The Case for the Dual Halo of the Milky Way

Abstract

Carollo et al. have recently resolved the stellar population of the Milky Way halo into at least two distinct components, an inner halo and an outer halo. This result has been criticized by Schönrich et al., who claim that the retrograde signature associated with the outer halo is due to the adoption of faulty distances. We refute this claim, and demonstrate that the Schönrich et al. photometric distances are themselves flawed because they adopted an incorrect main-sequence absolute magnitude relationship from the work of Ivezić et al. When compared to the recommended relation from Ivezić et al., which is tied to a Milky Way globular cluster distance scale and accounts for age and metallicity effects, the relation adopted by Schönrich et al. yields up to 18% shorter distances for stars near the main-sequence turnoff (TO). Use of the correct relationship yields agreement between the distances assigned by Carollo et al. and Ivezić et al. for low-metallicity dwarfs to within 6%-10%. Schönrich et al. also point out that intermediate-gravity stars (3.5 ≤log g < 4.0) with colors redder than the TO region are likely misclassified, with which we concur. We implement a new procedure to reassign luminosity classifications for the TO stars that require it. New derivations of the rotational behavior demonstrate that the retrograde signature and high velocity dispersion of the outer-halo population remain. We summarize additional lines of evidence for a dual halo, including a test of the retrograde signature based on proper motions alone, and conclude that the preponderance of evidence strongly rejects the single-halo interpretation.

Full text

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The Case for the Dual Halo of the Milky Way
Timothy C. Beers1, Daniela Carollo2,ˇZeljko Ivezi´ c3, Deokkeun An4, Masashi Chiba5, John E. Norris2, Ken
C. Freeman2, Young Sun Lee1, Jeffrey A. Munn6, Paola Re Fiorentin7, Thirupathi Sivarani8, Ronald
Wilhelm9, Brian Yanny10, Donald G. York11
ABSTRACT
Based on an analysis of the local kinematics of SDSS DR7 calibration stars, Carollo et al.
have resolved the stellar population of the Milky Way halo into at least two components. This
result has recently been criticized by Sch¨ onrich et al., who claim that the retrograde signature
associated with the outer halo is due to the adoption of faulty distances. We refute this claim,
and demonstrate that the Sch¨ onrich et al. photometric distances are themselves flawed because
they adopted an incorrect main-sequence absolute magnitude relationship from the work of Ivezi´ c
et al.. When compared to the recommended relation from Ivezi´ c et al., which is tied to a Milky
Way globular cluster distance scale and accounts for age and metallicity effects, the incorrect
relation adopted by Sch¨ onrich et al. yields, on average, 18% shorter distances (independent of
metallicity) for stars near the main-sequence turnoff (TO). When the correct relationship is
used, the distances assigned by Carollo et al. and Ivezi´ c et al. for low-metallicity dwarfs agree
to within 6-10%, depending on the color range considered. We have also compared the Carollo
et al. distances with the distances derived from the calibrated isochrones of An et al., and find
a similar level of agreement for low-metallicity dwarfs. Sch¨ onrich et al. also point out that stars
of intermediate gravity (3.5 ≤ logg < 4.0, based on spectroscopic determinations) are likely
misclassified, at least for colors significantly redder than the TO region, with which we concur.
We implement a new procedure to reassign luminosity classifications for the TO stars that require
it. New derivations of the rotational behavior for the Carollo et al. stars that are most likely
associated with the outer halo demonstrate that, when either a sample of exclusively dwarf
stars or the full sample of dwarf, TO, and subgiant/giant stars is used, the retrograde signature
and high velocity dispersion of the outer-halo population remains, with values similar to those
previously derived. An additional test of the reality of the retrograde signature is provided,
1Department of Physics & Astronomy and JINA (Joint Institute for Nuclear Astrophysics), Michigan State University, East
Lansing, MI 48824, USA; beers@pa.msu.edu; lee@pa.msu.edu
2Research School of Astronomy & Astrophysics, Australian National University, Mount Stromlo Observatory, Cotter Road,
Weston, ACT, 2611, Australia; carollo@mso.anu.edu.au, jen@mso.anu.edu.au; kcf@mso.anu.edu.au
3Department of Astronomy, University of Washington, Box 351580, Seattle, WA 98195, USA; ivezic@astro.washington.edu
4Department of Science Education, Ewha Womans University, Seoul 120-750, Republic of Korea; deokkeun@ewha.ac.kr
5Astronomical Institute, Tohoku University, Sendai 980-8578, Japan; chiba@astr.tohoku.ac.jp
6U.S. Naval Observatory, Flagstaff Station, 10391 W. Naval Observatory Road, Flagstaff, AZ 86001, USA; jam@nofs.navy.mil
7INAF-Osservatorio Astronomico di Torino, via Osservatorio 20, 10025 Pino Torinese, Italy; refiorentin@oato.inaf.it
8Indian Institute of Astrophysics, II Block, Koramangala, Bangalore 560 034, India; sivarani@iiap.res.in
9Physics and Astronomy Department, University of Kentucky, Lexington, KY 40506; rjwi222@uky.edu
10Fermi National Accelerator Laboratory, Batavia, IL 60510, USA; yanny@fnal.gov
11Department of Astronomy and Astrophysics, University of Chicago, Chicago, IL 60637, USA; don@oddjob.uchicago.edu
arXiv:1104.2513v1 [astro-ph.GA] 13 Apr 2011

