A kinematic study of the Andromeda dwarf spheroidal system
Michelle L. M. Collins, Scott C. Chapman, R. Michael Rich, Rodrigo A. Ibata, Nicolas F. Martin, Michael J. Irwin, Nicholas F. Bate, Geraint F. Lewis, Jorge Peñarrubia, Nobuo Arimoto, Caitlin M. Casey, Annette M. N. Ferguson, Andreas Koch, Alan W. McConnachie, Nial Tanvir
aa r X i v : . [ a s t r o - ph . C O ] F e b Draft version November 5, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
A KINEMATIC STUDY OF THE ANDROMEDA DWARF SPHEROIDAL SYSTEM
Michelle L. M. Collins , Scott C. Chapman , R. Michael Rich , Rodrigo A. Ibata , Nicolas F. Martin ,Michael J. Irwin , Nicholas F. Bate , Geraint F. Lewis , Jorge Pe˜narrubia , Nobuo Arimoto , Caitlin M.Casey , Annette M. N. Ferguson , Andreas Koch , Alan W. McConnachie , Nial Tanvir Draft version November 5, 2018
ABSTRACTWe present a homogeneous kinematic analysis of red giant branch stars within 18 of the 28 An-dromeda dwarf spheroidal (dSph) galaxies, obtained using the Keck I LRIS and Keck II DEIMOSspectrographs. Based on their g − i colors (taken with the CFHT MegaCam imager), physical posi-tions on the sky, and radial velocities, we assign probabilities of dSph membership to each observedstar. Using this information, the velocity dispersions, central masses and central densities of the darkmatter halos are calculated for these objects, and compared with the properties of the Milky WaydSph population. We also measure the average metallicity ([Fe/H]) from the co-added spectra ofmember stars for each M31 dSph and find that they are consistent with the trend of decreasing [Fe/H]with luminosity observed in the Milky Way population. We find that three of our studied M31 dSphsappear as significant outliers in terms of their central velocity dispersion, And XIX, XXI and XXV,all of which have large half-light radii ( ∼ > σ v < − ). Inaddition, And XXV has a mass-to-light ratio within its half-light radius of just [ M/L ] half = 10 . +7 . − . ,making it consistent with a simple stellar system with no appreciable dark matter component withinits 1 σ uncertainties. We suggest that the structure of the dark matter halos of these outliers havebeen significantly altered by tides. Subject headings: dark matter — galaxies: dwarf — galaxies: fundamental parameters — galaxies:kinematics and dynamics — Local Group INTRODUCTION
The underlying nature of the dark matter halos ofdwarf spheroidal galaxies (dSphs) has garnered signif-icant attention from the scientific community over thepast decade. The goal of recent observational studies ofthese objects has been to make critical tests of structureformation scenarios, particularly focusing on the viabilityof the canonical ΛCDM model. There is the long stand-ing issue of the relative dearth of these faintest of galax- Max-Planck-Institut f¨ur Astronomie, K¨onigstuhl 17, D-69117 Heidelberg, Germany Institute of Astronomy,Madingley Rise, Cambridge, CB30HA ,UK Dalhousie University Dept. of Physics and Atmospheric Sci-ence Coburg Road Halifax, B3H1A6, Canada Department of Physics and Astronomy, University of Cali-fornia, Los Angeles, CA 90095-1547 Observatoire astronomique de Strasbourg, Universit deStrasbourg, CNRS, UMR 7550, 11 rue de lUniversit, F-67000Strasbourg, France Sydney Institute for Astronomy, School of Physics, A28, Uni-versity of Sydney, NSW 2006, Australia Ram´on y Cajal Fellow, Instituto de Astrof´ısica de Andalucia-CSIC, Glorieta de la Astronom´ıa s/n, 18008, Granada, Spain Institute for Astronomy, University of Edinburgh, Royal Ob-servatory, Blackford Hill, Edinburgh, EH9 3HJ, UK Subaru Telescope, National Astronomical Observatory ofJapan 650 North A’ohoku Place, Hilo, Hawaii 96720, U.S.A. Graduate University for Advanced Studies 2-21-1 Osawa,Mitaka, Tokyo 181-8588, Japan Institute for Astronomy, 2680 Woodlawn Drive Honolulu,HI 96822-1839 USA Zentrum f¨ur Astronomie der Universit¨at Heidelberg, Lan-dessternwarte, K¨onigstuhl 12, 69117 Heidelberg, Germany NRC Herzberg Institute of Astrophysics, 5071 West SaanichRoad, British Columbia, Victoria V9E 2E7, Canada Department of Physics & Astronomy, University of Leices-ter, University Road, Leicester LE1 7RH, UK ies observed surrounding nearby galaxies when comparedwith the number of dark matter subhalos produced in N − body simulations, which is referred to as the “miss-ing satellite” problem (Klypin et al. 1999; Moore et al.1999). The extent to which this mismatch is consideredproblematic has decreased over recent years as both theo-rists and observers have sought to reconcile the simulatedand observable Universe. From a modelling point of view,one does not expect stars to be able to form within alldark matter subhalos seen in simulations, and at a cer-tain mass limit ( V max ∼ <
15 km s − , see Pe˜narrubia et al.2008a; Koposov et al. 2009), star formation is unableto proceed. Thus, there is a lower limit placed ongalaxy formation. This mass limit is also tied to feed-back processes that can remove the baryonic reservoirsrequired for star formation (e.g., Bullock et al. 2000;Somerville 2002; Kravtsov 2010; Bullock et al. 2010;Nickerson et al. 2011; Kazantzidis et al. 2011). Thiswould imply that only the most massive subhalos seenin simulations are able to form and retain luminous pop-ulations. Observers have also attempted to quantify cur-rent survey completeness and radial selection effects toaccount for the number of satellites we are not currentlyable to detect (e.g., Koposov et al. 2008; Tollerud et al.2008; Walsh et al. 2009). These studies suggest thatthere are of order a few hundred satellites within theMilky Way’s virial radius that we have yet to detect.The high dark matter dominance of dSph galaxiesalso singles them out as objects of interest. With to-tal dynamic mass-to-light ratios of [ M/L ] ∼ − r half ∼ − ab initio assumptions about the un-derlying density profiles, or the velocity anisotropy ofboth the dark matter and stars, such as those employedby Walker & Pe˜narrubia (2011) and Jardel & Gebhardt(2012).To date, the majority of studies involving the de-tailed kinematics of dSphs have revolved largely aroundthose belonging to the Milky Way, as these are nearbyenough that we can measure the velocities of theirmember stars to a high degree of accuracy. How-ever, there are currently only ∼
25 known MW dSphs,with luminosities ranging from 10 − L ⊙ . For thevery faintest, some controversy remains as to whetherthey are massively dark-matter dominated (see e.g.,Niederste-Ostholt et al. 2009; Simon et al. 2011), but al-most all of them have been shown to be consistentwith the universal mass profiles of Walker et al. (2009a)and Wolf et al. (2010). One notable exception to thisis the Hercules object (Ad´en et al. 2009), which somehave argued is currently undergoing significant tidal dis-ruption (Martin & Jin 2010). Andromeda representsthe only other system for which comparable kinematicanalyses can be performed. M31 now has 28 dSphcompanions known, whose luminosities range from ∼ − L ⊙ , the majority of which have been dis-covered by the CFHT Pan-Andromeda ArchaeologicalSurvey (PAndAS Martin et al. 2006; Ibata et al. 2007;Irwin et al. 2008; McConnachie et al. 2008; Martin et al.2009; Richardson et al. 2011). The relatively brighterlower bound for the luminosities of M31 dSphs com-pared to the MW is a detection limit issue, rather thana sign of differing stellar populations (Martin et al.2013, in prep). It has been noted by a number of au-thors (e.g., McConnachie & Irwin 2006b; Tollerud et al.2012; McConnachie 2012) that for the brighter dSphs( M V < − r half ) and tidal ( r t )radii compared with the MW. In these papers, the under-lying cause of this discrepancy was not identified, but ithas been argued that it could be an effect of environment,with the mass distribution of the host playing an impor-tant role. Subsequent work by Brasseur et al. (2011a),who included the fainter, non-classic M31 dSphs for thefirst time, showed that statistically, the relationship be-tween size and luminosity for dSphs in the MW and An-dromeda are actually largely consistent with one another,however there remain a number of significantly extendedoutliers within the Andromedean system (e.g., And II,And XIX, r half ∼ . . kinematically hotter than their MW counter-parts by a factor of ∼
2. At the time of writing, theyhad only 2 measured velocity dispersions for the M31dSphs, those of And II and And IX (Cˆot´e et al. 1999;Chapman et al. 2005). New studies of the kinematics ofM31 dSphs (Collins et al. 2010, 2011; Kalirai et al. 2010;Tollerud et al. 2012; Chapman et al. 2012) have dramat-ically increased the number of systems with a measuredvelocity dispersion, and have shown that instead of be-ing kinematically hotter, these systems are either verysimilar to, or in a number of cases (e.g., And II, AndXII, And XIV, And XV and And XXII), colder thantheir MW counterparts. In particular, a significant re-cent kinematic study of 15 M31 dSph companions us-ing the Keck II DEIMOS spectrograph by the Spectro-scopic and Photometric Landscape of Andromeda’s Stel-lar Halo (SPLASH, Tollerud et al. 2012) concluded thatthe M31 dSph system largely obeys very similar mass-size-luminosity scalings as those of the MW. However,they also identified 3 outliers (And XIV, XV and XVI)that appear to possess much lower velocity dispersions,and hence maximum circular velocities, than would beexpected for these systems. Such a result suggests thatthere are significant differences in the formation and/orevolution of the M31 and MW dSph systems.To investigate this further, our group has been sys-tematically surveying the known dSphs of M31 with theKeck I LRIS and Keck II DEIMOS spectrographs, andhave obtained kinematic data for 18 of the 28 galaxies.In this paper, we present new spectroscopic analysis forthe 11 dSphs, Andromeda (And) XVII, And XVIII, AndXIX, And XX, And XXI, And XXIII, And XXIV, AndXXV, And XXVI, the tidally disrupting And XXVII,And XXVIII and And XXX (Cassiopeia II) using an al-gorithm we have developed that implements a probabilis-tic method of determining membership for each galaxy.In addition we re-analyze the kinematics of 6 dSphs thatour group has previously observed (And V, VI, XI, XII,XIII, XXII) using this method with the aim of provid-ing a homogeneous analysis of all dSphs observed by ourgroup to date. We also provide the individual stellarvelocities and properties for every star observed in ourdSphs survey, allowing us to present a large catalog ofhe kinematics of Andromeda’s dSphs 3stellar kinematics that will be of interest to those study-ing dSph systems and Milky Way-like galaxies, whetherobservationally or theoretically.The outline of this paper is as follows. In § § § § § § OBSERVATIONS
Photometry and target selection
The PAndAS survey (McConnachie et al. 2009), con-ducted using the 3.6 metre Canada France Hawaii Tele-scope (CFHT), maps out the stellar density of the discand halo regions of the M31–M33 system over a pro-jected area of ∼ ( ∼ ,
000 kpc ), resolving in-dividual stars to depths of g = 26 . i = 25 . ∗ galaxy to date. Eachof the 411 fields in this survey (0 . × .
94 deg ) hasbeen observed for at least 1350s in both MegaCam g and i filters, in < . ′′ seeing. This survey was ini-tiated following two precursor surveys of the M31 sys-tem, the first of which surveyed the central ∼
40 deg conducted with the 2.5 metre Isaac Newton Telescope(Ferguson et al. 2002; Irwin et al. 2005), and revealed awealth of substructure in the Andromeda stellar halo,including the giant southern stream (Ibata et al. 2001).To better understand this feature, and to probe deeperinto the M31 (and M33) stellar halo, a survey of thesouth west quadrant of the M31 halo was initiated us-ing the CFHT (Ibata et al. 2007), and revealed yet moresubstructure, including the arc like stream Cp and Cr(Chapman et al. 2008) and a number of dwarf spheroidalsatellites (Martin et al. 2006). This CFHT survey wasthen extended into the full PAndAS project. For de-tails of the processing and reduction of these data, seeRichardson et al. (2011). This survey has introducedus to a wealth of stellar substructure, debris and glob-ular clusters within the Andromeda–Triangulum sys-tem. In addition, it has led to the discovery of 17dSphs. These objects were detected in the PAndAS sur-vey maps as over-densities in matched-filter surface den-sity maps of metal poor red giant branch (RGB) starsand were presented in Martin et al. (2006); Ibata et al.(2007); Irwin et al. (2008); McConnachie et al. (2008);Martin et al. (2009) and Richardson et al. (2011). Webriefly summarise the photometric properties of all dSphsdiscussed within this paper in Table 1.For the majority of these objects, the PAndASdataset formed the basis for our spectroscopic targetselection. Using the color selection boxes presentedin McConnachie et al. (2008); Martin et al. (2009) andRichardson et al. (2011), we isolated the RGBs of eachdSph, then prioritised each star on this sequence depend-ing on their color, i -band magnitude, and distance fromthe centre of the dSph. Stars lying directly on the RGB, with 20 . < i < . d < r half (where r half is the half-light radius, measured on the semi-majoraxis of the dSph) were highly prioritised (priority A),followed by stars on the RGB within the same distancefrom the centre with 22 . < i < . . < i < . . < g − i < § Keck Spectroscopic Observations
The DEep-Imaging Multi-Object Spectrograph(DEIMOS), situated on the Nasmyth focus of the KeckII telescope is an ideal instrument for obtaining mediumresolution (R ∼ . ◦ A) spectra of multiple, faint stellartargets in the M31 dSphs. The data for the dSphs withinthis work were taken between Sept 2004 and Sept 2012in photometric conditions, with typical seeing between0 . − ′′ . Our chosen instrumental setting covered theobserved wavelength range from 5600–9800 ◦ A and em-ployed exposure times of 3x20 minute integrations. Themajority of observations employed the 1200 line/mmgrating, although for 4 dSphs (And XI, XII, XIIIand XXIV) the lower resolution 600 line/mm grating( R ∼ . ◦ A FWHM) was used. The spectra from bothsetups typically possess signal-to-noise (S:N) ratios of > ◦ A − for our bright targets ( i ∼ < . ◦ A, these strong features areideal for determining the velocities of our observed stars.We determine the velocities by using an Markov ChainMonte Carlo procedure where a template Ca II spectrumwas cross-correlated with the non-resampled data, gen-erating a most-likely velocity for each star, and a likelyuncertainty based on the posterior distribution that in- Collins et al.
TABLE 1Details of the structural properties for each dwarf, as derived fromCFHT photometry by Ibata et al. (2007); Letarte et al. (2009);Irwin et al. (2008); McConnachie et al. (2008); Martin et al. (2009);Collins et al. (2010, 2011); Brasseur et al. (2011a); Richardson et al.(2011) and McConnachie (2012), updated for distances presented inConn et al. (2012). The photometry for And VI is derived from SubaruSuprimeCam photometry (Collins et al. 2011), and the values for AndXXVIII come from SDSS photometry (Slater et al. 2011).
