The Haunted Halos of Andromeda and Triangulum: A panorama of galaxy
  formation in action
Draft version October 24, 2018
Preprint typeset using LATEX style emulateapj v. 08/22/09
THE HAUNTED HALOS OF ANDROMEDA AND TRIANGULUM:
A PANORAMA OF GALAXY FORMATION IN ACTION
R. Ibata
, N. F. Martin
, M. Irwin
, S. Chapman
, A. M. N. Ferguson
, G. F. Lewis
, A. W. McConnachie
Draft version October 24, 2018
ABSTRACT
We present a deep photometric survey of the Andromeda galaxy, conducted with the wide-field
cameras of the CFHT and INT telescopes. The surveyed area covers the inner 50 kpc of the galaxy
and the Southern quadrant out to a projected distance of ∼ 150 kpc. A survey extension to M33
at > 200 kpc probes the interface between the halos of these two galaxies. This survey is the first
systematic panoramic study of this very outermost region of galaxies. We detect a multitude of large-
scale structures of low surface brightness, including several streams. Significant variations in stellar
populations due to intervening stream-like structures are detected in the inner halo along the minor
axis. This, together with the fact that the light profile between 0◦.5 < R < 1◦.3 follows the exponential
“extended disk”, is particularly important in shedding light on the mixed and sometimes conflicting
results reported in previous studies. Two new relatively luminous (MV ∼ −9) dwarf galaxies And XV
and XVI are found in the study; And XVI is a particularly interesting specimen being located 270 kpc
in front of M31, towards the Milky Way. Underlying the many substructures that we have uncovered
lies a faint, smooth and extremely extended halo component, reaching out to 150 kpc, whose stellar
populations are predominantly metal-poor. This is consistent with recent claims based on spectroscopy
of a small sample of stars. We find that the smooth halo component in M31 has a radially-decreasing
profile that can be fit with a Hernquist model of immense scale radius ∼ 55 kpc, almost a factor
of 4 larger than theoretical predictions. Alternatively a power-law with ΣV ∝ R
−1.91±0.11 can be
fit to the projected profile, similar to the density profile in the Milky Way. If it is symmetric, the
total luminosity of this structure is ∼ 109 L⊙, again similar to the stellar halo of the Milky Way.
This vast, smooth, underlying halo is reminiscent of a classical “monolithic” model and completely
unexpected from modern galaxy formation models where stars form in the most massive subhalos and
are preferentially delivered into the inner regions of the galaxy. Furthermore, over the region surveyed,
the smooth stellar halo follows closely the profile of the dark matter distribution predicted from earlier
kinematic analyses. M33 is also found to have an extended metal-poor halo component, which can be
fit with a Hernquist model also of scale radius ∼ 55 kpc. These extended slowly-decreasing halos will
provide a challenge and strong constraints for further modeling.
Subject headings: galaxies: individual (M31) — galaxies: individual (M33) — galaxies: structure —
galaxies: evolution — Local Group
1. INTRODUCTION
The outskirts of galaxies hold fundamental clues about
their formation history. It is into these regions that new
material continues to arrive as part of their on-going
assembly, and it was also into these regions that ma-
terial was deposited during the violent interactions in
the galaxy’s distant past. Moreover, the long dynami-
cal timescales for structures beyond the disk ensure that
1 Observatoire Astronomique, Universit de Strasbourg, CNRS,
11 rue de l’universit, 67000 Strasbourg, France
2 Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117
Heidelberg, Germany
3 Institute of Astronomy, Madingley Road, Cambridge, CB3
0HA, U.K.
4 Institute for Astronomy, University of Edinburgh, Royal Ob-
servatory, Blackford Hill, Edinburgh, UK EH9 3HJ
5 Institute of Astronomy, School of Physics, A29, University of
Sydney, NSW 2006, Australia
6 Department of Physics and Astronomy, University of Victoria,
Victoria, B.C., V8W 3P6, Canada
∗ 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 National Re-
search Council (NRC) of Canada, the Institute National des Sci-
ences de l’Univers of the Centre National de la Recherche Scien-
tifique of France, and the University of Hawaii.
the debris of accreted material takes a very long time
to be erased by the process of phase mixing, which in
turn means that we can hope to detect many of these
signatures of formation as coherent spatial structures
(Johnston, Hernquist & Bolte 1996).
Much theoretical effort has been devoted in re-
cent years to understanding the fine-scale structure of
galaxies (Abadi et al. 2003; Bullock & Johnston 2005;
Abadi et al. 2006), as researchers realized that cosmo-
logical models could be tested not only with the clas-
sical large-scale probes such as galaxy clusters, fila-
ments and voids, but also with observations on galac-
tic and sub-galactic scales (Freeman & Bland-Hawthorn
2002). Indeed, it is precisely in these latter re-
gions that the best constraints on cosmology are
expected to be put (Springel, Frenk & White 2006)
in the coming decades. Λ-CDM cosmologies, in
particular, are now sufficiently well developed the-
oretically (e.g., Bullock, Kravtsov & Weinberg 2001;
Bullock & Johnston 2005) that the Local Group provides
a means of directly testing and constraining these theo-
ries, by observing the profiles of density, age, and metal-
licity of the structure and substructure predicted to be
http://arxiv.org/abs/0704.1318v1
found in the outer parts of galaxy disks and in galaxy
halos.
1.1. The Andromeda galaxy
Andromeda, like the Milky Way, is a canonical galaxy,
and a laboratory for examining in close detail many of
the astrophysical processes that are investigated in the
more distant field. Studying Andromeda and Triangu-
lum in the Local Group has the advantage that it affords
us a view free from the problems that plague Galactic
studies due to our position within the Milky Way, yet
their location within the Local Group allows us to re-
solve and study individual stars and deduce population
properties in incomparably greater detail than is possible
in distant systems.
Andromeda is the closest giant spiral galaxy to our
own, and the only other giant galaxy in the Local Group.
In many ways Andromeda is the “sister” to the Milky
Way, having very similar total masses (including the
dark matter, Evans et al. 2000; Ibata et al. 2004), having
shared a common origin, and probably sharing the same
ultimate fate when they finally merge in the distant fu-
ture. However, there are significant differences between
these “twins”. M31 is slightly more luminous than the
Milky Way, it has a higher rotation speed, and a bulge
with higher velocity dispersion. M31 possesses a globular
cluster system with ∼ 500 members, approximately three
times more numerous than that of the Milky Way. The
disk of Andromeda is also much more extensive, with a
scale-length of 5.9±0.3 kpc (R-band value corrected for a
distance of 785 kpc, Walterbos & Kennicutt 1988) com-
pared to 2.3±0.1 for the Milky Way (Ruphy et al. 1996);
but which is currently forming stars at a lower rate than
the Galaxy (Avila-Reese, Firmani & Hernández 2002;
Walterbos & Braun 1994). There are indications that
the Milky Way has undergone an exceptionally low
amount of merging and has unusually low specific an-
gular momentum, whereas M31 appears to be a much
more normal galaxy in these respects (Hammer et al.
2007). Though possibly the consequence of low-number
statistics, it is tempting to attribute significance to the
fact that Andromeda has a compact elliptical (M32)
and three dwarf elliptical galaxies (NGC 205, NGC 147,
NGC 185) among its entourage of satellites, and no star-
forming dwarf irregulars (dIrrs) within 200 kpc, whereas
the Milky Way has no ellipticals but two dIrrs. How-
ever, it is perhaps in their purported halo populations
that the differences between the two galaxies are most
curious and most interesting.
1.2. Comparing the halos of Andromeda and the Milky
A large number of studies of the Milky Way halo (e.g.,
Ryan & Norris 1991; Chiba & Beers 2000, and references
therein), have revealed that this structure is very metal-
poor, with a median 〈[Fe/H]〉 = −1.6. It has a high veloc-
ity dispersion, with (U, V,W ) values in the solar neigh-
borhood of (141 km s−1 : 106 km s−1 : 94 km s−1), and
a small prograde rotation of 30 – 50 km s−1. There is
broad agreement that the stellar halo is flattened with
b/a ∼ 0.6 (e.g., Morrison et al. 2000; Yanny et al. 2000;
Chen et al. 2001; Siegel et al. 2002), though there are in-
dications that the distribution becomes spherical beyond
15 – 20 kpc (Chiba & Beers 2000).
The volume density profile and extent of this struc-
ture have been harder to pin down. This is perhaps not
surprising given the patchy sky coverage of most stud-
ies, since current expectations are that the stellar halo
is significantly lumpy (Bullock & Johnston 2005). The
stellar volume density is generally modeled as ρ(r) ∝
r−α, and recent studies (Wetterer & McGraw 1996;
Morrison et al. 2000; Yanny et al. 2000; Ivezic et al.
2000; Siegel et al. 2002; Vivas & Zinn 2006) have found
values of the exponent ranging from α = 3.55 ± 0.13
(Chiba & Beers 2000) to α = 2.5±0.3 (Chen et al. 2001),
with a general consensus of ρ(r) ∝ r−3. Note that in ex-
ternal systems, where we observe the projected density,
ρ(r) ∝ r−3 would correspond to Σ(R) ∝ R−2.
Recent wide-field studies have gone a long way in
improving our knowledge of the radial extent of the
Milky Way halo. Using the SDSS database, Yanny et al.
(2000) were able to follow A-colored stars in the halo to
∼ 25 kpc, and blue-straggler candidates out to ∼ 50 kpc.
From the same survey, Ivezic et al. (2000) followed the
profile of RRLyrae candidates, and found a sharp drop in
the star-counts between 50 – 60 kpc, though this discon-
tinuity in density has since been found to be due to the
intervening stream of the Sgr dwarf galaxy (Ibata et al.
2001c). From VLT spectroscopy of 34 faint A-stars se-
lected from the SDSS, Clewey et al. (2005) were able to
show that the stellar halo extends out to at least 100 kpc,
although again a sub-sample of their stars appears to be
associated to the stream of Carbon stars emanating from
the Sgr dwarf (Ibata et al. 2001a). Several other stud-
ies have found evidence for further lumpy structures in
the halo (e.g., Vivas & Zinn 2006; Martin et al. 2007a;
Belokurov et al. 2007, and references therein).
It has been believed for many years that M31 pos-
sesses a stellar halo that is fundamentally different to
that deduced from the above and earlier observations
in the Milky Way. The first deep CCD studies by
Mould & Kristian (1986) in a field in the inner halo
of M31 found a surprisingly high mean metallicity of
〈[M/H]〉 = −0.6. While the surface brightness profile
measured along the minor axis from integrated light
(Pritchet & van den Bergh 1994) is consistent with a de
Vaucouleurs R1/4-law out to R = 20 kpc, quite unlike the
power-law behavior deduced for the halo of the Milky
Way. Both the de Vaucouleurs profile and the high
metallicity are suggestive of an active merger history at
the time of halo (or bulge) formation.
The existence of the metal-rich halo population was
confirmed by several subsequent studies; notably among
these the wide-field (0.16 deg2) photometric study by
Durrell, Harris & Pritchet (2001) in a location 20 kpc
out along the minor axis. In addition to the main
〈[M/H]〉 = −0.5 component, Durrell, Harris & Pritchet
(2001) also discovered that 30-40% of of the stars at
this location belong to a metal-poor population. The
surface density of the metal-poor sub-sample falls off
rapidly as Σ(R) ∝ R−5.25±0.63, but slower than the
Σ(R) ∝ R−6.54±0.59 relation for the metal-rich sub-
sample. These results were later complemented by the
same authors with a minor axis field at R = 30 kpc
(Durrell, Harris & Pritchet 2004) , which showed essen-
tially identical abundance properties to their 20 kpc field,
leading them to conclude that the outer halo shows little
or no radial metallicity gradient.
As an alternative to the above “wide-field” ap-
proach, Bellazzini et al. (2003) analyzed a set of 16
HST/WFPC2 fields with much deeper photometry,
mostly in and around the M31 disk, but with some
fields extending out to a distance of 35 kpc. Through-
out this area they detect the previously-discussed dom-
inant metal-rich component with [Fe/H] ∼ −0.6, but
also an additional high metallicity component with
[Fe/H] ∼ −0.2. Interestingly, they found that the frac-
tion of metal-poor stars is constant from field to field,
though metal-rich stars are enhanced in regions contain-
ing substructure, especially along the extended path of
the Giant Stream (Ibata et al. 2001b).
The inclusion of kinematic information has been ex-
tremely useful, but has also added another dimension
of complexity to the puzzle. Reitzel & Guhathakurta
(2002) analyzed a sample of 29 stars in a field at R =
19 kpc on the minor axis, and found the mean metallicity
to be in the range 〈[M/H]〉 = −1.9 to −1.1, dependent on
calibration and sample selection issues, but significantly
lower than the results deduced from the above photomet-
ric analyses.
A wider-field view was obtained by Chapman et al.
(2006), who sampled the halo at 54 locations between
10 – 70 kpc, isolating 827 out of a sample of ∼ 104 stars
as having kinematics consistent with being halo mem-
bers. The population was found to have 〈[Fe/H]〉 ∼ −1.4
with a dispersion of 0.2 dex, indicating that kinematic se-
lection reveals a halo similar to that of the Milky Way un-
derneath the “halo” substructures, which in many cases
are metal-rich, and in general cannot have halo-like kine-
matics. The (central) velocity dispersion of 152 km s−1
deduced from the sample, is also comparable to that of
the Milky Way.
In an impressive effort of finding needles in a haystack,
Kalirai et al. (2006b) and Gilbert et al. (2006) extended
the kinematic coverage out to 165 kpc, and claim a de-
tection of the halo at R > 100 kpc based on a sample of
3 stars. To minimize contamination they implemented
a complex non-linear algorithm to assign likelihoods to
the observed stars, and as the algorithm was trained on
the inner region of M31, the biasses for the outer halo
population are not well known.
1.3. The Triangulum galaxy
If Andromeda is the twin of the Milky Way, the
Triangulum galaxy (M33) with a mass ∼ 10 times
lower than either of these two giants, is their little
sister. M33 is the third brightest galaxy in the Lo-
cal Group (MV = −18.9), and probably a satellite of
M31. The relatively undisturbed optical appearance of
M33 places strong constraints on the past interaction of
these two galaxies (Loeb et al. 2005), though it should be
noted that the gaseous component is extremely warped
(Rogstad, Wright & Lockhart 1976).
The early CCD study of the halo of M33 by
Mould & Kristian (1986) claimed an inner halo compo-
nent with a more “normal” metallicity (〈[M/H]〉 = −2.2)
than deduced for M31. In reality however, this field
lies within the disk of M33 and does not probe the
“halo”, as we show below in §9. Further progress in
understanding the elusive halo component of this galaxy
was only achieved recently. In their kinematic study of
star clusters in M33, Chandar et al. (2002) find evidence
for two sub-populations, with old clusters showing evi-
dence for a large velocity dispersion, which they inter-
pret as the sign of a halo population. Further signs of
this halo component were detected in the spectroscopic
study of McConnachie et al. (2006) with Keck/DEIMOS,
who distinguished halo field stars from stars in the disk
via their kinematics, and deduce a mean metallicity for
the halo component of 〈[Fe/H]〉 = −1.5, with a narrower
spread of abundance than the disk stars.
1.4. Halos of more distant disk galaxies
Due to their extremely faint nature the halos of spiral
galaxies beyond the Local Group have been extremely
challenging to observe. A major advance in detecting
extra-planar light in distant galaxies was made by stack-
ing 1047 edge-on spiral galaxies observed in the SDSS
(Zibetti, White & Brinkman 2004). The resulting stack
showed a flattened (c/a ∼ 0.6) distribution with a power-
law density profile ρ(r) ∝ r−3, similar to the properties
of the halo of the Milky Way deduced from the stud-
ies reviewed above. This structure could be detected
out to approximately 10 exponential scalelengths of the
disk (i.e., approximately 25 kpc for the case of the Milky
Way). An analogous structure was also detected di-
rectly from the surface brightness around a single isolated
galaxy in an ultra-deep HST survey (Zibetti & Ferguson
2004).
Extra-planar populations have also been detected via
star-counts of resolved RGB populations in nearby (<
10Mpc) galaxies from deep HST imaging. Notable
among these is the survey of Mouhcine et al. (2005a,b),
who employed WFPC2 to survey 8 nearby spirals. Their
fields probed the minor axis halo out to R = 13 kpc.
Interestingly, they find a correlation between galaxy lu-
minosity and the metallicity of the extra-planar popula-
tion, with low luminosity galaxies containing metal-poor
stars with a narrow abundance spread, while luminous
galaxies contain metal-rich stars and a wide abundance
spread. Their results for galaxies of similar luminosity to
M31 are in good agreement with the metallicity distri-
bution of minor axis fields in Andromeda at 10 – 20 kpc.
However, as we will show below, the minor axis fields in
M31, from which most of the information on the “halo”
or “spheroid” is derived, do not directly probe that
component. Furthermore, as we have reviewed above,
kinematically-selected halo stars in M31 display a simi-
lar metallicity to genuine halo stars in the Milky Way
(Chapman et al. 2006). These considerations suggest
that the Mouhcine relation is caused by small structures
accreted into the inner regions of the halo, and which
are largely supported by rotation, rather than random
motions. The correlation of the metallicity of the extra-
planar stars with galaxy luminosity found by Mouhcine
et al. may then simply reflect that more massive host
galaxies are able to accrete larger dwarf galaxies which
themselves have a higher metallicity.
Nevertheless, we stress that all of these observations
beyond the Local Group are derived from regions close
to the centre of the galaxy, and there is concern that con-
tamination from other components, such as streams or a
warped disk could be affecting the observations. Extend-
ing further out in radius, as we will do in this contribu-
tion, will allow us to eliminate this uncertainty. But most
importantly it will allow us to examine a different region
of the halo, one that is less dominated by the remnants
of massive accretions.
1.5. Theoretical motivation
Several theoretical studies have been undertaken in re-
cent years to attempt to understand and reproduce the
above observations and to make useful predictions for the
next generation of surveys.
Bullock & Johnston (2005) implemented a hybrid N-
body plus semi-analytic approach. Their simulations
provide very high spatial resolution compared to the
other studies discussed below, which they achieve by
concentrating on each merger event in turn, with the
rest of the galaxy modeled with analytic (but time vary-
ing) potentials. The drawback of this method is that
the dynamical evolution of the system is not fully self-
consistent, and star-formation is implemented with em-
pirical recipes. They find that the present-day density
profile of stars within 10 kpc of a Milky Way or M31-
like galaxy should be shallow, ρ(r) ∝ r−1, steepen-
ing to ρ(r) ∝ r−4 beyond 50 kpc, resembling a Hern-
quist profile with scale radius of ∼ 15 kpc. They also
find that the bulk of the stars that constitute a stellar
halo were formed more than 8Gyr ago, with most of
these stars originating from massive accretions (Mvir >
2×1010M⊙). Beyond 30 kpc, substructure begins to pre-
dominate in their simulations, and they find that most of
the stars beyond this radius arrived after the last major
merger.
