The large-scale structure of the halo of the Andromeda Galaxy Part I: global stellar density, morphology and metallicity properties
Rodrigo A. Ibata, Geraint F. Lewis, Alan W. McConnachie, Nicolas F. Martin, Michael J. Irwin, Annette M. N. Ferguson, Arif Babul, Edouard J. Bernard, Scott C. Chapman, Michelle Collins, Mark Fardal, A.D. Mackey, Julio Navarro, Jorge Penarrubia, R. Michael Rich, Nial Tanvir, Lawrence Widro
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THE LARGE-SCALE STRUCTURE OF THE HALO OF THE ANDROMEDA GALAXY PART I:GLOBAL STELLAR DENSITY, MORPHOLOGY AND METALLICITY PROPERTIES Rodrigo A. Ibata , Geraint F. Lewis , Alan W. McConnachie , Nicolas F. Martin , Michael J. Irwin ,Annette M. N. Ferguson , Arif Babul , Edouard J. Bernard , Scott C. Chapman , Michelle Collins , MarkFardal , A.D. Mackey , Julio Navarro , Jorge Pe˜narrubia , R. Michael Rich , Nial Tanvir , and LawrenceWidrow Draft version August 9, 2018
ABSTRACTWe present an analysis of the large-scale structure of the halo of the Andromeda galaxy, based onthe Pan-Andromeda Archeological Survey (PAndAS), currently the most complete map of resolvedstellar populations in any galactic halo. Despite the presence of copious substructure, the global halopopulations follow closely power law profiles that become steeper with increasing metallicity. We dividethe sample into stream-like populations and a smooth halo component (defined as the population thatcannot be resolved into spatially distinct substructure with PAndAS). Fitting a three-dimensional halomodel reveals that the most metal-poor populations ([Fe / H] < − .
7) are distributed approximatelyspherically (slightly prolate with ellipticity c/a = 1 . ± . f stream = 42%). The sphericity of the ancient smoothcomponent strongly hints that the dark matter halo is also approximately spherical. More metal-richpopulations contain higher fractions of stars in streams, with f stream becoming as high as 86% for[Fe / H] > − .
6. The space density of the smooth metal-poor component has a global power-law slopeof γ = − . ± .
07, and a non-parametric fit shows that the slope remains nearly constant from 30 kpcto ∼
300 kpc. The total stellar mass in the halo at distances beyond 2 ◦ is ∼ . × M (cid:12) , whilethat of the smooth component is ∼ × M (cid:12) . Extrapolating into the inner galaxy, the total stellarmass of the smooth halo is plausibly ∼ × M (cid:12) . We detect a substantial metallicity gradient,which declines from (cid:104) [ F e/H ] (cid:105) = − . R = 30 kpc to (cid:104) [ F e/H ] (cid:105) = − . R = 150 kpc for the fullsample, with the smooth halo being ∼ . Subject headings: galaxies: halos galaxies: individual (M31) galaxies: structure Based on observations obtained with MegaPrime/MegaCam,a joint project of CFHT and CEA/DAPNIA, at the Canada-France-Hawaii Telescope (CFHT) which is operated by the Na-tional Research Council (NRC) of Canada, the Institute Nationaldes Sciences de l’Univers of the Centre National de la RechercheScientifique of France, and the University of Hawaii. Observatoire astronomique de Strasbourg, Universit´e deStrasbourg, CNRS, UMR 7550, 11 rue de lUniversit´e, F-67000Strasbourg, France; [email protected] Institute of Astronomy, School of Physics A28, University ofSydney, NSW 2006, Australia NRC Herzberg Institute of Astrophysics, 5071 West SaanichRoad, Victoria, BC, V9E 2E7, Canada Max-Planck-Institut f¨ur Astronomie, K¨onigstuhl 17, D-69117 Heidelberg, Germany Institute of Astronomy, University of Cambridge, MadingleyRoad, Cambridge CB3 0HA, UK Institute for Astronomy, University of Edinburgh, BlackfordHill, Edinburgh EH9 3HJ, UK Department of Physics and Astronomy, University of Vic-toria, 3800 Finnerty Road, Victoria, British Columbia, CanadaV8P 5C2 Department of Physics and Atmospheric Science, DalhousieUniversity, 6310 Coburg Rd., Halifax, NS B3H 4R2 Canada University of Massachusetts, Department of Astronomy,LGRT 619-E, 710 N. Pleasant Street, Amherst, Massachusetts01003-9305, USA. RSAA, The Australian National University, Mount StromloObservatory, Cotter Road, Weston Creek, ACT 2611, Australia Department of Physics and Astronomy, University of Cali-fornia, Los Angeles, PAB, 430 Portola Plaza, Los Angeles, Cali-fornia 90095-1547, USA Department of Physics and Astronomy, University of Le-icester, University Road, Leicester, LE1 7RH, UK Department of Physics, Engineering Physics, and Astron-omy Queen’s University, Kingston, Ontario, Canada K7L 3N6 a r X i v : . [ a s t r o - ph . GA ] N ov Ibata et al. INTRODUCTION
The stellar halos of giant galaxies are repositories ofmuch of the stellar material that was accreted duringthe formation of their host galaxy. It is in these regionsalone that we can resolve and identify (in extra-Galacticsystems) the remnants of the numerous low-mass accre-tion events that contributed to the build-up of present-day galaxies. Halo studies are further motivated by thefact that modern simulations in the standard ΛCDM cos-mology make predictions for the spatial distribution, ageand metallicity of stars in the halo (e.g., Abadi et al.2006; Bullock & Johnston 2005; Johnston et al. 2008;Font et al. 2008; Cooper et al. 2010; Zolotov et al. 2010),so that detailed observations provide a means to test thiscosmological paradigm.It was for these reasons that we began, a full decadeago, an in-depth panoramic study of the Andromedagalaxy on the Canada-France-Hawaii Telescope (CFHT),an effort that morphed into the Pan-Andromeda Arche-ological Survey (PAndAS), which was set up as a “LargeProgram” on the CFHT in 2008. As the closest giantgalaxy, the choice of Andromeda (M31) for the target isobvious; at present (before the advent of Gaia or homoge-nous digital full-sky optical surveys) one can also arguethat for matters of homogenous spatial coverage the M31halo is a far better and easier specimen for study thanthe halo of our own Milky Way.The aim of the present paper is to update and comple-ment an earlier contribution on this subject (Ibata et al.2007, hereafter paper I). In that article we gave a full ex-position of the CFHT survey from data obtained up to2006, with almost all of the studied fields located in thesouthern quadrant of M31. That contribution also pro-vides a detailed review of the literature prior to 2007 ongalactic halos, focussing particularly on M31, to whichwe refer the interested reader.Since 2007 significant progress has been made in thephotometric and kinematic mapping of the haloes ofnearby galaxies. Perhaps the greatest surprises havecome from the analyses of the Milky Way halo, whichhas turned out to be much more complex than previ-ously imagined. Carollo et al. (2007) showed that theSloan Digital Sky Survey (SDSS) halo sample can bedeconstructed into two sub-components, the inner andouter halos, that have different morphological and chem-ical properties, with the outer halo being more metalpoor and possessing slightly retrograde mean rotation,but see also Sch¨onrich et al. (2011). In addition, theinner halo appears to contain itself a highly-flattenedsub-component (Morrison et al. 2009), with axis ra-tio c/a ∼ .
2. Nearby main sequence halo dwarfs inthe SDSS extending out to ∼
20 kpc (i.e. encompass-ing both the “inner” and “outer” halos) are found tobe distributed as a smooth oblate structure (axis ratio c/a ∼ . .