Property α ,J δ ,J M V r half (pc) D (kpc)And V 01:10:17.1 +47:37:41.0 -10.2 302 ±
44 742 +21 − And VI 23:51:39.0 +24:35:42.0 -10.6 524 ±
49 783 ± +9 − +29 − And XII 00:47:27.0 +34:22:29.0 -6.4 324 +56 − +40 − And XIII 00:51:51.0 +33:00:16.0 -6.7 172 +34 − +126 − And XVII 00:37:07.0 +44:19:20.0 -8.5 262 +53 − +39 − And XVIII 00:02:14.5 +45:05:20.0 -9.7 325 ±
24 1214 +40 − And XIX 00:19:32.1 +35:02:37.1 -9.6 1481 +62 − +32 − And XX 00:07:30.7 +35:07:56.4 -6.3 114 +31 − +42 − And XXI 23:54:47.7 +42:28:15.0 -9.8 842 ±
77 827 +23 − And XXII 01:27:40.0 +28:05:25.0 -6.5 252 +28 − +32 − And XXIII 01:29:21.8 +38:43:08.0 -10.2 1001 +53 − +31 − And XXIV 01:18:30.0 +46:21:58.0 -7.6 548 +31 − +28 − And XXV 00:30:08.9 +46:51:07.0 -9.7 642 +47 − +23 − And XXVI 00:23:45.6 +47:54:58.0 -7.1 219 +67 − +218 − And XXVII 00:37:27.2 +45:23:13.0 -7.9 657 +112 − +42 − And XXVIII 22:32:41.2 +31:12:51.2 -8.5 210 +60 − +150 − And XXX (Cass II) 00:36:34.9 +49:38:48.0 -8.0 267 +23 − +32 − corporates all the uncertainties for each pixel. Typicallyour velocity uncertainties lie in the range of 5 −
15 km s − .Finally, we also correct these velocities to the heliocentricframe. Telluric velocity corrections
With slit-spectroscopy, systematic velocity errors canbe introduced if stars are not well aligned within thecentre of their slits. Such misalignments can result fromastrometric uncertainties or a slight offset in the positionangle of the mask on the sky. For our astrometry, we takethe positions of stars from PAndAS photometry, whichhave an internal accuracy of ∼ . ′′ and a global accuracyof ∼ . ′′
25 (S´egall et al. 2007). This can translate to ve-locity uncertainties of up to ∼
15 km s − for our DEIMOSsetup. In previous studies, authors have tried to correctfor this effect by cross correlating their observed spectrawith telluric absorption features (e.g., Sohn et al. 2007;Simon & Geha 2007; Kalirai et al. 2010; Collins et al.2010; Tollerud et al. 2012). These atmospheric absorp-tion lines are superimposed on each science spectrum,and should always be observed at their rest-frame wave-lengths. Thus, if one is able to determine the offset ofthese features, shifts caused by misalignment of the sci-ence star within the slit can be corrected for, and thiscan be applied on a slit by slit basis. The strongest ofthese features is the Fraunhofer A-band, located between7595–7630 ◦ A. An example of this feature is shown in theleft panel of Fig. 1.While we believe this correction is robust in the highS:N regime, we argue against applying this correctionin studies of Andromedean satellites, where S:N is often quite low (typically less than 8–10 ◦ A − ) for 1 hour ob-servations of faint ( i ∼ >
21) RGB stars. We find thatwhen we compute this offset for all stars within our sam-ple, those with high S:N tend to cluster within a fewkm s − of the average telluric correction found for themask. As the S:N decreases below about 10 ◦ A − , thescatter about this mean value increases dramatically, asdo the uncertainties computed for each individual cor-rection. This is because the telluric feature is a single,very broad and asymmetric feature. It is therefore easyin the noisy regime for the cross correlation routine tomisalign the template and science spectrum whilst stillproducing a high confidence cross-correlation maximum.We show this effect explicitly in the right hand panel ofFig. 1 where we plot the deviation of the telluric correc-tion for every star within our sample from the averagecorrection determined for the spectroscopic mask it wasobserved with ( v tel − < v tel > ) as a function of S:N. Thecyan points represent the individual data, and the largeblack points represent the median of all points within1 ◦ A bins in S:N. The error bars represent the dispersionwithin each bin. It is plainly seen that the median valuefor each bin is consistent with zero (i.e., the median), andthat the dispersion increases with decreasing S:N. If wewere to apply these velocity corrections to all our stars,it is probable that we would merely increase the velocityuncertainties rather than reducing them.For this reason, we take a different approach. Usingsolely the telluric velocity corrections of stars from eachobserved mask whose spectra have S:N >
7, we measure(a) the average telluric correction for the mask and (b)the evolution of the telluric correction as a function ofhe kinematics of Andromeda’s dSphs 5
TABLE 2Details of spectroscopic observations
Object Date Instrument Grating Res. α ,J δ ,J P.A. Exp. (s) N Targ N Mem
And V 16 Aug 2009 LRIS 831/8200 3.0 ◦ A 01:10:18.21 +47:37:53.3 0 ◦ ◦ A 23:51:51.49 +24:34:57.0 0 ◦ ◦ A 00:46:28.08 +33:46:28.8 0 ◦ ◦ A 00:47:32.89 +34:22:28.6 0 ◦ ◦ A 00:52:00.22 +32:59:16.2 0 ◦ ◦ A 00:37:51.09 +44:17:51.9 280 ◦ ◦ A 00:02:14.50 +45:05:20.0 90 ◦ ◦ A 00:19:45.04 +35:05:28.8 270 ◦ ◦ A 00:19:30.88 +35:07:34.1 0 ◦ ◦ A 00:07:30.69 +35:08:02.4 90 ◦ ◦ A 23:54:47.70 +42:28:33.6 180 ◦ ◦ A 01:27:52.37 +28:05:22.3 90 ◦ ◦ A 01:27:52.37 +28:05:22.3 0 ◦ ◦ A 01:29:18.18 +38:43:50.4 315 ◦ ◦ A 01:29:21.87 +38:44:58.7 245 ◦ ◦ A 01:18:32.90 +46:22:50.0 30 ◦ ◦ A 01:18:32.90 +46:22:50.0 0 ◦ ◦ A 00:30:01.88 +46:50:31.0 90 ◦ ◦ A 00:23:41.42 +47:54:56.8 90 ◦ ◦ A 00:37:31.93 +45:23:55.4 45 ◦ ◦ A 22:32:32.71 +31:13:13.2 140 ◦ ◦ A 00:37:00.84 +49:39:12.0 270 ◦ Fig. 1.—
Left:
Keck II DEIMOS spectrum of a bright foreground star, centered on the region of the strong telluric absorption feature,the Fraunhofer A band.
Right:
The deviation of the telluric correction for every observed star within our sample from the averagecorrection determined for the spectroscopic mask ( v tel − < v tel > ) as a function of S:N. Cyan points represent the individual data, and thelarge black points represent the median of all points within 1 ◦ A bins in S:N. Error bars show the standard deviation within the bin. Themedian value for each bin is consistent with zero (i.e., the median), and the dispersion increases with decreasing S:N, arguing against usingthis correction in the low S:N regime.
Collins et al.mask position. In this way, we can track any gradientin our measurements that could be caused by e.g., ro-tational offsets in our mask. In general, we find thesecorrections to be slight. The average measured offsetacross all our masks is 3 . − (ranging from between − . − and +10 . − ). The measured gradientsare very slight, resulting in an average end-to-end maskdifference of 2.6 km s − , with a range of 0 . − . − ,typically within our measured velocity uncertainties. A PROBABILISTIC DETERMINATION OF MEMBERSHIP
Determining membership for Andromedean dwarfspheroidals is notoriously difficult in the best of cases.We only possess information about the velocity, CMDposition, distance from the centre of the dSph and spec-troscopic metallicity (although this carries large uncer-tainties of > . v hel & −
150 km s − )or M31 halo giants ( v halo ≈ −
300 km s − , σ v,halo ≈
90 km s − , Chapman et al. 2006). In the case of Galacticcontamination, our spectra also cover the region of theNa I doublets ( ∼ ◦ A). As this feature is dependenton the stellar surface gravity, it is typically stronger indwarf stars than in giants. However, there is a significantoverlap between the two, especially in the CMD color re-gion of interest for Andromedean RGB stars. In the past,groups have focused on making hard cuts on likely mem-bers in an attempt to weed out likely contaminants (e.g.,based on their distance from the centre of the galaxy ortheir velocity, Chapman et al. 2005; Collins et al. 2010,2011; Kalirai et al. 2010), but such ‘by eye’ techniquesare not particularly robust. Tollerud et al. (2012) re-cently presented an analysis of a number of M31 dSphswhere they used a more statistical method to ascertainlikely membership, using the distance from the centre of,and position in the CMD of stars targeted within theirDEIMOS masks. Here we employ a similar techniquethat will assess the probability of stars being members ofa dSph based on (i) their position on the CMD; (ii) theirdistance from the centre of the dSph and, in addition;(iii) their position in velocity space, giving the likelihoodof membership as: P i ∝ P CMD × P dist × P vel (1)Below, we fully outline our method, and implement aseries of tests to check it can robustly recover the kine-matics of the M31 dSphs. Probability based on CMD position, P CMD
For the first term, P CMD , we are interested in where agiven star observed in our mask falls with respect to theRGB of the observed dSph. Tollerud et al. (2012) use thedistance of a given star from a fiducial isochrone fit tothe dwarf photometry to measure this probability. Here,we determine this value from the data itself, rather thanusing isochrones. Using the PAndAS CFHT photometry,we construct a normalised Hess diagram for the centralregion (i.e., within 2 × r half ) of the dSph, and one ofa surrounding ‘field’ comparison region. By combiningthese two Hess diagrams, we can then map both the color distribution of the dSph and that of our contaminatingpopulations. We use both directly as probability maps,where the densest region would have a value of 1.So we are not dominated by shot noise of sparsely pop-ulated regions of the CMD, we use only the region ofthe RGB. We do this by assigning a generous boundingbox around the RGB as seen in the left hand panel ofFig. 2 where we display the PAndAS CMD for the wellpopulated And XXI RGB. We have zoomed in on theregion for which DEIMOS observations with reliable ve-locities can be obtained, e.g., i < .
