR = 232 ±
14 km s - – a histogram of the bootstrapresults is seen in the right panel of Figure 18. This mean valueis lower by ∼ . σ than the result using only µ l cos(b). For-mally, this is a better fit than the one-dimensional result (withuncertainty of 14 km s - compared to an uncertainty of 23 kms - from the fits using only longitudinal proper motions), butthe two are consistent within their 1 σ uncertainties.Finally, we performed the same exercise using all three di-mensions of Sgr debris motions, but excluding the less reli-able SA 71 field. The uncertain identification of Sgr debris inSA 71 is likely the reason this field (at Λ ⊙ = 128 ◦ ) is an out-lier from the predicted kinematical trends in Figures 15 and16. The bootstrap fit using only SAs 94, 93, and 117 yields Θ LSR = 244 ±
17 km s - . This slightly higher value for Θ LSR suggests that (as is evident in Figures 15 and 16) the Sgr can-didates in SA 71 skew our results toward lower Θ LSR .Ultimately, we have derived three estimates of Θ LSR – onebased on a simple one-dimensional analysis (using all fourfields) that gave 264 ±
23 km s - , another based on three-dimensional data yielding 232 ±
14 km s - , and a final 3-Dresult with SA 71 excluded, which gave 244 ±
17 km s - . Itis likely that the true result is somewhere between the two Figure 17.
Total χ residuals for the final mean proper motions relative tocorresponding model debris. Each point represents a χ for one of the fivemodels in which we vary Θ LSR from 190-310 km s - . A parabola fit to theresults (the red curve) yields a minimum χ at Θ LSR = 270 . - . Figure 18.
Resulting Θ LSR corresponding to the minimum χ of 100,000bootstrap resamplings of the individual stellar proper motions in each SAfield. The left panel shows fits using only the µ l cos(b) component of Sgrdebris motions in SAs 71, 94, 93, and 117. A Gaussian fit (overlaid as the redcurve) to the results yields Θ LSR = 264 ±
23 km s - . The right panel showsthe results using all three dimensions of Sgr debris motions (i.e., µ l cos(b), µ b , and V GSR ) as constraints, which yields Θ LSR = 232 ±
14 km s - . extremes (264 km s - and 232 km s - ) from our methods. Sgr Disruption Models For Best-Fitting Θ LSR
We now repeat the N -body analysis described in Section 4.1two times, first taking Θ LSR = 264 km s - as a constraint onthe models, then again using Θ LSR = 232 km s - . The result-ing N -body model for the 264 km s - case matches the angularposition, distance, and radial velocity trends of the observedSgr tidal streams (using all of the observational constraints in-cluded in the original LM10 model) almost equally as well asdid the LM10 model (formally, χ = 3 . Θ LSR = 264 kms - model, compared to χ = 3 . µ l cos(b)= - . - , µ b = 1 .
92 mas yr - ) is a substantially better matchto observations (e.g., Dinescu et al. 2005; Pryor et al. 2010)than was the LM10 model.However, the N -body model in a Milky Way halo with Θ LSR = 232 km s - fits equally well as does the 264 km s - case, χ = 3 .
1. For this model, the Sgr core proper motion (seenin the right panel of Figure 19) is intermediate between thoseof the LM10 model and the 264 km s - result, as might beexpected. In this case, the proper motions are discrepant withboth the Dinescu et al. (2005) and Pryor et al. (2010) resultsat the ∼ . σ level. In the following subsection we discuss theramifications of these Θ LSR results for the Milky Way halo.0 Carlin et al.
Figure 19.
Proper motion estimates for the Sgr core in Galactic coordinates.Blue and red shaded ellipses show 1 σ and 2 σ uncertainty regions around themeasurements of Dinescu et al. (2005) and Pryor et al. (2010) respectively.The proper motion of the Sgr model dwarf described by LM10 ( Θ LSR = 220km s - ) is indicated by a filled black square. In the left panel the 1 σ rangeof proper motions corresponding to the value Θ LSR = 264 ±
23 km s - wefound using only the µ l cos(b) component of Sgr debris motions is indicatedby the error bars surrounding the filled black circle. The right panel is similar,but for the result ( Θ LSR = 232 ±
14 km s - ) using all three dimensions of Sgrdebris kinematics. The orientation of the error bars represents the direction towhich changes in Θ LSR correspond in this diagram; the proper motion of theSgr core is constrained to lie along this line because the orbital plane is fixedby the observed position of the tidal debris leading and trailing Sgr, whichtrace its orbit.