8) with space density that follows a powerlaw of index − . −
3, once the known halo substruc-tures are removed (Juri´c et al. 2008). It is very interest-ing that the incidence of the halo substructures appearsto be similar to that found in cosmologically-motivatedstellar halo formation simulations (Bell et al. 2008). Notehowever, that recent analyses of distant blue horizontal-branch (BHB) stars (Xue et al. 2011; Deason et al. 2011),which represent very old stellar populations, and also of main sequence turn-off stars (Helmi et al. 2011), suggestthat the incidence of substructure may be slightly lowerthan expected from simulations.Great strides have also been made in the mapping ofthe halos of external galaxies. Through the use of noveldetection techniques, a great wealth of substructure hasbeen identified via integrated surface brightness measure-ments (Mart´ınez-Delgado et al. 2008, 2010; Paudel et al.2013) despite the extremely faint nature of the features(extending down to ∼
29 mag arcsec − ). While thesestudies are still in progress, integrated surface brightnesssurveys appear to be a promising avenue to identify andquantify fossil remnants of intermediate mass accretionsthat have occurred in the last few Gyr out to a distanceof several tens of Mpc.Halo surveys based on resolved stellar populations arenecessarily limited to nearer galaxies, although the in-formation that can be recovered is significantly more de-tailed. In this endeavor the Hubble Space Telescope hasbeen a powerful tool in recent years (see, e.g., Dalcan-ton et al. 2009, and references therein). A particularlyinteresting case is NGC 891, a Milky Way analogue, forwhich deep HST imaging showed evidence for clear signsof spatial substructure in its halo, with similar statisticalsignificance as was identified in the Milky Way by Bellet al. (2008), but in addition strong spatial variations inchemical abundance were also found (Ibata et al. 2009).Modern wide-field cameras on 8 m telescopes are nowbeginning to open up this field of study to ground-basedobservatories (Barker et al. 2009; Mouhcine et al. 2010;Jablonka et al. 2010; Bailin et al. 2011; Crnojevic et al.2013) for galaxies within ∼
10 Mpc.Nevertheless, M31 remains an important and uniquestepping stone in our efforts to explore those more dis-tant stellar halos, due to our current ability to probethe stellar populations in M31 both to extreme photo-metric depths (Richardson et al. 2009), including downto the main sequence turnoff in a handful of HST fields(Brown et al. 2006, 2007; Bernard et al. 2012), and overan extremely wide area, such as in the present study.A previous contribution (Cockcroft et al. 2013), basedalso on PAndAS data, detected the halo of M33 (a satel-lite of M31) out to very large radii, revealing hints ofasymmetric morphology. Recent spectroscopic studieshave shown evidence of a metal-poor halo in M31 (Chap-man et al. 2006; Kalirai et al. 2006; Koch et al. 2008),which had been largely missed in earlier work due to thepresence of substantial contamination from the so-calledsouthern Giant Stellar Stream (Ibata et al. 2001), whichpollutes almost all the inner halo region. The large spec-troscopic study of Gilbert et al. (2012, hereafter G12),which probed the halo at the location of 38 fields withKeck/DEIMOS, found that the projected stellar densityfalls off with a power-law index of − . ± .
2, and thatglobally the halo is slightly prolate. However, the effec-tively pencil-beam nature of the (relatively) small 5 (cid:48) × (cid:48) DEIMOS fields means that it is unclear to what extentthese results are affected by the substructure found inthe M31 halo (McConnachie et al. 2009; Tanaka et al.2011).The layout of the paper is as follows. Section 2 presentsan overview of the data and reductions, § § §
5, anddraw our conclusions in § THE SURVEY
The imaging data that provided the foundations forthe PAndAS survey were obtained with the MegaCamwide-field camera at the CFHT from 2003 to 2010. Allfields were observed in both the g and i bands. Althoughthe bulk of the fields were taken as part of the dedi-cated CFHT Large Program, a substantial number offields were taken from earlier programs (PIs Ibata andMcConnachie). A full account of the data and the dataprocessing will be provided in a future contribution (Mc-Connachie et al., in preparation), but we provide here asummary necessary for the present analysis.The CFHT MegaCam imager is a mosaic of 36 (usable)individual 2048 × × .
187 arcsec / pixel,its field of view is 0 ◦ .96 × ◦ .94. An overview of the chosentiling pattern is shown in Fig. 1, where the color codes theyear of observation. As can be seen from the diagram,the survey covers an extremely large field around theM31 galaxy almost fully encompassing a 150 kpc radiuscircle in projection, along with an extension out to M33(located at ξ = 11 ◦ .3, η = − ◦ .1 on this map).The Andromeda galaxy is located at relatively lowGalactic latitude ( (cid:96) = 121 ◦ .2, b = − ◦ .6), and conse-quently its environment suffers from non-negligible fore-ground extinction. Figure 2 shows the distribution of theinterstellar reddening E(B − V) over the PAndAS surveyregion, as estimated by Schlegel et al. (1998). It can beappreciated from this map that we refrained from ex-tending the survey further to the North so as to avoidmore highly extincted regions of sky. Within the PAn-dAS footprint (but avoiding the central 2 ◦ around M31),the minimum and maximum values of the extinction are0.034 and 0.24, with an average value of 0.077, and anr.m.s. scatter of 0.028. The reddening was convertedinto extinction in the MegaCam g and i bands, using thefollowing relations: g = g − E ( B − V ) × . i = i − E ( B − V ) × . . (1)All observations were undertaken in queue mode byCFHT staff. Generally, the observing conditions wereextremely good, and only a minor fraction of frames hadpoor image quality. During the final observing seasonin 2010, most of these poorer fields were re-observed ingood seeing conditions. The final set of fields used inthe analysis below have good image quality, with a g-band mean of 0 (cid:48)(cid:48) .67 (rms scatter 0 (cid:48)(cid:48) .10) and i-band mean0 (cid:48)(cid:48) .60 (rms scatter 0 (cid:48)(cid:48) .10). However, some good and badoutliers are present in the sample (in g, the best andworst seeing was 0 (cid:48)(cid:48) .41 and 0 (cid:48)(cid:48) .93, respectively, while inthe i-band the best and worst seeing frames has 0 (cid:48)(cid:48) .35 and0 (cid:48)(cid:48) .92, respectively). As a consequence of these variations,the photometric depth is not uniform over the survey.This can be appreciated in Fig. 3, where we display thelimiting magnitude in the g- (left panel) and i-band (rightpanel). The median (5- σ ) depth is 26 . . × σ from the stellar locus.In addition, sources in the stacked images were alsomeasured using the photometric package DAOPHOTand ALLSTAR Stetson (1987) so as to provide pointspread function (PSF) fitted photometry and additionalmorphological measurements to improve star/galaxy dis-crimination. While the DAOPHOT photometry and fitparameters were found to be very useful in crowded re-gions, in the outer halo the resulting catalogue was lesshomogenous (due to significant PSF variations betweenfields) than that derived from the CASU pipeline. In theanalysis below we therefore use only the CASU photom-etry.Unfortunately, the Elixir data products received overthe course of the project suffered from the several photo-metric problems that are discussed at length in Regnaultet al. (2009). Those authors propose corrections to ac-count for non-uniformities of the detector response aswell as for spatial variations in the effective passbands ofthe MegaCam filters. While we initially implemented thecorrections of Regnault et al. (2009), which were devel-oped for the Supernova Legacy Survey (SNLS) observa-tions, it became apparent from comparison to the SloanDigital Sky Survey (SDSS) that the corrections were notapplicable to our fields.Part of the problem was that the newer Elixir recipesdeveloped for the SNLS were only applied to a subset ofour images, but even those images had obvious residualpatterns. We therefore decided to proceed to calibrateour data empirically using the SDSS as a reference, con-structing two-dimensional correction functions over theMegaCam focal plane. Nevertheless, in order to min-imize the amplitude of the correction, we first appliedto all the images the most recent flat-field correctionimages derived by the CFHT for each observing run.In Fig. 4, we display the overlap of PAndAS with theSDSS Data Release 8 (DR8). Although the DR8 data aresubstantially shallower than the MegaCam photometrypresented in this contribution, they have the advantageof being (mostly) well-calibrated. Furthermore, the DR8observing pattern in “stripes” is very different to the ori- As of December 2011.
Ibata et al.
Figure 1.
The chosen CFHT tiling pattern of the region around M31 (on which the coordinates are centered) is displayed, with the colorsmarking the year of observation of the i-band images from 2003 to 2010, as indicated in the legend. The g-band data have an almostidentical tiling pattern and temporal (observing year) distribution. Each tile represents a CFHT/MegaPrime field. The inner red ellipserepresents a disk of inclination 77 ◦ and radius 1 ◦ .25 (17 kpc), the approximate edge of the “classical” regular stellar disk. This same ellipseis reproduced in the image insert on the top left, a view of M31 constructed from Palomar photographic plates. entation of the MegaCam camera (aligned with eclipticcoordinates), which makes it easy to identify regions inthe SDSS with suspicious calibration. These suspiciousareas have the size of the SDSS CCDs and follow anSDSS stripe rather than equatorial cardinal directions.Figure 4 shows the areas without SDSS comparison stars(red), where the SDSS calibration is good (green), andwhere the SDSS calibration appears incorrect or unreli-able (blue).For each observing season we constructed the empiricalphotometric correction function over the MegaCam focalplane using overlapping SDSS stars with magnitudes inthe range 18 < g <
20 or 18 < i < .