The problem of stellar halo formation was also tackled
by Renda et al. (2005), who used a chemodynamical code
to treat self-consistently gravity, gas dynamics, radiative
cooling, star formation and chemical enrichment. The
drawback of this approach was a very much lower spa-
tial resolution compared to Bullock & Johnston (2005).
Renda et al. (2005) find a large (∼ 1 dex) spread in the
mean metallicity of halos of galaxies of a given (final)
luminosity, where the large variations in the metallicity
distribution between their galaxy models is related to the
diversity in the galactic mass assembly history. This is
somewhat at odds with the finding that M31 and the
Milky Way have underlying halos of similar metallicity
(Chapman et al. 2006). They also find that a more ex-
tended assembly history gives more massive stellar halos,
and a higher halo surface brightness.
Yet another approach was adopted by Abadi et al.
(2006), who undertook SPH simulations that follow the
gas evolution in a small sample of galaxy models form-
ing in a ΛCDM cosmology. Overcooling early on leads
to large spheroid component in their simulations, though
they claim that the insensitivity of the halo parameters
to the final stellar halo mass implies that their simu-
lations are also applicable to Milky Way-like systems.
In their models stars formed in situ in the galaxy are
all confined to the inner luminous region, while accreted
stars dominate beyond 20 kpc, and are the main popula-
tion contributing to the spheroid. The stellar surface
density profile is very similar in all their simulations,
and has Σ(R) ∝ R−2.3 at r ∼ 20 kpc, steepening to
Σ(R) ∝ R−2.9 at r ∼ 100 kpc, and steepening further
to at Σ(R) ∝ R−3.5 near the virial radius. Furthermore,
they find that the stellar halo is a mildly triaxial struc-
ture (〈c/b〉 = 0.90, 〈c/a〉 = 0.84, with no obvious align-
ment of the triaxial halo with the angular momentum
vector of the galaxy. Old stars disrupted in the early
history of the galaxy are ejected into highly eccentric
and energetic orbits during close perigalactic passages,
and it is these stars that primarily populate the outer
halo.
Complementary studies using pure N-body simula-
tions were undertaken by Diemand et al. (2005) and
Gauthier, Dubinkski & Widrow (2006). Diemand et al.
(2005) focus on the evolution of high density peaks in
cosmological simulations that formMilky Way-like galax-
ies. Their result of relevance to the present study is the
asymptotic density profile of these peaks in the galaxy
simulation: they find that the outer profile behaves as
ρ(r) ∝ r−3.26 for 1σ peaks, steepening to ρ(r) ∝ r−4.13
for 2.5σ and ρ(r) ∝ r−5.39 for 4σ peaks. In contrast,
Gauthier, Dubinkski & Widrow (2006) simulate the evo-
lution of satellites around a fully-formed M31-like galaxy,
with the satellites modeled as a collection of NFW den-
sity profiles (Navarro, Frenk & White 1997). They do
not consider star-formation in the satellites, but instead
identify the 10% most bound particles as tracers of the
stars in the satellite. They predict that disrupted satel-
lites give rise to a halo luminosity profile that falls as
ρ(r) ∝ r−3.5 at large radii. Since massive satellites cor-
respond to rare overdense peaks in cosmological simu-
lations, the difference in the profile slope compared to
Diemand et al. (2005) suggests that taking the full cos-
mological evolution of the host galaxy into account is
important.
1.6. Purpose of the present study
In this contribution we are building upon an ear-
lier wide-field survey of Andromeda with the Wide
Field Camera camera at the Isaac Newton Telescope
(Ibata et al. 2001b; Ferguson et al. 2002; Irwin et al.
2005). This panoramic survey covered the entirety of the
disk and inner halo of the galaxy out to ∼ 55 kpc (see
Fig. 1), which combined with follow-up kinematics from
Keck/DEIMOS (Ibata et al. 2004, 2005; Chapman et al.
2006) and deep HST/ACS photometry in selected fields
(Ferguson et al. 2005; Faria et al. 2007) opened up a
new violent vision of an apparently normal disk galaxy.
We found that M31 possesses of order half a dozen
substructures, probably debris fragments from merg-
ing galaxies that have not yet lost all spatial coher-
ence (Ferguson et al. 2002, 2005); that it is surrounded
by a vast rotating disk-like structure, extending out to
∼ 40 kpc (Ibata et al. 2005); that it contains a giant stel-
lar stream of width greater than the diameter of the
disk of the Milky Way and > 100 kpc long (Ibata et al.
2001b; McConnachie et al. 2003); and that underlying all
of this substructure there is a kinematically hot, metal-
poor halo (Chapman et al. 2006).
Thus the inner halo region covered by the INT survey
is completely contaminated by these various structures.
Indeed it was a surprising result of that survey that it is
necessary to observe at much larger radius to obtain a
clear measurement of the accretion rate, the incidence of
sub-structures, the stellar mass of the accreted objects,
and the global properties of the halo. We therefore em-
barked on the deep imaging campaign of the outer halo
presented in this contribution, undertaken with Mega-
Fig. 1.— The coverage of our large panoramic survey of M31
with the INT camera, in standard coordinates (ξ, η). The inner
ellipse represents a disk of inclination 77◦ and radius 2◦ (27 kpc),
the approximate end of the regular HI disk. The outer ellipse
shows a 55 kpc radius ellipse flattened to c/a = 0.6, and the major
and minor axis are indicated with straight lines out to this ellipse.
This map is constructed from a total of 164 INT/WFC individual
pointings.
Cam, a state-of-the-art wide-field camera at the CFHT.
One of the main aims of the present survey was to in-
vestigate the prediction of CDM cosmology that upward
of 500 satellites reside in the halo of a galaxy like M31
(Klypin et al. 1999; Moore et al. 1999). The possibility
remains that many dwarf galaxies are being missed in
current surveys. However we defer all discussion of this
issue to a companion paper (Martin et al. 2007b).
The layout of this paper is as follows. In §2 we first
present the photometric data and data processing. The
color-magnitude distribution of detected sources is dis-
cussed in §3, and their spatial distribution in §4. The re-
sulting maps of the stellar populations of interest are pre-
sented in §5, continuing in §6 with the detected streams
and other spatial substructures, and in §7 with the prop-
erties of the outer halo. The radial profiles of the stellar
populations in M31 are analyzed in §8. A short discus-
sion of the properties of the halo of M33 are presented
in §9. Finally in §10 we discuss the implications of our
findings and compare to previous studies, and draw con-
clusions in §11.
Throughout this work, we assume a distance of 785 kpc
to M31 (McConnachie et al. 2005). We also adopt the
convention of using R to denote projected radius, s an
elliptical projected radius, and r a three-dimensional dis-
tance or radius.
2. OBSERVATIONS
2.1. INT observations
The Wide Field Camera (WFC) of the Isaac Newton
Telescope (INT) was used in four observing runs between
1998 and 2003 to map the Andromeda galaxy over the
area displayed in Fig. 1. The observations were taken
with the V and i filters, with exposures of 1200 sec and
900 sec, respectively, in each of these two bandpasses.
The data were obtained in dark skies, with typical seeing
of 1′′. A total of 164 individual fields were observed, each
Fig. 2.— The main area surveyed with the CFHT MegaCam
instrument. As we describe below, the image stability over the field
of view of the camera varied slightly from one year to another. We
therefore show the year that the field was observed in by a color
code: red, green and black mark fields obtained in 2003, 2004
and 2005–2006, respectively. The field T6, centered on M33, was
observed in primarily in 2004, with some data in 2003. The offset
fields colored turquoise mark the positions of the short exposure
fields. In the case of field H13, we also display the layout of the 36
CCDs. The meaning of the ellipses centered on M31 is described
in Fig. 1.
covering an “L”-shaped region of 0.33 deg2. A small
∼ 5% overlap between adjacent fields was adopted to
ensure a homogenous photometric survey.
The images were processed by the Cambridge Astro-
nomical Survey Unit (CASU) pipeline (Irwin & Lewis
2001), in an identical manner to that described in
Ségall et al. (2006). This includes corrections for bias,
flat-fielding, and for the fringing pattern. The software
then proceeds to detect sources, and measures their pho-
tometry, the image profile and shape. Based upon the
information contained in the curve of growth, the algo-
rithm classifies the objects into noise detections, galaxies,
and probable stars. (For comparison to previous studies
using this classification algorithm, throughout this paper
we adopt as stars those objects that have classifications
of either -1 or -2 in both colors; this corresponds to stars
up to 2σ from the stellar locus).
2.2. CFHT observations
The survey of the inner halo of M31 with the INT
was complemented with a deeper survey with the CFHT
MegaCam wide-field camera to probe the outer reaches
of the halo of this galaxy. MegaCam consists of a mosaic
of 36 2048 × 4612 pixel CCDs, covering a 0.96◦ × 0.94◦
field, with a pixel scale of 0.187 arcsec/pixel. The greater
photometric depth and field-of-view achievable with this
instrument makes it particularly powerful in such regions
of extremely low surface density of stars. The g and i-
band filters were used, totalling 5 × 290 sec of exposure
per field in each passband. Figure 2 displays the survey
fields, while Fig. 3 shows this area in relation to the en-
vironment around M31. The survey comprises 89 deep
fields, observed in service mode over the 2003 to 2006 sea-
sons. We chose a tiling pattern with no overlap between
the deep fields, using instead short (45 sec) exposures in g
Fig. 3.— The survey region (irregular blue polygon) is overlaid on a schematic diagram of M31 and surrounding Local Group structure.
Note that the survey extension along the M31 minor axis reaches M33 and therefore probes the halos of both these disk galaxies. In
addition to the ellipses reproduced from Fig. 1, the two concentric (dashed-line) circles show projected radii of 100 kpc and 150 kpc. A grid
in Galactic longitude and latitude has been marked. The extinction over the surveyed region, interpolated from the maps of Schlegel et al.
(1998) is also shown.
and i to establish a consistent photometric level over the
survey. These short exposure images were taken offset
by half a field size in the right-ascension and declination
directions. The fields were observed in photometric con-
ditions in good seeing conditions (typically better than
0′′.8). In addition, the two inner halo fields marked H11
and H13 were retrieved from the CFHT archive. These
g and i-band images are somewhat deeper that the main
survey fields with exposures of 5 × 289 sec in each pass-
band. A further field centered on M33 (marked field T6
in Fig. 2) was obtained from the archive. After elimina-
tion of frames with poorer seeing (> 1′′) or CCD con-
troller problems, 37 g-band frames and 32 i-band frames
were combined, for a total of 18306 sec in the g-band and
19165 sec in the i-band.
The solid angle covered by the INT survey corresponds
to a projected area of ∼ 9500 kpc2 at the distance of
M31 (∼ 7400 kpc2 not overlapping with the MegaCam
survey), while the MegaCam survey area subtends 1.6×
104 kpc
. This vast area encompasses several previously
known structures, as we show in Fig. 3. These are the
dwarf galaxies M32, NGC 205, And I, And II (though
we miss its center), And III, And IX, as well as the new
discoveries from this work: And XI, And XII, And XIII,
all discussed in (Martin et al. 2006), and And XV, and
And XVI presented below. We also mark the positions
of the known globular clusters in the MegaCam region:
GC 5, GC 6, EC 4 (Mackey et al. 2006, 2007), and GC-
M06 (Martin et al. 2006).
In addition to the INT fields and the 92 contiguous
MegaCam fields, we consider below two additional fields,
which will be used as background references: a compari-
son field taken for a study of the Draco dwarf spheroidal
(dSph) galaxy (field D7 of Ségall et al. 2006, located at
ℓ = 81◦.5, b = 34◦.9), and the field D3 of the Legacy Sur-
vey of the CFHT (CFHTLS). The observations on the
Draco dSph comparison field had slightly different expo-
sure times to those taken for the M31 survey (950 s in
g and 1700 s in i), though similar image quality. From
the public release data of the CFHTLS field D3 (located
at ℓ = 96◦.3, b = 59◦.7), we selected a subset of the best
seeing frames, totaling 2702 s in the g-band and 4520 s
in the i-band.
The MegaCam data were pre-processed by CFHT staff
using the “Elixir” pipeline; which accomplishes the usual
bias, flat and fringe corrections, and also determines the
photometric zero-point of the observations. These im-
ages were then processed by the Cambridge Astronomical
Survey Unit photometry pipeline in an identical manner
to that described above for the INT data. Using the mul-
tiple overlaps between deep and shallow fields we correct
the photometric solution provided by the “Elixir” algo-
rithm (by up to ∼ 0.5 mag), finding a global solution over
all 92 deep fields that has an RMS scatter of 0.02 mags.
Using observations of the Draco dwarf spheroidal
galaxy for which we had both INT-WFC and CFHT-
MegaCam data in the (V,i) and (g,r,i) bandpasses, re-
spectively, we determined colour transformations to put
the INT (Vega-calibrated) photometry onto the Mega-
Cam AB photometric system. The advantage of using
the Draco field is that the region has also been covered
by the Sloan Digital Sky Survey (SDSS), providing an
external check to the photometry. Note that the Mega-
Cam (g, i) bands are not identical to the SDSS (g′, i′),
though the conversions between these two systems have
been determined by the CFHT staff. We refer the in-
terested reader to Ségall et al. (2006) for further details.
The conversion between INT (V,i) and MegaCam (g,i)
were found to be:
iMC = iINT − 0.105 ,
gMC =
0.030 + 1.400× (V − i)INT + iMC
for (V − i)INT < 1.3 ,
0.491 + 1.046× (V − i)INT + iMC
for (V − i)INT > 1.3 .
In order to enable the construction of maps over the
combined area of the INT and CFHT surveys, we con-
verted the INT photometry to (g,i) using these relations.
The conversion appears to be adequately accurate, judg-
ing from the photometry of bright stars (with magnitudes
in the range 18 < g < 20 and 18 < i < 20) in the large
overlap region between the two surveys: the RMS scatter
around zero offset was found to be < 0.02 mags in both
bands.
Given the huge area of the survey it is necessary to be
aware of variations in the interstellar extinction which
will affect the depth of the photometry. In Fig. 3 the
surveyed area is superimposed on a map of the extinc-
tion derived from Schlegel et al. (1998); the maximum i-
band extinction over the halo region observed with Mega-
Cam is Ai = 0.27 mags, with a mean of Ai = 0.1 mags.
Thus the extinction is neither very high nor very vari-
able, though we nevertheless correct for it using the
Schlegel et al. (1998) maps. In all the discussion below,
g0 and i0 will refer to extinction-corrected magnitudes.
3. COLOR-MAGNITUDE DISTRIBUTION OF SOURCES
As well as encompassing a large fraction of the halo
of M31, the survey also intersects a substantial volume
of the foreground Milky Way. This is clearly seen in
Fig. 4.— The combined CMD of the MegaCam survey fields
of M31, except fields T5 and T6 which are excluded because
they are dominated by stars from M33 (including young stars
in the disk), and fields 6, H11, and H13 which are close to
the M31 disk. The fiducial RGBs correspond to, from left to
right, NGC 6397, NGC 1851, 47 Tuc, NGC 6553, which have
metallicity of [Fe/H] = −1.91, −1.29, −0.71, and −0.2, respec-
tively. The sequences have been shifted to a distance modulus
of (m−M)0 = 24.47. The dashed-line rectangles show the regions
selected to probe the foreground Galactic halo (blue) and Galactic
disk (red).
Fig. 4, where we show the combined color-magnitude
distribution of all stars in the deep MegaCam fields of
the main survey, except for fields T5 and T6, close to
M33, and fields 6, H11 and H13 close to M31. Prominent
at (g − i)0 > 1.5 and i0 < 23 is the sequence of Galactic
disk dwarfs; the vertical sequence is the result of low-
mass stars accumulating in a narrow color range, yet be-
ing seen over a large range in distance along the line of
sight. In addition, on the blue side of this diagram, at
(g − i)0 < 0.8 and i0 < 23, resides the Galactic halo se-
quence. Usually, this is seen as a smooth vertical struc-
ture, due to stars at or close to the main-sequence turnoff
at increasing distance through the Galactic halo. Curi-
ously, however in these fields towards M31 the sequence
bifurcates — indicating that the Galactic “halo” is not
spatially smooth along this line of sight. This issue is
explored in detail in a companion article (Martin et al.
2007a).
The stellar populations of immediate interest to this
study are revealed by the red giant branch (RGB) stars
that span the globular cluster fiducial sequences that
have been overlaid on the CMD. The bluemost and
redmost sequence correspond to clusters of metallicity
Fig. 5.— The left and right panels show the distributions of
photometric uncertainty in g0 and i0, respectively, together with
simple exponential fits (red lines). Some fields have slightly better
photometry than others, giving rise to the inhomogenous aspect at
faint magnitudes.
[Fe/H] = −1.91 and [Fe/H] = −0.2, respectively, so the
survey is sensitive to stars of a wide range of abun-
dance. At the limiting magnitude of i0 ∼ 24.5, the sur-
vey can in principle detect horizontal branch stars (see
Martin et al. 2006), though of course the contamination
at these magnitudes, mostly from unresolved background
galaxies and noise artifacts, is very large. Nevertheless
down to i0 ∼ 24.0 the photometric quality remains excel-
lent, as we show in Fig. 5, with δi < 0.1 mag.
There are substantial variations of stellar populations
between fields, as we demonstrate in Fig. 6. Here, panel
‘a’ displays the CMD of field 46, which lies in a dense area
of the so-called “Giant Stream” (Ibata et al. 2001b), and
clearly contains a numerous population of RGB sources
with a wide spread of metallicity. Panel ‘b’ shows the
photometry of field 106 in the far outer halo; no obvious
RGB is discernible visually in this diagram, though as we
shall see later in §7, the combination of this with several
other outer fields does allow a detection of the stellar halo
of M31. For comparison, we also display the CMDs of the
reference fields near the Draco dSph (panel ‘c’) and the
CFHTLS field D3 (panel ‘d’). The photometric depth of
the survey clearly varies slightly from field to field (note
that the images from which the CMDs in panels ‘a’ and
‘b’ were constructed had identical exposure times). The
data taken in the 2005 and 2006 runs (of which panel ‘b’
is an example) were very homogenous in depth, whereas
the earlier 2003 and 2004 runs were more patchy. It is
likely that the improvement in the 2005 and 2006 seasons
was a result of the correction of the detector plane tilt ††,
allowing a uniform focus to be achieved over the 0◦.96×
0◦.94 field of view. (For comparison to Fig. 6, in Fig. 7 we
show the color-magitude distribution of sources classified
as galaxies).