Robustness of the Galactic Mass Models
The results for Θ LSR from our analysis in the previous sub-section suggest that the true value of Θ LSR as constrained bySgr trailing tail debris likely lies between 232-264 km s - , butthat more (or more sensitive) proper motion measurements ofSgr trailing debris are needed to resolve this issue. In thissubsection, we will discuss the implications of the Θ LSR con-straints resulting from our two methods; we remind the readerthat the upper end of the range (i.e., the 264 km s - result) isless robustly determined than the results that produced lowervalues of the circular velocity. However, we include this valuein our discussion to present the reader with the range of possi-ble ramifications of what, in either case, represents an upwardrevision of Θ LSR from the accepted value.The value of Θ LSR = 232 ±
14 km s - we found using allthree dimensions of Sgr debris kinematics is consistent withthe canonical 220 km s - value at the roughly 1 σ level. How-ever, this value is also consistent (within the 1 σ uncertain-ties) with recent determinations of Θ LSR that have found therotation speed to be higher than the standard 220 km s - value [e.g., Reid et al. (2009) – Θ LSR = (254 ± R / . - ; Bovy et al. (2009) – Θ LSR = 244 ±
13 km s - ]. Fora change in Θ LSR of only about 10 km s - , it is difficult tomake any conclusions about whether the additional mass re-quired to increase the rotation speed must reside in the Galac-tic halo or the disk/bulge. We note that placing the addi-tional mass in the disk and bulge (with the halo fixed) yields M bulge = 3 . × M ⊙ and M disk = 1 . × M ⊙ for the 232km s - model – an increase of ∼
10% over the disk and bulgemass from the model of LM10. The relatively high value of Θ LSR = 264 ±
23 km s - found by our analysis using only the µ l cos(b) motions would require that the mass of the Galac-tic bulge and disk components be increased by ∼
50% fromthe values assumed by LM10 to M bulge = 5 . × M ⊙ and M disk = 1 . × M ⊙ . This disk mass is near the peak ofthe probability distribution ( M disk = 1 . × M ⊙ ) found byKoposov et al. (2010) based on fitting the GD-1 stream in athree-component gravitational potential similar to our own.We caution however that the orbit of Sgr is largely insensi-tive to the distribution of the excess mass between the two Figure 20.
Model Milky Way rotation curves as a function of radius fromthe Galactic center. Solid blue/green/red lines respectively represent rotationcurves with Θ LSR = 264 km s - achieved via scaling the Galactic bulge + disk,Galactic disk alone, and Galactic halo alone. Included for comparison is therotation curve of the original LM10 model (solid black line) normalized to Θ LSR = 220 km s - . The vertical dotted line represents the location of theSun at R ⊙ = 8 kpc. baryonic components, and solutions that yield similar χ canbe found by ascribing all or part of the needed adjustment in Θ LSR to changes in the mass of either the disk or bulge com-ponents alone. We do note, however, that the relative fractionof the total disk+bulge mass in each component is constrainedby the need to reproduce the shape of the observed Milky Wayrotation curve interior to R ⊙ (see Figure 20).The total mass of the Milky Way interior to 50 kpc inthe 264 km s - model is 5 . × M ⊙ , similar to the valueof 4 . × M ⊙ in the LM10 model. Since we have ac-counted for the increased Θ LSR = 264 km s - by increasingthe disk+bulge mass (which is a relatively small componentof the total virial mass), the mass of the Milky Way interiorto 200 kpc is M vir = 1 . × M ⊙ , similar to the value of1 . × M ⊙ derived by LM10 assuming that Θ LSR = 220km s - .We note that it was not possible to obtain a satisfactorymodel (within our parameterization of the Milky Way com-ponents; exploration of different dark halo models is beyondthe scope of this work) for the Sgr stream by leaving both thebulge and disk masses fixed at their LM10 values and account-ing for changes in Θ LSR by scaling the dark matter halo. Thedark matter halo profile is characterized by the parameters v halo and r halo (see Eqn. 3 of LM10) , which describe the totalmass normalization and radial scalelength of the halo respec-tively. Since dark matter in the LM10 model contributes only19% of the total centripetal acceleration in the solar neighbor-hood, v halo must be scaled up drastically (by a factor of ∼ Θ LSR from 220 km s - to 264 kms - , and necessitates a large increase in the space velocity ofSgr along its orbit (to ∼