5. For those seasons without SDSS reference data, we adopted thecorrection closest in time. Note that SDSS g,i passbandsare not identical to those of MegaCam, so the color trans-formations given in Regnault et al. (2009) were used toconvert between the two systems. It is also noteworthythat the original MegaCam i-band filter was damaged inJune 2007, and its replacement has a slightly differenttransmission. From PAndAS regions observed with bothi-band filters, we deduced the following simple transfor-he halo of M31 5
Figure 2.
The E(B − V) reddening over the survey region accord-ing to the (Schlegel et al. 1998) maps. Extinction increases north-ward toward the Galactic plane, and is typically E(B − V) ∼ . mation: i new = − .
010 + 0 . × ( g − i old ) + i old for ( g − i old ) < . , − .
081 + 0 . × ( g − i old ) + i old for ( g − i old ) > . . In the analysis below g,i refer to AB magnitudes in theCFHT system, with old i-band data transformed into thenew filter using this equation.Figure 5 shows the resulting distribution of residualsbetween the PAndAS and SDSS data over the opticalfield of MegaCam, after the empirical correction func-tions were applied (and the field-to-field zero-points).The distributions in both g and i are flat (with r.m.s.scatter below 0 .
02) and substantially better than the ini-tial “elixir” calibrations that had up to ∼ . . < g <
20, 18 < i <
19) in this region, which they
Figure 3.
Map of the photometric depths (5 σ limit) for pointsources in the g- (top) and i-band (bottom). Moderate inhomo-geneities are apparent over the survey region. The circles, linesand ellipse have the same meaning as in Fig. 2. (The light-coloredregion in the M31 disk is not a hole in the survey, but marks fieldswhere the limiting magnitude is shallower). generously granted. It transpired that, within the un-certainties, our calibration agreed very well with Pan-STARRS, with only 5 fields showing substantial errors(and which we corrected to be in-line with Pan-STARRS,as will be discussed in McConnachie et al. 2013). Thelarge-scale calibration of the photometric zero-point ap-pears to be within ∼ .
01 magnitudes, judging from thesmall change in the zero-point between our original pho-tometric calibration and the Pan-STARRS calibration,although we are aware that this test is not entirely in-dependent since Pan-STARRS also bootstrapped theircalibration from the SDSS. GLOBAL COLOR-MAGNITUDE AND SPATIALDISTRIBUTION
Ibata et al.
Figure 4.
The shallower SDSS survey (whose sources are markedwith black dots) overlaps a significant fraction of the PAndAS field.This provides a very convenient means to refine the calibration ofthe CFHT photometric zero-points. The CFHT fields hatched ingreen mark those fields where the SDSS calibration appears to beof good quality. Red fields have no SDSS counterparts, while bluefields contain either too few SDSS stars to be useful, or the SDSScalibration was found to be unreliable.
In Fig. 6 we display the color-magnitude distributionof point sources over the entire survey area, and the ex-pected loci of plausible stellar populations in the M31halo are marked by the fiducial RGB tracks. A largenumber of these sources are Galactic contaminants, prin-cipally from the Galactic thin and thick disks, and halo.Their color-magnitude distribution is complex and variesspatially, but for illustrative purposes in Fig. 6 we markthe color magnitude diagram (CMD) regions where theyare most visible. In addition to the foreground Galacticstars, the survey also contains unresolved backgroundgalaxies, which contaminate especially at faint magni-tudes. In an accompanying contribution (Martin et al.2013, hereafter M13), we have developed a detailed em-pirical model to account for both of these contaminat-ing populations. The model uses the area beyond a ra-dius of 9 ◦ (120 kpc) to sample the contamination, and soprovides an interpolation of the number of contaminantsΣ ( g − i,i ) ( ξ, η ), as a function of color-magnitude position( g − i, i ) and sky position ( ξ, η ).In the remainder of this contribution we will be inter-ested primarily in investigating the global properties ofthe M31 halo, and the analysis will be made more robustby considering a clean sample. After extensive tests wedecided to limit the survey to i < .
5, which showsa smooth distribution of foreground contaminants whilebeing typically more than a magnitude above the 5 σ de-tection limit (see Fig. 3). This will minimize field-to-fieldvariations in counts due to photometric incompleteness.A photometric metallicity was estimated for each starin the survey by comparing their colors and magnitudesto the Dartmouth isochrones (Dotter et al. 2008), shiftedinto the MegaCam filter system. A common age of13 Gyr was assumed for all stars, and [ α/ Fe] = 0, which
Figure 5.
The spatial distribution over the CFHT field of viewof the photometric differences in the g- (top) and i-band (bottom)with respect to well-measured stars in the SDSS after the CFHTflattening operation has been applied. (The samples consist of starswith 18 < g <
20 or 18 < i < . we consider a reasonable assumption for halo members.In order to estimate a photometric metallicity we alsoneed to know the distance to the star under examination,yet this information is unavailable to us . To overcomethis problem, we further assumed that all the halo starshave the same Heliocentric distance as M31 (taken to be785 kpc, McConnachie et al. 2005). Note however, thatwe observe major substructures at projected distancesof up to ∼
120 kpc; a similar extension along the line of The distance to a few substructures may be estimated fromthe tip of the RGB (Conn et al. 2012), but this is only probabilisticand not available for the bulk of the halo he halo of M31 7
Figure 6.
The combined CMD of the PAndAS survey at dis-tances beyond 2 ◦ of M31, showing the main RGB feature of inter-est as well as the contamination from foreground and backgroundsources that must be overcome. The fiducial RGBs (Ibata et al.2001) correspond to, from left to right, NGC 6397, NGC 1851,47 Tuc, NGC 6553, which have metallicity of [Fe / H] = − . − . − .
71, and − .
2, respectively. The sequences have beenshifted to a distance modulus of (m − M) = 24 .
47. The dashed-line rectangles highlight CMD regions where the contamination isespecially prominent: these are the foreground Galactic halo (blue)and Galactic disk (red). The orange box shows the adopted color-magnitude selection region, inside which we estimate the photo-metric metallicities of the stars in the survey (as discussed in § Figure 7.
Map of stars with ( g − i ) < . − . < [Fe / H] < i < .
5. The contamination from the foreground MilkyWay as well as that from unresolved background galaxies has beenremoved in a statistical manner. The dense regions around M31(radius 50 kpc) and M33 (radius 10 kpc) are shown as greyscaledensity images (with bin size 0 ◦ .02 × ◦ .02) while the outer data areshown with points. The pink circles indicate the positions of theknown satellites dwarf galaxies of M31. Figure 8.
Metallicity map of stars for the same parameter selec-tion as Fig. 7. The rich tangle of substructure is seen to possess awide range in metallicity. sight would result in changes in brightness of ∼ .
35 mag.Even though the isochrones on Fig. 6 are steep over thecolor interval of interest (especially for the metal-poorpopulations), changes of this size could substantially af-fect the inferred [Fe / H] and thus result in, for example,apparent metallicity gradients along streams. To give aquantitative appreciation of the size of this effect, con-sider a star with i = 22 . i < .
5) and ( g − i ) = 1 .
08; atthe nominal distance of M31 we would infer such a starto have [Fe / H] = − .
5. However, if the star were in real-ity 120 kpc closer (farther) the actual metallicity shouldhave been calculated to be [Fe / H] = − .
22 ( − . / H] ∼ . § / H] should ingeneral be substantially smaller than 0 . × g − i ) < . i < .
5, ( g − i ) < . − . < [Fe / H] <
0. Here, we have subtracted off the con-taminating populations; this is done in a statistical man-ner, treating the contamination as a distribution func- Ibata et al.
Figure 9.
As Fig. 7, but showing four different metallicity cuts. The two high metallicity cuts (upper panels) are dominated by thesouthern “Giant Stellar Stream”, although note that this structure changes shape slightly between the two panels. The low metallicity cutsin the bottom two panels display a more interesting spatial distribution. The − . < [Fe / H] < − . / H] < − .
7) appears, to first approximation, primarily smooth. In all panels we replacethe stars within an ellipse of radius 30 kpc and axis ratio 0 . tion in position, color, magnitude and metallicity. Thealgorithm generates a star at random from this distribu-tion function, and subtracts the real star that lies closestin the parameter space to the artificial contaminant .While the halo map changes slightly from one randomrealization to the next (depending on which stars weresubtracted) the advantage of this technique for visualiza- This multi-dimensional space clearly has different units. Tocalculate a “distance” we adopt a scale of 0 ◦ .25 for both ξ and η positions, a scale of 0 .