5. The boundingbox is shown with red dashed lines. Anything that fallsoutside this region is therefore assigned a probability of P CMD = 0. The resulting probability map for And XXIis shown in the right hand panel. Red points represent allDEIMOS stars that have P CMD > − , while the bluestars show stars from the DEIMOS mask that are far re-moved from the And XXI RGB, and thus not consideredto be members. Probability based on distance position, P dist The second term in our probability function, P dist can be easily determined from the known radial profileof the dSphs. The half-light radii of all these objectsare known and can be found in McConnachie & Irwin(2006a); Zucker et al. (2004, 2007); McConnachie et al.(2008); Martin et al. (2009); Collins et al. (2010, 2011);Richardson et al. (2011). We also know that their den-sity profiles are well represented by a Plummer profilewith a scale radius of r p ≡ r half . Therefore, we can de-fine the probability function as a normalised Plummerprofile (Plummer 1911), i.e.,: P dist = 1 πr p [1 + ( r/r p ) ] (2)The above equation assumes that the systems we arestudying are perfectly spherical. While the majority ofthese systems are not significantly elliptical, it is impor-tant to consider the effect of any observed deviationsfrom sphericity. We therefore modify r p based on a givenstars angular position with respect to the dwarfs majoraxis, θ i , such that: r p = r half (1 − ǫ )1 + ǫ cos θ i (3)where ǫ is the measured ellipticity of the dSph as takenfrom McConnachie (2012). Probability based on velocity, P vel The final term, P vel , contains information about thelikelihood of a given star belonging to a kinematic sub-structure that is not well described by the velocity pro-files of either the MW halo dwarfs or the Andromedahalo giants, both of which are determined empiricallyfrom our DEIMOS database of > v r,halo = − . − and σ v,halo = 96 . − , giving a probability density func-tion for a given star with a velocity v i and velocity un-certainty of v err,i of:he kinematics of Andromeda’s dSphs 7 And XXI i g-i Fig. 2.—
Left:
The PAndAS CMD for And XXI, showing all stars within 2 × r half of the dwarf centre. The red dashed lines showthe bounding box we use to construct our probability map for the RGB of the dSph. Right:
A background normalized Hess diagram forthe RGB region of And XXI. The color represents the probability, P CMD in each cell for a star in that position belonging to And XXI.This diagram is used as a probability map for all our spectroscopically observed stars. Red points represent stars DEIMOS stars for which P CMD > − , while the blue stars represent objects for which P CMD ≤ − . P halo = 1 q π ( σ v,halo + v err,i ) × exp h − v r,halo − v r,i q σ v,halo + v err,i i (4)The MW halo population is well approximated by 2Gaussians with v r,MW = − . − , σ v,MW =36 . − and v r,MW = − . − and σ v,MW =48 . − , resulting in a probability density functionfor a given star with a velocity v i and velocity uncer-tainty of v err,i of: P MW = R q π ( σ v,MW + v err,i ) × exp h − v r,MW − v r,i q σ v,MW + v err,i i + (1 − R ) q π ( σ v,MW + v err,i ) × exp h − v r,MW − v r,i q σ v,MW + v err,i i (5)where R is the fraction of stars in the first MW peak, and(1 − R ) is the fraction of stars in the second peak. Thevalue of R is determined empirically from our DEIMOSdata set.A strong kinematic peak outside of these two popula-tions can then be searched for using a maximum likeli- hood technique, based on the approach of Martin et al.(2007). We search for the maximum in the likelihoodfunction that incorporates the two contamination popu-lations plus an additional Gaussian structure with sys-temic velocity v r,substr and a dispersion of σ v,substr , de-fined as: P substr = 1 q π ([ ησ v,substr ] + v err,i ) × exp h − v r,substr − v r,i q [ ησ v,substr ] + v err,i )] i (6)Here, to ensure we haven’t biased our P substr stronglyagainst stars that lie within the wings of the Gaussiandistribution of dwarf spheroidal velocities, we have in-cluded a multiplicative free parameter, η , to our derivedvalue of σ v . To determine the ideal value of η , we ranour algorithm over all our datasets, changing the valueof η from 0 . − . η ∼ − η , however for those with sys-temic velocities within the velocity regime of the MilkyWay, the solution quickly destabilizes as more contami-nants are included as probable members. We show thisimplicitly in Fig. 4, where we present the effect of modi-fying η on 6 dSphs, And XII, XIX, XXI, XXII, XXIIIand XXV. These objects were selected as they nicelyprobe our datasets with low numbers of probable mem-ber stars ( ∼ Fig. 3.—
A velocity histogram for all observed stars in the fieldof And XXI. Our empirical Gaussian fits to the full Keck II dataset for the M31 and MW halos are overlaid in blue and greenrespectively. A cold, kinematic peak at −
400 km s − is also seen,and this is the likely signature of the dSph. Our coarse, initialML procedure identifies this peak, and the values of v sys and σ v it measures are used to derive our kinematic probability, P vel . η is therefore independently determined for each datasetseparately, and we report its final value in Table 4. P substr = 1 q π ( σ v,substr + v err,i ) × exp h − v r,substr − v r,i q σ v,substr + v err,i )] i (7)The likelihood function can then be simply written as:log[ L (v r , σ v )] = N X i=1 log (cid:16) α P i , halo + β P i , MW + γ P i , substr (cid:17) (8)where α , β and γ represent the Bayesian priors, i.e., theexpected fraction of stars to reside in each population.These are determined by starting with arbitrary fractions(for example, 0.2, 0.5 and 0.3 respectively) and are thenadjusted to the posterior distribution until priors andposteriors match. This technique will therefore identifyan additional kinematic peak, independent of the MWand M31 halo populations, if it exists. We stress thatthese are not the final systemic velocity and dispersionof the dSph, but merely indicate a region in velocity spacein which an excess of stars above the two contaminantpopulations is seen. In Fig. 3, we show the result of thisprocess for the And XXI dSph. Here, the substructureis clearly visible as a cold spike at ∼ −
400 km s − .Now that we have a velocity profile for our three com-ponents (MW, M31 halo and the dSph), we can assignprobabilities for each star within our sample belongingto each population using simple Bayesian techniques, i.e.,the probability that a given star belongs to the substruc-ture, P vel , is: P vel = γP substr αP halo + βP MW + γP substr (9)and the probability of being a contaminant is: P nvel = αP halo + βP MW αP halo + βP MW + γP substr (10) Measuring v r and σ v Upon applying this to our data, we can identify the mostprobable members of each dSph, without having to applyany additional constraints or cuts.Having established the membership probability foreach observed star (as detailed above) we now calculatethe kinematic properties of each dSph; namely their sys-temic velocities ( v r ) and velocity dispersions ( σ v ). Weuse the maximum likelihood technique of Martin et al.(2007), modified to include our probability weights foreach star. We sample a coarse grid in ( v r , σ v ) space anddetermining the parameter values that maximise the like-lihood function (ML), defined as:log[ L ( v r , σ v )] = − N X i =1 h P i log( σ )+ P i v r − v r,i σ tot 2 + P i log(2 π ) i (11)where N is the number of stars in the sample, v r,i is theradial velocity measured for the i th star, v err,i is the cor-responding uncertainty and σ tot = q σ v + v err,i . In thisway, we aim to separate the intrinsic dispersion of a sys-tem from the dispersion introduced by the measurementuncertainties. Testing our probabilistic determination ofmembership and calculations of kinematicproperties
Having developed the above technique, it is importantfor us to rigorously test that it is robust enough to ac-curately determine the global kinematic properties foreach of our datasets. In Appendix A, we examine indetail a number of potential issues that could cause ouralgorithm to return biased or incorrect results. These arethe inclusion of a velocity dependent term in our prob-ability calculation, the effect of including low S:N data(S:N < ◦ A) in our analysis and the effect of small samplesizes ( N ∗ <
8) on our measurements of kinematic prop-erties. We briefly summarize our findings here, and referthe reader to Appendix A for a more detailed description.This work has introduced the concept of assigning aprobability of membership for a given star to a dSphbased on the prior knowledge of the velocity profiles ofour expected contaminant populations, P vel , a techniquethat has not previously been used in the study of M31dSphs. To test that this is not biasing our results, wecan simply remove this term from Eqn. 1, and follow thetechnique of T12, where they use only P CMD and P dist terms and then cut all stars with P i < . σ from the mean of this samplefrom their final analysis. We find that both techniquesproduce very similar results, however our algorithm ishe kinematics of Andromeda’s dSphs 9 -564-562-560-558-556-554-552-550 v r ( k m s - ) And XII0 2 4 6 8 η σ v ( k m s - ) -118-116-114-112-110-108-106 v r ( k m s - ) And XIX0 1 2 3 4 η σ v ( k m s - ) -365-364-363-362-361-360 v r ( k m s - ) And XXI0 2 4 6 8 10 η σ v ( k m s - ) -134-132-130-128-126 v r ( k m s - ) And XXII0 1 2 3 4 5 η σ v ( k m s - ) -242-240-238-236-234-232 v r ( k m s - ) And XXIII0 2 4 6 8 10 η σ v ( k m s - ) -112-110-108-106-104 v r ( k m s - ) And XXV0 1 2 3 4 5 6 η σ v ( k m s - ) Fig. 4.—
The effect of modifying η – a multiplicative weight applied to the dispersion of the identified substructure in our P vel term – onthe final derived systemic velocities ( v r ) and dispersions ( σ v ) for six of our dSphs.The effect of increasing η is typically more pronouncedin objects with systemic velocities close to that of Milky Way contamination (such as And XIX and XXV) than for other objects. Dashedlines represent the optimal value of η for each system. more robust in regimes where the systemic velocity ofthe dSph is close to that of the MW, and in dSphs whereour number of probable member stars is low ( N ∗ < v r and σ v , we use our datasets for And XXI, XXIIIand XXV, all of which have ≥
25 associated members.For each dataset, we apply a series of cuts to the samplebased on S:N (at levels of S:N > , , ◦ A) andrerun our algorithm. In all cases we find that the derivedprobabilities do not significantly differ when the low S:Ndata are included, justifying our inclusion of all stars forwhich velocities are calculated by our pipeline.We also test the ability of our algorithm to measure v r and σ v in the small N ∗ regime. For some of our datasets, we are only able to identify a handful of stars as probablemembers. In theory, one can calculate velocity disper-sions accurately from only 3 stars if one is confident ofones measurement uncertainties, as is demonstrated byAaronson, (1983) measurement of the velocity disper-sion for Draco from only 3 stars, which remains consis-tent with modern day measurements from significantlylarger datasets (Walker et al. 2009b). We can test ifour results are similarly robust using our larger datasets(such as And XXI, XXIII and XXV) by randomly select-ing 4, 6, 8, 10, 15, 20 and 25 stars from these datasetsand rerunning our algorithm to determine v r and σ v fromthese subsets. We repeat this exercise 1000 times for eachsample size, and examine the mean and standard devia-tions for the computed quantities. We find that on aver-0 Collins et al.age, for all sample sizes, our routine measures systemicvelocities and velocity dispersions that are entirely con-sistent with those measured from the full sample, witha spread that is very comparable to typical errors pro-duced by our ML routine in these low N ∗ regimes. Assuch, we conclude that our technique is able to place sen-sible limits on these values, even when dealing with asfew as four member stars.Finally, as the individual positions, velocities and ve-locity uncertainties for all the stars analyzed in T12 arepublicly available (with the data from the non-memberstars having been kindly passed on to us by the SPLASHteam), we can check that our algorithm is able to repro-duce the values they measure for their M13 dSph sample.We find that, in all cases, we calculate systemic velocitiesand velocity dispersions that agree with their measuredvalues to well within their 1 σ uncertainties.These tests demonstrate that our method is robustenough to accurately determine the global kinematicproperties of M31 dSphs across a wide range of samplesizes and data quality. We therefore proceed to apply itto the datasets of all of the dSphs for which our grouphas acquired Keck II DEIMOS observations to date. THE KINEMATICS OF M31 DSPHS
With this vast dataset of dSph kinematics now in hand,we can begin to statistically probe their structures morefully. In Fig. 5 we display a summary of the velocities andpositions of 26 of the 28 dSphs for which kinematic dataare available, where the values are taken from this work,T12 and Kalirai et al. (2010). In the following sections,we will discuss the individual stellar kinematics, massesand chemistries of the dSphs analyzed within this work.
Andromeda XVII
And XVII was discovered by Irwin et al. (2008), andit is located at a projected distance of ∼
40 kpc to theNorth West of Andromeda. A detailed study of deepimaging obtained with the Large Binocular Camera onthe LBT was also performed by Brasseur et al. (2011b),and throughout, we use the structural properties as de-termined from this work. It is a faint, compact galaxy( M V = − . , r half = 1 . ′ or 262 +53 − pc). In the leftpanel of Fig. 6 we display the PAndAS color magnitudediagram for And XVII. Over-plotted we show the ob-served DEIMOS stars, color-coded by their probabilitiesof membership. The open symbols represent stars forwhich P i < − . We employ this cut solely to makeclarify which stars have the highest probability of be-longing to And XVII. In the right hand panel, we dis-play the basic kinematic information for And XVII. Inthe top panel of this subplot, we show a velocity his-togram for all stars observed within the LRIS mask, andstars with P i > − are highlighted with a filled red his-togram. The centre panel shows the velocities as a func-tion of distance from the centre of And XVII (and the reddashed lines indicate 1 , , × r half ), and the lowerpanel shows the photometric metallicities for all stars, asdetermined using Dotter et al. (2008) CFHT isochrones.Again, all points are color-coded by their probability ofmembership. Finally, the two lower panels show the re-sulting, one dimensional, probability weighted, marginal-ized maximum likelihood distributions for v r and σ v forthis data set. From the kinematics presented in Fig. 6, which represent the first spectroscopic observations ofthis object, we see the signature of the dwarf galaxy as acold spike at v r ∼ −
250 km s − . From the lower panels ofthis figure and the accompanying CMD we see that thereis a cluster of 7 stars sitting within this spike that arecentrally concentrated and are consistent with the RGBof the dwarf itself, leading us to believe that our algo-rithm has cleanly detected the signature of the galaxy.Interestingly, we also see 3 stars that, kinematically, areindistinguishable from the stars that have been dubbedas probable members in our analysis. However, they allsit at large distances from the centre of And XVII, equiv-alent to greater than 6 times the half-light radius of thedwarf, and hence the routine has classified them as likelymembers of the M31 halo rather than And XVII mem-bers. But, given their tight correlation in velocity to thesystemic velocity of And XVII the possibility exists thatthese are extra-tidal stars of And XVII. No sign of extra-tidal features were cited in either the discovery paper ofAnd XVII or the LBT followup, but given its position inthe north M31 halo where contamination from the MWbecomes increasingly problematic, and its relatively lowluminosity ( M V = − . v r = − . +1 . − . km s − and σ v = 2 . +2 . − . km s − . Andromeda XVIII
Andromeda XVIII (And XVIII) was detected byMcConnachie et al. (2008) in the PAndAS CFHT maps.Located at a projected distance of ∼
110 kpc to theNorth-West of M31, it is one of the most distant of itssatellites, sitting ∼
600 kpc behind the galaxy, makingspectroscopic observations of its individual RGB starstaxing, as they are all relatively faint ( i ∼ > . v r = − . ± . − , and we are unable to resolve a ve-locity dispersion, finding σ v = 0 . +2 . km s − where theupper bound is determined from the formal 1 σ confidenceinterval produced by our maximum likelihood analysis.This suggests that the 4 stars we are able to confirm asmembers do not adequately sample the underlying ve-locity profile. The systemic velocity we measure is dif-ferent to that presented in T12 of v r = − . ± . σ . Our 1 σ limit of 2.7 km s − is also at oddswith the dispersion determined by T12 ( σ v = 9 . ± . § − from those values. The true systemic velocityhe kinematics of Andromeda’s dSphs 11 −10−50510152025 RA (deg) D e c ( d e g ) III III VIIXIVV VIIXX XIXIIXIIIXV XVI XVII XVIIIXXXXIIXXIII XXIV XXVIXXVIICassII XXIXXV XIX
M31M33
PAndAS −550−500−450−400−350−300−250−200−150 v r ( k m / s ) Fig. 5.—
Positions of 26 of the 28 Andromeda dSphs, color coded by their heliocentric velocity, v r (taken from this work, Kalirai et al.2010 and T12). The solid line represents the PAndAS survey foot print. M31 is shown by the double ellipse, where the outer ellipse showsa segment of a 55 kpc radius ellipse flattened to c/a = 0.6, and the major-axis and minor-axis are indicated with straight lines out to thisellipse. The inner ellipse corresponds to a disc of radius 2 ◦ (27 kpc), with the same inclination as the main M31 disc. M33 is shown as asingular ellipse. of And XVIII therefore remains unclear. However, giventheir larger sample size, the T12 systemic properties aremore statistically robust than those we present here. Andromeda XIX
Andromeda XIX (And XIX) was first reported inMcConnachie et al. (2008), and is a relatively bright,very extended ( M V = − . r half = 1 . ∼
180 kpc to thesouth west of M31. Its unusual morphology, very lowsurface brightness Σ v = 30 . , and evidencein the photometry for a possible link to the majoraxis substructure reported in Ibata et al. (2007) causedMcConnachie et al. (2008) to question whether And XIXwas truly a dynamically relaxed system, or whether ithad experienced a significant tidal interaction. Here, wepresent the first spectroscopic observations of the AndXIX satellite in Fig. 8 from two DEIMOS masks placedat different position angles. These data allow us to com-ment on its dark matter content, and on the likelihoodof a tidal origin for its unique structure. We identify27 stars where P i > − within the system. Thesemeasurements were made increasingly challenging as the systemic velocity we measure is v r = − . +1 . − . km s − ,placing it within the regime of Galactic contamination.However, we are confident that our algorithm is robustto this unfortunate location of And XIX in velocity space(see discussion in § ∼ ◦ A). These gravity-sensitive absorption linesare typically significantly stronger in foreground dwarfstars than M31 RGB stars, although there is some over-lap between the two populations. For the stars taggedas probable members by our algorithm, we find no ev-idence of strong absorption in the region of the Na Idoublet, indicating that we are not selecting foregroundstars as members. We measure a relatively cold velocitydispersion for this object of σ v = 4 . +1 . − . km s − , which issurprising given the radial extent of this galaxy. This re-sult will be discussed further in § Andromeda XX −0.5 0.0 0.5 1.0 1.5 2.0 2.5 g-i i And XVII P i F r e q . And XVII D i s t a n c e ( a r c m i n ) −500 −400 −300 −200 −100 0 100 v hel (km/s) −3.0−2.5−2.0−1.5−1.0−0.5 [ F e / H ] P i -280 -260 -240 -220v hel (kms -1 )0.010.101.00 R e l a t i v e li k e li hood And XVII - v r =-251.6 +1.8-2.0 (kms -1 ) σ v (kms -1 )0.010.101.00 σ v =2.9 +2.2-1.9 (kms -1 ) Fig. 6.—
CMD of And XVII, from PAndAS photometry (not extinction corrected). All stars observed with DEIMOS are color coded bytheir probability of membership.