400 km s - ) to produce a leading armdebris stream at an observed peak distance of ∼
50 kpc (seeFigure 6 of LM10). However, such a rapidly moving satellitemodel yields radial velocities along the tidal debris streamsthat are systematically discrepant from observations by ∼ - . Similarly, it is neither possible to obtain a satisfac-tory fit for larger Θ LSR values ( Θ LSR &
280 km s - , for which The halo triaxiality is an added complication that has little bearing onthe present discussion. inematics of Sgr Tidal Debris in Kapteyn’s Selected Areas 21the halo mass scaling problem is even more extreme), nor formuch lower values ( Θ LSR ∼
190 km s - , because the bary-onic bulge+disk mass component alone require Θ LSR > - ).Another possibility we considered was to again fix the bary-onic mass (i.e., the bulge+disk component), but to a smallervalue than the LM10 model, and allow the halo mass to vary.In particular, we attempted to fit a model with Θ LSR = 232 kms - , but with the bulge+disk mass decreased by 10% from theLM10 values. Even this small change in the baryonic massrequired scaling up the dark matter halo mass by ∼
50% tokeep Θ LSR = 232 km s - . The best-fit N -body model in thiscase fit the Sgr trailing-tail velocities, but was a poor fit to theleading arm SDSS distances because of the increased speed ofthe Sgr core necessitated by the much larger halo. This illus-tration highlights the large changes in the halo mass effectedby even small changes in the baryonic mass or the LSR ve-locity when fitting to observational data on the Sgr system. Infact, it is a testament to how well-constrained the Sgr systemis by the current observational data that we are unable to fitthe data if we change the dark halo model substantially.One possible way to construct an N -body model of the Sgrdwarf that fits the observational data relatively well while dra-matically changing Θ LSR is to adopt a Galactic halo whosescalelength is a factor of ∼
10 shorter than commonly adopted(from r halo = 12 kpc in the LM10 model to r halo = 1 kpc).However, the Galactic rotation curve implied by such a shorthalo scalelength declines steeply outside the solar circle (Fig-ure 20), in conflict with observations (e.g., Sofue et al. 2009).We therefore conclude that it is not possible to satisfacto-rily model the Sgr dwarf in a Milky Way model with thebulge and disk masses fixed at the LM10 values of M bulge =3 . × M ⊙ , M disk = 1 . × M ⊙ , and the Milky Way haloscaled to produce Θ LSR much higher than 220 km s - . Thusour (and other recent) suggestions that Θ LSR is due an upwardrevision implies that the disk and/or bulge components – but not the halo – of the Milky Way are more massive than previ-ously thought. ABUNDANCES
While the spectra in the Selected Areas were obtained pri-marily with kinematics in mind, they have sufficient resolu-tion and, for a large fraction of stars, sufficient S / N , to obtaininformation not only on metallicity but also abundance pat-terns. This allows us an independent estimate of abundancedistributions that, while of lower precision than the echellework of Monaco et al. (2005, 2007) and Chou et al. (2007,2010), is derived for many Sgr stars, and is less biased thanthose M-giant studies. Sgr Metallicity
Metallicities were measured for all stars using a softwarepipeline entitled "EZ_SPAM" (Easy Stellar Parameters andMetallicities), details of which will appear in a forthcom-ing paper (Carlin et al. 2011, in prep. ). EZ_SPAM relieson the well-understood and calibrated Lick spectral indices(see, e.g., Worthey et al. 1994; Friel 1987) to measure stel-lar properties from low-resolution spectra. In particular, esti-mates of [Fe/H] are derived for target stars using eight Fe in-dices combined with the H β index. Calibration of these multi-dimensional data comes from fits of known [Fe/H] values asa function of the Lick Fe and H β indices for stars in the atlasof Schiavon (2007, based on the spectra of Jones 1998). The EZ_SPAM code yields [Fe/H] measurements with 1 σ preci-sion of ∼ . S / N ≈
20, decreasing to ∼ . S / N & Table 6
Mean [Fe/H] for Sgr Debris in Kapteyn Selected Areas of This StudySA < [Fe/H] > σ [Fe / H] N [Fe / H]a Λ ⊙ (degrees)71 -1.14 ± ± ± ± ± ± ± b ± ± ± ± a Number of spectra with S / N >
20 providing reliably-measured [Fe/H]. b Cannot be measured for this field – too few spectra.