25 mag for the magnitude dimension, and0 .
25 dex for the metallicity dimension. Possible matches are con-sidered up to a “distance” of 5 scale lengths. tion is that it keeps the full resolution of the data.The corresponding metallicity distribution of thesehalo (and disk) stars is displayed in Fig. 8. This color-ful map reveals vividly the multitudinous accretions thathave taken place during the formation of the Andromedagalaxy. The variations in metallicity, size, and orbit high-light differences in mass, age, and accretion time (see,e.g., Johnston et al. 2008). By splitting the sample intothe four wide bins shown in Fig. 9, one can further appre-ciate the variation in the behavior of the halo populationsas a function of metallicity. It is interesting to note thatby far the strongest signal of metal-rich stars (beyondhe halo of M31 9
Figure 10.
The substructure masks generated by the halo fittingalgorithm are displayed in black. Note that data within the central2 ◦ of M31 was ignored, as we deemed the spatial distribution tobe too complex in that region. Similarly, a 2 ◦ .5 region around M33was excised. The bottom panel shows the union of the four uppermasks. In each panel the underlying colored distribution shows thebest-fit halo model for the corresponding metallicity selection. Thehalo fits (the parameters of which are listed in Table 2) are clearlyalmost spherical. the bound galaxies) is due to the so-called “Giant Stel-lar Stream” that protrudes down to the south of M31(Ibata et al. 2001, 2004; Fardal et al. 2006, 2007, 2012;Gilbert et al. 2009). This structure is likely the latestand most significant accretion event that has taken placein the last several ( ∼ −
3) Gyr. While the progenitor(or its remnant) has not been identified, it is likely thatits dismemberment also produced many of the metal richfeatures that surround M31 at distances of ∼ / H] = − . − . < [Fe / H] < − .
7, is the only one ofthese maps that begins to approximate the classical pic-ture (commonly accepted in the 1990s) of a smooth, el- lipsoidal, stellar halo. DECONSTRUCTING THE M31 HALO
The maps presented in Fig. 9 show clear evidence fora multitude of accretion structures overlaid on what ap-pears to be a relatively smooth centrally-concentratedcomponent. To some extent, this is exactly what is ex-pected. Hierarchical halo formation scenarios are well-known to predict copious stream-like substructures (Bul-lock & Johnston 2005). But a smooth halo componentis also expected. In a recent contribution, Pe˜narrubia(2013) demonstrated that in hierarchical time-dependentpotentials, stellar clumps tend to be effaced from theintegral-of-motion space. The same process that leadsto the formation of substructures, namely the accretionof satellites, induces an evolution of the host potential,which in turn speeds up the diffusion of pre-existing sub-structures. This is a dynamical process from which a“smooth” stellar halo must necessarily arise (in this pic-ture the smooth stellar halo is nothing but diffused ac-creted substructures).Nevertheless, a reliable identification of this smoothhalo poses significant practical problems: how does onedistinguish the smooth and clumpy halo components?Indeed, how can these components be suitably definedin an observational survey, given signal to noise limita-tions at the spatial resolutions required to discriminatebetween residual faint substructure and the diffuse halo?One could propose that the smooth halo is whateveris not in a “clump”. However, there is no clear defi-nition for “clumps”, since streams can show an infinitenumber of phase-space configurations and metallicity dis-tributions. Furthermore, these structures are transient,and will eventually diffuse away, so any distinction isstrongly dependent on the system observed. Also even ifwe had access to perfect data, the analysis of Pe˜narrubia(2013) indicates that there should not be a clear-cut dis-tinction between “smooth” and “clumpy” components inintegral-of-motion space, let alone in projected density.These considerations would suggest that the best com-promise is simply to ignore the distinction betweensmooth and clumpy halo, and to present the global prop-erties of the population. This will be the approachadopted in § § demands close examination. The caveat forthis pragmatic alternative analysis is that what we willcall a “smooth” halo, is only smooth to the limits ofthe PAndAS survey. While this observational definitionmay appear somewhat arbitrary, the well-defined selec-tion function for PAndAS means that modelers may pro-cess their simulations in order to produce PAndAS-likemock catalogs, and so compare directly to our findings. Three-dimensional fits with masks
For the purposes of this study we developed a newalgorithm to help disentangle the stream and shell-likeoverdensities from a possible smooth large-scale compo-nent. Starting from a trial density profile ρ ( s ) for thesmooth stellar halo (which we implement to be either bea power-law or a spline interpolation function to log( ρ )0 Ibata et al.vs. log s ), the algorithm integrates the density along theline of sight cone. In the following, we denote the lineof sight coordinate l , the M31 tangent plane coordinates( ξ, η ) (aligned with the North and South directions, asdisplayed in all our maps), and we define an M31-centricelliptical coordinate s = (cid:112) x + y + z /q . Here x, y liein the plane of the M31 disk, with z perpendicular to thedisk. The coordinate s also depends on the flatteningparameter q , which allows for oblateness or prolateness.The integration along a cone is necessary to account forthe fact that the M31 halo extends over a huge distancerange, such that the observed volume behind M31 is sub-stantially larger than the observed volume in front ofthe galaxy. While the increased volume behind M31 willtend to favor the detection of distant stars, there is alsoan opposing tendency that these more distant stars willbe fainter, and hence correspondingly less numerous in amagnitude limited survey like PAndAS. To account forthe dimming of the RGB, we assume that the RGB lumi-nosity function of all populations has the form (M´endezet al. 2002): L ( M ≥ M TRGB ) ∝ . M − M TRGB ) , (2)where M TRGB is the absolute magnitude of the RGBtip. The density profile is defined as a spline profile inlog(density) versus log(radius), constrained at an arbi-trary number of radial anchor points. To allow for a flat-tening of the smooth halo, we permit ρ to be a functionof s , so that the ellipsoid has the same axis of symme-try as the disk of M31. The flattening q is introducedas a global variable or, optionally, as a non-parametricsplined function of ellipsoidal radius. The halo densitymodel ρ ( s ) is thus forced to have the same axis of sym-metry as the disk of M31. We refrained from testingother axes of symmetry for the halo, since any flatteningdirected along (or close to) our line of sight would bealmost entirely unconstrained, due to the lack of gooddistance information along the line of sight. In any case,we feel that it is a natural assumption for an axisymmet-ric halo to have the same axis of symmetry as the disk,as a non-spherical halo in another configuration wouldgive rise to non-circular motions of gas in the disk.We proceed to calculate the model over the ( ξ, η ) plane,subject to the spatial footprint S of the survey, takingbins of 0 ◦ .1 × ◦ .1 on the sky. With the above definitions,the normalized projected density of the halo model in achosen range in [Fe / H] at position ( ξ, η ) is: D halo ( ξ, η ) = (cid:82) ∞ ρ ( s ) L c ( l ) l dl (cid:82) (cid:82) S (cid:82) ∞ ρ ( s ) L c ( l ) l dl dξ dη , (3)where L c ( l ) is a correction function to account for thedimming of the population with distance. This cor-rection function can be evaluated simply by integrat-ing Eqn. 2 between a bright apparent magnitude cut-off i b (= 20 .