Though the globular cluster RGB ridge-lines shown in
Figs. 4 and 6 are useful to show the behavior of known
stellar populations, the set of 4 templates is too sparse to
allow accurate comparisons to be made with the distant
†† See http://www.cfht.hawaii.edu/News/Projects/MPIQ/
Fig. 6.— The upper panels show sample CMDs of point-sources
in the MegaCam survey. The panel ‘a’ is for field 46, in a dense
region within the giant stream, while panel ‘b’ is for field 106,
in the outer halo. The lower panels correspond to the comparison
fields: ‘c’ lies near the Draco dSph, while ‘d’ is contructed from the
CFHTLS field D3. As in Fig. 4, the lines in panel ‘a’ are the RGB
ridge-lines of globular clusters of metallicity (from left to right)
[Fe/H] = −1.91, −1.29, −0.71, and −0.2. The dense grouping of
objects with −0.5 < (g − i)0 < 1.5 are mostly due to misclassified
compact galaxies.
M31 population. Instead we chose to adopt the Padova
isochrones (Girardi et al. 2004), which conveniently have
been calculated in the Sloan passbands. Figure 8 shows
the isochrones we used, converted into the MegaCam
photometric system, which were chosen for a population
age of 10Gyr. For each star in the survey, a photomet-
ric metallicity was calculated by interpolating between
the RGB curves. The assumption that the stellar pop-
ulations have an age of 10Gyr over the entirety of the
survey is clearly incorrect (Brown et al. 2006b), but this
is probably a reasonable estimate for the majority of the
stars at large radius.
As we have shown in Fig. 3, the region surveyed with
MegaCam includes several known sources. For compari-
son to the populations we will encounter below, we dis-
play their CMD structure in Fig. 9.
4. SPATIAL DISTRIBUTION OF SOURCES
Although the MegaCam camera covers a large area,
there are large inter-CCD gaps in the mosaic, that were
not filled by our chosen dithering pattern with 5 sub-
exposures. These gaps are partially filled by the short
exposures, but of course reach to a much shallower lim-
iting depth. These inter-CCD gaps are seen in Fig. 10,
http://www.cfht.hawaii.edu/News/Projects/MPIQ/
Fig. 7.— As Fig. 6, but for sources classified as galaxies by the
image analysis algorithm.
Fig. 8.— The Padova isochrones superimposed on the CMD of
field 47. The isochrone models are all for 10Gyr, and [Fe/H] metal-
licity (from left to right) of −3 (actually Z = 0), −2.3, −1.7, −1.3,
−0.7, −0.4, 0.0 and +0.2. The continuous line part of each of these
curves corresponds to the RGB, while the horizontal branch and
asymptotic giant branch are indicated with dashed lines.
Fig. 9.— CMDs of known satellite galaxies in the MegaCam
survey region. The Padova isochrones from Fig. 8 are repro-
duced here. For M33 we show the sources within an annulus
between 1◦ and 2◦ while for And II, And III and the remaining
dwarfs, we show the sources within a circular region of 12′, 6′, and
12′, respectively. For the purposes of overlaying the isochrones,
we adopt the following distance moduli. M33: 24.54 ± 0.06;
And II: 24.07±0.06 (both from McConnachie et al. 2004a; And III:
24.37± 0.07 (McConnachie et al. 2005); while for And XI, XII and
XIII (Martin et al. 2006) we assume the distance modulus of M31:
24.47± 0.07 (McConnachie et al. 2005).
which shows the stellar density in one of the MegaCam
fields. Another problem that is not limited to the Mega-
Cam data are the “halos” of bright stars that effectively
render useless certain regions of the detector mosaic. The
effect of these halos is also illustrated in Fig. 10. Both the
gaps and bright star holes could easily be accounted for in
the analysis of the surface density, by simply correcting
for the missing area. However, we found this approach to
be somewhat unsatisfactory when making maps of spatial
resolution smaller than the area of the bright star “ha-
los”. Instead we chose to replace the affected areas with
nearby counts: the inter-CCD gaps were filled with the
detections of the CCD immediately to the South, while
the bright star halos were filled with detections either to
the East or West of the hole (depending on the location
of the field edge or other nearby bright stars). Figure 10
shows an example of the procedure adopted. A further
problem was that in several fields observed in 2003 the
data for CCD 4 of the MegaCam mosaic was absent due
to a CCD controller malfunction. For these fields, which
comprise fields 48, 63, 77, 92, H11, H13, T2, T3, T4 and
T5, we copied over the sources from CCD 3, adjacent on
the mosaic. All the sources that were added artificially
in these various ways were flagged.
The final catalog contains a total of 19 million sources.
However, many of these sources are foreground and back-
ground contaminants, so we must assess their numbers
and distribution before being able to analyze the dis-
tribution of genuine M31 stars. In Fig. 11 we show
the spatial distribution of Galactic disk dwarf stars with
1.5 < (g−i)0 < 3.0 and 15.0 < i0 < 19.5; from an inspec-
tion of Fig. 4 it can be seen that these stars are located
at brighter magnitudes than the tip of the M31 red giant
branch (RGB) and should therefore be an almost pure
Galactic sample. Figure 11 shows that this is not entirely
Fig. 10.— As an example of our correction technique for the effect
of bright stars, we show in the left-hand panel the distribution
of stellar sources in field 70, a field containing several unusually
bright stars. The two horizontal gaps are due to a physical gap
between the first two and the last two rows of detectors on the
mosaic camera. The lower source density at ξ ∼ −1◦.1, η ∼ −5◦.9
is due to a bright star “halo”. In the right-hand panel, we show
the corrected counts in this region, where the stars in the affected
region have been deleted, and replaced with artificial sources (red
points) that were copied from adjacent areas of the sky.
Fig. 11.— The distribution of stars within the color-magnitude
selection box 1.5 < (g − i)0 < 3.0 and 15.0 < i0 < 19.5, which
outside of the inner regions of M31 and M33, which contain blue
loop and AGB stars, gives a clean sample of Milky Way disk dwarf
stars. The map is a linear representation of the star counts, with
pixels of size 0◦.1× 0◦.1.
correct, as a strong enhancement of sources is seen in the
inner regions of M31 and M33, due to the presence of blue
loop stars and asymptotic giant branch (AGB) stars in
the disks of those galaxies. Ignoring these disk regions,
we detect a smooth gradient towards the Galactic plane
in the North, with no obvious structures.
In addition to the Galactic disk dwarfs, there is some
contamination from distant bright main-squence halo
stars, as we showed in Fig. 4. We select a representa-
tive sample of this population by choosing stars within
Fig. 12.— As Fig. 11, but showing the distribution of Milky
Way halo stars over the survey region, selected within the color-
magnitude box 0.0 < (g − i)0 < 0.8 and 20.0 < i < 22.5. The
concentration of sources inside the disks of M31 and M33 is due to
young blue main sequence stars in those galaxies.
the box 0.0 < (g − i)0 < 0.8 and 20.0 < i0 < 22.5. The
resulting spatial distribution is presented in Fig. 12. The
contamination to this sample from the disks of M31 and
M33 is not at all surprising, as young blue supergiant
stars in these galaxies will fall into this color-magnitude
selection box. However, excluding a 2◦ and 1◦ circle
around M31 and M33, respectively, shows the remain-
ing Galactic population to have a very uniform density
over the survey region.
A further source of contaminants are background
galaxies. Most of these are readily identifiable from their
image parameters, though there will be some distant
compact galaxies that are unresolved with the typical
depth and seeing achieved in this survey. The map of the
sources classified as galaxies by the algorithm is displayed
in Fig. 13. Apart from the usual filamentary signature
of large-scale structure there is no apparent correlation
with either the Milky Way, Andromeda or M33, beyond
the disks of these latter two galaxies (where some sources
are classified as being extended due to image crowding).
The colour-magnitude distribution of these contaminants
is displayed in Fig. 7 for four selected fields. These re-
solved galaxies are approximately as numerous as the
point-sources in the dense Giant Stream fields, but be-
come up to 6 times more numerous than point-sources
in the outer halo fields. Clearly a small error in image
classification towards fainter magnitudes could have a
significant repercussion in the measured density of point-
sources. We return to this issue below.
4.1. Foreground subtraction
We had envisaged using the MegaCam comparison
fields presented in Fig. 6 to subtract off the background
counts, however since the Galactic contamination varies
substantially from these fields to our M31 fields of in-
terest, and even varies significantly over the main area
of this vast survey, we decided to investigate whether
Galactic models could be used instead to predict the
contamination more reliably. To this end we tessellated
the survey area with 0◦.5 × 0◦.5 bins, and generated sim-
Fig. 13.— As Fig. 11, but showing the distribution of objects clas-
sified as extended sources over the survey region. Due to the high
source density in the disks of M31 and M33, some point sources are
blended and are classified as galaxies by the photometry software.
A pixel size of 0◦.05× 0◦.05 has been used.
Fig. 14.— The map of the fractional residuals between the Galac-
tic disk selection previously presented in Fig. 11, and the Besançon
model predictions (calculated as (Data −Model)/Model for each
0◦.5 × 0◦.5 bin). Ignoring a 2◦ circle around M31 and a 1◦ circle
around M33, the average difference is less than 2%.
ulated catalogues using the Besançon Galactic popula-
tions model. All stellar populations in the model with
i-band magnitudes between 15 < i0 < 26 were accepted.
To reduce shot noise in the randomly generated catalogs,
at each spatial bin we simulated a 10 times larger solid
angle, and later corrected the density maps for this fac-
tor. Finally, the artificial photometry was convolved with
the observed magnitude-dependent uncertainty function
(from Fig. 5).
We were impressed to discover the accuracy to which
the Besançon model predicts the starcounts towards
our fields. For the Galactic disk sample selected with
1.5 < (g−i)0 < 3.0 and 15.0 < i0 < 19.5 (red dashed-line
box in Fig. 4), whose observed spatial distribution was
presented previously in Fig. 11, the Besançon model cor-
Fig. 15.— The luminosity function of point sources in the color
range 0.8 < (g− i)0 < 1.8 for the sample fields shown previously in
Figs. 6 and 7: field 46 (a), field 106 (b), the Draco dSph comparison
field (c) and the CFHTLS field D3 (d). The observed luminosity
functions are shown in black, while the red lines show the Besançon
model predictions. In panel ‘a’ the stellar populations of the Giant
Stream cause the large increase in counts beyond i0 = 21. The
correspondence between observations and model in panels ‘b’ and
‘c’ is excellent, though there is a significant departure in panel ‘d’.
A limiting g-band magnitude of g0 < 25.5 was imposed to data
and models alike.
rectly predicts the observed counts over the survey area
to better than 2%. The fractional residuals between the
observations and the model are shown in Fig. 14.
Evidently the Besançon model has the correct ingredi-
ents to reproduce very accurately the Galactic disk star-
counts towards these fields around M31. However, we
need to investigate the model further before we can use
it with confidence. The color-magnitude region that is of
particular interest to us, is the region where the RGB of
M31 has its greatest contrast over the contaminants. We
will return to this in more quantitative detail later, when
we discuss the matched filter method, yet a visual inspec-
tion of Fig. 4 shows that the color interval will be approx-
imately in the range 0.8 < (g− i)0 < 1.8, where we avoid
the bulk of the Galactic disk contamination, and also the
faint blue contaminants, which are most likely unresolved
background galaxies. In Fig. 15 we display the observed
luminosity function in this color interval (in black), as
well as the corresponding Besançon model predictions
(in red) for the two representative fields and the two ref-
erence fields that we presented previously in Figs. 6 and
7. The correspondence is excellent from i0 = 15 down
to i0 = 20.0, with Kolmogorov-Smirnof (KS) test proba-
Fig. 16.— The color-magnitude distribution of sources from the
Besançon model for the MegaCam comparison fields is shown in
panel (a), where the model predictions have been smoothed with
the observational errors in Fig. 5. The corresponding observed dis-
tribution is given in panel (b). Clearly, in reality the stellar popu-
lations have a much wider color spread than the model predicts. To
alleviate this problem we have introduced an additional smoothing
to the model, as detailed in the text. In panel ‘c’ the ratio of the
luminosity function in the color range 2.0 < (g − i)0 < 3.0 of the
model (red) and the data (black) is used to compute an empiri-
cal completeness correction, which applied to the color-magnitude
data, gives the distribution shown in panel ‘d’. (A g-band limit of
g0 = 25.5 has been imposed throughout).
bility that the observations are drawn from the model of
greater than 10% for all four fields. In panel ‘a’ the ob-
servations depart strongly from the model for i > 21, this
is however completely expected, as the field contains the
RGB of Andromeda at these magnitudes. Panel ‘b’ is for
field 106 in the outer halo, and panel ‘c’ is the Draco dSph
comparison field; in both cases the model predictions are
extremely close to what is observed: the KS test over the
range 15 < i0 < 24 gives 27% and 9% probability, respec-
tively, that the observed and modeled distributions are
identical, and the total counts agree to within better than
2σ. However, for the CFHTLS field D3, shown in panel
‘d’, the Besançon model predictions over the full range
15 < i0 < 24, do not accurately match the observations
(KS-test probability < 0.01%). This failure towards the
direction (ℓ = 96◦.3, b = 59◦.7), is likely due to a slightly
inaccurate model of the Galactic halo component, or due
to local deviations from a globally correct halo model.
Despite this shortcoming, we consider these comparisons
to have been very encouraging. The Besançon model
predicts reasonably well the details of the star counts to-
wards our two comparison fields, and it predicts perfectly
well the star counts in the outer halo field (panel ‘b’).
Very similar results were found upon widening the color
range to 0.5 < (g − i)0 < 1.8, to include the bluest RGB
stars of interest. Given the variations in the luminosity
function that are clearly visible in Fig. 15, it is evidently
better to use the model to subtract off the expected con-
tamination rather than use a comparison field located at
a different Galactic latitude and longitude. This is true
even for relatively nearby fields: the difference in the pre-
dicted luminosity function of foreground stars in panels
‘a’ and ‘b’ is substantial.
The excellent agreement between the observations and
the model predictions in panels ‘b’ and ‘c’ of Fig. 15
is somewhat surprising given the fact that we did not
apply any incompleteness corrections to the model, and
have not corrected for contaminating background unre-
solved galaxies. We chose not to perform artificial star
completeness tests for this survey as it would have been
a prohibitively expensive undertaking, and refer instead
to a previously computed comparison between MegaCam
and Hubble Space Telescope photometry from the center
of the Draco dSph. As we show in Fig. 2 of Ségall et al.
(2006), the completeness of MegaCam down to i = 24
from data of similar exposure time is greater than 80%.
Note however, that this completeness was calculated in
a relatively crowded central field of the Draco dSph (not
the Draco comparison field shown in panel ‘c’ of Figs. 6, 7
and 15), and is therefore likely to be substantially worse
than what we face in the almost empty fields in the outer
halo of M31.
Despite these successes of the Besançon model, it un-
fortunately fails to predict the correct color-magnitude
distribution. The reason for this is apparent from a visual
inspection of panel ‘a’ of Fig. 16, in which we present the
predicted color-magnitude distribution over the Mega-
Cam fields 93, 105, 106, 115, 120 and 121, which are all
located at the outer edge of the survey near a projected
radius of 150 kpc (In the analysis below we shall refer
to these fields as “background” fields). Comparing this
distribution to its observed counterpart in panel ‘b’, we
see that the model has features that are too sharp, de-
spite the convolution with the photometric uncertainties.
This is likely due to the model not containing a realis-
tic spread of stellar populations types, in particular the
color-magnitude sequences are evidently not as varied in
the model as in reality.
To alleviate this problem we have introduced an ad-
ditional smoothing to the model. From a Gaussian fit
to the color distribution of Galactic “halo” and Galactic
disk populations in the magnitude range 20 < i0 < 21
(where the sequences are almost vertical in the CMD),
we measured the intrinsic FWHM of the observed dis-
tributions. By introducing a color-dependent additional
Gaussian spread to the model of σ = 0.05+0.075(g− i)0,
we find a similar color spread in the halo and disk pop-
ulations to the observations.
In panel (c) we compare the luminosity function in the
color range 2.0 < (g−i)0 < 3.0 in the resulting smoothed
model (red) with that of the data. We see an excellent
match down to g0 = 23.25, after which the model begins
to diverge, due to the effects of incompleteness. We use
the ratio of these distributions beyond g0 = 23.25 to
correct the model for incompletness; the resulting final
model for the background region is displayed in panel ‘d’.
The excellent agreement of the Besançon model with
our observations to g0 = 23.25, indicates that the number
of background galaxies masquerading as point-sources
cannot be a substantial fraction of the total counts down
to these photometric limits. Beyond this limit, some
background galaxy contamination may offset the incom-
pleteness, in which case it will be hidden in the empiri-
cal completeness correction adopted for the background
fields.
The Besançon model, smoothed and corrected for in-
completeness, as discussed previously, can now be used
Fig. 17.— The spatial distribution of the Besançon model (cal-
culated for each 0◦.5×0◦.5 bin) over the survey region for two differ-
ent color-magnitude selections. Panel ‘a’ is for Galactic stars that
have color and magnitude in the region occupied by stars in M31
of metallicity in the range −3.0 < [Fe/H] < +0.2 according to the
10Gyr Padova models. Panel ‘b’ is for the more restricted range
−3.0 < [Fe/H] < −0.7.
to predict the expected foreground contamination, for
stars of color and magnitude that will masquerade as
M31 halo stars. In Fig. 17 we show two such predic-
tions over the area of the study. The top panel shows
the equivalent surface brightness of the star-count model
for stars with metallicities −3 < [Fe/H] < +0.2 interpo-
lated from the Padova models shifted to the distance
of M31. The bottom panel shows a similar map for
−3 < [Fe/H] < −0.7, which is substantially fainter than
that of panel ‘a’ because this metallicity interval excludes
most red stars from the Galactic disk sequence (as can
be seen in Fig. 16).
To construct Fig. 17 we have converted the predicted
Galactic star-counts to an “equivalent surface bright-
ness” ΣV in the V-band, as if these contaminants were
RGB stars in M31. The motivation for converting the
measured star-counts into surface brightness is of course
to be able to compare our observations to previous stud-
ies and also to theoretical predictions. However the pro-
cedure requires some further explanation. Both for the
model and for the survey data, we convert the MegaCam
g and i-band photometry into the V-band using the color
equation above. The resulting V-band luminosities are
summed for the stars in a spatial and/or color-magnitude
bin, but we must still correct for the fact that we are only
observing RGB stars which represent only a fraction of
the total luminosity. By comparing the RGB star-counts
of And III down to a limiting magnitude of i0 = 23.5
with the integrated magnitude of mV = 14.4± 0.3 of this
dwarf galaxy (McConnachie & Irwin 2006), we measure
an offset of 2.45 mag. This is consistent, and similar, to
the value of 2.3 mag estimated in the same manner by
Martin et al. (2006) for a limiting magnitude of i0 = 24.