Figure 21.
Measured values of [Fe/H] for all stars having spectra with S / N >
20 in each SA field. The (red) hashed histogram is made up of Sgr candidatesfrom our final samples in each field, and the solid black line represents allother stars (i.e., mostly Milky Way field stars, with perhaps some unidentifiedSgr debris included) for which we obtained spectra. The distribution of Sgrmetallicities is clearly different from that of the field stars in all of theseregions (except perhaps SA 117, which is somewhat ambiguous), peaking ata more metal-poor mean value in each field. The bottom panel shows themetallicity distribution function (MDF) for all four fields in the 88 ◦ < Λ ⊙ < ◦ portion of the trailing tail in our study. This fractional MDF consists ofall the Sgr debris metallicities (red histograms) from the previous four panels,normalized by the total number of stars (147) in the sample. The metallicity distribution for all well-measured stars (i.e.,those with spectra having S / N >
20) in each of the four fields(SAs 71, 94, 93, and 117) in which Sgr debris are reliablyidentified is given in Figure 21. For each field, the solid(black) histogram shows [Fe/H] of non-Sgr stars, and the2 Carlin et al.hashed (red) histogram gives the distribution of [Fe/H] forstars selected to be Sgr members. The bottom panel repre-sents the distribution of metallicities for all Sgr members fromthe four trailing-tail fields, normalized by the total number ofstars (147) in the sample to produce a fractional distribution.In each field, Sgr members are typically more metal-poor thanthe field stars, with the possible exception of those in SA 117.For each SA field in the survey, a maximum likelihood es-timate for [Fe/H] was derived from all well-measured stars inthe final Sgr candidate sample. The resulting values for Sgrdebris metallicities in each field are given in Table 6 alongwith σ [Fe / H] , the dispersion in [Fe/H] about the mean. Aswas the case for the kinematics in SAs 92 and 116, we re-gard the [Fe/H] results in these fields (and, to a lesser de-gree, those in SA 71) with some skepticism, because theidentification of Sgr debris in these fields is rather unreli-able. The mean metallicities for Sgr stars are displayed inFigure 22 as a function of Λ ⊙ ; solid squares depict SAs 71,94, 93, and 117 (i.e., the “well-measured" fields), with opensymbols included for SAs 92 and 116. Error bars repre-sent the uncertainties in the mean value from the maximumlikelihood estimator; however, the scatter of [Fe/H] for Sgrcandidates in each field is rather large. Typical fields have σ [Fe / H] = 0 . - . Λ ⊙ = 128 ◦ ); this may arisefor a number of reasons. As can be discerned from Figure 1,SA 71 may be sampling Sgr debris stripped on multiple peri-centric passages (i.e., both gold and magenta debris may bepresent in this field). Furthermore, this is the lowest-latitudefield among those in this study, and thus may be also sufferingmore contamination from Galactic thick disk stars. Finally,we note that SA 71 has been shown by Casetti-Dinescu et al.(2008) to contain a significant number of stars from the"Monoceros stream" overdensity, which could contribute tothe inflation of the metallicity dispersion in this field, thoughit is unlikely that many Monoceros stars would lie within ourSgr radial velocity criteria for this field. Also shown in Fig-ure 22 is a solid line at constant [Fe/H] = -1.15, which is themean value from the four well-measured fields; the tight cor-respondence of the mean values of each field to this line isconsistent with the notion that debris along this narrow stretchof the trailing tail has constant metallicity. However, there isa hint of a shallow gradient, which we confirm by fitting alinear trend to the four good data points. This fit, overlaidas a dashed line in Figure 22, is [Fe/H] = -0.991 ± ± Λ ⊙ . While suggestive of a slight gradient,the slope given is also consistent with zero within the errorsof the fit. This is not surprising considering that nearly all de-bris in the portion of the stream contained within this study isexpected to have been stripped on the same pericentric pas-sage of the Sgr core, as evidenced by the fact that all of ourfields overlap gold-colored debris in Figure 1 (i.e., debris thatbecame unbound during the last two perigalactic passages;see Law & Majewski 2010a for more detail about the colorscheme used).Our measured metallicity of [Fe/H] ∼ -1.2 for Sgr trailingdebris is ∼ . Figure 22.