5) and the apparent magnitude limit of thesurvey i l (= 23 . L c ( l ) = exp[ a ( i l − i (cid:48) T RGB ( l ))] − exp[ a ( i b − i (cid:48) T RGB ( l ))]exp[ a ( i l − i T RGB )] − exp[ a ( i b − i T RGB )] , (4) if the population is in front of M31, or: L c ( l ) = exp[ a ( i l − i (cid:48) T RGB ( l ))] − a ( i l − i T RGB )] − exp[ a ( i b − i T RGB )] , (5)if the population is behind that galaxy. The quantity i T RGB is the i-band magnitude of the RGB tip at thenominal distance of M31 (785 kpc), while i (cid:48) T RGB ( l ) is theapparent magnitude of the RGB tip at the line of sightdistance l . The numerical constant a = 0 . ( g − i,i ) ( ξ, η ) that we discussed above in § . Unfortu-nately, there are no other suitable background fields inthe CFHT archive that could be used to constrain betterthis contamination. We overcame this modeling problemby including an additional parameter F into our fit, inthe form of a simple global factor to multiply the con-tamination model by. For convenience, we define a newquantity C bg to be the sum over all color-magnitude binsof the M13 model that have metallicity in the chosen[Fe / H] range: C bg ( ξ, η ) = (cid:88) CMD Σ ( g − i,i ) ( ξ, η ) . (6)Thus the final model probability of finding a star in asmall bin centered on ( ξ i , η i ) becomes: P model ( ξ i , η i ) = ( n − n bg ) D halo ( ξ i , η i ) + F C bg ( ξ i , η i ) n , (7)where n is the number of stars in the sample, and n bg = F (cid:80) S C bg is the sum of the background contaminationmodel over the survey area S . Finally, we calculate thelikelihood of the model given the data via:ln L = n (cid:88) i =1 ln[ P model ( ξ i , η i )] . (8)We use the Markov Chain Monte Carlo (MCMC) en-gine described in Ibata et al. (2013a) to refine the ini-tial guessed halo density model and the parameter F .This MCMC solver uses multiple “temperature” parallelchains to probe the likelihood surface at different levels ofsmoothing, thereby greatly diminishing the chances thatthe algorithm will get caught in local maxima. The rou-tine also uses a population of affine-invariant “walkers”,which propagate across the likelihood surface; the scatterin the population adapts automatically to the steepnessof the likelihood function in each dimension, and therebyprobes the parameter space very efficiently.All runs consisted of 10 iterations of the lowest tem-perature chain, and used a population of 100 walk-ers. The algorithm was tested extensively using artificialdata, in which we included streams from N-body sim-ulations as additional “contamination”, mimicking thestructures observed in our maps. For artificial samples This “background” is composed primarily of foregroundGalactic contaminants. he halo of M31 11
Figure 11.
The residual maps of the smooth power-law halo fits (data − model). Each pixel is 0 ◦ .1 × ◦ .1. of 10 stars, our tests showed that the input parametersof the artificial smooth halo could be accurately recov-ered, including the flattening as a function of radius.Returning to the real PAndAS data, we used as beforestars limited to i < .
5, 0 . < ( g − i ) < .
8, andwith color-magnitude consistent with stars that have aphotometric metallicity in the range − . < [Fe / H] < ◦ .15) where the result-ing residuals were found to be in excess of 2 . σ ; a visualcomparison to Fig. 9 shows that this procedure has nicelyidentified the substructures, as intended. The maskedfractions of the available area (A masked , from which wehave excluded the circular regions around the satellites)are listed in Table 1 for the various metallicity selections;note that these remove only ∼
10% of the available haloarea. For completeness we also give the contaminationfraction ( f contam ) in the metallicity interval according tothe M13 model.The faintest of the masked structures is “stream A”previously reported in Paper I, which has a surfacebrightness of Σ V ∼
32 mag arcsec − , and which is vis-ible in Fig. 9c at ( ξ ∼ ◦ .5, η ∼ − ◦ ). We propose thisas an estimate of the limiting surface brightness beyondwhich we can no longer resolve the detections into sep-arate structures (this is not a hard limit since it alsodepends on the size of the feature and the background2 Ibata et al. Table 1
The foreground/background contamination fraction and thefraction of the total area suppressed by the masks shown inFig. 10.Selection panel f contam A masked n (fraction) a (fraction) a − . < [Fe / H] < . .
56 0 .
08 223107 − . < [Fe / H] < − . .
56 0 .
08 288425 − . < [Fe / H] < − . .
66 0 .
09 196259 − . < [Fe / H] < − . .
68 0 .
09 94839 − . < [Fe / H] < . .
56 0 .
13 802630
Notes. a Fraction of the total number of stars (before masking, but afterrejecting the circular regions around M31 and its satellites) con-sidered to be contamination according to the M13 contaminationmodel. The multiplicative factor F is not applied. a Total number of stars in metallicity selection (unmasked andwith no contaminants removed). level).Having identified the over-dense areas, we use themto define masks that will facilitate the study of the un-derlying smooth component. It is worth reiterating atthis juncture that we are of course aware that with asufficiently fine resolution and sufficiently deep data, itis possible that we would find that what we are callingthe smooth component is composed of a (probably quitelarge) number of correlated families of stars. However,given our observational limitations, we feel that it is auseful approximation to group the unresolved structuresinto a single entity, and explore how this may be modeledas an ellipsoidal structure.The algorithm was subsequently re-run, this time fix-ing the substructure masks defined from the initial iter-ation, and with the previous prior on negative residualsdisabled. The halo fits to the masked samples using asimple power-law profile and a single global flattening areshown in color in Fig. 10, the corresponding residuals inFig. 11, and the details of the fits are listed in Table 2.The table shows that the power-law exponent γ of thesmooth component becomes progressively shallower withdecreasing metallicity. (We define γ to be the exponent ofthe three-dimensional density distribution, while Γ belowwill refer to the two-dimensional projected distribution.Likewise, r below refers to 3-D radius, while R is pro-jected radius). In all cases, the algorithm finds a veryclose to spherical stellar halo. Note that the putativesmooth component represents a relatively small fraction(14%) of the total number of stars more metal rich than[Fe / H] = − .
6. It is only for the most metal-poor se-lection that the smooth component becomes dominant(58%). We note also that the contamination model cor-rection factor F is, as expected, slightly lower than unity.Given the paucity of candidate stars that could belongto the smooth halo in the higher metallicity bins, we de-cided to only attempt the spline profile fitting of the halodensity profile with the − . < [Fe / H] < − . q = 1 . ± .
04. It is in-teresting to note that the algorithm finds a profile thatfalls off as γ ∼ − γ = − Two-dimensional fits
Figure 12.
The non-parametric density profile fit to the smoothhalo for the metallicity range − . < [Fe / H] < − .
7, as a functionof (three-dimensional) radius r . The filled circles show the an-chors of the most likely halo model, with the corresponding errorbars marking 1 σ uncertainties derived from the Markov chain. Thecontinuous line demonstrates the smooth spline function that thealgorithm generates to interpolate the density. To aid visual in-terpretation, we have overlaid a γ = − γ = − q = 1 . ± . Table 2
Parameters of the three dimensional fits to the smooth halocomponent (power law model), using the masked samples.Selection γ q f smooth F a b (fraction) c d − . < [Fe / H] < . − .
34 1 .
01 0.14 0 . ± . ± . ± . − . < [Fe / H] < − . − .
62 1 .
05 0.22 0 . ± . ± . ± . − . < [Fe / H] < − . − .
16 1 .
07 0.42 0 . ± . ± . ± . − . < [Fe / H] < − . − .
08 1 .
09 0.58 0 . ± . ± . ± . − . < [Fe / H] < . − .
59 1 .
11 0.21 0 . ± . ± . ± . Notes. a Power law exponent. b Density flattening parameter. c Fraction of the halo between 2 ◦ (= 27 . d Multiplicative correction factor applied to the M13 “back-ground” contamination model.
As an alternative to the three-dimensional halo modelfits discussed in the previous section, we present inFig. 13 the direct (i.e. projected) star-counts profile forthe − . < [Fe / H] < − . − . ± . − . ± .
02; giventhat this has been fit to a projected profile, it is fairlyhe halo of M31 13
Figure 13.
The star-counts profile of the smooth metal poor ( − . < [Fe / H] < − .
7) population as a function of projected radial distance.Panel (a) corresponds to the full unmasked survey (but regions around known satellites are excluded), while panel (b) is masked with themask shown in Fig. 10d. In both panels the data for all azimuthal angles is shown in black. We also show the profiles of the four quadrantsindividually, color-coded according to quadrant as indicated in the diagram. A small radial offset has been applied to the colored datapoints in order to make them easier to see. The overall normalization (i.e the vertical offset) has been set by comparison to Dartmouthstellar population models. For the models we assumed an age of 13 Gyr, [ α/F e ] = 0 .
0, and a log-normal initial mass function; we alsoexamined 9 Gyr models, but the differences (which can be appreciated from Table 4) were found to be relatively small. The dashed lineis a linear fit to the full profile, implying a (projected) power-law slope of Γ = − . ± .
02 and Γ = − . ± .
02, respectively for theunmasked and masked samples. The larger uncertainties marked in brackets on the diagrams are derived from taking the root mean squarescatter in azimuthal bins as an estimate of the uncertainty in the profile.
Table 3
Power-law fits to the projected distribution.Selection Γ unmasked Γ maskeda b − . < [Fe / H] < . − . − . ± . ± . ± . ± . − . < [Fe / H] < − . − . − . ± . ± . ± . ± . − . < [Fe / H] < − . − . − . ± . ± . ± . ± . Notes. a Power law exponent fit to the unmasked sample. The uncertaintyin brackets reflects the uncertainty due to the azimuthal scatter inthe profiles. b Power law exponent fit to the masked sample. similar to the corresponding MCMC model fit listed inTable 2. In Fig. 13 we also show the data split into fourquadrants (colored points); clearly there are significantdifferences between the profiles, but the radial profile ap-pears similar between quadrants. Fig. 14 shows the sameinformation for the − . < [Fe / H] < − . − . ± .