Top right:
Kinematic information for all stars observed with DEIMOS. The top subplot shows a velocityhistogram for our sample, with all stars with P i > − highlighted as a filled red histogram. The central subplot shows the distance ofeach star from the centre of And XVII as a function of velocity, and the lower subplot shows the photometric metallicity for each star,interpolated from Dotter et al. (2008) isochrones in the CFHT-MegaCam g − and i − bands (after correcting the observed colors of the starsfor extinction using the Schlegel et al. (1998) dust maps), as a function of velocity. Stars that lie far from the RGB of the dSph are notwell matched by the isochrones, and as a result there is no estimate of their [Fe/H]. Lower panels:
Resulting probability distributionsfrom ML analysis of the kinematics of And XVII. The left hand panel shows the systemic velocity ( v r ) likelihood distribution and the rightshows the intrinsic velocity dispersion ( σ v ) likelihood distribution. The dashed lines represent canonical 1 , σ confidence intervals,derived assuming Gaussian uncertainties. he kinematics of Andromeda’s dSphs 13 −0.5 0.0 0.5 1.0 1.5 2.0 2.5 g-i i And XVIII P i F r e q . And XVIII D i s t a n c e ( a r c m i n ) −500 −400 −300 −200 −100 0 100 v hel (km/s) −3.0−2.5−2.0−1.5−1.0−0.5 [ F e / H ] P i -400 -380 -360 -340 -320v hel (kms -1 )0.010.101.00 R e l a t i v e li k e li hood And XVIII - v r =-346.8 ± -1 ) σ v (kms -1 )0.010.101.00 σ v =0.0 +2.7 (kms -1 ) Fig. 7.—
As Fig. 6, but for And XVIII. −0.5 0.0 0.5 1.0 1.5 2.0 2.5 g-i i And XIX P i F r e q . And XIX D i s t a n c e ( a c m i n ) −500 −400 −300 −200 −100 0 100 v hel (km/s) −3.0−2.5−2.0−1.5−1.0−0.5 [ F e / H ] P i -140 -120 -100 -80v hel (kms -1 )0.010.101.00 R e l a t i v e li k e li hood And XIX - v r =-111.6 +1.6-1.4 (kms -1 ) σ v (kms -1 )0.010.101.00 σ v =4.7 +1.6-1.4 (kms -1 ) Fig. 8.—
As Fig. 6, but for And XIX.
And XX was the third of three dSphs discovered byMcConnachie et al. (2008), and is notable for being oneof the faintest dSph companions detected surroundingAndromeda thus far. With M V = − . r half =114 +31 − pc, it is a challenging object to study spectro-scopically as there are very few stars available to tar-get on its RGB, as shown in the top left subplot inFig. 9. As a result, our algorithm is only able to find4 stars for which P i > − . These are found to clus-ter around v r = − . +3 . − . km s − , with a dispersion of σ v = 7 . +3 . − . km s − . Despite the low number of stars, weare confident in this detection, as the systemic velocityplaces it in the outer wings of the velocity profile of theM31 halo. And XX is also located at a large projecteddistance from M31 of ∼
130 kpc, where we expect thedensity of the M31 halo to be very low. As such, seeing 4halo stars so tightly correlated in velocity in the wings ofthe halo velocity profile within such a small area of thesky (all stars are within 1 arcmin of the centre of AndXX) is highly unlikely. We caution the reader that, whilehe kinematics of Andromeda’s dSphs 15we are confident that our algorithm is able to measurevelocity dispersions for sample sizes as small as 4 stars,as we are not probing the full velocity profile of this ob-ject this measurement ideally needs to be confirmed withlarger numbers of member stars.
Andromeda XXI
Andromeda XXI (And XXI) was identified within thePAndAS imaging maps by Martin et al. (2009). It isa relatively bright dSph ( M V = − . ∼
150 kpc from M31, and ithas a half-light radius of r half = 842 ±
77 pc. Wepresent our spectroscopic observations for this object inFig. 10, and in the top right subplot, we can clearlysee the signature of And XXI as a cold spike in ve-locity with 32 probable member stars, located at v r = − . ± . − , with a curiously low velocity dis-persion of only σ v = 4 . +1 . − . km s − . These results arecompletely consistent with those of T12, where they mea-sured v r = − . ± . − and σ v = 7 . ± . − .As their sample contained only 6 likely members com-pared with the 29 we identify here, ours constitute a morestatistically robust measurement of the global kinematicsfor this object than those presented in T12. Andromeda XXII
Andromeda XXII (And XXII) was identified within thePAndAS imaging maps by Martin et al. (2009), and isa relatively faint dSph, with M V = − .
5. Its physicalposition in the halo, located at a distance of 224 kpcin projection from M31, but only 42 kpc in projectionfrom M33, led the authors to postulate that it could bethe first known dSph satellite of M33. Subsequent workanalysing the kinematics of And XXII by T12 measureda systemic velocity for And XXII of − . ± . − from 7 stars, more compatible with the systemic velocityof M33 ( −
178 km s − , Mateo 1998) than that of M31.Another study by Chapman et al. (2012) using the samedata and the same method we present here concluded thesame, measuring a systemic velocity for the satellite of − . ± . N − body simulations of the M31-M33 system, concludingthat And XXII was a probable M33 satellite.In Fig. 11, we present the same data as analyzedby Chapman et al. (2012) for completeness. The ve-locity dispersion of And XXII is just resolved at σ v =2 . +1 . − . km s − , completely consistent with the value of σ v = 3 . +4 . − . km s − from T12. As our values are calcu-lated from a 50% greater sample size, we posit that theyare the more statistically robust. Andromeda XXIII
Andromeda XXIII (And XXIII) was the first of fiveM31 dSphs identified by Richardson et al. (2011). Lo-cated at a projected distance of ∼
130 kpc to the eastof Andromeda, it is relatively bright, with M V = − . r half = 1001 +53 − pc. Our routineclearly detects a strong cold kinematic peak for AndXXIII located around −
230 km s − and calculates a sys-temic velocity of v r = − . ± . − , and a veloc-ity dispersion of σ v = 7 . ± . − from 40 probable member stars, as show in Fig. 12. This small, positive ve-locity relative to M31, combined with its large projecteddistance from the host suggests that And XXIII is notfar past the apocentre of its orbit, heading back towardsM31. Andromeda XXIV
And XXIV was also first reported in Richardson et al.(2011). Relatively faint and compact ( M V = − . r half = 548 +31 − pc), spatially it is located ∼
200 kpc fromM31, along its northern major axis. And XXIV was ob-served on two separate occasions as detailed in Table 2.For the first mask, there was an error in target selection,and as a result, only one star that lay on the RGB of AndXXIV was observed. The second mask was observed inMay 2011, however owing to target visibility, only a shortintegration of 45 minutes was obtained, which resultedin higher velocity uncertainties than typically expected( ∼ − vs. ∼ − ). For this reason, we haveonly included stars from this mask with i < .
0, as thespectra for fainter stars were too noisy to determine reli-able velocities from. The systemic velocity of And XXIValso unsatisfactorily coincides with that of the MW halocontamination, as can be seen in Fig. 13. As for AndXIX, we check the strength of the Na I doublet of allthe stars classified as potential members for And XXIV,and find no significant absorption, making them unlikelyforeground contaminants. But, given the lower qualityof this dataset, this check is far from perfect, and it ispossible that we have included contaminants from theMW within our sample. Owing to the larger velocity un-certainties of the And XXIV dataset, and the overlap ofAnd XXIV with the MW, the determination of probabil-ity of membership for stars within this dataset is basedlargely on their position in the color magnitude diagram(e.g., location on the RGB) and their distance from thecentre of And XXIV.When we run our machinery over the data acquiredfrom both masks, we identify only 3 probable membersand determine a systemic velocity of v r = − . ± . − and we resolve a velocity dispersion of σ v =0 . +7 . km s − . Given the lower quality of this dataset incomparison to the remainder of those we present in thiswork, and the overlap of And XXIV in velocity spacewith contamination from the MW, a robust kinematicdetection and characterisation of this galaxy is made in-credibly challenging. As such, we present these resultsas a tentative identification of And XXIV, and do notinclude its measured properties in the remainder of ouranalysis. Further kinematic follow up of And XXIV is re-quired to understand this system. We present the veloc-ities of all bright stars for which velocity measurementswere possible in Table 3 so that they may be helpful forany future kinematic analysis of this system. Andromeda XXV
And XXV was identified in Richardson et al. (2011)as a relatively bright ( M V = − . r half =642 +47 − pc) dwarf spheroidal, located at a projected dis-tance of ∼
90 kpc to the north west of M31. As with AndXXIII, we present here a kinematic analysis of And XXV.The results are displayed in Fig. 14. We see that the sys-temic velocity of And XXV ( v r = − . ± . − ),6 Collins et al. −0.5 0.0 0.5 1.0 1.5 2.0 2.5 g-i i And XX P i F r e q . And XX D i s a n c e ( a r c m i n ) −500 −400 −300 −200 −100 0 100 v hel (km/s) −3.0−2.5−2.0−1.5−1.0−0.5 [ F e / H ] P i -500 -480 -460 -440 -420v hel (kms -1 )0.010.101.00 R e l a t i v e li k e li hood And XX - v r =-456.2 +3.1-3.6 (kms -1 ) σ v (kms -1 )0.010.101.00 σ v =7.1 +3.9-2.5 (kms -1 ) Fig. 9.—
As Fig. 6, but for And XX. places it in the regime of the Galactic foreground. How-ever, given the strong over-density of stars with this ve-locity relative to the expected contribution of MW stars,we are confident that our routine has detected 25 likelymembers for this object. We check the strength of the NaI doublet in these likely members, and find no significantabsorption, making them unlikely foreground contami-nants. As for And XIX and XXI, we find that And XXVhas a curiously low velocity dispersion for its size, with σ v = 3 . +1 . − . km s − . We discuss the significance of this further in § Andromeda XXVI
And XXVI is a relatively faint ( M V = − .
1) dSph with r half = 219 +67 − pc, also first reported in Richardson et al.(2011). Its low luminosity makes observing large num-bers of member stars difficult, owing to the paucityof viable targets on the RGB that can be observedwith DEIMOS. As a result, our routine has identi-fied only 6 stars as potential members, highlighted inhe kinematics of Andromeda’s dSphs 17 −0.5 0.0 0.5 1.0 1.5 2.0 2.5 g-i i And XXI P i F r e q . And XXI D i s t a n c e ( a c m i n ) −500 −400 −300 −200 −100 0 100 v hel (km/s) −3.0−2.5−2.0−1.5−1.0−0.5 [ F e / H ] P i -400 -380 -360 -340v hel (kms -1 )0.010.101.00 R e l a t i v e li k e li hood And XXI - v r =-362.5 ± -1 ) σ v (kms -1 )0.010.101.00 σ v =4.5 +1.2-1.0 (kms -1 ) Fig. 10.—
As Fig. 6, but for And XXI
Fig. 15. The dwarf has a systemic velocity of v r = − . +3 . − . km s − , and a fairly typical velocity disper-sion of σ v = 8 . +2 . − . km s − . As with And XX, while webelieve our routine can robustly measure the velocity dis-persions of systems with only 6 confirmed members, tobe truly confident of this value, follow up of And XXVIto increase the number of likely members is required.In Conn et al. (2012), from an analysis of the photom-etry of And XXVI, they determined a distance modulus to the object of ( m − M ) = 24 . +0 . − . from a Markov-Chain-Monte-Carlo analysis of the PAndAS photometryof And XXVI. This value corresponds to an i − band mag-nitude for the TRGB of And XXVI of m i, = 21 . +0 . − . .Our CMDs for the dwarfs are not extinction corrected,but using the extinction values from Richardson et al.(2011) of E ( B − V ) = 0 .
110 (Schlegel et al. 1998), thiswould correspond to an i − band magnitude of m i,T RGB =21 . +0 . − . . Three targets were observed with magnitudes8 Collins et al. −0.5 0.0 0.5 1.0 1.5 2.0 2.5 g-i i And XXII P i F r e q . And XXII D i s t a n c e ( a c m i n ) −500 −400 −300 −200 −100 0 100 v hel (km/s) −3.0−2.5−2.0−1.5−1.0−0.5 [ F e / H ] P i -160 -140 -120 -100 -80v hel (kms -1 )0.010.101.00 R e l a t i v e li k e li hood And XXII - v r =-129.8 ± -1 ) σ v (kms -1 )0.010.101.00 σ v =2.8 +1.9-1.4 (kms -1 ) Fig. 11.—
As Fig. 6, but for And XXII and colors that should be consistent with their belongingto And XXVI. However. we find that all these objectshave velocities that are consistent with being Galacticforeground contaminants. Given the position of AndXXVI in the northern M31 halo, where contaminationfrom the MW increases, this is not unexpected. Thebrightest star we observe that is likely associated withAnd XXVI has m i = 21 . m i, = 21 . m i, = 21 .
7, with colors consistent with the And XXVIRGB was observed, this value merely represents an upperlimit, on the distance to And XXVI and highlights thedifficulty of calculating distances to these faint galaxieswhere RGB stars are sparse.
Andromeda XXVII he kinematics of Andromeda’s dSphs 19 −0.5 0.0 0.5 1.0 1.5 2.0 2.5 g-i i And XXIII P i F r e q . And XXIII D i t a n c e ( a r c m i n ) −500 −400 −300 −200 −100 0 100 v hel (km/ ) −3.0−2.5−2.0−1.5−1.0−0.5 [ F e / H ] P i -300 -280 -260 -240 -220v hel (kms -1 )0.010.101.00 R e l a t i v e li k e li hood And XXIII - v r =-237.6 ± -1 ) σ v (kms -1 )0.010.101.00 σ v =7.1 ± -1 ) Fig. 12.—
As Fig. 6, but for And XXIII.
Andromeda XXVII (And XXVII) is a somewhat un-usual object as it is currently undergoing tidal disrup-tion, spreading its constituent stars into a large stellarstream, named the northwestern arc, discovered in thePAndAS survey by Richardson et al. (2011). As such, itis unlikely to be in virial equilibrium, if it remains boundat all.When determining the kinematics of And XXVII, wefind the results somewhat unsatisfactory. Our rou-tine determines v r = − . +4 . − . km s − and σ v = 14 . +4 . − . km s − from 11 stars. However, from an inspec-tion of Fig. 16, we see that there is significant substruc-ture around v hel ∼ −
500 km s − , much of which is consid-ered to be unassociated with And XXVII in this analysisas it does not fall within a cold, well-defined Gaussian ve-locity peak. Given the disrupting nature of And XXVII,it is likely that a different analysis is required for this ob-ject, and we shall discuss this further in a future analysis,where the kinematics of the northwestern arc itself arealso addressed. From this first pass however, it would ap-0 Collins et al. TABLE 3Details of probable dSph members (This table is available in its entirety in machine-readable form inthe online journal. A portion is shown here for guidance regarding its form and content)
Field Star ID α ,J δ ,J g i v hel ( km s − ) v err ( km s − ) S:N ( ◦ A − ) P i And V 9 1:10:2.38 47:37:48.5 23.640 22.402 -371.270 5.080 1.700 0.014And V 12 1:10:5.540 47:36:41.6 23.100 21.530 -406.500 3.600 2.000 0.111... ... ... ... ... ... ... ... ... ... pear that And XXVII may no longer be a gravitationallybound system.