Measured values of [Fe/H] for Sgr candidates in each SA field asa function of Sgr longitude, Λ ⊙ . Filled squares and diamonds (and associ-ated error bars) show the maximum likelihood estimate from the individualSgr candidates in each field (diamonds are the two fields lacking secure iden-tification of candidates). The mean value of the four well-measured fields(the filled squares), [Fe/H] = -1.15, is represented by the solid line that repro-duces the measurements well. A linear fit to the same four fields is shown asa dashed line, and is suggestive of a slight metallicity gradient of 1.4 × - dex degree - along the stream (though the fit is consistent with zero slopewithin the uncertainties). the more metal-rich M-giants, we measure a shallow gradientin [Fe/H] as a function of Λ ⊙ , with a slope consistent withthe Keller et al. (2010) measurement, and just a simple offsetin the zero-point metallicity. A more apt comparison for themean metallicity of Sgr debris in our SA fields is the workof Sesar et al. (2010), who used SDSS Stripe 82 data to de-velop a new technique for estimating metallicity from photo-metric data, which relies on combined information from bothRR Lyrae variables and main-sequence stars from the samestructure. Because SAs 94, 93, and 92 are within Stripe 82(and, in fact, we have used those SDSS data in our analysis),the Sesar et al. study probes identical stellar populations fromthe Sgr trailing tail as our work. This is borne out by the factthat our measured [Fe/H] = -1.15 is in excellent agreementwith the value of [Fe/H] = -1.20 ± Metallicity Distribution Function
Previous attempts to measure the metallicity distributionfunction (MDF) of the Sgr stream have suffered from bothsmall number statistics and stellar tracers that have an inher-ent metallicity bias. For example, Chou et al. (2007) mea-sured the MDF for M giant stars at several points along theSgr leading stream as well as its core; using these data theyattempted to reconstruct the MDF that the Sgr stream progen-itor would have had several Gyr ago. However, because Mgiants only form in metal rich stellar populations, this anal-ysis, while able to show that the mean metallicity of starsvaries along the stream, was inadequate to assess the MDFacross the full metallicity range of the system. In addition,the analysis was based on a relatively small sample (about7 dozen stars), nearly half of which are in the core of theSgr dSph. Monaco et al. (2007) derived abundances of SgrM giants along the trailing tidal tail, from which they derived h [Fe/H] i = - . ± .
13 between 80 ◦ < Λ ⊙ < ◦ (from 6M giants), and h [Fe/H] i = - . ± .
11 (mean of 4 stars) fordebris even further along the trailing tail. The existence ofa metallicity gradient among Sgr stream M giants along bothinematics of Sgr Tidal Debris in Kapteyn’s Selected Areas 23
Figure 23.
The normalized MDF from all 147 Sgr candidates in SAs 71, 94,93, and 117 with spectra having S / N >
20 is shown as a solid black histogramwith grey fill. For comparison, in the upper panel we show the MDFs fromChou et al. (2007) of the Sgr core (black dashed line) and Sgr leading armM-giants (green dot-dashed line). In the lower panel the red (dot-dashed)and blue (dashed) histograms show the approximate Sgr MDF from severalGyr ago reconstructed by Chou et al. from linear combinations of the coreand leading arm samples. The first of these was created by interpolating theMDFs at different orbital longitudes, and MDF 2 was created by assigningobserved MDFs to particles in the Law et al. (2005) Sgr model by the timesthey became unbound. the trailing and leading tails was confirmed by Keller et al.(2010), who combined their additional measurements of 5stars at Λ ⊙ = 66 ◦ ( h [Fe/H] i ∼ - .
5) and 6 stars at Λ ⊙ = 132 ◦ ( h [Fe/H] i ∼ - .
7) with the Chou et al. and Monaco et al. re-sults to confirm the gradient in [Fe/H] among Sgr stream Mgiants. However, all of these M-giant studies suffer an inher-ent bias toward metal-rich stellar populations, and are likelynot showing the true MDF of the Sgr system.Blue horizontal branch stars (BHBs) are another easily-identified and rather unambiguous tracer of halo substructurethat has been used to probe the Sgr stream. However, BHBstars arise only in old, metal-poor populations, and are thusnot ideal tracers of the global MDF of a system consisting ofmultiple stellar populations. Yanny et al. (2009b) performedan extensive study of the Sgr tails using SDSS and SEGUEspectroscopy of BHB stars in both the northern and southernGalactic caps. BHB stars in the portions of both the leading(200 ◦ < Λ ⊙ < ◦ ) and trailing (70 ◦ < Λ ⊙ < ◦ ) tails inthis study have MDFs peaking at h [Fe/H] i ∼ - .