02, identical within the uncertainties withthat of the most metal poor selection. It is interesting to note that both of these profiles show no steepening ofthe profile at large radius.Due to the small number of stars in the putativesmooth halo component at metallicities greater than[Fe / H] = − .
1, we combined the two metal-rich binsto construct the profile shown in Fig. 15b. Given thelarge variations between quadrants, it is obvious that ourmasks have not removed all of the substructure, and theresidual presence of the Giant Stellar Stream in the SEminor axis quadrant is particularly striking. In the un-masked profiles displayed in Fig. 15a, it is surprising tofind that the azimuthally-averaged profile follows quiteclosely a (very steep) power law whereas the profiles fromindividual quadrants show huge scatter.
Metallicity structure
We now turn our attention to the variation of metal-licity with radius. The stellar sample with i < . . < ( g − i ) < . / H] = − . / H] = 0 .
0, using the 13 Gyr Dartmouth isochronemodel, as discussed above. The upper color limit wasimposed on the sample as we deemed that it was theonly practical way of avoiding overwhelming contamina-tion by foreground dwarf stars, but it can be appreciatedfrom an inspection of Fig. 6 that the limit excludes mostof the evolved metal-rich RGB stars from our sample.Fortunately, it is possible to use the same isochrone mod-4 Ibata et al.
Figure 14.
As Fig. 13, but for the − . < [Fe / H] < − . Figure 15.
As Fig. 13, but for stars more metal rich than [Fe / H] = − .
1. The very large variations between quadrants in the profilederived from the masked sample (panel b) are almost certainly due to residual substructures that have not been eliminated by the masks(Figs. 10a and 10b), the Giant Southern Stream in particular. The marked power law has slope Γ = − .
66, but it is clearly not applicablefor the profile in all quadrants beyond the inner halo. he halo of M31 15els to estimate the number of stars that were missed bythe cut and correct for the absent members. The modelestimates that no stars are missing below [Fe / H] = − . . / H] = 0 .
0. For younger popu-lations the correction is somewhat smaller: for instancea 9 Gyr old model predicts a correction of a factor of 3 . / H] = 0 . ∼ − − R = 27 . ◦ ) and R = 150 kpc. Theraw star counts are displayed as points with uncertain-ties connected by a dashed line. We also show the countscorrected for the incompleteness of the red stars beyond( g − i ) = 1 .
8; these are connected with the continuousline.The left column of Fig. 16 shows the full sample (mi-nus satellites), while the distributions in the right columnhave had the substructure masked out (using the maskdisplayed in Fig. 10e). These data show a clear metallic-ity gradient in both the full and masked samples. Thebottom row of Fig. 16 displays the different radial bins onthe same scale to allow the reader an appreciation of therelative density present in each interval. Note that forthe masked populations (panel l), the metal-poor pop-ulations (Fe / H] ∼ − .
5) have roughly the same countlevel, consistent with Γ ∼ −
Mass and luminosity of the halo
The total mass and luminosity of stellar halos areamong their most fundamental properties, and it isclearly important to provide this information on the M31halo derived from a panoramic study such as PAndAS.But while the present data set is superb for quantifyingthe populations at large radius, the superposition of thecentral components towards the inner galaxy precludes atrue global analysis.Obviously it makes little sense to extrapolate thepower-laws we have fitted in § R = 0, since theywill diverge. Furthermore, very little real information onthe stellar halo exists in the inner few kpc of M31 thatis not highly dependent on the modeling choices (andin particular, on the dominant bulge and disk compo-nents that must be subtracted to reveal the halo). So weagain take a pragmatic approach and measure the stellarhalo’s properties where we have detected this componentwith confidence in PAndAS, namely from R = 27 . R = 150 kpc.To calculate the mass and luminosity of the stellar pop-ulations, we need to correct again for the stars that arenot present in the color-magnitude selection box (Fig. 6),notably all of the stars below i = 23 . g − i ) = 1 . Figure 16.
The metallicity distribution of the M31 halo in fivelogarithmically-spaced intervals covering the range 27 . < R <
150 kpc. All stars within small circular regions of all the knownsatellites have been removed. The left column presents the metal-licity distributions of the full sample, while the column on theright shows the sample subject to the mask of Fig. 10e (which isappropriate for the full metallicity range − . < [Fe / H] < . g − i ) < .
8, there is significant incompleteness atthe metal-rich end; we correct for this using a 13 Gyr Dartmouthpopulation model, as described in the text. The resulting correctedcounts are connected with the full line curve. The error-bars showncorrespond to Poisson counting uncertainties. The dotted verticalline in magenta shows the mean metallicity of each distribution,whose value is indicated. The bottom two panels reproduce theprevious rows on the same vertical scale to aid their comparison.A prominent trend towards lower metallicity as a function of radiusis revealed by these data, both for the full and masked samples,with the masked distributions being more metal-poor than the un-masked distributions at the same radial position. radial selection of the halo. It can seen that for theseplausible choices of population age, the derived quanti-ties do not change substantially. The alternative mea-surements for the halo sample with substructure maskedout are given in Table 5, where we have accounted forthe missing area under the masks.It can be seen that for the unmasked population, thehalo beyond 2 ◦ amounts to ∼ M (cid:12) , or approximately10% of typical estimates of the total baryonic mass ofM31 (Klypin et al. 2002). The smooth halo in the samedistance range amounts to approximately one third ofthis value.6 Ibata et al. Figure 17.
The fraction of the halo present in the PAndAS samplebeyond 2 ◦ . Assuming that the halo has a cored power-law form(1 + ( R/R c ) ) Γ / , we calculate the fraction of the halo we havemeasured beyond 2 ◦ , as a function of the core radius R c . The linesshow the relations for various Γ values measured in Figs. 13-15.The reader may hereby easily use their preferred core radius valueto correct our halo mass measurements for the missing central 2 ◦ . How much mass or light are we likely missing byrejecting the central 2 ◦ ? Figs. 13-15 show that theazimuthally-smoothed stellar halo follows a power lawquite closely, so it may be instructive to consider a coredpower law (1 + ( R/R c ) ) Γ / behavior in the central re-gions, as is commonly assumed (see, e.g., Courteau et al.2011). Clearly the core radius R c must be significantlysmaller than 27 kpc, since we do not see a turnover inthe star counts profiles. In Fig. 17 we integrate thiscored power law to calculate the fraction of the totallight or mass we have measured in our samples beyond2 ◦ as a function of the value of R c . One can see, for in-stance, that for the smooth metal-poor population withΓ = − .
08, most of the mass is already accounted forin Table 5, even if R c is as small as 1 kpc. On theother hand, for the unmasked metal-rich selection withΓ = − .
72, the values listed in Table 4 would only be asmall fraction of the total population, if the true profilereally were a cored power-law all the way to the galaxycentre.To take a concrete example, if we adopt a core ra-dius value of R c = 5 . ∼ × M (cid:12) . This is substantiallylarger than the total mass of the Galactic halo, which isestimated at ∼ × M (cid:12) (see discussion in Bullock &Johnston 2005). We refrain from attempting to extrapo-late inwards the unmasked clumpy halo, since the answerwe would obtain would be non-sensical. DISCUSSION
What is the nature of the smooth halo component?