Furthermore, as we shall see below in §8, with this off-
set we obtain a good correspondence between the pro-
file of metal-poor stars and the V-band surface bright-
ness profile derived from integrated light (Irwin et al.
2005). Clearly the uncertainties in this simple correc-
tion are large: we are implicitly assuming that the un-
derlying population has the same luminosity function
as And III for all metallicities. The equivalent surface
brightness measurements we shall present below must
therefore be interpreted with caution, as they are likely
to contain substantial systematic errors. However, the
interested reader who may wish to convert these sur-
face brightness profiles back to the reliable measure of
luminosity-weighted star-counts (to a limiting magnitude
of i0 = 23.5) can do so by simply subtracting 2.45 mag.
The predicted distributions such as those shown in
Fig. 17 are the best means we have to subtract fore-
ground contamination from the spatial maps. However,
we found that we could improve upon the foreground
subtraction in color-magnitude (Hess) diagrams by us-
ing the observed color-magnitude distribution in the 6
background fields (93, 105, 106, 115, 120 and 121) ap-
propriately scaled according to the model to account for
the predicted density variations over the survey. A dif-
ferent scaling correction is adopted for each metallicity
interval; we show in Fig. 18 an example of the scal-
ing factor applied to the stars with colors consistent
with being M31 stars with metallicity in the interval
−0.7 < [Fe/H] < −0.4, according to the Padova models.
The density of contaminants subtracted from the higher
latitude fields is more than a factor of two larger than
from the lower latitude fields.
Panel ‘a’ of Fig. 19 shows the color-magnitude dis-
tribution of the MegaCam fields shown previously in
Fig. 4, with the contamination removed statistically.
The subtracted CMD displays a clear RGB-like popu-
lation, with a broad range of metallicity, although the
detection of the more metal-rich populations is clearly
hampered by the observational g-band limit. In or-
der to investigate the luminosity function along this
RGB, we select stars with interpolated metallicities in
the range −2.3 < [Fe/H] < −0.7 (i.e., between the green
and pink isochrones). The result is shown on panel ‘b’,
together with a simple fit. A linear fit in log(Counts),
is precisely what is expected for an RGB population
(Bergbusch & Vandenberg 2001). If this statistical fore-
ground subtraction is reliable, over 105 halo RGB stars
belonging to M31 are detected over these MegaCam
fields.
5. STELLAR POPULATION MAPS
Fig. 18.— An example of a map of the density scaling factor
applied to the background fields (marked in green) to compensate
for the expected variations in foreground stellar populations over
the survey. In this case, we have chosen stars with colors between
the Padova isochrones of metallicity −0.7 < [Fe/H] < −0.4.
Fig. 19.— Panel ‘a’ shows the Hess diagram of the MegaCam
fields previously shown in Fig. 4, with foreground and background
contamination subtracted by comparison to six background fields
as detailed in the text. The Padova isochrone models from Fig. 8
are reproduced to help guide the eye. Panel ‘b’: the luminos-
ity function of stars with −2.3 > [Fe/H] > −0.7. Panel ‘c’: the
matched filter weight map, trimmed to the color-magnitude region
encompassing stars of metallicity −3.0 < [Fe/H] < +0.2. (Both
gray-scale maps are shown on a linear scale, with the photome-
try limited to g0 < 25.5).
Having shown that there is a relatively clean signal of
the expected RGB of M31 in the combined data, we now
proceed to mapping out these stellar populations. A very
powerful technique for revealing a signal buried under
heavy contamination is the so-called “Matched Filter”
method, which is an optimal search strategy (in a least-
squares sense) if one has a precise idea of the properties of
the signal and the contamination. The properties could
be, for instance, the spatial properties of the population
of interest (a characteristic size or shape) as well as those
of the contamination. Alternatively (or in addition), one
Fig. 20.— Matched-filter map to i0 = 24.5 (i0 = 22.8 over the
INT survey region). The artifacts of the MegaCam fields observed
in the 2003 and 2004 seasons are clearly seen. A logarithmic scale
is used for the representation.
Fig. 21.— As Fig. 20, but to the limiting depth of the INT survey
(i0 = 22.8 for S/N∼ 10). The map is virtually free of obvious
artifacts over the entire region observed with MegaCam.
may use the color-magnitude distribution, or whatever
other physical properties of these populations that have
been measured.
To apply the matched filter method one simply weights
each datum by the ratio of signal to contamination ex-
pected for that datum given its parameters. The re-
sulting ensemble of weighted data can then be analyzed
in the usual way. However, the advantage this effort
has afforded us is that the distribution of weighted data
will optimally suppress the contamination, revealing best
whatever signal is present. In the particular situation
confronting us here, we know the color-magnitude distri-
bution of the signal of interest, as we have just presented
in panel ‘a’ of Fig. 19, and as discussed above the Mega-
Cam “background” fields (93, 105, 106, 115, 120 and
121) give us a reasonable model for the color-magnitude
behavior of the contamination in the absence (or near
absence) of that signal. The ratio of these two CMD
distributions gives the weight matrix, which we show in
panel ‘c’ of Fig. 19. Here we have trimmed the weight
matrix down to the maximum possible physical inter-
val (−3.0 < [Fe/H] < +0.2). Note that, as expected, the
greatest weight arises at faint magnitudes in the color
range 0.75 < (g − i)0 < 1.5, so of course stars with this
photometric property will contribute most strongly in the
following matched filter maps.
Figure 20 displays a matched filter map over the entire
survey region, where we have chosen a limiting magni-
tude (i0 = 24.5), a metallicity range (−3.0 < [Fe/H] < 0)
and a gray-scale representation to highlight the survey
defects. The sky region surveyed by the INT is clearly
not as deep as the outer MegaCam region, causing the
sharp edge along the MegaCam survey boundary. How-
ever, the most important defect visible here are the long
horizontal stripes, which are present on the top and bot-
tom row of CCDs in the 2003 and 2004 data, but not
after the camera refurbishment in 2005. The effect is due
to a deterioration of the point spread function (PSF) in
those areas, causing stars to appear elliptical and simi-
lar to barely-resolved galaxies. We spent a considerable
amount of effort adapting our processing software to cor-
rect for this effect, but though substantial improvement
was obtained compared to the starcounts derived assum-
ing a constant PSF, the problem could not be removed
entirely, since some galaxies intrinsically have ellipticity
and major axis position angle similar to the deformed
PSFs. We also attempted to correct the maps by calcu-
lating the equivalent of a flat-field for star-counts from
the median of many fields. However this was not im-
plemented for the maps presented here, as the defects
were found to be insufficiently stable, so that the com-
puted corrections introduced other artifacts of almost the
same amplitude as those they corrected for. Instead, the
problem is largely removed by choosing a brighter lim-
iting magnitude, and virtually disappears if we adopt
i0 = 22.8 as in Fig. 21, the limit of the INT photome-
try (Ibata et al. 2001b). Of the remaining artifacts, the
most obvious remaining are the handful of shallow INT
fields mainly clustered around (ξ = 0◦,η = −3◦) which
were observed in conditions of poorer seeing than av-
erage, and of course the hole in the star-counts at the
center of M31, where the photometry of individual stars
broke down due to very high crowding.
In Fig. 22 we present the matched filter maps for six
different ranges in metallicity. The limiting magnitude
over the MegaCam region was chosen to be i0 = 23.5,
and we kept a limit of i0 = 22.8 (S/N ∼ 10) for the
INT survey, which gives rise to the obvious discontinu-
ity around η ∼ −3◦. These maps possess a bewilder-
ing amount of information on a large range of spatial
scales and surface densities, so it is impossible to dis-
play all the information at a given pixel scale or with
a given color representation. The diagrams in Fig. 22
have been constructed to show the large-scale distribu-
tion of stellar populations in the MegaCam region of the
survey, while retaining some sensitivity to small struc-
tures such as dwarf galaxies which have scales of a few
arcmin; in each row the right-hand panel shows a higher
resolution version of the selection in the left-hand panel;
the lower-resolution maps are useful for appreciating the
large-scale behavior of the diffuse components. We start
our discussion with panel ‘b’, which displays the metal-
rich selection (−0.7 < [Fe/H] < 0.0). Though noisy, we
can discern many features:
• The elliptical but irregular distribution of stars
with axis ratio ∼ 0.5 and major axis diameter ∼ 5◦
(∼ 70 kpc), containing several previously reported
substructures (Ferguson et al. 2002). As we have
argued elsewhere (Ibata et al. 2005), this is a giant
rotating component which is dominant beyond the
end of the classical disk, and possibly the residue
of a significant merger that occurred many Gyr ago
(Peñarrubia, McConnachie & Babul 2006).
• The large (∼ 1◦ diameter) overdensity to the north-
east (ξ ∼ 1◦.5, η ∼ 3◦), almost certainly unbound
debris (Zucker et al. 2004; Ibata et al. 2005).
• The “G1” clump at (ξ ∼ −1◦, η ∼ −1◦.5), a
structure surrounding but unrelated to the lumi-
nous globular cluster “G1” (Ferguson et al. 2002;
Rich et al. 2004; Reitzel, Guhathakurta & Rich
2004; Faria et al. 2007).
• The stream-like “Eastern shelf” (Ferguson et al.
2002), at (ξ ∼ 2◦, η ∼ 0◦.5).
• A fainter stream on the western side of the galaxy,
the “Western shelf” at (ξ ∼ −1◦, η ∼ 0◦.5), and
seen in the map of Irwin et al. (2005).
• The “Giant Stream” (Ibata et al. 2001b, 2004),
which in the INT data appears to be a linear struc-
ture stretching from very close to the center of M31
to (ξ ∼ 1◦.5, η ∼ −3◦), but which shows up as a
substantially wider structure in the MegaCam sur-
vey extending to (ξ ∼ 3◦, η ∼ −6◦).
• A previously unknown stream is seen extending be-
tween (ξ ∼ 4◦, η ∼ −1◦.5) and (ξ ∼ 3◦, η ∼ −4◦);
we will refer to this as “Stream C” in the discussion
below.
• Vast expanses apparently devoid of stars over most
of the Southern half of the survey MegaCam.
• A faint diffuse component is detected approxi-
mately 4◦ from M33.
In panel ‘c’ we show an intermediate metallicity selec-
tion (−1.7 < [Fe/H] < −0.70), somewhat “overexposed”
to bring out better the fainter structures. In addition to
the previously-discussed features, we now notice:
• The inner ellipse, attributed to the giant rotating
component, has become larger and even more irreg-
ular. The more irregular aspect is of course con-
sistent with the expected longer mixing times of
debris at larger radius. An interesting point is that
the distribution appears now to be less flattened,
suggesting that this extreme color stretch may be
revealing another rounder structure previously hid-
den beneath the flattened rotating component.
• The dwarf galaxies And II and And III (cf. Fig. 3)
become apparent.
Fig. 22.— Logarithmic scale matched-filter maps to a limiting magnitude of i0 = 23.5, g0 = 25.5. Low resolution images (0
◦.2 × 0◦.2
pixels) are shown on the left, high resolution versions (0◦.05× 0◦.05 pixels) on the right-hand column.
Fig. 22 — continued.— Logarithmic scale matched-filter maps to a limiting magnitude of i0 = 23.5, g0 = 25.5. Low resolution images
(0◦.2× 0◦.2 pixels) are shown on the left, high resolution versions (0◦.05 × 0◦.05 pixels) on the right-hand column.
Fig. 23.— Star-count map of the MegaCam region, with the
foreground contamination subtracted using the Besançon model. A
limiting magnitude of i0 = 23.5 has been adopted. The red, green,
blue and pink polygons delineate the regions chosen to sample,
respectively, the Giant Stream, the major axis structure, the minor
axis stream and the empty outer halo region.
• Two strong localized structures, at (ξ ∼ 6◦.23,
η ∼ −2◦.89) and (ξ ∼ 6◦.23, η ∼ −8◦.89), which as
we will discuss below, are two new dwarf satellite
galaxies.
• A faint low surface brightness fuzz is detected on
the extension of the major axis of M31, out to (ξ ∼
−5◦, η ∼ −7◦), we will refer to this as the “Major
axis diffuse structure”.
• A strong stream-like structure is detected between
(ξ ∼ 3◦, η ∼ −1◦.5) and (ξ ∼ 2◦, η ∼ −2◦.5), which
we call “Stream D” below.
• A further faint low surface stream-like structure is
detected towards (ξ ∼ 6◦, η ∼ −6◦), which we will
refer to as “Stream A”.
• The extended structure near M33 is stronger.
• The region (ξ < 4◦, η < −9◦) remains devoid of
stars.
The more metal-poor selection in panel ‘d’
(−2.3 < [Fe/H] < −1.1) displays essentially the same
properties as in panel ‘c’, except that a considerable
amount of localized density spikes are detected, covering
one to a few contiguous pixels. Among these are the
newly-discovered dwarf galaxies And XI, XII, and
XIII (Martin et al. 2006). Panel ‘e’ shows the most
metal-poor sample (−3 < [Fe/H] < −1.70). Now the
Giant Stream has almost disappeared, and only And
II and III are still clearly visible as substructures, yet
one also discerns a radial gradient from M31 over the
MegaCam survey region. For completeness, in panel
‘a’ we show the most metal-rich selection considered
here (0.0 < [Fe/H] < +0.2) in which only the inner disk
of M33 and a small portion of the Giant Stream are
discernible, while panel ‘f’ shows the map over the full
metallicity range. The increased sensitivity with the
full metallicity range reveals a further feature on the
Fig. 24.— Cartoon of the main structures presented in §5. The
circled dots and ‘star’ markers are reproduced from Fig. 3, and
show the positions of dwarf galaxies and selected globular clusters,
respectively.
minor axis with a stream-like structure between (ξ ∼ 5◦,
η ∼ −2◦.5) and (ξ ∼ 3◦, η ∼ −5◦), which we will refer to
as “Stream B”.
The maps displayed in Fig. 22 show the distribution
of the matched filter statistic, so the resulting counts
are therefore somewhat difficult to interpret directly.
The reason for this is primarily that the matched fil-
ter method relies on a model of the stellar population
that one desires to detect, and the statistic we mea-
sure will depend on the assumed luminosity function and
how we choose to weight populations of different metal-
licity. A secondary reason is that, as discussed above,
the foreground Galaxy counts do vary over this vast sur-
vey, so the contamination model also varies. For these
reasons we also present in Fig. 23 a straightforward sur-
face density map, where we have counted up stars in
the color-magnitude interval 0.8 < (g − i)0 < 1.8 and
20.5 < i0 < 23.5, and have subtracted off the correspond-
ing Besançon model counts over the same area of sky.
The main structures previously seen in Fig 21 are nicely
confirmed, and which we highlight in Fig. 23, namely
the very extended Giant Stream (red polygon), the dif-
fuse major axis structure (green polygon), the minor axis
stream-like structure (blue polygon), the extended out-
skirts of M33, and the voids elsewhere (pink polygon).
The advantage of this map is that we can now interpret
the physical meaning of the color scale, which is shown
with the wedge at right-hand edge of the diagram. Black
corresponds to 10−4 RGB stars per square arcsecond
down to i0 = 23.5. Using the conversion of star-counts to
surface brightness discussed above, the saturated black
level translates to ΣV = 30.3mag arcsec
In the next section we discuss in more detail the popu-
lations that are highlighted in Fig. 23. To ease interpre-
tation, in Fig. 24 we show a cartoon of the positions of
these populations with respect to the various structures
discussed above.
Fig. 25.— The spatial distribution of point-sources in a 9′ × 9′
area in the vicinity of And XV (panel ‘a’). The parallel red lines
mark the CCD boundaries, though there is no gap at this location
due to the adopted dithering pattern. The CMD of the stars within
the 2′ circular region is shown in panel ‘b’. Selecting those stars
with color and magnitude within the red dashed polygon, yields
the spatial distribution shown in panel ‘c’ whose radial profile is
given in panel ‘d’. The continuous, dashed and dot-dashed lines
in panel ‘d’ are, respectively, a Plummer model, an exponential
model, and a King model fit to the profile inside of 5′.
6. SPATIAL SUBTRUCTURES
6.1. Discovery of 2 bright satellites
A thorough analysis of these data regarding the inci-
dence of low mass satellites around M31 and its impli-
cations for galaxy formation theory and cosmology will
be presented in a later publication in this series (Martin
et al. 2007b). However, we discuss briefly here two new
dwarf galaxies which were discovered immediately from
simple visual inspection of the starcounts maps. Since
the analysis is identical for both objects we include the
results for And XVI in brackets.
And XV (XVI), located at α0 = 1
h14m18.7s, δ0 =
38◦7′3′′ (α0 = 0
h59m29.8s, δ0 = 32
◦22′36′′) can be
noticed as an obvious enhancement in the matched-
filter maps presented previously. In panel ‘a’ of Fig. 25
(Fig. 26), we show the distribution of all detected point
sources in a 9′ × 9′ region around the dwarf galaxy.
The color-magnitude distribution of the sources within
the 2′ (1′.5) radius circle centered at the point of max-
imum density is shown in panel ‘b’. A very clear and
strong RGB is present. Assuming that the stars out-
side of the irregular polygon are contaminants, we pro-
ceed to estimate the distance of the structure using
the tip of the RGB. We adopt MTRGB = −4.04± 0.12
from Bellazzini, Ferraro & Pancino (2001) for the ab-
solute I-band magnitude of the RGB tip, and con-
vert into the Landolt system using the color equations
above and those given by McConnachie et al. (2004a);
this yields a distance modulus of m−M = 24.0± 0.2
(m−M = 23.6± 0.2) or alternatively a distance of 630±
60 kpc (525 ± 50 kpc). With this distance modulus we
find a reasonable visual fit to the RGB with a Padova
isochrone of metallicity [Fe/H] = −1.1 ([Fe/H] = −1.7).
Given the angular distance of 6◦.8 (9◦.5) fromM31, the ob-
ject lies at an M31-centric distance of 170 kpc (270 kpc).
Fig. 26.— As Fig. 25, but for And XVI. The presence of several
bright stars causes the irregular spatial distribution in the left hand
panels.
With the CMD selection polygon from panel ‘b’, we
filter out foreground contamination, which gives the dis-
tribution shown in panel ‘c’. The corresponding density
profile is given in panel ‘d’, where we have subtracted off
a background count determined from an annulus between
10′ and 15′. Fitting the distribution with an exponential
profile (dashed line), yields a scale length of 0′.72 ± 0′.03
(0′.53 ± 0′.03), though a Plummer model (solid line) of
scale size 1′.2 (0′.9) also fits acceptably well, as does a
King (1962) model (dot-dashed line) with core radius of
0′.91 (0′.64) and tidal radius of 5′.7 (4′.3). By integrating
the star-counts up to the half-light radius, and correct-
ing by 2.45 mag (as above) to account for stars below
i0 = 23.5, we estimate a total absolute magnitude of
MV = −9.4 (MV = −9.2).