7, with sig-nificant numbers of stars as low as [Fe/H] ∼ -2.5. Althoughthis result turns up metal-poor populations not seen in M gi-ants, it is difficult to make conclusions about the overall MDFof the Sgr stream or progenitor based on biased metallicitytracers such as BHB stars and M giants.Fortunately, because the present analysis makes use ofMSTO stars, it is far less susceptible to metallicity biases andcan provide new insights into the MDF (particularly at the in-termediate to metal-poor end) of the stream (and therefore theprogenitor) MDF. Of course, our spectra have ∼ × worseresolution than the various echelle resolution studies, but oursample of Sgr stream stars is significantly larger, including147 with good enough S/N ( >
20) for [Fe/H] measurementsto the approximately . < - .
0) stars.Indeed, our sample includes some rather metal-poor stars as-sociated with the Sgr system, with stars as metal-poor as the-2.5 dex BHBs seen by Yanny et al. (2009b).Figure 23 shows the MDF derived from our data in the88 ◦ < Λ ⊙ < ◦ portion of the Sgr trailing tail. The MDFwe derive is significantly broader and extending to much moremetal-poor stars than indicated by the biased, M giant studies(shown in the upper panel of Figure 23 as a black dashed his-togram for the Sgr core and green dot-dashed lines for theleading arm), encompassing both the M-giant and BHB re-sults. A comparison of our MDF to the Chou et al. (2007)reconstruction of the Sgr M-giant MDF from several Gyr agobased on their core and leading-arm samples is given in thelower panel of Figure 23. Clearly our Sgr trailing-tail sam-ple is lacking the metal-rich component seen in the present-day core, but shows a similar distribution to the metal-poortail of the reconstructed MDF. Additional metal-poor stars arepresent in our sample that are not seen in the M giant samples;these are likely drawn from similar populations to those in theYanny et al. (2009b) study.Obviously, as has been shown by Chou et al. and others, thetotal MDF of the entire Sgr system will include a higher con-tribution of metal-rich stars when the core is included, but wealso expect more metal-poor stars from those parts of the tailswith larger separation from the core than we explore. Thus,while we cannot yet accurately reconstruct the total MDF ofthe Sgr system, at least we now have a better feel of the breadth of the Sgr MDF from the data shown in Figures 21and 23. Comparison of the latter MDF with those of otherMW dSphs (summarized, e.g., in Kirby et al. 2011) shows Sgrto be more typical of other MW satellites. In particular, theSgr MDF resembles even more that of the LMC (as has beenpreviously suggested by, e.g., Monaco et al. 2003, Cole et al.2005, and Monaco et al. 2005), which has been argued to bea chemical analog to the Sgr progenitor by Chou et al. (2010)and a morphological analog by Łokas et al. (2010). “Alpha” Abundances As shown in Section 5.1, we have identified metal-poorpopulations in (at least) four of the fields from our study,which explore a different segment of the stellar populationsin the Sgr stream than previous M-giant studies. We haveobserved stars in these fields only at low resolution, andthus cannot do detailed element-by-element chemical analysissuch as that enabled by high-resolution spectroscopy. How-ever, we can use the low-resolution Lick indices to explorerelative α -abundances for the stars in our study. Specifically,we explore the relative Mg abundances using the Lick Mg bindex centered at 5160-5190 Å. Calibrating the Mg b index toan actual [Mg/Fe] abundance is difficult, because the strengthof Mg lines is highly sensitive to surface gravity, with someadditional sensitivity to effective temperature and [Fe/H]. Dis-entangling these effects is difficult with low-resolution spec-tra, but we can still explore a subset of the stars in our sam-ples in a way that is relatively free of the effects of surfacegravity and temperature of individual stars. To do so, we se-lect only blue (0 . < g - r < .
7, or B - V < .
9) stars, whichshould be mostly main-sequence dwarfs (thus, with similarsurface gravity), since no giants are found at such blue col-ors. Furthermore, the temperature sensitivity of the Mg linestrength, which is already much smaller than the log g sensi-4 Carlin et al. Figure 24.