The Keck/DEIMOS spectroscopic survey of G12 (acollaboration known as “Spectroscopic and PhotometricLandscape of Andromeda’s Stellar Halo” or SPLASH)presented kinematics from a total of 38 DEIMOS fields(covering approximately 1 /
500 of the area of the presentCFHT survey) distributed in an irregular fashion aroundM31. Their fields probe the halo primarily along the mi-nor axis, but they also targeted dwarf galaxies and othersubstructures (see Figure 1 of G12). In terms of the re-gion surveyed, all fields except one (targeting the satel-lite And VII) are contained within a projected circle of150 kpc of M31, which makes their study a very usefulcomplement to PAndAS.Both PAndAS and SPLASH are dominated by con-taminants, but the two studies identify and correct forthese in different ways. G12 de-contaminated their sam-ple by using kinematics and several diagnostic parame-ters to minimize the number of Milky Way dwarf stars.However, since not every candidate star in their color-magnitude selection box within the DEIMOS fields couldbe observed, they further used the Besan¸con Galacticmodel (Robin et al. 2003) to weight the relative numberof M31 RGB stars in each field. In the present analysis,we use an empirical fit to the contamination, as we foundthat the Besan¸con model does not give a sufficiently goodrepresentation of the foreground populations over the en-tire PAndAS survey (with errors exceeding ∼
50% forsome populations).G12 measure the velocity distribution in each field,and remove features in velocity space that are related tothe known substructure. They also performed a multi-Gaussian fit to the velocity distribution in all fields toidentify any additional kinematically cold components.Slightly under a third of their fields (12/38) containedsuch kinematically identified substructure. In addition,a high velocity dispersion “hot” spheroid was fit in allfields, though they note that beyond a projected distanceof 90 kpc the statistics were not sufficient to disentanglekinematic substructure if it were present.While we do not have the information to relate di-rectly our smooth halo component to the hot kinematiccomponent detected in the G12 fields, it is highly plau-sible that the two populations are closely related. Theyappear to have the same power-law exponent (furtherdiscussion below), and in both analyses they are whatis left over after the most obvious substructure has beenremoved. However, it is unclear whether cosmologicalhalo formation simulations (e.g., Bullock & Johnston2005; Cooper et al. 2010) are compatible with the sig-nificant fraction of stars in this “smooth” component,given that all stars at these distances in the simulationswill have been accreted from disrupted satellite galaxies,and such debris has not had enough time to phase-mix.It is of course completely plausible that future deeperphotometric and spectroscopic surveys will manage toresolve this “smooth” halo component into further sub-structure (beyond Σ
V > ∼
32 mag arcsec − ). Given the ap-parent smoothness in the spatial distribution and thehigh dispersion of the kinematic distributions, it is likelythat this would have to involve a large number of sepa-rate accretions.However, it seems difficult to accommodate these manyhe halo of M31 17 Table 4
Properties of the full M31 halo sample in the projected radial range from 27 . ◦ ) to 150 kpc.Selection M
13 Gyr
V,V ega M V,V ega M
13 Gyr i,AB M i,AB ( mass10 M (cid:12) )
13 Gyr ( mass10 M (cid:12) ) ( L L (cid:12) )
13 Gyr ( L L (cid:12) ) − . < [Fe / H] < − . − . < [Fe / H] < − . − . < [Fe / H] < − . − . < [Fe / H] < . − . < [Fe / H] < . Table 5
Properties of the masked M31 halo sample in the projected radial range from 27 . ◦ ) to 150 kpc, corrected for the masked-out area.Selection M
13 Gyr
V,V ega M V,V ega M
13 Gyr i,AB M i,AB ( mass10 M (cid:12) )
13 Gyr ( mass10 M (cid:12) ) ( L L (cid:12) )
13 Gyr ( L L (cid:12) ) − . < [Fe / H] < − . a -14.3 -14.5 -15.1 -15.2 0.35 0.35 0.08 0.08 − . < [Fe / H] < − . − . < [Fe / H] < − . − . < [Fe / H] < . − . < [Fe / H] < . Notes. a The masks of Fig. 10 corresponding to each of these metallicity intervals are used, hence the final row is not simply the sum of theprevious rows. accretions into this smooth component, since the total lu-minosity integrated over projected radii between 30 kpcand 150 kpc is modest ( ∼ . × L (cid:12) for [Fe / H] < − . ∼
12 Gyr that is relatively free of stream-like structure.
Radial profile of the halo
Despite the above-mentioned differences in the elimi-nation of contamination between PAndAS and SPLASH,the power-law fits to the projected counts of metal-poorstars (Figs. 13b and 14b, with index of − . ± .
02 and − . ± .
02, respectively) are in excellent agreementwith the Gilbert et al. (2012) fit of − . ± . V ∼
32 mag arcsec − ) to identify the properties of the under-lying “smooth” halo population. The analysis in Paper Iwas hampered by the presence of copious sub-structuresin the Southern quadrant of M31, but excising the obvi-ous over-densities we found Σ V ( R ) ∝ R − . ± . , consis-tent with the present work. A number of other studiesthat attempted to measure the halo profile are reviewed in G12, but these either probe small fields (and hence arehighly prone to unidentified substructure) or probe onlythe inner halo region, and so are not directly comparableto G12 and the present contribution.It is fascinating that in addition to the spatialsmoothness, and apparent high velocity dispersion, the“smooth” metal-poor halo component additionally pos-sesses a smooth power-law profile (Figs. 13 and 14). Thisreinforces the notion that it is probably an ancient, well-mixed structure (or that it is composed of many ancient,smoothed-out remnants).In the simulations of Bullock & Johnston (2005), whoused a hybrid semi-analytic plus N-body approach tomodel galaxy formation, the halo density profiles tendto steepen with radius from approximately − − . ∼ − . γ = − γ = − . ± . ∼
25 kpc (Watkins et al. 2009), in main sequence turn-offstars at ∼
28 kpc (Sesar et al. 2011), and in BHB starsat 27 kpc (Deason et al. 2011). Yet at these distances inM31, the halo is clearly highly contaminated, especiallyby the Giant Stellar Stream. We suspect that a usefulcomparative study of the outer halos of the two LocalGroup giants will have to await the advent of the LSSTand, more imminently, HyperSuprimeCam.
Metallicity distribution
The metallicity measurements presented in § (cid:104) [Fe / H] (cid:105) ∼ − . − .
0. The differences between authors are account-able to differences in the techniques of the measurementand calibration of the Ca II triplet equivalent widths,and probably also due in part to field-to-field variance.While no similar panoramic survey has been conductedin another more distant giant spiral galaxy, we find thatour measurements are qualitatively similar to resultsin other systems: e.g., extra-planar stars resolved withHST in NGC 891 show (cid:104) [Fe / H] (cid:105) = − . R = 20 kpc(Ibata et al. 2009), while integrated light at a distance of R = 8 . (cid:104) [Fe / H] (cid:105) = − . / H] > − .
1; Fig. 15) is substantially steeper thanthat of more metal poor stars ([Fe / H] < − .
1; Figs. 13and 14), which of course implies that there is a largemetallicity gradient through the halo. This broad prop-erty was again predicted by the Font et al. (2006) simu-lations.However, it is the combination of the smooth power-law profiles (Figs. 13b and 14b) and the metallicity gradi-ent (Figs. 16g-k) in the “smooth” component that is par-ticularly interesting. It indicates the presence of differentfamilies of stars. As we proceed inwards from the outerboundary of the survey, we detect more and more metal-rich families with smaller apocenters. A large number offamilies is required since there is no break in the profiles.This is remarkable fossil evidence of the formation of thehalo, and is consistent with a picture in which more mas-sive satellites, which due to their deeper potential wellsare able to hold on to more stellar ejecta and hence en-rich further in [Fe / H], are also those satellites that suffermore orbital decay due to dynamical friction.
Extent of halo
The PAndAS survey shows that the M31 halo is a vaststructure, extending out in every direction to at least aprojected distance of 150 kpc, i.e. approximately half ofthe virial radius (estimated to be 290 kpc, Klypin et al.2002). Indeed, our three-dimensional fit is consistentwith stars being distributed along the line of sight allthe way out to the virial radius.Of course, given that orbital time-scales are close to aHubble time at such distances, it is inconceivable that theoutermost reaches of the stellar halo should be smoothand azimuthally uniform. This is indeed what we see inthe projected star-counts profiles of the smooth metal-poor populations (Figs. 13b and 14b), where the scatterbetween quadrants appears to increase beyond 100 kpcin projection. (It has not escaped our attention thatthe scatter is also larger at small radius). The variancebetween the different quadrants in the outermost two ra-dial bins is clearly very large. However, we will returnto the statistics of substructure, and the quantificationof the variance in the halo in a future contribution (Mc-Connachie et al., in preparation, Paper II in this series).
Shape of the stellar halo
One of the most interesting results presented above isthe finding that the smooth halo component underlyingthe identifiable substructure is approximately spherical.Formally, the solutions are slightly prolate, with massflattening q progressing from q = 1 . ± .
07 for the mosthe halo of M31 19metal-rich selection to q = 1 . ± .