And XVI will be a particularly interesting object for
further study given its extreme distance from M31, and
its location between M31 and the Milky Way, where it
presumably has felt a non-negligible perturbation from
the potential of our Galaxy. It is also curious that
And XV appears to be structurally disturbed and elon-
gated, which is suggestive of the action of galactic tides.
Yet how this very distant galaxy might have been affected
by tides is hard to imagine. (The irregular morphology
seen in the distribution of And XVI stars in Fig. 26 is an
artifact of nearby bright star “holes”).
6.2. Giant Stream
The Giant Stream around M31 has been the subject of
numerous studies, due to the fact that it is a nearby in-
termediate mass merging event, and that it can be used
to measure the potential of M31. The initial discovery in
the INT survey (Ibata et al. 2001b) showed the structure
to be (in projection) an approximately linear and radial
stream, with a metallicity slightly higher than that of
47 Tuc ([Fe/H]− 0.71), and a total absolute magnitude of
MV ≈ −14. We probed more fully its extent and the line
of sight depth with the CFHT12K (McConnachie et al.
2003), a precursor wide-field camera to MegaCam at the
CFHT. These photometric and positional data were then
complemented by radial velocities obtained at 4 loca-
Fig. 27.— Panel ‘b’ displays the stellar populations in the core of
the Giant Stream (sampled in the spatial region shown with a red
polygon in panel ‘a’); while panel ‘c’ displays those on the periphery
of this structure (dark blue polygon in panel ‘a’). The foreground
contamination has been removed from the two Hess diagrams.
Fig. 28.— The metallicity distribution functions (with error bars
denoting 1σ uncertainties) for the Giant Stream core sample (red)
and the envelope sample (blue), as interpolated from the chosen
Padova isochrones. Photometric limits of i0 = 23.5 and g0 = 25.5
have been imposed. The background fields, normalized with the
Besançon model, have been used to subtract off the expected fore-
ground counts in each of the metallicity bins. The two distributions
are completely inconsistent with each other to high confidence.
tions along the stream with the DEIMOS multi-object
spectrograph at the Keck Observatory, which allowed a
measurement of the mass of the halo of Andromeda out
to 125 kpc (Ibata et al. 2004), and enabled us to develop
a model of the orbital path of the stream progenitor. We
found the orbit to be highly radial, and predicted that
the stream fans out towards the East after passing very
close to the nucleus of M31, losing its stream-like spatial
coherence. This analysis also posed an interesting puz-
zle, which is still unsolved: since the stream is on such
a highly destructive radial orbit, how did the progenitor
survive until so recently?
Subsequently, Guhathakurta et al. (2006) also used
Keck/DEIMOS to obtain spectra in one stream
field, where they measured a mean metallicity of
〈[Fe/H]〉 = −0.51. The kinematic data sets were reana-
lyzed by Font et al. (2006), who undertook N-body simu-
lations to attempt to reproduce the stream morphology.
They found that the progenitor must have been more
massive than 108M⊙, and that the time since its disso-
lution is a mere 0.25Gyr. Recently, Fardal et al. (2006)
have shown how the fanning-out of the stream into shells
to the East and West can be used to place constraints
on the galaxy potential. We defer a full re-analysis of
the Giant Stream to a subsequent contribution, focussing
here on the salient new features that are revealed in the
MegaCam survey.
An inspection of Fig 22, shows that the Giant Stream
extends out to a projected radius of ∼ 100 kpc (the in-
ner dashed circle). With the maximum line of sight
distance to the stream of 886 ± 20 kpc estimated by
McConnachie et al. (2003) (at ξ = 2◦, η = −4◦), this cor-
responds to an apocenter distance of ∼ 140 kpc. Though
this is further than it had been mapped out before, the
possibility that the stream reaches this projected dis-
tance was anticipated by one of the orbit models pre-
sented in Ibata et al. (2004) (cf. Fig. 4 of that paper).
Fig. 29.— Counts in a 1◦-wide East-West band between −4◦.5 <
η < −3◦.5 for different metallicity intervals.
That particular orbit model, however, does not agree well
with the measured line of sight distance gradient, though
we note that debris does not exactly follow the orbit of
the progenitor. Further detailed modeling is clearly re-
quired to understand the dynamics of this stream.
The MegaCam data also shows that there are stel-
lar populations variations in the stream. We illustrate
the evidence for this in Fig. 27, where the colour magni-
tude distribution in the core of the Giant Stream (panel
‘b’) is compared to a region on the western periphery
of the structure. Both of these spatial selections con-
tain stars over a wide range of metallicities, and peak at
high mean metallicity, consistent with the mean photo-
metric metallicity of 〈[Fe/H] = −0.51〉 measured from a
kinematically-selected sample of stars on the periphery of
the Giant Stream (Guhathakurta et al. 2006). It is clear
from an inspection of this diagram, however, that relative
to the outer field the core is lacking the blue stellar popu-
lations (around the isochrone with [Fe/H] = −1.3). The
concentration of very “metal-rich” stars to the core of
the stream can also be seen in Fig. 22 (compare panel ‘a’
to panel ‘c’). We stress here that these red stars need not
be as metal-rich as they appear from comparison to these
ancient isochrones, due to the well-known age-metallicity
degeneracy. While the majority of other “halo” popula-
tions studied in this contribution are very likely old, this
is not the case for the Giant Stream. In the spectral
sample of bright stream stars obtained by Ibata et al.
(2004), many targets could be identified as Asymptotic
Giant Branch (AGB) stars from their spectral features,
which indicates that a fraction of these stars are of in-
termediate age. This is consistent also with the deep
photometric survey in a Giant Stream field undertaken
by Brown et al. (2006b) with the Advanced Camera for
Surveys (ACS) on board the HST. They detected a dom-
inant population of age ∼ 8Gyr, as well as a younger
∼ 5Gyr component. We will continue to label these red
stars as “metal-rich” for the sake of brevity, though the
above caveat should be kept in mind.
The stellar populations differences can be put on a
more quantitative basis by constructing the metallicity
distribution functions for the “stream core” and “outer
stream” selections; this is displayed in Fig. 28, which
shows the striking difference very clearly. The core of
the stream clearly has a very large fraction of red stars.
Fig. 29 shows the star-counts in different metallicity in-
tervals as a function of ξ in a 1◦-wide band between
−4◦.5 < η < −3◦.5. The distribution, which peaks near
ξ ∼ 1◦.5 for [Fe/H] > −0.4, becomes broader for the
metallicity intervals −1.3 < [Fe/H] < −0.4.
6.3. Major axis structure
The faint diffuse population detected on the major axis
between a projected distance of 50 kpc and 100 kpc (de-
lineated with the green polygon in Fig. 23) is a con-
spicuous feature of the MegaCam survey. The average
surface brightness in this region is ≈ 31 mag arcsec2.
The dwarf galaxy And III lies on the edge of this re-
gion, so to avoid contamination we remove the data from
a 0◦.5 radius circle around And III for the subsequent
analysis. The color-magnitude distribution of the area
is displayed in panel ‘a’ of Fig. 30, which clearly pos-
sesses a well-populated RGB with a dominant population
of color similar to the Padova isochrones of metallicity
[Fe/H] ∼ −1.3. The corresponding MDF in Fig. 31 (red
line) confirms this visual impression.
Thus despite the visual impression that the “overex-
posed” density map of Fig. 23 gives that the major axis
population merges with the Giant Stream, we find that
these two stellar populations are very different and likely
unrelated. This diffuse low-constrast feature has no clear
spatial structure as one would expect of a stream. In-
deed, it could be the inner regions of the halo, though it
appears not to be a smooth roughly spherical structure
since there is an obvious deficit of stars at (ξ ∼ −0◦.6,
η ∼ −6◦) compared to (ξ ∼ −3◦, η ∼ −5◦). We re-
frain from estimating the total luminosity of the struc-
ture, since we have clearly only detected a fraction of
the entire object. Additional photometry to the North
and West and possibly even kinematics will be needed to
understand this structure further.
6.4. Distant minor axis stream ‘A’
In contrast, the structure on the minor axis (delineated
with the blue polygon in Fig. 23, which covers 1.7 deg2)
at R ∼ 120 kpc is much more confined spatially as can be
perceived from an inspection of the matched-filter maps
in Fig. 22. Curiously, this population (which we refer to
as stream ‘A’ in the discussion below) has a very similar
color-magnitude distribution to that of the major axis
structure, with a dominant population again just slightly
redward of the [Fe/H] = −1.3 Padova isochrone, as can
be seen in panel ‘b’ of Fig. 30. The corresponding MDF
Fig. 30.— Panel ‘a’ shows a foreground-subtracted Hess diagram
of the major axis diffuse population over the region marked out
with the green polygon in Fig. 23, while panel ‘b’ presents the
foreground-subtracted Hess diagram of the minor axis stream pop-
ulation over the region marked out with the blue polygon in Fig. 23.
The gray scale wedge on the right shows the count level per CMD
bin of size 0.05mag × 0.05mag.
Fig. 31.— The metallicity distribution function of the major
axis diffuse structure and the minor axis stream ‘A’ population, as
derived from the data in Fig. 30.
is compared to that of the diffuse major axis feature in
Fig. 31.
The structure is very faint, with an average surface
brightness of ΣV ∼ 31.7± 0.2mag arcsec
−2 . Integrating
over the blue polygon in Fig. 23, and subtracting the
average counts at this radius calculated from the “outer
halo” region (contained in the pink polygon), gives a to-
tal luminosity of LV sin 2.3 × 10
6 L⊙ (MV ∼ −11.1). If
we are detecting the entirety of the stars in the original
structure, the progenitor must have been a galaxy simi-
lar to the Sculptor dwarf spheroidal (MV = −10.7± 0.5,
Irwin & Hatzidimitriou 1995).
6.5. Minor axis streams at R < 100 kpc
Figure 32 shows a close-up map of the minor axis region
in the proximity of M31 and the Giant Stream. Here we
have used the matched-filter technique to detect struc-
tures of metallicity in the range−3.0 < [Fe/H] < 0.0, and
have chosen a grayscale representation that highlights
the three linear structures that appear almost perpendic-
ular to the minor axis and merge into the Giant stream.
Three arrows have been added to the diagram to indicate
the approximate location of these stream-like features,
which we denote ‘B’, ‘C’ and ‘D’ in order of increasing
declination.
The nature of these streams becomes more appar-
ent if we investigate the color profile along the minor
axis region. We choose to remove the Giant Stream
stars by selecting only those point-sources within the
yellow-line polygon in Fig. 32, and sum stars perpen-
dicular to the minor axis (rather than taking radial bins)
so as to enhance the density peaks. The correspond-
ing foreground-subtracted surface brightness profiles are
shown in Fig. 35, where the blue line shows the metal-
poor populations with −3.0 < [Fe/H] < −0.7 and the red
line those with −0.7 < [Fe/H] < +0.2. The foreground,
as before, is estimated using the Besançon model. As ex-
pected, several strong peaks are detected, however, the
locations of the peaks in the metal-poor subsample do not
coincide with those of the metal-rich subsample, suggest-
ing very strong stellar populations differences between
Fig. 32.— Matched-filter map of the minor axis populations with
metallicity in the range −3.0 < [Fe/H] < 0.0. The map is, as be-
fore, a superposition of MegaCam and INT photometry, the differ-
ences in depth of which account for the discontinuous density distri-
bution. The region surrounded by the yellow polygon encloses the
MegaCam area used to investigate the minor axis density profile in
Fig. 33. The red, green and blue polygons enclose the stream-like
structures labeled, respectively, ‘B’, ‘C’ and ‘D’. (These structures
can be appreciated better in panel ‘a’ of Fig. 27).
Fig. 33.— The surface density profile along the minor axis, se-
lected from the region within the yellow polygon in Fig. 32. The
arrows point out significant peaks in the profile. The positions of
the labeled peaks correspond to the streams seen in Fig. 32.
these stream-like features.
This deduction is borne out by the variations in the
color-magnitude distributions in adjacent spatial loca-
tions. In Fig. 34 we display the Hess diagrams of the
stream-like structures enclosed within the green, red and
blue polygons of Fig. 32, and also show the stellar pop-
ulation between streams ‘B’ and ‘C’. The corresponding
MDFs are given in Fig. 35. These data show that stream
‘D’ is a relatively metal-poor structure, while stream ‘C’
is predominantly metal-rich. Curiously, the population
contained within gap between streams ‘B’ and ‘C’ has a
narrow range of metallicity and is metal-rich.
These stream-like structures overlap along the line of
Fig. 34.— Background-subtracted Hess diagrams for four adja-
cent MegaCam fields near the minor axis. In panels ‘a’, ‘b’, ‘c’ and
‘d’ we display the data for fields 13, 14, 23 and 24, respectively.
Fig. 35.— The MDF determined from the four fields of Fig. 36:
13 (black), 14 (red), 23 (green) and 24 (blue).
sight (which is why we chose not to extend the stream
‘D’ spatial selection polygon in Fig. 32 up to the north-
eastern end of the survey region). A spectacular example
of this can be seen in Fig. 36, which shows the CMD of
MegaCam field 14, where streams ‘C’ and ‘D’ cohabit
over essentially the entirety of the field.
Thus, although these stream-like structures appear to
merge spatially with the Giant Stream, such that it is
tempting at first sight to associate them to that huge
structure, their stellar populations properties are so dif-
ferent both from each other and from the Giant Stream,
that this proposition is untenable.
In the present survey these streams or stream-like
structures are clearly truncated at the Eastern edge of
the dataset, so it is impossible to determine their full ex-
tent or nature. Instead, we obtain a first and very rough
estimate of their luminosities by integrating within the 3
stream polygons in Fig. 32. In this way we estimate that
stream ‘B’, which lies at R ∼ 80 kpc, has a luminosity
Fig. 36.— The color-magnitude diagram for field 14, showing
the presence of two co-spatial populations with very different RGB
tracks.
within the red polygon of ∼ 1.0 × 107 L⊙; stream C at
R ∼ 60 kpc has ∼ 1.4 × 107 L⊙ in the green polygon;
while stream ‘D’ at R ∼ 40 kpc has ∼ 9.5×106 L⊙ in the
blue polygon. In estimating these luminosities we have
ignored the complex background in this region. Never-
theless, these estimates indicate that the progenitors of
the streams were sizable dwarf galaxies, likely more lumi-
nous than the Fornax dSph. We note that the extended
globular cluster (Huxor et al. 2005) EC4 (Mackey et al.
2007) lies within or superimposed on stream ‘C’.
7. THE OUTER HALO
The primary reason for undertaking this survey was
initially to investigate the large-scale structure of the ha-
los of M31 and M33, and to some extent the substruc-
tures discussed above are a hindrance for this purpose. In
particular, we had not expected the Giant Stream to be
as extended and polluting of the inner halo as it turned
out to be, and the various “contaminating” streams along
the minor axis were a surprise, as we had chosen those
fields from the shallower INT survey to probe the surface
density profile of the “clean” inner halo.
However, there is a relatively empty region of the sur-
vey free from obvious substructures towards the South-
west. This ∼ 30 deg2 region previously surrounded
with a pink polygon in Fig. 23, is reproduced in Fig 37,
where we have converted the counts of stars in the var-
ious metallicity ranges shown into an equivalent surface
brightness. The four white pixels within the polygon in
the diagram are pixels discarded from the analysis as
they contain the dwarf galaxies And XI, XII, XIII and
The equivalent mean surface brightness of the outer
halo stars for the full [Fe/H] range given in panel ‘a’ of
Fig. 37 is ΣV = 33.0± 0.05mag arcsec
−2, where the un-
certainty is calculated using Poisson statistics, assuming
no uncertainty in the background subtraction. Note that
a 2% error in the subtraction (the average difference of
the residuals between the Galactic model and observed
Galactic disk found in Fig. 14), will incur a 0.25 mag
systematic error. However, the rms scatter in the pixel
values in Fig. 37 (calculated in counts and then converted
Fig. 37.— Background-subtracted maps of the equivalent sur-
face brightness in the outer halo region. Panel ‘a’ shows stars in
the metallicity range −3.0 < [Fe/H] < +0.2, while panel ‘b’ is re-
stricted to −3.0 < [Fe/H] < −0.7, a range which suffers much less
from uncertainties in the background correction.
into magnitudes) is 1.1 mag; for this calculation, we only
took into account those (128) pixels in Fig. 37 for which
the surface area correction was less than 10%. The fact
that this rms scatter is larger than the 0.2 mag random
uncertainty expected from Poisson uncertainties in the
total measured star counts, could be due to an intrinsic
lumpiness in the star distribution on the 0◦.5× 0◦.5 scale
of the pixels in Fig. 37, but we consider it likely that it
is largely due to slight variations in observing conditions
between fields, and slight variations of image quality over
the camera. Panel ‘b’ gives the map for the metal-poor
range −3.0 < [Fe/H] < −0.7, which has the advantage of
reducing the amount of residual Galactic contamination.
The equivalent mean surface brightness for this selection
is ΣV = 33.7± 0.08mag arcsec
−2. It is pertinent to point
out here that the six fields chosen to probe the back-
ground all lie within this outer halo region, indeed they
are the fields closest to the outer dashed circle segment
marking a projected radius of 150 kpc (cf. Fig. 18).
The Hess diagram for the outer halo region is shown
in Fig. 38, with the foreground subtracted as before.
Though noisy, a low contrast RGB population can iden-
Fig. 38.— Foreground-subtracted Hess diagram of the outer halo
region shown in Fig. 37.
tified that is strongest between the [Fe/H] = −1.7 and
[Fe/H] = −0.7 isochrones. Clearly for [Fe/H] > −0.7,
residual foreground subtraction errors dominate the
data.
8. HALO PROFILES
Before presenting the radial profiles of the stellar popu-
lation present in the survey, we first investigate whether
our conversion from star-counts to “equivalent surface
brightness” (first presented in §4.1) yields consistent re-
sults with previous studies. To this end we compare our
measurements to those of Irwin et al. (2005) who ana-
lyzed the profile along the minor axis of M31. We at-
tempted to reproduce as closely as possible the spatial
selection chosen by Irwin et al. (2005), a band between
±0◦.5 of the minor axis (see their Fig. 1). The MegaCam
survey covers most, but not all, of this area (there is a
small gap near ξ ∼ 1◦.5, η ∼ −1◦.5, as can be seen in
Fig. 32, for example). In panel ‘a’ of Fig 39 the black
dots mark the surface brightness measurements from in-
tegrated light by Irwin et al. (2005), while the blue his-
togram shows the MegaCam profile. Though the mea-
surements from integrated light end at R = 0◦.5, just
before the beginning of the MegaCam survey, there is
good consistency between these two profiles.