Relative values of Lick index ratio log (Mg b/ < Fe > ), where the indices are as described in the text and Carlin et al. 2011 ( in prep. ), for all bluestars (0 . < g - r < . B - V < . S / N >
30 in the four SA fields with securely identified Sgrdebris. When comparing only predominantly dwarf stars of similar, blue photometric colors, the log (Mg b/ < Fe > ) ratio can be thought of as a proxy for [Mg/Fe],because variations in [Mg/Fe] with log g and color (i.e., temperature) are then minimized. Colored points represent all stars within the initial Sgr candidate RVselections, with color codes as in the legend. Black dots are all other stars outside the Sgr velocity range. For [Fe/H] & -1.5, Sgr candidates (colored points)typically occupy a region of lower Mg abundance at a given [Fe/H] than the black dots that are likely Galactic foreground stars. This behavior is typical for starsfrom most Galactic dSphs (relative to Galactic disk populations). At lower metallicities, the distributions converge. tivity, is mitigated by concentrating on a limited color range.In Figure 24 we show a “pseudo-[Mg/Fe]" ratio, given as thelogarithm of the ratio of the Lick Mg b index to the mean ofall eight Lick Fe indices (after transforming them to a com-mon scale), for all of the blue stars in SAs 71, 94, 93, and117 for which we have high enough signal-to-noise ( >
30) toprecisely measure indices and [Fe/H]. Black points in this di-agram are all stars with non-Sgr radial velocities, while oursamples of all stars with Sgr-like RVs in each field are shownas colored points. It is readily apparent that the black (MW)points mostly occupy a different region of the diagram thanthe colored (Sgr) dots, which suggests an intrinsic chemicaldifference between the populations (though some overlap isexpected, especially at low metallicities, where many MWhalo stars likely resemble dSphs in their abundance patterns).Indeed, the behavior seen in Figure 24 is exactly that seen formany MW dSphs – for more metal-rich dSph stars, the Mg (or α ) abundance is lower (on average) at a given [Fe/H] than inthe Galactic populations, with the two populations convergingat lower metallicities (i.e., at the "knee" in the dSph’s distri-bution). Among the more metal-rich (and younger) M-giantpopulations of the Sgr stream, there is some indication thatthe knee in [ α /Fe] occurs at -1.2 . [Fe/H] . -1.0 (Chou et al.2010; Monaco et al. 2007), but this is difficult to assess be-cause of the lack of M-giants at lower metallicity. Thus theapparent convergence of Sgr trailing tail [Mg/Fe] with theplateau seen in Galactic stars at [Fe/H] . -1.5 may be an ex-tension of the same behavior seen in the M-giant studies. Al-ternatively, since we’ve already shown that the mean [Fe/H]along the trailing tail differs between the M-giant sample ofMonaco et al. (2007), who find [Fe/H] ∼ -0.6, and our resultof [Fe/H] ∼ -1.2 (which is also consistent with the findingsof Sesar et al. 2010), our study may be sampling a distinctlyolder, more metal-poor population of Sgr debris than the M-giant tracers. Further characterization of the α -element be-havior along the Sgr trailing tail would benefit from either acalibration of our Mg b/ < Fe > index onto [Mg/Fe] abundanceor the identification of bona fide stream giant stars that arebright enough for echelle-resolution spectroscopic follow-up. SUMMARY
We have presented the first large-scale study of the 3-Dkinematics of the Sagittarius trailing tidal stream, with dataspanning ∼ ◦ along the trailing tail. The data include deep,precise proper motions derived from photographic plates witha ∼ >
150 have beenidentified as Sgr debris stars. Mean absolute proper motionsof these Sgr stars in four of the six 40 ′ × ′ fields from oursurvey have been derived with ∼ . - . - per fieldprecision in each dimension (depending on the quality anddepth of plate material and the number of spectra obtainedin each field). Mean three-dimensional kinematics in each ofthese four fields have been shown to agree with the predicted V GSR and µ b from the Sagittarius disruption models of LM10.However, there is a systematic disagreement in the µ l cos(b)proper motions (with the exception of the somewhat problem-atical SA 71 field), which we use to assess refinements to themass scale of the Milky Way (particularly its disk and bulgecomponents).While proper motions along the portion of the trailing tailin this study provide constraints on Sgr tidal disruption mod-els, the fortuitous orientation of the Sgr plane also allows usto use the measured proper motions to derive the circular ve-locity at the Solar circle (or “Local Standard of Rest”), Θ LSR .Our first-order approximation using only the µ l cos(b) propermotions as constraints yields Θ LSR = 264 ±