03 for the most metal-poor. While our analysis method differed from that ofG12 (we integrated M31 halo models along the line ofsight, accounting for the dimming luminosity function,and took the disk plane as the plane of symmetry of thehalo), our results are again very similar. G12 also foundthat their spectroscopic sample favored a prolate halo with q = 1 . +0 . − . . The fact that a kinematically se-lected sample from a small number of pencil-beam fieldsyields the same result as a panoramic photometrically-selected sample lends strong support to both studies. Arobust result from these studies is that at large radii theM31 stellar halo is closely spherical.In contrast, measurements of the flattening of theMilky Way stellar halo find a much more oblate struc-ture, with q ∼ . . q ∼ . Shape of the dark matter distribution
Our decomposition of the M31 halo into “lumpy” and“smooth” components carries all the caveats we laid outin §
4. Nevertheless, the apparent large-scale homogene-ity of the smooth component, as well as the high veloc-ity dispersion seen in the individual G12 spectroscopicfields, strongly suggests that this component is a reason-ably well phase-mixed population and hence a reasonabletracer of the underlying gravitational potential.In collisionless cold dark matter simulations, cosmo-logical halos possess an approximate triaxial shape, withaxis ratios c/a ∼ . c/b ∼ . c ≤ b ≤ a ). However, these triaxial structuresbecome approximately oblate when baryonic physics isincluded in the simulations (see, e.g. Abadi et al. 2010),with c/a ∼ . c/b ∼ . ∼
30 kpcin M31 (Zemp et al. 2012, see their Figure 11). Be-yond that radius the dark matter halo is expected tobecome (on average) more triaxial, attaining c/a ∼ . c/b ∼ . ∼
100 kpc. It has been extremely difficult totest these predictions observationally, and unfortunatelyour best measurements of the shape of dark matter haloson galaxy scales, which came from weak lensing studies,have recently been shown to be fraught with difficulties(see Howell & Brainerd 2010; Bett 2012, and referencestherein). Obtaining constraints on the galactic dark mat-ter distribution from nearby galaxies is therefore of greatinterest.The approximate sphericity of the smooth stellar halomeasured in this contribution is surprising in the contextof the above predictions of dark matter morphology. Inprinciple, there is a large amount of freedom to populate There is a typo on the lower uncertainty limit on page 17 ofG12. the dark matter halo with a stellar tracer population, andundoubtedly one could find equilibrium solutions withpeculiar velocity dispersion tensors that would allow forthe observed spherical stellar distribution. Nevertheless,we suspect that such solutions are contrived in the sensethat there will be very few ways to form a spherical stel-lar system within a triaxial dark matter halo, whereasthere is a vast number of ways to form a triaxial stellarsystem in the same potential. Moreover, the sphericity ofthe stellar halo is detected in several bins in metallicity,and as we have seen in § The M31 satellite alignment in light of the smoothhalo
In a recent study that was also based on PAndAS data,Ibata et al. (2013b) showed that 50% of the satellitegalaxies of Andromeda (13 of the then known 27) arecontained within a very thin plane (Conn et al. 2013)and possess a common sense of rotation about M31. Al-though the exact formation mechanism of this structureis unknown, and indeed poses quite a puzzle (Hammeret al. 2013; Goerdt & Burkert 2013), it is clear that itimplies that the formation of this sub-set of M31 satel-lites was highly correlated. The nature of the remaining50% of satellites is unclear, but one could imagine an ex-treme scenario in which the satellites that are not part ofthe plane might also originate in a similar way, perhapscoming from a small number of additional families.However, the detection in the present contribution ofa smooth, spherical halo with a well-behaved power-lawprofile that is the dominant component at low metal-licity, requires, almost certainly, many progenitors withdifferent angular momenta to fill out the vast volume inthis regular manner. The alternative would be that themetal poor smooth halo formed in situ, but this is notpossible in standard galaxy formation models. If therewas a significant number of uncorrelated satellites in thepast, it would therefore seem likely that the present-daysatellites that are not in the correlated planar structureare mostly not related to each other. CONCLUSIONS
We have analyzed the large-scale properties of the haloof the Andromeda galaxy, using photometric data fromthe Pan-Andromeda Archaeological Survey. This largeendeavor has measured stellar sources down to g = 26 . i = 24 . > ∼
10 Gyr); withthis assumption the age-metallicity degeneracy is largelyavoided, and a simple conversion from color and mag-nitude to metallicity is possible using stellar populationmodels. In order to examine the population propertieswe divided the sample into four wide metallicity bins.Our main findings are:1. For stars more metal-rich than [Fe / H] = − . ∼
50 kpc.2. The populations with metallicity in the range − . < [Fe / H] < − . − . < [Fe / H] < − .
7, the contrast of the streamsis greatly diminished and a clear sign of what ap-pears to be a diffuse smooth halo is perceived.3. Despite the numerous substructures, and sub-stantial azimuthal variations in density, theazimuthally-averaged projected star-counts profilesare remarkably featureless and possess power-lawbehavior. The power-law fits become steeper withincreasing metallicity, being Γ = − . ± .
02 forstars in the range − . < [Fe / H] < − . − . ± .
01 for − . < [Fe / H] < ± ∼
300 kpc) is a large fraction ofthe distance to that galaxy, it was necessary to in-tegrate the model in a cone along the line of sight,taking into account the dimming of the stellar pop-ulations with distance. The algorithm automati-cally identifies regions with overdense substructure.Applying this technique to the data, we find thata “smooth” halo component is present in all of ourmetallicity subsamples, albeit in a minor fraction( ∼ ∼
58% for the most metal-poor stars.5. This “smooth” halo follows closely a power-lawprofile in projection, with an exponent of Γ = − . ± .
02 for the most metal-poor stars. Fitsusing our three-dimensional non-parametric modelhave a space density that follows a power law withexponent γ ∼ − γ ∼ − .
5, in good agree-ment with the simulations of Bullock & Johnston(2005).6. The fits also show that the shape of the smoothhalo population is close to spherical in the four metallicity sub-samples. The global structurewe are calling a smooth halo can be identi-fied with the hot kinematic component detectedwith Keck/DEIMOS spectroscopy by Gilbert et al.(2012) in 38 pencil-beam fields. This strongly sug-gests a formation from a large number of satellitesarriving in an uncorrelated way with a range of an-gular momentum, energy and metallicity. We ar-gue that the sphericity of the stellar distribution ineach metallicity sub-sample suggests that the darkmatter distribution is not strongly triaxial, but alsoclose to spherical.7. By summing the stars in our survey and accountingfor the stars outside of the color-magnitude selec-tion box, we estimate that the total stellar mass inthe halo beyond 2 ◦ is ∼ . × M (cid:12) , while thatof the “smooth” component is ∼ × M (cid:12) . If thesmooth halo follows a cored-power law profile intothe center of M31, we estimate (very roughly) a to-tal mass of ∼ × M (cid:12) for this component. Theseare considerable fractions ( ∼ (cid:104) [Fe / H] (cid:105) = − . R =27 . (cid:104) [Fe / H] (cid:105) = − . R = 150 kpc.The smooth halo follows the same trend, but ap-proximately 0.2 dex more metal poor at a givenradius.So we find that Andromeda’s halo is indeed in roughagreement with the expectations of hierarchical galaxyformation, but to go beyond these relatively broad-brushtests, we now need to confront a new generation of mod-els to our data. This will be the subject of a subsequentcontribution.We thank the staff of the Canada-France-Hawaii Tele-scope for taking the PAndAS data, and for their con-tinued support throughout the project. R.A.I. gratefullyacknowledges support from the Agence Nationale de laRecherche though the grant POMMME (ANR 09-BLAN-0228). G.F.L thanks the Australian research council forsupport through his Future Fellowship (FT100100268)and Discovery Project (DP110100678). REFERENCESAbadi, M. G., Navarro, J. F., Fardal, M., Babul, A., & Steinmetz,M. 2010, MNRAS, 407, 435Abadi, M. G., Navarro, J. F., & Steinmetz, M. 2006, MNRAS,365, 747Bailin, J., Bell, E. F., Chappell, S. N., Radburn-Smith, D. J., &de Jong, R. S. 2011, ApJ, 736, 24Barker, M. K., Ferguson, A. M. N., Irwin, M., Arimoto, N., &Jablonka, P. 2009, AJ, 138, 1469Bell, E. F., et al. 2008, ApJ, 680, 295Bernard, E. J., et al. 2012, MNRAS, 420, 2625Bett, P. 2012, MNRAS, 420, 3303Brown, T. M., et al. 2007, ApJ, 658, L95Brown, T. M., Smith, E., Ferguson, H. C., Rich, R. M.,Guhathakurta, P., Renzini, A., Sweigart, A. V., & Kimble,R. A. 2006, ApJ, 652, 323 he halo of M31 21he halo of M31 21