In panel ‘b’ the black dots now show the star-counts
profile of the blue RGB selection of Irwin et al. (2005)
converted into an equivalent surface brightness. This
V-band profile was determined from a color cut in the
INT (V,i) system, designed to select metal poor stars.
Fig. 39.— Panel ‘a’ compares the surface brightness profile from
integrated light (black points) deduced from the INT survey by
Irwin et al. (2005), with the converted star-counts derived from the
present survey in a ±0◦.5 band around the minor axis of M31. The
color variations as a function of radius are attributable to substruc-
tures with different stellar populations intersecting this area. The
blue RGB star-counts profile of (Irwin et al. 2005) is compared in
panel ‘b’ to the metal-poor MegaCam selection in the same spatial
region. The differences between these curves at r < 2◦.5 are likely
due to the fact that the two stellar selections, though similar, are
not identical. For r > 2◦.5 the Irwin et al. (2005) profile decreases
sharply due to over-subtraction of foreground contaminants in that
analysis. Panel ‘c’ is similar to panel ‘a’ but the profile is derived
over a wider minor axis area (contained within the yellow polygon
of Fig. 32).
Here we have chosen not to adopt that approach, relying
on interpolation between Padova isochrones. This dif-
ference in stellar populations must account for some of
the differences between the two profiles. However, the
shape of the Irwin et al. (2005) profile at large radius
drops rapidly unlike the MegaCam profile derived from
the same region. This effect is due to the foreground
subtraction method chosen by Irwin et al. (2005), who
selected fields within 4◦ of M31 to probe and remove
the contaminating foreground populations. With hind-
sight this is clearly not appropriate given that the present
MegaCam data shows that the halo is very extended, and
has a rather flat profile. However, out to R ∼ 2◦.5 the
INT and MegaCam profiles agree very well.
To complement the profiles derived from the narrow 1◦
band shown in panels ‘a’ and ‘b’, we present in panel ‘c’
the surface brightness profile derived from data over the
wider minor axis area enclosed within the yellow polygon
in Fig. 32. This is of course less noisy at large radius. The
various peaks in the profile correspond to the locations
Fig. 40.— Panel ‘a’ shows the radial profile of all the stellar
structures present in the MegaCam survey to a limiting magnitude
of i0 = 23.5. The points show the V-band surface brightness profile
from integrated light, as derived by Irwin et al. (2005). The profiles
colored in blue and red show the MegaCam data for the metal-poor
and metal-rich selections, respectively. Panel ‘b’ gives the “metal-
licity” distribution of this entire region (and down to i0 = 23.5),
derived from the stellar color by comparison to 10Gyr old Padova
isochrone models. The corresponding background-subtracted Hess
diagram is shown in panel ‘c’.
of the stream-like structures discussed above.
Having shown that the minor axis profile is consis-
tent with previous measurements in the inner regions (for
R < 2◦.5), we now proceed to determine the radial trend
of the halo populations over the full survey area. The
large amount of substructure detected in the maps above
means that the result we find will depend sensitively on
what populations we decide to include or reject in the
analysis. We therefore adopt a pragmatic approach, tak-
ing in turn various population selections, which may be
helpful when comparing these data to cosmological sim-
ulations.
We begin by showing the profile of all stellar popu-
lations present in the survey down to a limiting mag-
nitude of i0 = 23.5 (Fig. 40, panel ‘a’). The counts
in each radial bin are derived from averaging over
the entire azimuthal coverage of the MegaCam sur-
vey, with the foreground subtracted using the Besançon
model. The V-band surface brightness profile measured
from the integrated light in the INT data (Irwin et al.
2005) is reproduced here with black dots. The pro-
files measured from the present MegaCam data are dis-
played in blue for −3.0 < [Fe/H] < −0.7, and in red for
−0.7 < [Fe/H] < 0.0. As discussed above, we expect the
metal-rich selection to be compromised by foreground
correction uncertainties, though this is likely only to be
an issue at low surface brightness levels where the signal
is small.
This sample contains all populations – including satel-
lites and streams, so the profile is not obvious to inter-
pret. However, it transpires that the peak near 4◦ is due
to the presence of the Giant Stream at that location. The
metal-rich nature of that structure enhances the metal-
rich (red) profile in the region between 3◦.5 < R < 6◦,
giving the impression that the halo becomes more metal
poor at large radius. This is, however, purely an artifact
Fig. 41.— As Fig. 40, but removing the inner halo of M31 out
to r = 2◦ and that of M33 out to r = 5◦, as well as all known
satellites. For the satellites we excised data within 0◦.5 of And II
and III, and within 0◦.2 for the remaining satellites in the MegaCam
region.
of the presence of that one stream.
A clear radial decrease is detected in the surface bright-
ness of this combined population up to a distance of
about R ∼ 10◦, where it begins to rise again towards
M33. Given that M31 and M33 lie at approximately the
same Heliocentric distance (McConnachie et al. 2005),
this is a spectacular demonstration that the stellar halos
of the two galaxies actually pass through each other like
ghostly bodies.
Panels ‘b’ and ‘c’ show the MDF and background sub-
tracted Hess diagram of these stellar populations. In
this situation the distributions are overwhelmingly dom-
inated by stars close to M31 and in the disk of M33.
In Fig. 41 we repeat this analysis, after removing large
areas around the inner halos of the two main galaxies
and their known satellites. Clearly the tiny bound satel-
lites found within the MegaCam survey do not have a
significant effect on the global surface brightness profile.
However the Giant Stream does have a large effect, and
the MDF and Hess diagram in panels ‘b’ and ‘c’ are dom-
inated by that population (compare to panels ‘b’ and ‘c’
of Fig. 27).
Removing the Giant Stream in addition to the inner
halo and bound satellites, reveals a fascinating profile
(Fig. 42). We find a very flat decrease as a function of
radius, visually resembling an exponential profile in the
log-linear diagram of panel ‘a’. Moving outwards from 2◦
to 5◦.5 the offset between the metal-poor and the metal-
rich profile remains approximately constant. This data
comes primarily from the minor axis area previously pre-
sented in Fig 34 (the region within the yellow polygon).
At a radius of R ∼ 5◦.5 the metal-rich population drops
significantly, and again appears to mimic the metal-poor
profile out to R ∼ 7◦. The fact that the metal-poor and
metal-rich profiles track each other fairly well in each of
these two radial ranges, suggests that the mix of stellar
populations present does not change considerably over
each range. Whether the drop at R ∼ 5◦.5 reflects a
real change in stellar populations at this radius (75 kpc)
remains to be confirmed.
Fig. 42.— As Fig 41, but with the additional removal of the
Giant Stream, as contained within the red polygon of Fig. 23.
Fig. 43.— As Fig. 42, but containing only diffuse stellar popula-
tions not identified as streams.
Finally, we show in Fig. 43 the result of removing all of
the identified structures from the survey, leaving only the
widely-distributed diffuse population behind. For this we
have excised the inner halos of M31 and M33, as well as
the satellites as detailed previously. We have also re-
moved the areas within the red, green and blue polygons
in Fig. 23, and the region contained within the yellow
polygon in Fig. 32. As can be appreciated from panel
‘c’ of Fig. 43, we cannot have much confidence in the
metal-rich selection, and correspondingly the red profile
of panel ‘a’ is very uncertain. However, the metal-poor
profile appears fairly smooth.
Indeed, the outer halo profile appears remarkably flat
in log-linear representation, essentially an exponential
function. The blue dashed line in Fig. 44 shows an
exponential model fit to the outer halo data (blue his-
togram); we find an extremely long exponential scale
length of hR = 46.8 ± 5.6 kpc. We also show a pro-
jected Hernquist model fit (blue dot-dashed line) to these
data, a model choice motivated by the simulations of
Fig. 44.— The radial profile from the metal-poor selection of the
diffuse outer halo (previously shown in Fig. 43) is displayed with
the blue histogram. The blue dashed line is an exponential fit to
these data with hR = 46.8 ± 5.6 kpc, while the blue dot-dashed
line is a Hernquist model with scale length of 53.5± 0.2 kpc. The
black histogram reproduces the metal-poor minor axis profile of
panel ‘c’ of Fig. 39. We reject the data below R = 30 kpc, as the
profile is dominated by the inner R1/4 de Vaucouleurs profile in this
region (Pritchet & van den Bergh 1994; Irwin et al. 2005). As we
have shown, between 35 < R < 90 kpc there are copious stream-
like substructures on the minor axis, so we reject these regions
as well. The best exponential model fit to the remaining data
(marked with red points) is shown with a black dashed line, and
has hR = 31.4± 1.0 kpc. The black dot-dashed line shows the best
fit Hernquist model, which has a scale length of 53.7±0.1 kpc. The
red line shows a power-law model fit to these data, which has an
exponent of 1.91± 0.11. In addition, with the green line, we show
the NFW model halo mass profile fit by Ibata et al. (2004) to the
kinematics of the Giant Stream, with an offset (arbitrarily) chosen
to fit the outer halo data. The virial radius of this model is 191 kpc.
(Bullock & Johnston 2005); the best model has a scale
radius of 53.5±0.2 kpc, more that a factor of 3 larger than
predicted by Bullock & Johnston (2005). The black his-
togram in Fig. 44 reproduces the metal-poor minor axis
profile from panel ‘c’ of Fig. 39. Recall that this minor
axis selection contains the stream-like structures ‘B’, ‘C’
and ‘D’, so it does not represent the underlying halo.
Nevertheless, beyond R = 6◦.5 there was no obvious sub-
structure in that region of the halo, and we see that the
profile from the minor axis agrees reasonably well with
that deduced from the “outer halo”.
For R > 6◦.5 the minor axis profile appears slightly
higher than the “outer halo” profile. It is possible that
this may reflect the real geometry of the halo, the differ-
ence would be consistent with the halo being a slightly
prolate structure. We do not favor this interpretation,
however. The copious substructures seen at R < 80 kpc
testify to the dominance of stochastic accretion events in
the halo. Given this, its seems more natural to postu-
late that the variation in the profile that we see here is
another consequence of this messy merging process.
If such a thing as a smooth dynamically relaxed halo
exists underneath all of the substructure, it cannot have
a hole, so the interval 30 < R < 35 kpc is a good place
to probe the upper limit to the radial profile in the in-
ner region. We therefore fit models to the data in that
region and also at R > 90 kpc (the data points used
are marked red in Fig. 44). The best-fit exponential
Fig. 45.— The radial surface brightness profile for stars with
−3.0 < [Fe/H] < −0.7 is shown for the minor axis data (black),
and for three sub-samples of the outer halo region: −7◦ < ξ <
−1◦ (in red), −1◦ < ξ < 2◦ (in green), and 2◦ < ξ < 7◦ (in
blue). The similar radial decease indicates that an underlying halo
population is present in all these samples, which are separated by
up to 150 kpc.
model to these minor axis data (black dashed line) has
hR = 31.4 ± 1.0 kpc; while the best fit projected Hern-
quist model (black dot-dashed line) has a scale radius of
35.7 ± 0.1 kpc. We also fit a power-law model, and find
that an exponent of 1.91 ± 0.11 is preferred. Thus we
find again a similar slow decline and a long scale length.
This is a very important, and rather unexpected re-
sult, and therefore deserves to be checked carefully. In
Fig. 45 we have split the “outer halo” sample into three
sub-samples (contained within the regions red: −7◦ <
ξ < −1◦, green: −1◦ < ξ < 2◦ and blue: 2◦ < ξ < 7◦);
the same slow decline with radius is seen in each sub-
sample, and in the minor axis sample shown in black,
indicating that we are not simply detecting the effects of
some localized substructure: approximately 150 kpc sep-
arate the red and black profiles! It is possible that the
signal arises from an incorrect subtraction of the Galactic
contamination. Since the density of stars decreases away
from the Galactic plane, which also happens to be the
direction away from the centre of M31, an insufficient
subtraction of the contaminants could leave a residual
that decreases with R as observed. Furthermore, the
Galactic disk has an exponential profile, which would
naturally explain the observed decline. To examine this
possibility we recalculate the surface brightness profiles
as before, selecting on metallicity, but this time in ad-
dition using a draconian color-magnitude selection. We
limit the data to i0 < 22.5 and retain stars only in the
color interval 0.8 < (g−i)0 < 1.8. An inspection of panel
‘b’ of Fig. 16 reveals that this selection avoids the bulk
of the Galactic disk and halo. The results are shown in
Fig. 46, and reassuringly they are qualitatively and quan-
titatively identical to the previous selection with deeper
data and the full color interval. The predicted behav-
ior of the Galactic foreground contamination (with this
same color-magnitude selection) is also shown in Fig. 46
(turquoise line). The profile of the contamination is
nearly flat in this log-linear representation, so contam-
Fig. 46.— As Fig. 44, but for stars restricted to the small color-
magnitude region 0.8 < (g − i)0 < 1.8 and i0 < 22.5, to ensure a
minimal contamination from the Galactic halo and disk. Since
this selection is for the purpose of verification only, we make no
attempt to calibrate the absolute surface brightness values; hence
the ordinate includes an unknown constant. The exponential fit
to the outer halo (blue dashed line) has hR = 48.8 ± 8.8 kpc,
while the Hernquist fit (blue dot-dashed line) has a scale radius
of 53.6 ± 0.3 kpc. The black histogram is the metal-poor minor
axis selection, also constrained to the narrow color-magnitude re-
gion. The exponential fit to these data (black dashed line) has
hR = 32.5 ± 1.5 kpc, while the Hernquist model has a scale ra-
dius of 53.9 ± 0.1 kpc. The power-law fit to these same data (red
line) has an exponent of 1.85±0.16. For comparison, we also show
the profile of the Galactic foreground as predicted by the Besançon
model (turquoise line). The same color-magnitude selection is used
as for the observed profiles, although we show here the model pre-
diction over the entire MegaCam survey area (not just the “outer
halo” or minor axis regions). The model predicts a decrease in
the foreground contamination with radial distance over the survey
region, but it is essentially flat compared to the observed decrease
in the M31 populations.
Fig. 47.— The expected spread in distance modulus as a function
of projected radius if the underlying halo component falls off as
ρ(r) ∝ r−2.91. The dashed line shows the distance modulus to
M31, while the full lines shows the limit of r = 191 kpc (the virial
radius estimated by Ibata et al. 2004). The dashed and dot-dashed
lines mark the region enclosing 50% and 90% of the stars.
Fig. 48.— Matched filter map (logarithmic representation) to
search for structures around M33 constituted of stars with metal-
licity in the range −3.0 < [Fe/H] < 0.0. A limiting magnitude of
i0 = 23.5 was used. The two red ellipses mark elliptical radii
of s = 0◦.5 and s = 0◦.75 around M33. The pink square at
ξ = 0◦.30, η = −0◦.24 marks the location of the “halo” field of
Mould & Kristian (1986), which is in fact clearly probing the disk
of the galaxy.
ination cannot account for the observed profile. Thus a
slow decline with an exceeding long scale length for the
outer halo population is a robust result of this survey.
This slow decline has important consequences on the
detectability of halo populations. In particular one may
worry about the distance spread in the halo, whether
we are able to detect stars on the far side of M31,
and the corresponding spread in the CMD. Assuming
an ρ(r) ∝ r−2.91 profile, we display in Fig. 47 the ex-
pected spread as a function of projected radius. We see
that even with this extended profile, the distance spread
should be relatively modest, ∼ 0.5 mag.
9. M33
The South-eastern corner of the survey extends out to
the Triangulum galaxy, M33. The motivation for this
part of the study was to attempt to investigate the in-
terface region between the halos of M33 and M31. Four
fields were positioned along the extension of the minor
axis of M31, as shown in Fig. 48, connecting to the
archival data centered on the disk of M33. The map
reveals clearly the very regular outer disk of M33, as
well as the presence of an extended component out to
∼ 3◦, possibly the stellar “halo” of this galaxy. A more
detailed discussion of the structural and stellar popula-
tions properties of M33 based upon a much wider survey
conducted with the INT will be presented in a compan-
ion paper (Ferguson et al. 2007, in prep.). We note
here that a previous claimed detection of the stellar halo
component of this galaxy (Mould & Kristian 1986), was
in reality studying the outer disk (their field is marked
with a pink square in Fig. 48).
We adopted the geometry of the model of
McConnachie et al. (2006) for the disk of M33,
namely a position angle of 23◦ and an inclination of
53◦.8. The outer red dashed ellipse in Fig. 49 shows the
corresponding elliptical radius s = 0◦.75, approximately
Fig. 49.— The radial profile as a function of elliptical coordinate
distance from M33, in 3 color-magnitude selection regions corre-
sponding to locations between Padova isochrones. We truncate
the “metal-rich” profile (which is more heavily affected by Galac-
tic foreground contamination), where the noise begins to dominate.
where the disk appears to truncate in this diagram.
As we have mentioned before, the applicability of the
isochrones to estimate metallicity is only justified in re-
gions composed of old stars, so the “metallicity” profiles
displayed in Fig. 49 must be interpreted with extreme
caution. Here we show the trends as a function of ellipti-
cal coordinate s for three different CMD bins, as shown.
The data interior to s = 0◦.5 is severely affected by crowd-
ing, and we therefore neglect that region. In the region
to 0◦.75 < s < 1◦, the blue selection becomes more pro-
nounced with increasing radius relative to the other two
selections, indicating strong radial variations in the stel-
lar populations. The exponential profile of the inner disk
ends changes abruptly at s ∼ 0◦.9 into an apparently flat
distribution for 1◦ < s < 2◦.5. Fitting the profiles in the
interval 1◦ < s < 2◦.5 with an exponential function gives
exceedingly long scale-lengths, or even rising profiles.
The spatial extent of the MegaCam survey around M33
is very limited, so it is impossible to construct a global
model for the extended outer component. Thus it is not
clear whether the appropriate geometry for calculating
the profiles is spherical or ellipsoidal. If we adopt a spher-
ical coordinate as in Fig. 50, the profile of the extended
component for the selection −3.0 < [Fe/H] < −0.7 seems
more reasonable, as it descends monotonically apart from
a bump at 1◦.6.
Fitting the data between 1◦ < R < 4◦ (but reject-
ing the bin at 1◦.6) yields a scale length of 18 ± 1 kpc
for an exponential model, or alternatively a scale radius
of 55 ± 2 kpc for a projected Hernquist model. These
scale lengths are surprisingly large, reminiscent of the
large values measured above for the outer halo of M31.