23 km s - . Fromour measured 3-D kinematics, we find this fundamental MilkyWay parameter to be Θ LSR = 232 ±
14 km s - , or ∼ σ higherthan the IAU standard value of 220 km s - . When we removeSA 71, a field in which it is more difficult to unambiguouslyidentify Sgr debris, from the sample we find Θ LSR = 244 ± - . We suggest that the true value of Θ LSR lies some-where between 232-264 km s - , while noting that all three ofthese estimates are consistent with each other within their 1 σ uncertainties.Our general result that the circular velocity at the Solar ra-dius is higher than the IAU standard of 220 km s - agrees withinematics of Sgr Tidal Debris in Kapteyn’s Selected Areas 25the recent derivation of Θ LSR = 254 ±
16 km s - by Reid et al.(2009) using trigonometric parallaxes of star forming regionsin the outer disk. The same maser data from the Reid et al.study were reanalyzed by Bovy et al. (2009), and yield a re-sult of 246 ±
30 km s - (244 ±
13 km s - if priors on theproper motion of Sgr A* are included, and 236 ±
11 km s - if the additional contribution of orbital fitting to the GD-1stellar stream is included). Again, our independent result isconsistent with these studies, and inconsistent with the IAUaccepted value of 220 km s - for this fundamental constantat the 1-2 σ level. Identification of additional Sgr candidatescould increase the accuracy of our determination of Θ LSR , ascould the addition of another epoch of accurate data to theproper motion measurements.We note that while Reid et al. (2009) argued that their mea-surement of 254 km s - would imply an upward revision ofthe total Milky Way mass by a factor of ∼ Θ LSR even higher than that of Reid et al. Scal-ing the Milky Way dark matter halo up in mass to a levelthat yields Θ LSR = 264 km s - while simultaneously reproduc-ing known leading arm debris requires the Sgr core to have ahigh ( ∼
400 km s - ) space velocity, resulting in RVs in thetidal streams that are discrepant by ∼
75 km s - from mea-sured values. Instead, we show that because >
80% of thecentripetal force at the location of the Sun is contributed bymass in the Galactic disk and bulge, an increase of ∼ - rotation at the solarcircle, while contributing only a small ( ∼ Θ LSR , we have found a satisfactory model of Sgr disruptionthat matches all of the constraints used in fitting the LM10model, while additionally predicting a proper motion for theSgr dwarf that is in much better agreement with observationsthan the LM10 model.Stellar metallicities have been derived from the low-resolution spectra of Sgr candidates, and the mean metallic-ity of Sgr tidal debris derived in each field. We find that aconstant [Fe/H] = -1.15 is consistent with the observations ofall four fields for which Sgr members were reliably identi-fied. However, a linear fit to these four data points suggeststhat a gradient of (1 . × - ) dex degree - is also reason-able (though this value is consistent with zero slope within theuncertainty), in line with previous findings (e.g., Chou et al.2007; Keller et al. 2010) of a metallicity gradient among M-giants along both the leading and trailing tidal tails. The scat-ter of [Fe/H] in each of the survey fields is & < Fe > indices; the behavior of log (Mg b/ < Fe > ) with [Fe/H]for Sgr main-sequence candidates is markedly different fromGalactic stars of similar photometric colors (identified by ra-dial velocity) from among the same datasets. Furthermore,the trend is similar to that typically seen for dSphs, in that[Mg/Fe] is deficient at a given [Fe/H] for Sgr stars relative to the Milky Way field populations, and converges to a “knee”in Figure 24 at lower ([Fe/H] ∼ -1.5) metallicity. This is alower [Fe/H] than previously reported for Sgr M giants, andmay reflect a bias intrinsic to those earlier M-giant studies.High-resolution spectroscopic follow-up will be necessary toconfirm this trend among the old, metal-poor populations ofrecently-stripped Sgr debris.We appreciate the useful comments provided by the anony-mous referee. We thank Mei-Yin Chou for kindly sharing theSgr MDF data used in Figure 23, and Heidi Newberg for manyuseful discussions. JLC acknowledges support from NationalScience Foundation grant AST-0937523, and observing travelsupport from the NOAO thesis student program for proposalID 2008B-0448. JLC and SRM acknowledge partial fundingof this work from NSF grant AST-0807945 and NASA/JPLcontract 1228235. DIC and TG acknowledge NSF grant AST-0406884. DRL acknowledges support provided by NASAthrough Hubble Fellowship grant Facilities:
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