Andromeda XXVIII
And XXVIII was recently discovered in the 8th datarelease of the SDSS survey (Slater et al. 2011). It has M v = − . r half = 210 +60 − pc. It is also potentiallyone of Andromeda’s most distant satellites, with a host-satellite projected separation of 365 +17 − kpc. The AndXXVIII satellite is not covered by the PAndAS footprint,so we must instead use the original SDSS photometry forour analysis. A CMD with the SDSS i − band and r − i colors for And XXVIII is shown in Fig. 17, where alltargets brighter that i ∼ . r half are shown.The photometry here do not show an RGB that is asconvincing as those from the PAndAS survey, so to guidethe eye, we also overplot an isochrone from Dotter et al.(2008) with a metallicity of [Fe / H] = − .
0, corrected forthe distance of And XXVIII as reported in Slater et al.(2011).In a recent paper, Tollerud et al. (2013) discussed thekinematics of this object as derived from 18 membersstars. They find v r = − . ± . − and σ v =8 . ± . − from their full sample. They then removetwo stars that they categorize as outliers based on theirdistance from the centre of And XXVIII, which alterstheir measurements to v r = − . ± . − and σ v =4 . ± . − . Analyzing our own DEIMOS datasetfor this object, we find v r = − . ± . − and σ v = 6 . +2 . − . km s − based on 17 probable members. Thisis fully consistent with the results from the full samplein Tollerud et al. (2013). However, the systemic velocitywe measure is offset at a level of ∼ σ from their finalvalue (calculated after excluding 2 outliers). This offsetis small, and is probably attributable to our differingmethodologies for classifying stars as members. As webelieve our method is more robust (as discussed in § And XXX/Cassiopeia II
And XXX – also known as Cass II owing to its spatiallocation, overlapping the Cassiopeia constellation – is arecently discovered dSph from the PAndAS survey (Irwinet al. in prep). It has M v = − . r half = 267 +23 − pc.Located to the north west of Andromeda, it sits within60 kpc of the two close dwarf elliptical M31 companions,NGC 147 and NGC 185. With these 3 objects found soclose together in physical space, it is tempting to supposethem a bound system within their own right, but this canonly be borne out by comparing their kinematics.Conspiring to confound us, we find that Cass II haskinematics that place it well within the regime of Galac- tic foreground, as can be seen in Fig. 18. However,our analysis is able to detect the dSph as a cold spikeconsisting of 8 likely members. As for And XIX, wecheck the strength of the Na I doublet in these likelymembers, and find no significant absorption, makingthem unlikely foreground contaminants. We measure v r = − . +6 . − . km s − , and a fairly typical velocity dis-persion of σ v = 11 . +7 . − . km s − .The systemic velocity of Cass II ( v r = − . +6 . − . km s − ) puts it within ∼
50 km s − ofthose of NGC 147 and NGC 185 ( v r = − ± − and v r = − ± − , Mateo 1998), lendingfurther credence to the notion that these 3 systems areassociated with one another. This will be discussed inmore detail in Irwin et al. (2013, in prep). A note on previous work
Finally, we also use our new algorithm to reanalyze allour previously published M31 dSph datasets. These in-clude And V, VI (Collins et al. 2011), XI, XII and XIII(Chapman et al. 2007; Collins et al. 2010). Details of theresults of this reanalysis can be found in Appendix B. Insummary, we find that our algorithm measures systemicvelocities and velocity dispersions that are fully consis-tent with our previous work. We present these results inTable 4. And V, XI, XII and XIII are also analyzed byT12, so we compare our findings with theirs. For AndXI and XII, our results are based on two and four timesthe number of stars respectively, and as such, supercedethose presented in T12. In the case of And V and XIII,the T12 measurements are based sample sizes with fourtimes the number of stars as our datasets, making theirfindings more robust.In previous studies by our group (Chapman et al.2005; Letarte et al. 2009; Collins et al. 2010), we alsopublished kinematic analyses for three additional M31dSphs; And IX, And XV and And XVI. In T12, it wasnoted that the values presented in these works for sys-temic velocities and velocity dispersions were not con-sistent with those measured in their analyses. We re-visited these datasets in light of this discrepancy, to seeif our new technique could resolve this issue. We foundthat these discrepancies remained. For And IX, we mea-sure a systemic velocity of v r = − . ± . − cf. v r = − . ± . − in T12 and a velocity dispersionof σ v = 2 . +2 . − . km s − cf. σ v = 10 . ± . − . Notonly are their measurements determined from 4 times themember stars that we possess, we also experienced prob-lems with our radial velocity measurements for the starsobserved with this mask, due to the use of the minislitletapproach pioneered by Ibata et al. (2005). This setupresulted in poor sky subtraction for many of the sciencehe kinematics of Andromeda’s dSphs 21 −0.5 0.0 0.5 1.0 1.5 2.0 2.5 g-i i And XXIV P i F r e q . And XXIV D i s t a n c e ( a c m i n ) −500 −400 −300 −200 −100 0 100 v hel (km/s) −3.0−2.5−2.0−1.5−1.0−0.5 [ F e / H ] P i -160 -140 -120 -100 -80v hel (kms -1 )0.010.101.00 R e l a t i v e li k e li hood And XXIV - v r =-128.2 ± -1 ) σ v (kms -1 )0.010.101.00 σ v =0.0 +7.3 (kms -1 ) Fig. 13.—
As Fig. 6, but for And XXIV. spectra, lowering the quality of our radial velocity mea-surements. As such, the T12 results supercede those ofour previous work (Chapman et al. 2005; Collins et al.2010).For And XV and XVI, we measure a systemic velocitiesof v r = − . ± . − and v r = − . ± . − cf. v r = − . ± . − and v r = − . ± . − from T12. We also note offsets in our ve-locity dispersions for And XV and XVI, where we mea-sure σ v = 9 . +4 . − . km s − and σ v = 17 . +6 . − . km s − cf. σ v = 3 . ± . − . In this instance, the data for bothAnd XV and XVI were taken in poor conditions, withvariable seeing that averaged at 1 . ′′ and patchy cirrus.These conditions significantly deteriorated the quality ofour spectra, and made the measurement of reliable ra-dial velocities extremely difficult. Again, this leads us toconclude that the measurements made in T12 supercedethose presented by our group in Letarte et al. (2009).2 Collins et al. −0.5 0.0 0.5 1.0 1.5 2.0 2.5 g-i i And XXV P i F r e q . And XXV D i s t a n c e ( a c m i n ) −500 −400 −300 −200 −100 0 100 v hel (km/s) −3.0−2.5−2.0−1.5−1.0−0.5 [ F e / H ] P i -160 -140 -120 -100 -80v hel (kms -1 )0.010.101.00 R e l a t i v e li k e li hood And XXV - v r =-107.8 ± -1 ) σ v (kms -1 )0.010.101.00 σ v =3.0 +1.2-1.1 (kms -1 ) Fig. 14.—
As Fig. 6, but for And XXV. THE MASSES AND DARK MATTER CONTENT OF M31DSPHS
Measuring the masses and mass-to-light ratios ofour sample
As dSph galaxies are predominantly dispersion sup-ported systems, we can use their internal velocity dis-persions to measure masses for these systems, allowing usto infer how dark matter dominated they are. There areseveral methods in the literature for this (e.g., Illingworth 1976; Richstone & Tremaine 1986), but recent work byWalker et al. (2009a) has shown that the mass containedwithin the half-light radius ( M half )of these objects canbe reliably estimated using the following formula: M half = µr half σ v, half (12)where µ = 580 M ⊙ pc − km − s , r half is the spherical half-light radius in pc and σ v, half is the luminosity- averagedvelocity dispersion. This mass estimator is independenthe kinematics of Andromeda’s dSphs 23 −0.5 0.0 0.5 1.0 1.5 2.0 2.5 g-i i And XXVI P i F r e q . And XXVI D i t a n c e ( a r c m i n ) −500 −400 −300 −200 −100 0 100 v hel (km/ ) −3.0−2.5−2.0−1.5−1.0−0.5 [ F e / H ] P i -280 -260 -240 -220 -200v hel (kms -1 )0.010.101.00 R e l a t i v e li k e li hood And XXVI - v r =-261.6 +3.0-2.8 (kms -1 ) σ v (kms -1 )0.010.101.00 σ v =8.6 +2.8-2.2 (kms -1 ) Fig. 15.—
As Fig. 6 but for And XXVI. of the (unknown) velocity anisotropy of the tracer pop-ulation, however, it is sensitive to the embeddedness ofthe stellar component within the DM halo. Particularly,the mass tends to be slightly over-estimated the moreembedded the stars are (Walker & Pe˜narrubia 2011), es-pecially if the dark matter halo follows a cored densityprofile.As numerous authors have shown that the veloc-ity dispersion profiles of dSphs are constant withradius (e.g., Walker et al. 2007, 2009b), we assume our measured values of σ v are representative of theluminosity-averaged velocity dispersion ( σ v, half ) used byWalker et al. (2009b). However, if it transpired that thevelocity dispersion profiles of the Andromedean dSphswere not flat, but declined or increased with radius, thiswould no longer true. We see no evidence for this be-haviour in our dataset, although low-number statisticsmeans we are unable to completely rule out this pos-sibility. We calculate this for all our observed dSphs(including those we reanalyzed from previous works, see4 Collins et al. −0.5 0.0 0.5 1.0 1.5 2.0 2.5 g-i i And XXVII P i F r e q . And XXVII D i s t a n c e ( a r c m i n ) −600 −500 −400 −300 −200 −100 0 100 v hel (km/s) −3.0−2.5−2.0−1.5−1.0−0.5 [ F e / H ] P i -560 -540 -520 -500 -480v hel (kms -1 )0.010.101.00 R e l a t i v e li k e li hood And XXVII - v r =-539.6 +4.7-4.5 (kms -1 ) σ v (kms -1 )0.010.101.00 σ v =14.8 +4.3-3.1 (kms -1 ) Fig. 16.—
As Fig. 6, but for And XXVII.
Appendix B) using results from the Keck LRIS andDEIMOS dataset, and report their masses within r half ( M half ) in Table 4.From these masses, it is trivial to estimate the dynami-cal central mass-to-light ratios for the objects, [ M/L ] half .We list these values for each dSph in Table 4, where theassociated uncertainties also take into account those fromthe measured luminosities and distances to these dSphs(McConnachie 2012; Conn et al. 2012), as well as thoseon the masses measured in this work. Comparing the mass-to-light ratios of M31 andMilky Way dSphs
By combining our measurements of the kinematicof M31 dSphs in this work with those from T12 andTollerud et al. (2013), we find ourselves with a set ofkinematic properties as measured for 27 of the 28 An-dromeda dSphs (owing to the difficulties experiencedwith the And XXIV dataset, we do not include thisobject in our subsequent analysis). This near-completehe kinematics of Andromeda’s dSphs 25 −0.5 0.0 0.5 1.0 1.5 2.0 2.5 r-i i And XXVIII P i F r e q . And XXVIII D i s t a n c e ( a r c m i n ) −500 −400 −300 −200 −100 0 100 v hel (km/s) −3.0−2.5−2.0−1.5−1.0−0.5 [ F e / H ] P i -360 -340 -320 -300v hel (kms -1 )0.010.101.00 R e l a t i v e li k e li hood And XXVIII - v r =-326.2 ± -1 ) σ v (kms -1 )0.010.101.00 σ v =6.6 +2.9-2.1 (kms -1 ) Fig. 17.—
As Fig. 6, but for And XXVIII. sample allows us to fully compare the masses and mass-to-light ratios for the M31 satellite system with thosemeasured in the Milky Way satellites. Before beginningthis analysis, we compile Table 5 which presents the kine-matics for the full M31 satellite system, which combinesthe results from this work, T12, Kalirai et al. (2010), andTollerud et al. (2013). In cases where two measurementsfor a dSph exist, we use those that were calculated fromlarger numbers of likely members, as these are the morerobust. We begin by comparing the mass-to-light ra- tios (which indicate the relative dark matter dominanceof these objects) of the two populations as a functionof luminosity. In Fig 19 we show these values for allMW (red triangles, with values taken from Walker et al.2009b), and M31 (blue circles) dSphs as a function oftheir luminosity. We can see that all these objects areclearly dark matter dominated, excluding And XII andAnd XVII where we are unable to resolve the mass withcurrent datasets. We also see that they follow the trendof increasing [
M/L ] half with decreasing luminosity, as is6 Collins et al. −0.5 0.0 0.5 1.0 1.5 2.0 2.5 g-i i Cass II P i F r e q . Cass II D i s a n c e ( a r c m i n ) −500 −400 −300 −200 −100 0 100 v hel (km/s) −3.0−2.5−2.0−1.5−1.0−0.5 [ F e / H ] P i -180 -160 -140 -120 -100v hel (kms -1 )0.010.101.00 R e l a t i v e li k e li hood Cass II - v r =-139.8 +6.0-6.6 (kms -1 ) σ v (kms -1 )0.010.101.00 σ v =11.8 +7.7-4.7 (kms -1 ) Fig. 18.—
As Fig. 6, but for Cass II seen in their MW counterparts.The one tentative exception to this is the And XXVdSph. From our dataset, we measure a value of[
M/L ] half = 10 . +7 . − . for this object, making it consis-tent with a stellar population with no dark matter withinits 1 σ uncertainties. This result is surprising and wouldbe of enormous importance if confirmed with a largerdataset than our catalog of 26 likely members as it wouldbe the first dSph to be observed with a negligible darkmatter component. And XXV is also one of the mem- bers of the recently discovered thin plane of satellites inAndromeda (Ibata et al. 2013), and so the presence orabsence of dark matter in And XXV might tell us moreabout the origins of this plane which are currently poorlyunderstood. Comparing the masses of M31 and Milky WaydSphs
Finally, we discuss how the masses for the full sam-ple of Andromeda dSphs for which kinematic data arehe kinematics of Andromeda’s dSphs 27
TABLE 4Kinematic properties of Andromeda dSph galaxies as derived within this work,from Keck I LRIS and Keck II DEIMOS data.