Curiously, the central surface brightness of the extrapo-
lated exponential models are rather similar too. In M33
the model has ΣV (0) = 29.7 ± 0.1, while in M31 the
two exponentials fit in Fig 44 bracket this value with
ΣV (0) = 30.6 ± 0.3 and ΣV (0) = 29.0 ± 0.06 (taking
the metallicity selection −3.0 < [Fe/H] < −0.7 for both
objects). We stress here that the detection of a halo
component around M33 gives further confirmation that
Fig. 50.— The radial light profile in M33 as a function of the
radial coordinate r. We display a fitted exponential model with
scale length 18±1 kpc and a projected Hernquist model with scale
radius 55± 2 kpc.
Fig. 51.— Background-subtracted Hess diagrams in four selected
regions near M33. In panel ‘a’, we show the region 0◦.5 < s < 0◦.75,
panel ‘b’ is for 0◦.75 < s < 1◦, panel ‘c’ is for 1◦ < r < 2◦ and
panel ‘d’ is for 2◦ < r < 3◦.
the M31 detection is not due to errors in the foreground
subtraction, since the foreground contamination profile
has the opposite slope as a function of galactic radial
distance in the M33 survey fields compared to the M31
fields.
The bump in the surface brightness profile at 1◦.6 is
(just) visible as a faint arc on the map in Fig. 48, but
we are unsure of the reality of the structure, since it
is a very faint feature and only extends over one field.
Further imaging is required to determine whether this is
a substructure in the halo of M33 or not.
Finally, we show in Fig. 51 the progression in the stel-
lar populations as we move from the outer disk into the
halo component. Of particular interest is the difference
between panels ‘b’ at the disk edge (0◦.75 < s < 1◦) with
panel ‘c’ (1◦ < R < 2◦) in the halo. The “halo” compo-
nent contains a higher proportion of blue stars, compared
to the broader distribution in panel ‘b’.
10. DISCUSSION
10.1. The underlying halo
The analysis presented above in §8 indicates that un-
derneath the many substructures that we have uncovered
in M31 lurks an apparently smooth and extremely ex-
tended halo. A similar structure is also detected in M33.
By “smooth” what we mean here is not necessarily that
the component is perfectly spatially smooth, but instead
that any substructures that may be present are below
detectability with the current survey. The detectability
threshold is a function of radius, but it corresponds to
approximately 1 mag arcsec−2 brighter than the smooth
background over spatial scales >∼ 1 deg
The existence of a stellar halo component which ap-
pears smooth at these surface brightness levels is com-
pletely unexpected given recent numerical models that
implement recipes for star-formation in merging CDM
subhalos (Bullock & Johnston 2005; Abadi et al. 2006).
Those models predict that the light at large radius is
confined to arcs, shells and streams, with essentially no
smoothly-distributed stars beyond ∼ 50 kpc in a Milky-
Way (or M31) analogue. The reason for this is that
dynamical times at large distances from the galaxy are
extremely long, so material has not had anywhere near
enough time to mix. The more recent the accretion, in
general the more spatially confined the stars should be.
Given these considerations, one would expect a smooth
component to be made in the early violent phases of
galaxy formation, and since the disk is a fragile structure
(Toth & Ostriker 1992), the formation of the structure
would have had to have occurred before the formation
of the thin disk. This scenario still poses problems how-
ever, since the proto-Andromeda at z ∼ 2 would have
been much less massive than it is today, so the extreme
distances of these halo stars — most likely beyond the
virial radius of the galaxy at that redshift — are hard to
explain.
Interestingly, the radial profile of this smooth halo
component in M31 is similar to what is deduced for
the Milky Way. As we have reviewed in §1.2, in the
case of the Milky Way, current data probe the halo well
up to r ∼ 20 kpc, we have reasonable constraints up to
r ∼ 50 kpc, but beyond that distance the information is
very scanty indeed. However, at least up to r = 50 kpc,
and given variations from study to study (which are prob-
ably due to halo substructures) the density can be ap-
proximated by ρ(r) ∝ r−3. For instance, the study of
Siegel et al. (2002), which made use of good distance
estimates to halo stars found ρ(r) ∝ r−2.75±0.3. Simi-
larly, analysis of the RRLyrae sample of Vivas & Zinn
(2006) yielded ρ(r) ∝ r−2.7±0.1 or ρ(r) ∝ r−3.1±0.1,
depending on model assumptions of the shape of the
halo. This is completely consistent with the present
Σ(R) ∝ R−1.91±0.11 fit to the minor axis selection in
In modern galaxy formation simulations stars are
formed only within the most massive sub-haloes that
merge to form a galaxy. This is because star-formation
recipes used in the simulations impose a threshold
in gas density below which stars cannot form, bas-
ing this condition on observed correlations between
Hα emission and gas surface density in galaxy disks
(Kennicutt 1989). Furthermore, those satellites that
were not massive enough to accrete sufficient gas be-
fore the epoch of reionization are expected not to
have been able to form stars subsequent to that epoch
(Bullock, Kravtsov & Weinberg 2000). Dynamical fric-
tion acts more strongly upon the most massive subhalos,
making them fall rapidly into the potential well, where
they become disrupted and their contents mixed into the
evolving galaxy. Because of this, stars accreted from sub-
halos are expected to have a more rapidly falling pro-
file than the dark matter, as we have reviewed in §1.5,
with the light profile falling as r−4 or steeper. Neverthe-
less, this prediction does not appear to hold out. If dark
matter is distributed according to the “Universal” NFW
profile (Navarro, Frenk & White 1997), the density pro-
file in the outer regions of the halo will be ρ(r) ∝ r−3,
consistent with what we have measured from the stars.
This suggests that stars in these tenuous outer reaches
of giant galaxies trace the dark matter.
We stress here that the present analysis of M31 is based
on a dataset that is much more spatially extensive than
has been possible for the Milky Way. We have covered
substantially more than a quarter of the halo of M31.
In comparison, even the SDSS studies of Yanny et al.
(2000); Ivezic et al. (2000) or Chen et al. (2001) covered
only 1% of the sky.
Another measure of the halos of these two galaxies that
we may now compare is their total luminosity. Integrat-
ing the lower of the two exponential profiles shown in
Fig. 44 out to 140 kpc, gives a conservative lower limit
to the smooth halo of LV ∼ 2.2 × 10
8L⊙. We estimate
an upper limit by integrating the power-law up to the
virial radius (which we take to be 191 kpc), assuming that
the halo density inside 0.5 kpc is constant; this yields a
value of LV ∼ 1.3× 10
9L⊙. For the Milky Way, we esti-
mate the total luminosity by assuming a Solar Neighbor-
hood V-band luminosity of halo stars of 22300L⊙/ kpc
(Morrison 1993); for a density law ρ(r) ∝ r−3, inte-
gration out to 50 kpc gives LV ∼ 7 × 10
8L⊙ or alter-
natively LV ∼ 1.2 × 10
9L⊙ for ρ(r) ∝ r
−3.5 (follow-
ing Robin et al. 2003 we also assume that the density of
the halo is constant in the inner 0.5 kpc). These esti-
mates both for M31 and the Milky Way are very crude,
but taken at face value they indicate that the stellar
halo of M31 is very similar in total luminosity to that
of the Milky Way. Thus it appears that previous esti-
mates (e.g. Reitzel, Guhathakurta & Gould 1998) who
reported that the halo in M31 is ∼ 10 times denser than
that of the Milky Way apply only to the inner regions
of the galaxy, where contamination from the large bulge,
extended disk and intervening substructures are clearly
a concern.
As reviewed above, Chapman et al. (2006) were able
to detect the true inner halo of M31 by observing mostly
major axis fields where halo stars have a very different
kinematic signature to other components. At radii be-
tween 10 and 70 kpc, the halo component was found to
have a mean metallicity of [Fe/H ∼ −1.4. This is con-
sistent with the photometric estimate derived for the
outer halo component in Fig. 43 over the radial range
75 < R < 140 kpc, and suggests that the halo has a
small or negligible metallicity gradient. This result pro-
Fig. 52.— Spectroscopically-observed fields. Kalirai et al.
(2006b) fields are shown in red, Chapman et al. (2006) fields in
green. Many of these pointing were chosen without knowledge of
the underlying populations, so only now is it possible to properly
interpret the spectroscopic results.
vides further support for the case of a smooth monolithic
halo formed in a single merging event.
10.2. Comparison to Kalirai et al. (2006b)
Our discovery of a smooth very extended halo
component covering the entire southern quadrant of
Andromeda was anticipated by the kinematic study
of Kalirai et al. (2006b). These authors used the
Keck/DEIMOS spectrograph to survey a number of fields
in this region of the sky, targeting known dwarf galax-
ies as well as “empty” halo fields. The position of the
fields presented in Kalirai et al. (2006b) are shown with
red dots in Fig. 52, green dots mark the positions of
fields observed with this instrument by our own group
(Ibata et al. 2004, 2005; Chapman et al. 2006).
The Kalirai et al. (2006b) fields marked ‘d2’ and ‘d3’
being located on the satellites And II and III, are not of
relevance to the current discussion. But for many of the
remaining of their fields our present panoramic survey is
invaluable, as it allows one to identify the stellar popu-
lations that study actually targeted. In particular, their
fields “m6” were placed on the edge of stream ‘B’, while
their fields ‘a13’ and ‘b15’ lie on the extended cocoon of
the Giant Stream. Likewise, in Chapman et al. (2006)
we serendipitously targeted streams ‘C’ (fields F25 and
F26) and ‘D’ (field F7).
Thus we see that only fields ‘m8’ and ‘a19’ were tar-
geted in regions where we can be sure that no substruc-
ture was present, while field ‘m11’ lies outside of the cur-
rent survey region. In these fields, Kalirai et al. (2006b)
report 1 probable M31 halo star in ‘m8’, 4 stars in ‘a19’,
and 3 stars in ‘m11’.
Are these counts consistent with our results? We nor-
malize with respect to the Kalirai et al. (2006b) field ‘a0’
at 30 kpc, where we deduce ΣV ∼ 30mag arcsec
−2. In
that field 67 halo stars were detected in observations over
3 spectroscopic masks (i.e. 3 subfields were observed).
Whereas in their field ‘m11’ at 165 kpc, where a mild
extrapolation from our survey region gives ΣV ∼ 34 –
35mag arcsec−2, 3 halo stars were detected using 4 spec-
troscopic masks. We therefore expect 40 to 100 times
lower stellar density in ‘m11’ compared to ‘a0’, that is,
we expect 0-2 stars to be detected in the 4 masks ob-
served in field ‘m11’ (taking the best-case scenario that
all available halo stars were observed and correctly clas-
sified). This is then consistent with the sample of 3 halo
stars that were reported by Kalirai et al. (2006b) in field
‘m11’. We note however, that their field lies ∼ 4◦ from
M33, where we have found that the halos of M31 andM33
overlap, and are approximately of equal surface bright-
ness. Though it is dangerous to draw conclusions from
such a minuscule sample, one out of the 3 halo stars in
m11 has a velocity of −150 km s−1, and is highly unlikely
to belong to M31, but could be perfectly consistent with
being a member of the halo of M33. Likewise, in field
‘m8’ we expect 2.5 stars, while in field ‘a19’ we expect
2.2 stars, consistent with the number of stars detected
spectroscopically.
In summary, despite the very small number of stars
in their sample, and despite the probable contamination
from M33 in their most distant (and interesting) field,
we take the results of Kalirai et al. (2006b) as confirma-
tion that a smooth extended stellar halo is present in
M31 out to at least 150 kpc. We note in passing that
Kalirai et al. (2006b) estimate the photometric metal-
licity of their outer halo sample (R > 60 kpc) to be
〈[Fe/H]〉 = −1.26± 0.1. Although this is apparently con-
sistent with the MDF shown in Fig. 43, their sample
is almost entirely dominated by “contamination” from
substructure, which as we have shown above, in predom-
inantly metal-poor.
10.3. Shape of the smooth stellar halo
As reviewed in §1.2, most studies of the halo of
the Milky Way find that this component is oblate in-
terior to r ∼ 20 kpc, with flattening b/a ∼ 0.6.
Studies of the halo component in external galax-
ies, be it from a medianed stack of edge-on spirals
(Zibetti, White & Brinkman 2004), or from an individ-
ual edge-on galaxy (Zibetti & Ferguson 2004) find an
identical measurement of b/a ∼ 0.6, within roughly the
same radius. The data we have presented on M31 do not
allow us to make any statement about the halo flatten-
ing in the same volume, and it is very hard to imagine
that such a measurement will be possible in the fore-
seeable future given the difficulty of disentangling bulge,
disk and halo in the inner regions of M31. Previous mea-
surements of the flattening of M31 in this region (e.g.
Pritchet & van den Bergh 1994: a/b = 0.55 ± 0.05 at
10 kpc), give an indication of the shape of the total light
distribution, but do not constrain the shape of the halo.
However, we believe we have been able to identify the
main substructures beyond a distance of R = 6◦.5, giv-
ing a relatively uncontaminated measurement of the den-
sity profile beyond that radius. We find, however, that
the minor axis profile is higher than the profile from the
broad region we have termed “outer halo” and which lies
closer to the major axis. This allows us to firmly reject
an oblate halo with b/a ∼ 0.6 at these distances, and
suggests instead the possibility that the halo is prolate,
with c/a >∼ 1.3. Further data in other quadrants is re-
quired to assess the reliability of this estimate. However,
in any case, the shape of the outer halo of M31 is mani-
festly different to that of the inner halos of other galaxies
observed to date.
10.4. Substructures
Every step we have taken in obtaining a wider view of
Andromeda has awarded us with new discoveries in the
form of previously unknown substructure. The large area
surveyed with MegaCam in the present contribution has
continued this trend showing new dwarf galaxies, and
several diffuse stellar populations in the form of arcs,
streams or shell segments. These structures testify that
accretion and therefore galaxy buildup is still continuing
to the present time.
Of the substructures that are present in the survey
region the Giant Stream is by far the most significant.
The data presented in §6.2 shows that the Giant Stream
is a long cigar-shaped structure made up of metal rich,
or young, stars with a metal-poor envelope or cocoon,
possibly ∼ 3◦ wide. This lack of homogeneity of the
stellar populations in the Giant Stream indicates that
so far the system has not been fully mixed during the
course of the tidal disruption process, so it is likely a
dynamically very young stream. The requirement that
the center and the cocoon remain spatially distinct will
likely provide very useful additional constraints for the
modeling of the system.
We count up the Giant Stream stars to i0 = 23.5, and
as before use And III to normalize the total luminosity.
(We caution the reader again that using And III as a ref-
erence introduces a large uncertainty into the luminosity
estimate). Integrating within the red polygon shown in
Fig 23 (and removing a 0◦.5 circle around both And I and
And III), and subtracting off the expected foreground
from the Besançon model, we find LV ∼ 1.5 × 10
(MV ∼ −15.6) over this region. This corresponds to ap-
proximately a tenth of the luminosity of M33, and given
that the MegaCam region only probes a fraction of the
total stream, it is plausible that the progenitor of the
Giant Stream was initially a galaxy of similar luminos-
ity to M33. The width of the stream appears consistent
with this possibility, though of course it must have been
broadened in the merging process. The core and cocoon
dichotomy support further the analogy with a dwarf disk
galaxy like M33. Indeed, the metal-poor cocoon may be
the remnant of a vestigial halo. It will be interesting to
conduct new simulations in which a small disk galaxy is
accreted by M31.
This luminosity of the Giant Stream, measured from
the southern quadrant, is between a factor of 1 and a
factor of 10 less luminous than that of the total smooth
halo component estimated above. This indicates that the
Giant Stream is a very significant, probably the largest,
merging event into the halo that has ever taken place in
Andromeda. If merging dwarf galaxies are responsible
for contributing globular clusters into halos, one should
therefore expect to find a commensurate number of halo
globular clusters with kinematics compatible the Giant
Stream and its extension.
In Fig. 53 we present an RGB image of the
survey region, in which the red, green and blue
channels contain, respectively, the matched filter
maps for metal-rich (−0.7 < [Fe/H] < 0.0), inter-
mediate (−1.7 < [Fe/H] < −0.7) and metal-poor
(−3.0 < [Fe/H] < −1.7) stars. This image shows the
striking differences in stellar populations of the halo
Fig. 53.— RGB color composite map, in which red shows stars with −0.7 < [Fe/H] < 0.0, green shows −1.7 < [Fe/H] < −0.7 and blue
shows −3.0 < [Fe/H] < −1.7. To render the inner region within the 4◦ ellipse easier to interpret, we have removed the MegaCam data from
that region. Dwarf satellite galaxies, being essentially the only structures with a strong metal-poor population appear blue on this map.
The differences in stellar populations between the Giant Stream and the several minor axis streams can be seen as striking differences in
color. At the center of the galaxy we have added to scale an image of the central regions of M31 constructed from Palomar sky survey
plates.
substructures we have identified in this survey. Even
though the Giant Stream remains the most significant
accretion, many more smaller systems are being ac-
creted. M31 is evidently still leading a colorful life
assimilating its small neighbors.
We see also that halo formation is evidently a stochas-
tic process. The halo profile and detailed properties of
the halo can therefore be expected to differ from galaxy
to galaxy depending on the amount of substructure and
merging debris that is present. This makes it all the more
surprising that the profile of the smooth halo discussed
above resembles well that of the Milky Way, suggesting
that the reason for this is an underlying similarity in the
mass distributions, which is independent of the detailed
assembly history.
10.5. The inner minor axis
The several streams detected on the minor axis from
∼ 6◦.5 all the way into the edge of the disk are partic-
ularly important in that they shed light on the numer-
ous previous studies (reviewed in §1) made in this region
because it has been considered “clean halo” for many
years. Indeed, it is not obvious that there exists a region
of “clean halo” in the inner galaxy. This is demonstrated
in Fig. 54, which shows a RGB color composite similar
to Fig. 53, but using only INT data and with a smaller
pixel scale. The variations in stellar populations are ap-
parent as color differences, and one can readily see that
the G1 clump and NE structure have a different distribu-
tion of stellar populations to the Giant Stream and the
two “shelves” to the East and West (the figure caption
Fig. 54.— RGB color composite map, as Fig. 53, but for the
INT data within the 4◦ ellipse (the blue area around the center of
the image is an artifact of crowding in certain central fields). We
again see the presence of many streams and structures that have
been discussed in earlier articles by our group. This RGB image,
however, shows vividly the differences and similarities in the stellar
populations of these structures. In particular, one notices that the
color of the Giant Stream is similar to that of the two “shelves” (at
ξ ∼ 2◦, η ∼ 0◦.5 and ξ ∼ −1◦.5, η ∼ 0◦.5) that appear on this map
(see Ferguson et al. 2002). Other structures, such as the diffuse
NE structure (ξ ∼ 1◦.5, η ∼ 2◦.5) and the G1 clump (ξ ∼ −1◦.5,
η ∼ −1◦.7) possess a different distribution of stellar populations.
This diagram also allows one to understand the nature of popula-
tions seen at various distances along the minor axis. It is clear that
at R ∼ 10 kpc on the minor axis the dominant stellar population
is that of the extended messy ellipsoidal structure that we have
shown previous is a giant rotating component (Ibata et al. 2005).
Beyond that radius out to R ∼ 20 kpc we discern a stellar popula-
tion with the same color as the Giant Stream. The contours show
the approximate location of ΣV = 27, 28 and 29 mag/arcsec
2. The
locations of the ACS fields of Brown et al. (2003, 2006a,b, 2007)
are indicated with purple squares (the ACS field sizes have been
exaggerated for display purposes).
states their location).
The contours in Fig. 54 show the iso-luminosity
surfaces derived from star-counts for stars with
−3.0 < [Fe/H] < 0.0, with contour separation of
1 mag/arcsec2 (the levels correspond approximately to
ΣV = 27, 28 and 29 mag/arcsec
2). It is immediately
apparent from this diagram that at a projected radius
from R ∼ 10 kpc to R ∼ 20 kpc on the minor axis,
the dominant component is a large irregular ellip-
soidal structure whose major axis size extends out to
R ∼ 40 kpc. We have shown previously from kinematics
in many fields around the galaxy that this is an extended
rotating disk-like component (Ibata et al. 2005). Thus,
although the surface brightness profile on the minor axis
follows approximately an R1/4 law out to 1◦.4, or 19 kpc
(Pritchet & van den Bergh 1994; Irwin et al. 2005), it
is unlikely that the bulge itself extends out to those
radii. Indeed the bulge in near infrared wavelengths is
a relatively compact structure that dominates out to
Fig. 55.— The black points in both panels reproduce the V-band
minor axis surface brightness profile from Irwin et al. (2005). The
radial interval 8 < R < 18 kpc (marked with red points in panel ‘a’)
is clearly almost straight in this log-linear representation. Fitting
the data in this region with an exponential function (dashed line),
yields a scale length of 3.22 ± 0.02 kpc (where the uncertainty is
the formal error on the fit). We also indicate the regions where the
various components are dominant. Recent analysis of the 2MASS
6X imaging data of M31 shows a high-contrast bulge that domi-
nates the near infrared light out to ∼ 2.6 kpc on the major axis
(Beaton et al. 2007). The bumps in the disk-dominated region (at
projected radii between 2 kpc <∼ R
∼ 6 kpc on the minor axis) are
due to spiral arms and the star-forming ring. The dashed line in
panel ‘b’ shows a de Vaucouleurs model fit using an effective ra-
dius of Re = 0
◦.1 as found by Pritchet & van den Bergh (1994),
equivalent to 1.4 kpc (Irwin et al. 2005), which overestimates the
starcounts between 1◦ < R < 1◦.5.
∼ 2.6 kpc on the major axis (Beaton et al. 2007). It is
therefore pertinent in the current context to review the
evidence for the R1/4 law profile. In Fig. 55 we repro-
duce the V-band minor axis profile from Irwin et al.
(2005); in the interval 8 < R < 18 kpc the light profile is
actually remarkably similar to an exponential function
with a scale length of 3.22 kpc. We stress that this
exponential behavior is not confined to the minor axis
data alone: it is present with the same density profile
(and normalization) at all azimuth angles (see Fig. 3
of Ibata et al. 2005). In contrast, the de Vaucouleurs
profile of Pritchet & van den Bergh (1994), shown in
panel ‘b’ of Fig. 55, over-predicts the counts in the
radial range 1◦ < R < 1◦.5.
The “extended disk” component was found to have an
intrinsic scale length of 6.6± 0.4 kpc (Ibata et al. 2005),
and to follow an exponential profile out to ∼ 40 kpc (after
which the profile flattens out). For the minor axis scale
length of 3.22 kpc to be consistent with that intrinsic
scale length, the inclination of the outer disk would have
to be 60◦.8, very close to the value of 64◦.7 estimated
by Ibata et al. (2005). Furthermore, the intrinsic break
at 40 kpc (deprojected) would correspond to 1◦.4 on the
minor axis, exactly where it is seen.
If one wishes to adhere to the previously-held assump-
tion that the minor axis is dominated out to R ∼ 20 kpc
by an immense R1/4-law “bulge” or “spheroid”, it re-
quires a considerable stretch of credibility. It means that
this “spheroid” has to be substantially flattened to be
consistent with the contours of Fig. 54; the “spheroid”
must have an exponential-like profile between (depro-
jected) radii of 15 <∼ R
∼ 40 kpc at all azimuth angles;
and it must be rotationally-supported, but with a ro-
tation rate almost as fast as that of the H I disk. We
therefore judge that the “extended disk” picture is a
far more likely and less contrived model. This confirms
the visual impression of Fig 54: in the distance range
10 <∼ R
∼ 15 kpc the minor axis profile is dominated by
a disk-like population, with only minor contribution from
the bulge or spheroid.
Since we now understand the kinematic and chemical
behavior of the “extended disk” from observations close
to the major axis (where stars of different components
may be more easily distinguished by their differences in
kinematics), we can use these insights to interpret the
radial variation in the properties of the stellar popula-
tions on the minor axis. Interior to ∼ 0◦.2 on the minor
axis the dominant population will clearly be the bulge;
further out between 0◦.2 < R < 0◦.4, the normal disk
contributes in a non-negligible fashion to the profile, as
noted by Irwin et al. (2005); then from 0◦.5 < R < 1◦.3
the extended disk component becomes dominant; finally
beyond 1◦.5 the underlying smooth halo becomes impor-
tant, though spatially confined streams dominate at var-
ious locations.
Consequently, one should also expect strong radial
variations in metallicity and kinematics. The kinematics
on the minor axis in particular will be complex, and dif-
ficult to disentangle, since all populations have the same
mean velocity and their velocity distributions overlap.
Going out from the center one should therefore expect
to find the bulge, with high metallicity and high velocity
dispersion; then in the bulge plus disk region, a wide
metallicity range, but a narrower velocity dispersion;
then with the addition of the extended disk, the mean
metallicity should decrease towards [Fe/H] ∼ −0.9± 0.2,
and the velocity distribution should contain a signifi-
cant fraction of stars in a peak with dispersion in the
range 20 km s−1 to 50 km s−1 (Ibata et al. 2005); then the
halo component should appear with [Fe/H] ∼ −1.4 and
with a large velocity dispersion of σv ∼ 140 km s
−1 at
R = 20 kpc, decreasing outwards (Chapman et al. 2006).
In addition to these smooth structures one will find the
multiple streams detected (and not yet detected!) in this
area, which as we have shown can have quite different
stellar populations, but which are likely to be dominated
by the metal-rich Giant Stream. The velocity distribu-
tion of these streams in a small field will in general be
a narrow velocity spike of dispersion ∼ 10 km s−1. How-
ever, we stress that the minor axis is a very complex
region interior to ∼ 30 kpc, with a complex mix of many
stellar populations, each component overlapping consid-
erably with the others in terms of radial velocity, metal-
licity, spatial location, color-magnitude structure, etc.
This finding that the minor axis region between
8 <∼ R
∼ 20 kpc is dominated by the extended disk, and
not bulge, halo or spheroid as has been assumed in nu-
merous earlier articles, goes a long way towards clarifying
the diverse and confusing results that have been deduced
from observations in this region. In particular, it helps
interpret the findings of Brown et al. (2003, 2006a,b,
2007). These authors obtained ultra-deep HST/ACS
photometry in two minor axis fields, a Giant stream
field, and a field at the edge of the NE disk, in order to
determine ages of the underlying populations via main-
sequence turnoff fitting (field locations are shown with
purple squares in Fig. 54). Their two minor axis fields lie
at projected radii of R = 11 and 21 kpc. Due to the rea-
sons detailed above, their “spheroid” field at R = 11 kpc
probes a location which is dominated by the extended
disk population. From their photometry in this region
they deduce a best fitting stellar populations model that
has 〈[Fe/H]〉 = −0.6 and 〈age〉 = 9.7Gyr. Brown et al.
(2006b) dismiss the possibility that the field is related
to the extended disk partly on the grounds that the
field lies at a de-projected distance of 51 kpc, yet any
small warping of the plane of the galaxy, such as we de-
duced in (Ibata et al. 2004), invalidates this argument.
The remaining argument is the velocity dispersion mea-
surement of ∼ 80 km s−1, which appears high for the ex-
tended disk (σv
∼ 50 km s
−1), until one considers the mix
of components that must be present at this location.
Further out on the minor axis at R ∼ 20 kpc one can
discern a diffuse component that appears of the same
red hue as the Giant Stream with this color representa-
tion. This is clearly a metal-rich region, and possibly re-
lated to the extension of the “NE shelf” of Ferguson et al.
(2002), itself the likely continuation of the orbit of the
Giant Stream (Ibata et al. 2004). Indeed, Ferguson et al.
(2005) showed that the Giant Stream and NE shelf are
connected on the basis of near identical stellar popu-
lations to 3 magnitudes below the horizontal branch.
With hindsight it is therefore not surprising that the
R = 21 kpc field of Brown et al. (2006b) contains in-
termediate age stars that have a distribution of stellar
populations essentially identical to that of their Giant
Stream field (which is itself on the outskirts of the “ex-
tended disk” region). Fig. 53 also suggests that their NE
disk field is also a complex mixture of disk, extended disk,
and possibly metal-rich debris from the Giant Stream.
We note also in passing that the geometry of the
minor axis populations has important consequences for
microlensing studies in M31 (e.g., Calchi Novati et al.
2005). With most of the stellar populations previously
assumed to lie in the spheroid, being confined primarily
in a disk, we predict a much lower self-lensing rate.
10.6. Kinematics of substructures
The above discussion also clarifies some previous
claims for the existence of kinematic substructure around
M31. In a field at R = 19 kpc, Reitzel & Guhathakurta
(2002) find four metal-rich stars in their sample with
similar radial velocity of ≈ −340 km s−1, which they in-
terpreted as evidence for accretion debris. This position
lies within the diffuse region that has stellar populations
similar to Giant Stream (Fig. 54), so the kinematic sub-
structure in the Reitzel & Guhathakurta (2002) sample
is likely related to that structure.
Further kinematic substructure in this region was
found by Kalirai et al. (2006a) who in studying the
kinematics of the Giant Stream find a secondary kine-
matic peak R = 20 kpc with v = −417 km s−1 and
σv ≈ 16 km s
−1. The location of this field (H13s) lies at
ξ = 0◦.29,η = −1◦.53, clearly within the ellipsoidal con-
tours in Fig. 54, and furthermore the expected mean ve-
locity of the “extended disk” model of Ibata et al. (2005)
predicts v = −381 ± 22 km s−1 in this field. The veloc-
ity dispersion of the cold component is also similar to
what has been found in certain regions of the extended
disk (e.g., 17 km s−1 in field F3 of Ibata et al. 2005). We
speculate therefore that the cold kinematic structure in
field H13s is clumpy structure of the edge of the “ex-
tended disk”.
Most recently Gilbert et al. (2007) have presented a
kinematic survey of several fields along the minor axis
of M31. They detect kinematic substructure in three
fields, with dispersions of 55.5+15.6−12.7 km s
−1 (R = 12 kpc)
51.2+24.4−15.0 km s
−1 (R = 13 kpc) and 10.6+6.9−5.0 km s
−1 (R =
18 kpc). It is probable that the two structures of velocity
dispersion ∼ 50 km s−1 are also related to the “extended
disk” component. The large de-projected distances they
deduce along the minor axis (51 – 83 kpc) are acutely
dependent on the assumption of constant inclination of
the disk, which as we have shown is not supported by the
data (Ibata et al. 2005). In particular, the R = 12 and
13 kpc fields of Gilbert et al. (2007) lie in the distance
regime where the extended disk is dominant in Fig. 55.
The cold kinematic component observed in their R =
18 kpc field is likely related to the Giant Stream for the
same reason as is the cold kinematic structure in the
Reitzel & Guhathakurta (2002) sample.
11. CONCLUSIONS
This article has presented a deep panoramic view of the
Andromeda galaxy and part of the Triangulum galaxy.
Though it is not the deepest external galaxy survey ever
undertaken, nor the most extended, we have for the first
time covered a substantial fraction of a galaxy out to a
substantial fraction of the virial radius to sufficient depth
to detect several magnitudes of the red giant branch and
with sufficient photometric accuracy to estimate stellar
metallicity. To our knowledge this is the first deep wide-
field view of the outermost regions of galaxies.
The new CFHT data presented here are combined with
an earlier survey of the inner regions of M31 (s <∼ 55 kpc)
taken with the INT (Ibata et al. 2001b; Ferguson et al.
2002; Irwin et al. 2005). We summarize below the main
findings from these surveys.
• A huge amount of confusion in the literature has
arisen from assuming that the minor axis region
between projected radii of 0◦.5 < R < 1◦.3 (7 kpc <
R < 18 kpc) is representative of the spheroid. We
have shown here that it is not. Instead it is likely
to be a complex mix of stellar populations, dom-
inated over much of this radial range by the “ex-
tended disk”. Many of the previous claims that
the spheroid or stellar halo of M31 is very differ-
ent to that of the Milky Way were based upon a
comparison of the properties of genuine Milky Way
halo stars to those of stars in M31 in quite different
components.
• Beyond the inner (∼ 20 kpc) disk, Andromeda con-
tains a multitude of streams, arcs, shells and other
irregular structures. Some of these structures ap-
pear to be related (they have a similar mix of stellar
populations) others are manifestly due to separate
accretion events.
• The largest of these structures, the Giant Stream,
is very luminous, possessing LV ∼ 1.5×10
8L⊙ over
the region surveyed with MegaCam. This body
dominates the luminosity budget of the inner halo,
and once it becomes fully mixed, may double the
luminosity of the smooth underlying halo. This
ongoing accretion event must be among the most
significant the halo has suffered since its initial for-
mation.
• Ignoring regions with obvious substructure, we find
that the remaining area of the survey exhibits a
smooth metal-poor stellar halo component. This
structure need not be perfectly spatially smooth,
but the intrinsic inhomogeneities are below the sen-
sitivity of this study. The smooth halo is vast, ex-
tending out to the radial limit of the survey, at
150 kpc. The profile of this component can be mod-
eled with a Hernquist profile as suggested by sim-
ulations, but the resulting scale radius of ∼ 55 kpc
is almost a factor of 4 larger than modern halo for-
mation simulations predict. A power-law profile
with Σ(R) ∝ R−1.91±0.11 (i.e. ρ(r) ∝ r−2.91±0.11)
can also be fit to the data. Simulations predicted
a sharp decline in the power law exponent beyond
the central regions of the galaxy to ρ(r) ∝ r−4 or
ρ(r) ∝ r−5. This is not observed. Instead, and
unexpectedly, the stellar profile mirrors closely the
expected profile of the dark matter.
• Since dynamically young accretion events give rise
to arcs and streams, and because dynamical times
are very long in the outer reaches of the halo, the
smoothness of the component over huge areas of
the outskirts of the galaxy suggests that the com-
ponent is very old. It therefore seems plausible that
the structure was formed in a cataclysmic merging
event early in the history of the galaxy, probably
before the formation of the fragile disk.
• The outer halo of M31 (R >∼ 80 kpc) is not oblate.
On the contrary, the stellar distribution appears to
be slightly prolate with c/a >∼ 1.3, though we judge
that a reliable measurement of this parameter will
require further data in other quadrants.
• Both the density profile of the smooth halo in M31
and its total luminosity (∼ 109 L⊙) are very simi-
lar to the Milky Way. Their metallicity and kine-
matic properties also resemble each other closely
(Chapman et al. 2006; Kalirai et al. 2006a). This
is somewht surprising if halo formation is a stochas-
tic process as suggested by simulations (see, e.g.
the discussion in Renda et al. 2005).
• Lumping all stellar populations together, we de-
tect a stellar population gradient in the survey such
that the more metal-rich populations are more cen-
trally concentrated, consistent with the predictions
of Bullock & Johnston (2005). However, this is al-
most entirely due to the presence of the metal-rich
Giant Stream “contaminating” the inner halo.
• An extended slowly-decreasing halo is also detected
around M33. Fitting this distribution with a Hern-
quist model gives a scale radius of ∼ 55 kpc, es-
sentially identical to that of M31, though we cau-
tion that the poor azimuthal coverage of the survey
around M33 makes this result sensitive to uniden-
tified substructures and to assumptions about the
geometry of the halo.
• The stellar halos of M31 and M33 touch in projec-
tion, and are probably passing through each other.
The kinematics of stars in this overlap region will
be fascinating to analyze, though large samples will
probably be needed to disentangle the structures.
• Two new dwarf satellite galaxies of M31, And XV
and And XVI, are presented, which together
with those reported in a previous contribution
(Martin et al. 2006), brings the number of new
satellites detected in the MegaCam survey region
up to five. Follow-up studies are currently under-
way to understand the nature of these objects and
those of lower S/N satellite candidates found in the
survey.
Many questions remain open. What is the radial de-
pendence of the metallicity and stellar populations in the
smooth component? Is there a discontinuity in proper-
ties between the inner halo and the outer halo similar
to the simulations of Abadi et al. (2003, 2006), reflecting
native and immigrant stars?
It will be very interesting to extend the survey out to
the virial radius of the Galaxy and verify whether the
correlation between the observed stellar profile and the
expected dark matter surface density continues to that
radius. Further photometric coverage to the East of the
minor axis will also be helpful to study fully the mor-
phology and extent of the stream-like structures detected
from R = 30 to ∼ 120 kpc and to determine whether
these objects are indeed streams, and so make plausible
judgements about their origin and evolution and com-
pare them to theoretical predictions of the formation of
the outer halo.
This panorama of the outer fringes of Andromeda and
Triangulum has shown that halos are truly misnamed:
they are in reality dark galactic graveyards, full of the
ghosts of galaxies dismembered in violent clashes long
ago. Other, even more ancient remnants, have lost
all memory of their original form, and in filling these
haunted halos with the faintest shadow of their former
brilliance, they follow faithfully the dark forces to which
they first succumbed. The true nature of this most som-
bre of galactic recesses is finally beginning to be revealed.
ACKNOWLEDGMENTS
This study would not have been possible without the
excellent support of staff at the CFHT telescope, and the
careful and meticulous observations performed in queue
mode. RI wishes to thank Annie Robin for allowing
us privileged access to the Besançon model via UNIX
scripts which greatly facilitated the construction of the
foreground model, and also many thanks to Michele Bel-
lazzini for helpful comments on this work. AMNF is sup-
ported by a Marie Curie Excellence Grant from the Eu-
ropean Commission under contract MCEXT-CT-2005-
025869.
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