Property η v r σ v M half [ M/L ] half [Fe / H] spec ( km s − ) ( km s − ) (10 M ⊙ ) ( M ⊙ / L ⊙ )And V 2.0 − . ± . . +2 . − . . +0 . − . . +22 . − . − . ± . − . ± . . +1 . − . . ± . . +4 . − . − . ± . − . +3 . − . . +4 . ∗ ) − . . +0 . − . +115 − − . ± . − . ± . . +4 . . +0 . . +194 − . ± . − . ± . . +8 . ∗ ) . +0 . . +330 − . ± . − . +1 . − . . +2 . − . . +0 . − . +22 − − . ± . − . ± . . +2 . . +0 . +5 − . ± . − . +1 . − . . +1 . − . . +0 . − . . +37 − − . ± . − . +3 . − . . +3 . ∗ ) − . . +0 . − . . +147 . − . − . ± . − . ± . . +1 . − . . +0 . − . . +9 . − . − . ± . − . ± . . +1 . − . . +0 . − . . +58 . − . − . ± . − . ± . . ± . . ± . . ± . − . ± . − . ± . . +7 . ∗ ) . +0 . − . +157 − − . ± . − . ± . . +1 . − . . +0 . − . . +7 . − . − . ± . − . +3 . − . . +2 . ∗ ) − . . +0 . − . +243 − − . ± . − . +4 . − . . +4 . − . . +2 . − . +1039 − − . ± . − . ± . . +2 . − . . +0 . − . +30 − − . ± . − . +6 . − . . +7 . − . . +1 . − . +269 − − . ± . Note . — ( ∗ ) - indicates velocity dispersions derived from fewer than 8 members stars, andrequire confirmation from further follow-up. Fig. 19.—
Dynamical mass-to-light ratio within the half-lightradius, [
M/L ] half , as a function of half-light radius for all M31 (bluecircles), MW (red triangles) and isolated dSphs (cyan squares). available compare with those of the MW dSphs. For theM31 dSph population, we again use our compilation ofkinematic properties assembled in Table 5. We plot thevelocity dispersions, mass within the half-light radius,and central densities for all M31 (blue circles) and MW(red triangles, Walker et al. 2009b; Ad´en et al. 2009;Koposov et al. 2011; Simon et al. 2011) dSphs as a func-tion of radius. We then overplot the best-fit NFW andcored mass profiles for the MW, taken from Walker et al. (2009b). In general, we see that the M31 and MWobjects are similarly consistent with these profiles, anagreement that was also noted by T12. However, thereare 3 objects which are clear outliers to these relations.These are And XIX, XXI and XXV, with velocity dis-persions of σ v = 4 . +1 . − . km s − , σ v = 4 . +1 . − . km s − and σ v = 3 . +1 . − . km s − , as derived in this work. Given theirhalf-light radii ( r half =1481 +62 − pc, r half =842 ±
77 pcand r half =642 +47 − pc), one would expect them to havedispersions of closer to 9 km s − in order to be consistentwith the MW mass profile. As they stand, these threeobjects are outliers at a statistical significance of 2 . σ ,3 . σ and 3 . σ (calculated directly from their likelihooddistributions as presented in Figs. 8, 10 and 14). Sim-ilarly, in T12 they noted that And XXII and And XIVwere outliers in the same respect as And XIX, XXI andXXV, albeit at a lower significance. These difference canalso be observed in terms of the enclosed masses anddensities within r half .In Collins et al. (2011) we argued that the low veloc-ity dispersion seen in some Andromeda dwarfs were aresult of tidal forces exerted on their halos by the hostover the course of their evolution, and that this effectwas predominantly seen in dSphs where their half-lightradii were more extended for a given luminosity than ex-pected, such is the case our three outliers, And XIX, XXIand XXV. This result therefore adds weight to the trendpresented in that work. A number of recent works tryingto account for the lower than predicted central masses ofdSph galaxies within the Local Group also support thisnotion. For example, Pe˜narrubia et al. (2010) demon-strated that the presence of a massive stellar disk in thehost galaxy (such as those of the MW and M31) can sig-nificantly reduce the total masses of its associated satel-8 Collins et al. Fig. 20.—
Top:
Half-light radius ( r half ) vs. velocity dispersion for the MW (red triangles) and M31 (blue circles) dSphs. The bestfit NFW and cored mass profiles to the whole Local Group dSph population are over-plotted as dashed and dot-dashed lines respectively. Middle:
As above, but in the M half − r half plane. Lower:
As above but in the ρ half − r half plane. lites. In addition, recent, papers by Zolotov et al. (2012)and Brooks & Zolotov (2012), where the effect of baryonswithin dark matter only simulations was measured alsofind that tidal forces exerted by host galaxies where amassive disk is present will serve to reduce the masses ofits satellite population at a far greater rate than hostswithout baryons. And XIX, XXI and XXV may thusrepresent a population of dSph satellites whose orbitalhistories about M31 have resulted in substantial fractionsof their central mass being removed by tides. It shouldbe noted, however, that tides not only reduce the centralmasses and densities of dSph halos, they also reduce thespatial size of the luminous component (Pe˜narrubia et al.2008b, 2010), albeit at a slower rate. The tidal scenariois therefore slightly difficult to reconcile with these outly-ing M31 dSphs having the largest sizes, unless they were both more massive and spatially larger in the past.Other recent theoretical works have also shown thatthe removal of baryons from the very centres of darkmatter halos by baryonic feedback (from star forma-tion and supernovae, for example) can also help tolower the central masses and densities of satellite galax-ies (e.g., Pontzen & Governato 2012; Zolotov et al. 2012;Brooks & Zolotov 2012). For this method to work ef-fectively, however, very large ‘blow outs’ of gas are re-quired, of the order ∼ − M ⊙ , equivalent to ∼ M V < −
12 (Zolotov et al. 2012;Garrison-Kimmel et al. 2013), significantly brighter thanthe current luminosities of our outliers ( M V ∼ − METALLICITIES
Our observational setup was such that we cover thecalcium triplet region (Ca II) of all our observed stars.This strong, absorption feature is useful not only forcalculating velocities for each star, but also metallici-ties. For RGB stars, such as we have observed, thereis a well known relation between the equivalent widths(EWs) of the Ca II lines, and the iron abundance,[Fe / H], of the object. The calibration between thesetwo values has been studied and tested by numerous au-thors, using both globular clusters and dSphs, and isvalid down to metallicities as low as [Fe / H] ∼ − / H] ∼ −
4, we fit Gaussian functions to the three CaII peaks to estimate their equivalent widths (EWs), andcalculate [Fe/H] using equation 13:[Fe / H] = − .
87 + 0 . V RGB − V HB ) + 0 . − . − . + 0 . RGB − V HB )(13)where ΣCa=0.5EW +EW +0.6EW , V RGB isthe magnitude (or, if using a composite spectrum, theaverage, S:N weighted magnitude) of the RGB star, and V HB is the mean V -magnitude of the horizontal branch(HB). Using V HB − V RGB removes any strong depen-dence on distance or reddening in the calculated value of[Fe/H], and gives the Ca II line strength at the level ofthe HB. For M31, we set this value to be V HB =25.17(Holland et al. 1996) . As the dSphs do not all sit atthe same distance as M31, assuming this introduces asmall error into our calculations, but it is at a far lowersignificance than the dominant uncertainty introducedby the noise within the spectra themselves. For individ-ual stars, these measurements carry large uncertainties( ∼ > . ≥ . ◦ A − )and measure the resulting EWs. In a few cases, not all3 Ca II lines are well resolved. For And V, IX, XVII,XVIII XXVI and XXVIII, the third Ca II line is signif-icantly affected by skylines, whilst for And XXIV, thefirst Ca II line is distorted. In the case of And XIII,only the second Ca II line appears well resolved. Inthese cases, we neglect the affected lines in our esti-mate of [Fe/H], and derive reduced equivalent widths This assumed value is sensitive to age and metallicity effects,see Chen et al. 2009 for a discussion, however owing to the largedistance of M31, small differences in this value within the M31system will have a negligible effect on metallicity calculations from the unaffected lines. Where the third line is af-fected, this gives ΣCa=1.5EW +EW . Where thesecond line is affected, we find ΣCa=EW +EW .Finally, where only the second line seems reliable we useΣCa=1.7EW . These coefficients are derived empir-ically from high S:N spectra where the absolute valuesof [Fe/H] are well known. We test these variations ofΣCa by applying them to our high S:N co-added spectrawhere all three lines are well resolved, such as And XXIand XXV, and we find that all three formulae produceconsistent values of [Fe/H]. The composite spectra foreach satellite are shown in Figs. 21 and 22. In all cases,we find that our results are consistent with photometricmetallicities derived in previous works.In the MW, it has been observed that the averagemetallicities of the dSph population decrease with de-creasing luminosity (e.g., Kirby et al. 2008, 2011). InFig. 23, we plot the spectroscopic metallicities of the M31dSphs (blue dSphs) as a function of absolute magnitude.We plot the MW dSphs as red triangles (Martin et al.2007; Kirby et al. 2008, 2011; Belokurov et al. 2009;Koch et al. 2009). We also include those M31 dSphsfor which only photometric measurements of [Fe/H] areavailable (And I, II, III, VII and XIV, Kalirai et al. 2010;Tollerud et al. 2012), and these are highlighted as encir-cled blue points. The dashed line represents the best-fitto the MW dSph population from Kirby et al. (2011).The three relatively metal rich ([Fe/H] ∼ − . − . L ∼ ⊙ ) MW points are the three ultra faintdSphs Willman I, Bo¨otes II and Segue 2, and these threewere not included in the Kirby et al. (2011) analysis,where the best fit MW relation was determined. Wesee that the metallicities for a given luminosity in theM31 dSphs also loosely define a relationship of decreasingmetallicity with decreasing luminosity, and they agreewith that defined by their MW counterparts within theirassociated uncertainties. However, it is also noteworthythat for dSphs with L < L ⊙ , the Andromeda satel-lites are also consistent with having a constant metallic-ity of ∼ − .
8. The same levelling off of average metal-licity at lower luminosities was noted by McConnachie(2012), where they note that this break occurs at thesame luminosity as a break in the luminosity-surfacebrightness relation for faint galaxies. As such, it couldimply that the denisty of baryons in these systems, ratherthan the total number of baryons, could be the most im-portant facor in determining their chemical evolution.The error bars we present here are still significant, soit is hard to fully interpret this result, but the hint ofa metallicity floor in these lower luminosity systems isintriguing.In Fig. 23, we highlight the positions of our three kine-matic outliers, And XIX, XXI and XXV, and we seethat they fall almost exactly on the MW relation. Inthis figure, systems that have experienced extreme tidalstripping would move horizontally to the left, as their lu-minosity would gradually decrease as stars are stripped,but their chemistry would remain unaffected. One wouldexpect to see such behaviour only after the stellar com-ponent began to be removed in earnest, after the major-ity of the dark matter halo had been removed. If theircentral densities were lowered by some active feedbackmechanism, such as SNII explosions (e.g., Zolotov et al.2012), one would expect the objects to become more en-0 Collins et al. N o r m a li s ed f l u x And XVII N * = 4[Fe/H] = -1.7 ± N o r m a li s ed f l u x And XVIII N * = 1[Fe/H] = -1.4 ± N o r m a li s ed f l u x And XIX N * = 12[Fe/H] = -1.9 ± N o r m a li s ed f l u x And XX N * = 4[Fe/H] = -2.3 ± N o r m a li s ed f l u x And XXI N * = 12[Fe/H] = -1.9 ± N o r m a li s ed f l u x And XXII N * = 3[Fe/H] = -1.8 ± N o r m a li s ed f l u x And XXIII N * = 19[Fe/H] = -2.1 ± N o r m a li s ed f l u x And XXIV N * = 1[Fe/H] = -1.8 ± Fig. 21.—
Figures of the S:N weighted composite spectra for each dSph. The average metallicity for each dSph, plus the associateduncertainty is printed on each panel (continued over page) he kinematics of Andromeda’s dSphs 31 N o r m a li s ed f l u x And XXV N * = 17[Fe/H] = -1.9 ± N o r m a li s ed f l u x And XXVI N * = 3[Fe/H] = -2.0 ± N o r m a li s ed f l u x And XXVII N * = 6[Fe/H] = -1.9 ± N o r m a li s ed f l u x And XXVIII N * = 5[Fe/H] = -2.1 ± N o r m a li s ed f l u x Cass II N * = 4[Fe/H] = -1.8 ± Fig. 22.—
Figures of the S:N weighted composite spectra for each dSph (excluding And XV and And XVI). The average metallicity foreach dSph, plus the associated uncertainty is printed on each panel (continued over page)
Fig. 23.—
Spectroscopically derived [Fe/H] vs. luminosity for allMW (red triangles, taken from Kirby et al. 2011, with additionalmeasurements taken from Martin et al. 2007; Belokurov et al.2009; Koch et al. 2009) and M31 dSphs (blue circles, this work).The solid line represents the best fit relationship between thesetwo parameters as taken from Kirby et al. (2011). The dashedlines represent the 1 σ scatter about this relationship. We see thatthe M31 dSphs follow this relationship very well within their as-sociated uncertainties. As we discuss in §
6, those galaxies with
L < L ⊙ are also consistent with having a constant metallicity,which could indicate a metallicity floor in these fainter systems. riched and perhaps brighter, moving them up and to theright, potentially allowing them to remain on the MWrelation. To confirm that this was the case for And XIX,XXI and XXV, we would require more information onthe abundances of these objects and their star formationhistories, which we do not currently possess. CONCLUSIONS
Using new and existing spectroscopic data from theKeck I LRIS and Keck II DEIMOS spectrographs, wehave homogeneously derived kinematic properties for 18of the 28 known Andromeda dSph galaxies. Using a com-bination of their g − i colors, positions on the sky andradial velocities, we determine the likelihood of each ob-served star belonging to a given dSph, thus filtering outMW foreground or M31 halo contaminants. We havemeasured both their systemic velocities and their velocitydispersions, with the latter allowing us to constrain themass and densities within their half-light radii. For thefirst time, we confirm that And XVII, XIX, XX, XXIII,XXVI and Cass II are dark matter dominated objects,with dynamical mass-to-light ratios within the half-lightradius of [ M/L ] half >
10 M ⊙ / L ⊙ .For And XXV, a bright M31 dSph ( M V = − . M/L ] half =10 . +7 . − . M ⊙ / L ⊙ from a sample of 26 stars, meaning thatit is consistent with a simple stellar system with no ap-preciable dark matter component within its 1 σ uncer-tainties. If this were confirmed with larger datasets, itwould prove to be a very important object for our un-derstanding of the formation and evolution of galaxies. We compare our computed velocity dispersions andmass estimates with those measured for MW dSphs, andfind that the majority of the M31 dSphs have very sim-ilar mass-size scalings to those of the MW. However, wenote 3 significant outliers to these scalings, namely AndXIX, XXI and XXV, who possess significantly lower ve-locity dispersions than expected for their size. Theseresults builds on the identification of three potential out-liers in the Tollerud et al. (2012) dataset (And XIV, XVand XVI). We suggest that the lower densities of the darkmatter halos for these outliers could be an indication thatthey have encountered greater tidal stresses from theirhost over the course of their evolution, decreasing theirmasses. However, these bright systems still fall on theluminosity-metallicity relation established for the dSphgalaxies of the Local Group. If these objects had under-gone significant tidal disruption, we would expect themto lie above this relation. As such, this remains puzzling,and requires dedicated follow up studies to fully map outthe kinematics of these unusual systems.We measure the metallicities of all 18 dSphs from theirco-added spectra and find that they are consistent withthe established MW trend of decreasing metallicity withdecreasing luminosity.This work represents a significant step forward in un-derstanding the mass profiles of dwarf spheroidal galax-ies. Far from residing in dark matter halos with identi-cal mass profiles, we show that the halos of these objectsare complex, and differ from one to the next, with theirenvironment and tidal evolution imprinting themselvesupon the dynamics of their stellar populations. The An-dromeda system of dSphs presents us with an opportu-nity to better understand these processes, and our futurework will further illuminate the evolutionary paths takenby these smallest of galaxies. ACKNOWLEDGMENTS
We would like to thank Hans-Walter Rix for helpfuldiscussions regarding this manuscript. We are also grate-ful to the referee for their helpful and detailed suggestionsfor improving this work. We thank the SPLASH collabo-ration for providing us with details of their observationsof dSphs as presented in T12.Most of the data presented herein were obtained at theW.M. Keck Observatory, which is operated as a scientificpartnership among the California Institute of Technol-ogy, the University of California and the National Aero-nautics and Space Administration. The Observatory wasmade possible by the generous financial support of theW.M. Keck Foundation.Based in part on observations obtained withMegaPrime/MegaCam, a joint project of CFHT andCEA/DAPNIA, at the Canada-France-Hawaii Telescope(CFHT) which is operated by the National ResearchCouncil (NRC) of Canada, the Institute National des Sci-ences de l’Univers of the Centre National de la RechercheScientifique of France, and the University of Hawaii.Based in part on data collected at Subaru Telescope,which is operated by the National Astronomical Obser-vatory of Japan.The authors wish to recognize and acknowledge thevery significant cultural role and reverence that the sum-mit of Mauna Kea has always had within the indigenousHawaiian community. We are most fortunate to have thehe kinematics of Andromeda’s dSphs 33
TABLE 5Compilation of kinematic and structural properties of all known Andromeda dSphs. Half-light radii are taken fromMcConnachie (2012), and updated to the distances provided in Conn et al. (2012).
Name M V N ( a ) ∗ [Fe/H] phot [Fe/H] spec v r σ v r half D Ref.(dex) (dex) ( km s − ) ( km s − ) (pc) (kpc)And I -11.8 80 -1.45 ± ± . ± . +68 − +18 − (1),(2),(3)And II -12.6 95 -1.64 ± ± . ± ±
46 630 ±
15 (1),(3),(4)And III -10.2 43 -1.78 ± ± . ± . +44 − +18 − (1),(2),(3)And V -9.6 85 -1.6 ± . ± ± . ( b ) ± . ( b ) ±
44 742 +21 − (2),(3),(5)And VI -11.5 38 -1.3 ± . ± ± . +1 . − . ±
49 783 ±
28 (3),(5),(6)And VII -13.3 18 -1.4 ± ± . ± ±
42 762 ±
35 (1),(2),(3)And IX -8.1 32 -2.2 ± . ± ± . ( b ) ± . ( b ) +68 − +91 − (1),(2),(3)And X -8.1 22 -1.93 ± ± . ± . +21 − +24 − (1),(2),(3)And XI -6.9 5 -2.0 ± . ± +3 . − . +4 . − . +9 − +29 − (3),(6),(7)And XII -6.4 8 -1.9 ± . ± ± . +4 . +56 − +40 − (3),(6),(7)And XIII -6.7 12 -2.0 ± . ± ± . ( b ) ± . ( b ) +34 − +126 − (2),(3),(7)And XIV -8.3 38 -2.26 ± ± . ± +185 − +23 − (1),(2),(3)And XV -9.4 29 -1.1 N/A -323 ± . ( b ) ± . ( b ) +29 − +79 − (1),(2),(3)And XVI -9.4 7 -1.7 -2.0 ± ± . ( b ) ± . ( b ) +13 − +44 − (1),(2),(3)And XVII -8.5 7 -1.9 -1.7 ± . +1 . − . +2 . − . +53 − +39 − (1),(3),(6)And XVIII -9.7 22 -1.8 ± . ± . ( b ) ± . ( b ) ±
24 1214 +40 − (1),(2),(3)And XIX -9.3 27 -1.9 ± . ± . +1 . − . +1 . − . +62 − +32 − (1),(3),(6)And XX -6.3 4 -1.5 ± . ± . +3 . − . +3 . − . +31 − +42 − (1),(3),(6)And XXI -9.9 32 -1.8 -1.8 ± . ± . +1 . − . ±
77 827 +23 − (1),(3),(6)And XXII -6.5 12 -1.8 -1.85 ± ± . +1 . − . +28 − +32 − (1),(2),(3),(8)And XXIII -10.2 42 -1.8 ± . ± . ± . ± . +53 − +31 − (1),(3),(6)AndXXIV -7.6 3 -1.8 ± . ± . − . ± . ( c ) . +7 . c ) +31 − +2842 (1),(3),(6)And XXV -9.7 25 -1.8 ± . ± . ± . +1 . − . +47 − +23 − (1),(3),(6)And XXVI -7.1 6 -1.9 ± . ± . +3 . − . +2 . − . +67 − +218 − (1),(3),(6)AndXXVII -7.9 11 -1.7 ± . ± .
28 -539.6 +4 . − . +4 . − . +112 − +42 − (1),(3),(6)AndXXVIII -8.5 17 -2.0 ± . ± . ± . +2 . − . +60 − +150 − (6),(9)AndXXIX -8.3 24 -1.8 ± . − . ± . . ± . ±
60 730 ±
75 (10),(11)And XXX (Cass II) -8.0 8 -1.6 ± . ± . +6 . − . +7 . − . +23 − +32 − (3),(6),(12) Note . — ( a ) Number of spectroscopically confirmed member ( b ) Kinematics taken from T12 rather than this work, as they possessgreater numbers of member stars. stars. ( c ) Owing to shorter than typical exposure time, lower resolution data and difficult observingconditions, this kinematic identification of And XXIV remains tentative, and needs to be confirmed with further follow-up. References:(1) McConnachie (2012), (2) Tollerud et al. (2012), (3) Conn et al. (2012), (4)Kalirai et al. (2010) (5)Collins et al. (2011), (6) Thiswork, (7) Collins et al. (2010), (8) Chapman et al. (2012), (9) Slater et al. (2011), (10) Tollerud et al. (2013), (11) Bell et al. (2011),(12) Irwin et al. (in prep).
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A.1.
The inclusion of a velocity term in the calculation of P i In T12, the authors do not impose a velocity probability criterion for their membership calculations. Instead theyrequire all member stars to have a total probability, based on their positions and colors, of P member > .
1, and thenapply a 3 σ clipping to this final sample to prevent any outliers from significantly inflating their calculated velocitydispersions. In our analysis, we have avoided making any hard cuts to our sample by also utilising prior information onthe velocities of our expected contaminant populations and member stars. In § η , that allows us to add additional weight to stars in the tails of the Gaussianvelocity distribution. However, we can further test our velocity criterion by removing it entirely from the probabilisticdetermination, and instead implementing the same cuts presented by T12. This involves cutting stars where P i < . P CMD and P dist ), and also by iteratively removing all stars that have velocities that do not liewithin 3 σ of the mean of the remaining sample. In Table A1, we present the results of this on our measured values of v r and σ v for our full sample of dSphs. For all objects (bar And XXVII, which is a unique case, as described in § ∼ − − of one another. The velocity dispersions we measure fromour full algorithm tend to be slightly higher on average, and this is to be expected as we do not cut any stars from ouranalysis, and therefore outliers in the velocity profile may be assigned non-negligible membership probabilities thatwill allow them to increase this measurement. By and large, these differences are not significant, with the final valuesagreeing to well within their 1 σ uncertainties.It is interesting that our algorithm appears to perform better when dealing with dSphs where the number of memberstars is low. This is best demonstrated by And XI (see Fig. A1). Our algorithm identifies 5 stars with non-negligibleprobabilities of membership, clustered around v r ∼ −
430 km s − . Our full algorithm measures a systemic velocity of v r = − . +3 . − . km s − and a velocity dispersion of σ v = 7 . +4 . − . km s − . One of these stars is slightly offset from theother 4 with a more negative velocity of v r = − . − . Although this star has a reasonably high probability ofbeing a member based on its distance from the centre of And XI, and its position in the CMD, it does not survivethe 3 σ velocity clipping procedure of T12. As the number of member stars is so low, cutting one star from the samplecan have a significant effect, and as such, while the T12 procedure determines a very similar systemic velocity of v r = − . ± . − it is unable to resolve a velocity dispersion. This effect is also seen other systems (such asAnd XIII, XVII, XXII and XXVI), although it is typically less pronounced.Another regime where our algorithm performs better than that of T12 is where the systemic velocity of the systemin question is within the regime of the contaminating Milky Way K-dwarfs. An example of this is the unusual system,And XIX, where our algorithm measures a systemic velocity of v r = − . +1 . − . km s − and a velocity dispersionof σ v = 4 . +1 . − . . However, the procedure of T12 is less able to resolve the kinematics of the system, measuring v r = − . ± . − and a velocity dispersion of σ v = 1 . +9 . − . . The much larger uncertainty on the dispersion isa result of including Milky Way contaminants in the sample which can be difficult to cut out without applying priorknowledge of the velocity profile of this population. 3 σ clipping allows outliers to contribute more significantly to themeasured profile in this instance, increasing the uncertainty. A similar effect is seen in the And XXIV and And XXX(Cass II) objects, which also have systemic velocities in the Milky Way contamination regime.6 Collins et al. −0.5 0.0 0.5 1.0 1.5 2.0 2.5 g-i i And XI P i F r e q . And XI D i s t a n c e ( a c m i n ) −500 −400 −300 −200 −100 0 100 v hel (km/s) −3.0−2.5−2.0−1.5−1.0−0.5 [ F e / H ] P i -480 -460 -440 -420 -400v hel (kms -1 )0.010.101.00 R e l a t i v e li k e li hood And XI - v r =-427.5 +3.5-3.4 (kms -1 ) σ v (kms -1 )0.010.101.00 σ v =7.6 +4.0-2.8 (kms -1 ) Fig. A1.—
As Fig. 6, but for And XI. Using our full probabilistic algorithm (including our P vel term), 5 stars are identified as likelymembers. When implementing the 3 σ clipping of T12, the star with v r ∼ −
450 km s − is removed from the analysis, despite having a highprobability of membership based on its color ( P CMD ) and distance from the centre of the dSph ( P dist ). This has a substantial effect ofthe calculated velocity dispersion, as shown in Table A1. These results lead us to conclude that the inclusion of a P vel term in our analysis allows us to more effectivelydetermine the true kinematics of the systems we are studying. Further, as no cuts to the sample are required usingthis method, it allows for a more unbiased study of the kinematics of dSphs than that of T12.he kinematics of Andromeda’s dSphs 37 TABLE A1Measured velocities ( v r ) and dispersions ( σ v ) for our full sample ofdSphs as calculated using cuts on probability of membership calculatedfrom only color and position of stars, combined with σ clipping onvelocities vs. those calculated using our full probabilistic algorithm. Object v & P i cuts Full algorithm v r ( km s − ) σ v ( km s − ) v r ( km s − ) σ v ( km s − )And V − . ± . . +3 . − . − . ± . . +2 . − . And VI − . ± . . +2 . − . − . ± . . +1 . − . And XI − . ± . +3 . − . +3 . − . . +4 . − . And XII − . ± . +6 . − . ± . +4 . And XIII − . ± . +16 . − . ± . . +8 . And XVII − . +8 . − . . +9 . − . − . +3 . − . . +5 . − . And XVIII − . ± . +4 . − . ± . +2 . And XIX − . ± . . +6 . − . − . +1 . − . . +1 . − . And XX − . +4 . − . . +8 . − . − . +3 . − . . +3 . − . And XXI − . +2 . − . . +2 . − . − . ± . . +1 . − . And XXII − . ± . +3 . − . ± . . +1 . − . And XXIII − . ± . . +1 . − . − . ± . . ± . − . ± . +6 . − . +4 . − . . +6 . − . And XXV − . +1 . − . . +2 . − . − . ± . . +1 . − . And XXVI − . ± . +4 . − . +3 . − . . +2 . − . And XXVII − . +42 . − . . +17 − − . +4 . − . . +4 . − . And XXX (CassII) − . +8 . − . . +12 . − . − . +6 . − . . +7 . − . TABLE A2The effect of including low S:N data in our analysis on determining v r and σ v . Object And XXI And XXIII And XXV N ∗ v r ( km s − ) σ v ( km s − ) N ∗ v r ( km s − ) σ v ( km s − ) N ∗ v r ( km s − ) σ v ( km s − )S:N > − . ± . . +0 . − . − . ± . . ± . − . ± . ± . > − . ± . . ± . − . ± . . +1 . − . − . ± . . ± . > − . ± . . +1 . − . − . ± . . +1 . − . − . ± . . +1 . − . S:N > − . +2 . − . . +2 . − . − . ± . . +4 . − . ± . . +1 . − . Note . — xxx
A.2.
The effect of low signal-to-noise data on measuring v r and σ v For our brightest targets ( i ∼ < .
5) the S:N of our spectra is typically > ◦ A − . However, as our targets becomefainter, so too their S:N falls. For spectra with S:N ∼ > . ◦ A − , our pipeline is still able to measure velocities based onthe Ca II triplet, with reasonable measurement uncertainties. However, it is prudent to check whether the inclusionof these velocities, calculated from significantly noisier spectra, has a detrimental effect on our ability to measure thekinematic properties of our dSph sample.Such a test is straightforward to implement. We have a number of dSphs within our sample for which our probabilisticanalysis identifies ∼
30 likely members (such as And XXI, XXIII and XXV). We can therefore use these samples toimpose S:N cuts on our data to see the effect of this on our measurements of v r and σ v . We present the results of thistest in Table A2, and our finding is that, as the level of our imposed S:N cut increases (and so the number of includedstars decreases), the systemic velocity remains more or less constant. The measured velocity dispersion, however,shows some variation. In the case of And XXI and XXV, the dispersion increases with increased S:N, however notsignificantly. In both cases the dispersion calculated from the higher S:N data lies well within 1 σ of that calculatedfrom the lower S:N data. Intuitively, this makes sense as the spectra with higher S:N are likely to have lower velocityuncertainties, and so our maximum-likelihood analysis will attribute more of the spread in measured velocities to anintrinsic dispersion, rather than to our measurement errors. In the case of And XXIII, we find the opposite to be true.As our S:N cut increases, we find that our measured dispersion decreases. This may be because the number of memberstars in subsequent quality cuts drops off more rapidly for And XXIII than And XXI and XXV. This suggests that weshould be extra cautious when interpreting our measured velocity dispersions for dSphs where both the average S:Nof member stars, and the number of member stars, is low.8 Collins et al. TABLE A3The effect of varying sample size ( N ∗ ) on the measurements of systemic velocity, v r , andvelocity dispersion, σ v . N stars from And XXI, XXIII and XXV are randomly selected, and theirproperties are derived using our full probabilistic analysis. This was repeated 1000 times. Valuesreported below are the averages from 1000 realizations, with the uncertainties represent thestandard deviation of the 1000 realizations. Object And XXI And XXIII And XXV N ∗ v r ( km s − ) σ v ( km s − ) v r ( km s − ) σ v ( km s − ) v r ( km s − ) σ v ( km s − )4 − . ± . . ± . − . ± . . ± . − . ± . ± . − . ± . . ± . − . ± . . ± . − . ± . . ± . − . ± . . ± . − . ± . . ± . − . ± . . ± . − . ± . . ± . − . ± . . ± . − . ± . . ± . − . ± . . ± . − . ± . . ± . − . ± . . ± . − . ± . . ± . − . ± . . ± . − . ± . . ± . − . ± . . ± . − . ± . . ± . − . ± . . ± . − . ± . . ± . − . ± . . ± . Full sample − . ± . . +1 . − . − . ± . . ± . − . ± . . +1 . − . A.3.
The effect of small sample sizes on determining kinematic properties of dwarf galaxies
Obtaining reliable velocities for member stars of faint and distant systems is a difficult task that can only be achievedwith the largest optical telescopes, such as Keck. Given the demand for facilities such as this, any observing timeawarded must be used as effectively as possible, and this often means compromising between deep pointings for a fewobjects, and shallower pointings for a number of objects. With longer or multiple exposures on a single target, one canbuild up impressive samples of member stars for an individual dSph. For example, the SPLASH collaboration observeda total of 95 members in And II, one of the brightest M31 dSph companions (Kalirai et al. 2010) by taking 2 separateexposure fields over this large object. However, multiple exposures such as these produce diminishing returns as youmove down the luminosity scale to fainter, more compact dSphs. This is both because of their smaller size with respectto the DEIMOS field of view, and the fewer number of bright stars available on the RGB to target. In this case, theonly way to identify more members is by integrating for longer, but given the paucity of stars, the trade-off betweentime spent exposing and additional members observed can be quite expensive. Such difficulties inevitably lead to theinference of dynamical properties for an entire system from a handful of stars. It is important for us to understandthe effect this bias has on our results, and how reliable the quoted values are. We test this using our datasets forwhich we identify >
25 member stars, namely And XIX, XXI, XXIII and XXV using the following method. We select4, 6, 8, 10, 15, 20, 25 and 30 stars at random from each dataset and then measure the systemic velocity and velocitydispersion using our probability algorithm. This was repeated 1000 times for each sample size. In cases where thealgorithm is unable to resolve a velocity dispersion, we throw out the result and resimulate, as null results here willaffect our averages and will not inform us whether the instances in which we are able to resolve a velocity dispersionfrom small numbers of stars are producing valid, reliable result. We display the resulting values in Table A3, with thetrue value recovered from the full sample shown in bold in the final row for comparison. We show that in all these cases,the systemic velocity and velocity dispersion are recovered well within the scatter of the 1000 simulations even whendealing with sample sizes as small as 4 stars, so long as the measurement is resolved. In cases where we are unable toresolve a dispersion, we find that our resulting uncertainties are not meaningful. This is shown explicitly in the case ofAnd XVIII, where we can compare our upper limit for the velocity dispersion as determined from our algorithm withthe dispersion calculated in T12 from a much larger dataset. We see that our uncertainty is not consistent with theirresult. As such, we advise that in all cases where we calculate velocity dispersions from small samples ( N ∗ <
8, AndXI, XII, XX XXIV and XXVI), the dispersion measurements should be treated as indications of the likely dispersion,and need to be confirmed with follow-up studies.
A.4.
Testing our algorithm on the SPLASH sample of M31 dSphs
In T12, the authors reported on the kinematic properties of 15 M31 dSphs, And I, III, V, VII, IX, X, XI, XII,XIII, XIV, XV, XVI, XVIII, XXI and XXII, and the positions, and measured velocities (plus uncertainties) for eachlikely member stars were published as part of that work. The authors were kind enough to also give us access tothese properties for their non-member stars so that we might run our algorithm over the full samples to see if wereproduce their results. Our technique for assigning membership probability differs from theirs in that we use thevelocities of stars as an additional criterion for membership, whereas they use a cut on both the resulting probability( P (m ember > . σ clipping on the velocity. In addition, where we use PAndAS CFHT MegaCam g − and i − band photometry for our membership analysis,the SPLASH team use their own Washington-DDO51 filterphotometric dataset, in membership classification. As such, small differences might be expected, but if our techniqueis robust our results should well mirror those of T12. In Table A4 we compare our calculated values of v r and σ v tothose published in T12. As the measurements made in T12 for And XI and XII are made from only 2 stars, we donot include these in this test. In general, the results from both analyses agree to within 1 σ of one another, with themajority of them being well within this bound. Typically, we find that our procedure measures slightly larger valuesfor σ v than that of T12 (with the exception of And IX, And XVIII and And XXII). This is to be expected, as we dohe kinematics of Andromeda’s dSphs 39 TABLE A4
Object T12 analysis Our analysis v r ( km s − ) σ v ( km s − ) v r ( km s − ) σ v ( km s − )And I -376.3 ± . ± . − . ± . . ± . ± . ± . − . ± . . ± . ± . ± . − . ± . . ± . ± . ± − . ± . . ± . ± . ± . − . ± . . +1 . − . And X -164.1 ± . ± . − . ± . . +1 . − . And XIII -185.4 ± . ± . − . +2 . − . . +2 . − . And XV -323 ± . ± . − . ± . . +2 . − . And XVI -367.3 ± . ± . − . +4 . − . . +4 . − . And XVIII -332.1 ± . ± . − . +3 . − . . +4 . − . And XXI − . ± . . ± . − . +5 . − . . +6 . − . And XXII − . ± . . +4 . − . − . +4 . − . . +5 . not cut stars from our analysis based on their velocity, instead we down-weight their probability of membership. Assuch, those stars considered as outliers would naturally inflate our dispersions above those measured by T12, but theeffect is marginal. These results demonstrate that our technique for assigning probability of membership of individualstars within M31 dSphs based on their photometric properties and velocities is robust, and comparable to that of T12.However, as discussed in § A.1, we find that our technique is superior as it requires no cuts to the final dataset to bemade, reducing the bias in these measurements. B. REANALYZING OUR PREVIOUSLY PUBLISHED RESULTS
To ensure our analysis of the global properties of the M31 dSph population in § B.1.
Andromeda V
Andromeda V (And V) was observed using the LRIS instrument on Keck I rather than the DEIMOS instrument onKeck II. LRIS has a lower resolution than DEIMOS, and a smaller field of view, which lowers the accuracy of velocitymeasurement and limits us to only ∼
50 targets within a mask compared with 100 −
200 for a DEIMOS mask. Theraw data were also not reduced using our standard pipeline, owing to problems with the arc-lamp calibrations, andwere instead analyzed using the NOAO.ONEDSPEC and NOAO.TWODSPEC packages in IRAF. The results fromthis reduction, plus an analysis of the data using hard cuts in velocity, distance and color to determine membershipwere first published in Collins et al. (2011). Our full probabilistic analysis identifies 17 stars with a non-negligibleprobability of belonging to And V. Our technique determines a systemic velocity of v r = − . ± . − and σ v = 12 . +2 . − . km s − . Comparing these values to our previously published results ( v r = − . ± . − and σ v = 11 . +5 . − . km s − , Collins et al. 2011) we find them to be consistent within the quoted uncertainties. We alsocompare our results to those of T12, who measured v r = 397 . ± . − and σ v = 10 . ± . − from a largersample of stars (85 members cf. 17) using the higher resolution DEIMOS spectrograph. The velocity dispersions ofboth are consistent within their 1 σ uncertainties, as are the systemic velocities. Given the difference of a factor of 5 innumber of probable member stars between our study and that of T12, this consistency is reassuring, and demonstratesthe ability of our technique to accurately determine the kinematics of M31 dSph galaxies from small sample sizes. B.2.
Andromeda VI
As And VI sits at a large projected distance from the centre of M31 ( ∼
270 kpc), it was not observed as part ofthe PAndAS survey and we were unable to use CFHT data for our P CMD determination. Instead, we use SubaruSuprime-cam data (PI. N. Arimoto, see Collins et al. 2011 for a full discussion of this data). Using our full probabilisticanalysis, we identify 45 stars with P i > − . Our technique determines a most-likely v r = − . ± . − ,with σ v = 12 . +1 . − . km s − . Comparing these values with the results of Collins et al. (2011) who measured v r = − . ± . − and σ v = 9 . +3 . − . km s − , we see that both the systemic velocities and the velocity dispersions areconsistent within quoted uncertainties. The slight differences between our previous study and this work are simply aresult of the application of our new technique. B.3.
Andromeda XI
The kinematic properties for Andromeda XI as measured from this DEIMOS data set were first published inCollins et al. (2010). Here we identify 5 stars as probable members. We determine most-likely parameters of0 Collins et al. v r = − . +3 . − . km s − and σ v = 7 . +4 . − . km s − . In Collins et al. (2010) we measured v r = − . +4 . − . km s − and we were unable to resolve the velocity dispersion for the dSph, measuring σ v = 0 . +4 . km s − (where the upperbound represents the formal 1 σ uncertainty on the unresolved dispersion), which implied a higher systemic velocityand lower velocity dispersion for And XI. However, in that analysis, one star with a velocity of ∼ −
440 km s − wasconsidered to be an outlier based on its velocity, and thus excluded from the kinematic analysis. Here, our algorithmgives this star a non-zero probability of membership, which likely decreases the systemic velocity and increases thedispersion. T12 also presented observations for And XI, but they were not able to cleanly detect the galaxy. Theyidentified 2 stars with highly negative velocities ( ∼ −
460 km s − ), which are offset from our systemic velocity by ∼
30 km s − . Given the very negative velocities of their 2 stars, the probability of them both being M31 contaminantsseems low, and some other explanation may be more suitable. Between observations, there is one star common to both( α =00:46:19.10, δ =+33:48:4.1), for which we measure a velocity of − .
16 km s − compared with − . − .This amounts to a statistical difference at the level of 5 σ . One obvious avenue to check is that there has been novelocity offset introduced by a rogue skyline that falls within the region of one of the three Ca II lines. We havecarefully checked the spectra of each of our 5 probable members to see if this has been the case. We also rederivethe velocity based on cross-correlations with each of the three lines individually, rather than with the full triplet. Wefind these results, and their average to be entirely consistent within the associated errors from the velocities derivedusing the technique discussed in § ∼ − ◦ A − ). Therefore, our results should be considered as more robustthan those of T12. B.4.
Andromeda XII
Kinematic properties for Andromeda XII as determined from the DEIMOS data set presented here were previouslypublished in Chapman et al. (2007) and Collins et al. (2010), and in both cases, membership was largely determinedusing hard cuts in velocity. This object has been of particular interest as it possesses an extremely negative systemicvelocity with respect to Andromeda, suggesting that it is on its first infall into the local group (see Chapman et al. 2007for a full discussion). Using our new algorithm, we measure v r = − . − and an unresolved velocity dispersionof σ v = 0 . +4 . km s − , where the upper bound represents the formal 1 σ uncertainty on the measurement. As thedispersion is unresolved, the lower error bound is undefined, as having a negative velocity dispersion is unphysical.These values are completely consistent with the results of Chapman et al. (2007) and Collins et al. (2010) ( v r = − . ± . − and σ v = 2 . +5 . − . km s − ). T12 also presented observations for And XII, but as for And XI, theywere not able to cleanly detect the galaxy. They identified 2 stars with highly negative velocities ( ∼ −
530 km s − ),which are offset from our systemic velocity by ∼
30 km s − . In this instance, both the stars they observed overlap withtwo of our likely members, situated at α =00:47:28.63, δ =+34:22:43.1 and α =00:47:24.69, δ =+34:22:23.9, and thesevelocities are offset from those that we measure at a statistical level of 3 . σ . This suggests that the self-same calibrationeffect that causes an offset between our results for And XI and those of T12, is present here also. In the case of AndXII, our mask was observed over two separate nights, giving us two velocity measurements for each star (as discussedin Chapman et al. 2007 and Collins et al. 2010), and we saw no evidence for systematic offsets of this magnitude inthe night to night velocities, making a calibration error within our dataset seem unlikely, though not impossible. Wetherefore conclude that, owing to our larger sample of members and repeat observations, our measurements for thekinematic properties of And XII are more robust than those of T12. B.5.
Andromeda XIII
The kinematic properties of Andromeda XIII were also presented in Collins et al. (2010), And XIII sits at a largeprojected distance from Andromeda ( ∼
120 kpc) in the southern M31 halo, so we expect contamination fromthe Milky Way and Andromeda halo to be low. It is surprising then, that we see significant structure within ourDEIMOS field. This is also seen within the 3 fields observed by T12, who attribute this over-density of stars locatedat v r ∼ −
120 km s − to an association with the TriAnd over-density within the Galactic halo. We too see a numberof stars between −
140 km s − and −
100 km s − . From their positions within the CMD of And XIII, they appear moreconsistent with MW foreground K-dwarfs than M31 RGB stars. As such, these are also likely associated to this MWsubstructure.Using our full probabilistic analysis, we identify the most probable And XIII stars as those 4 that cluster around v ∼ −
200 km s − , and we determine v r = − . ± . − and are unable to resolve a velocity dispersion, with σ v = 0 . +8 . , where the upper limit indicates the formal 1 σ uncertainty on the likelihood distribution. Given the verylarge uncertainties on these values (mostly a factor of the low number of member stars) it comes as no surprise perhapsthat these results are consistent with the results in Collins et al. (2010) ( v r = − . +7 . − . km s − and σ v = 9 . +8 . − . ),he kinematics of Andromeda’s dSphs 41although not with those of T12 ( v r = − . ± . − and σ v = 5 . ± . −1