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based exclusively on the observed proper motions of low-metallicity stars. Further evidence for
a complex halo comes from inspection of the metallicity distribution function of the Carollo et
al. sample as a function of distance from the Galactic plane. We summarize additional lines of
evidence for a dual halo, based on different stellar samples from the SDSS and other surveys. We
conclude that the overwhelming body of evidence rejects the single-halo interpretation beyond
reasonable doubt.
Subject headings: Galaxy: Evolution, Galaxy: Formation, Galaxy: Halo, Galaxy: Kinematics,
Galaxy: Structure, Stars: Surveys
1. Introduction
The nature of the stellar halo of the Milky Way has been debated for many decades. Among the
questions that have been asked: Is the halo a monolithic structure, well-described by a simple Gaussian
velocity ellipsoid? If so, is it in zero net rotation, and does that rotational character apply to all of its
constituent stars? Do the stars in the halo comprise a single stellar population, with similar ages and drawn
from a common metallicity distribution function (MDF)? Can the spatial distribution of the halo stars be
adequately described by a single density law (power-law or otherwise)? Due to the difficulty of teasing out
the properties of such a low density component (as compared, e.g., to the bulge and disk systems) the basic
data required to address these and other questions has only recently begun to arrive. Not surprisingly,
multiple interpretations have emerged.
Massive new datasets from, e.g., SkyMapper (Keller et al. 2007), Gaia (Perryman et al. 2001), and
eventually, LSST (Ivezi´ c et al. 2008a), will provide definitive answers to the above questions, and of course,
raise new ones. However, it is critical to address these issues with presently available data, so that the most
meaningful probes of future datasets can be developed.
The two largest spectroscopic datasets available today for examination of the stellar populations of the
Milky Way are the RAdial Velocity Experiment (RAVE; Steinmetz et al. 2006; Zwitter et al. 2008) and the
Sloan Digital Sky Survey (SDSS; York et al. 2000), in particular the subsurvey Sloan Extension for Galactic
Understanding and Exploration (SEGUE; Yanny et al. 2009). The SEGUE-2 subsurvey (Rockosi et al., in
preparation) has recently been publicly released as part of SDSS DR8 (Aihara et al. 2011), and will add to
this bounty of information. For now, we concentrate on the information available from the previous public
release from SDSS, DR7 (Abazajian et al. 2009), and in particular address the criticisms raised by Sch¨ onrich
et al. (2010; S10) of the previous work of Carollo et al. (2007; C07) and Carollo et al. (2010; C10).
C07 performed a kinematic analysis (within a local volume) for a large sample of calibration stars from
SDSS DR5 (Adelman-McCarthy et al. 2007), and argued for the existence of at least a two-component
halo. In their view the Galactic halo comprises two broadly overlapping structural components, an inner
and an outer halo. These components exhibit different spatial density profiles, stellar orbits, and stellar
metallicities. It was found that the inner-halo component dominates the population of halo stars found at
distances up to 10-15 kpc from the Galactic center, while the outer-halo component dominates in the region
beyond 15-20 kpc. The inner halo was shown to comprise a population of stars exhibiting a flattened spatial
density distribution, with an inferred axial ratio on the order of ∼ 0.6. According to C07, inner-halo stars
possess generally high orbital eccentricities, and exhibit a small (or zero) net prograde rotation around the
center of the Galaxy. The MDF of the inner halo peaks at [Fe/H] = −1.6, with tails extending to higher
and lower metallicities. By comparison, the outer halo comprises stars that exhibit a more spherical spatial

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density distribution, with an axial ratio ∼ 0.9. Outer-halo stars possess a wide range of orbital eccentricities,
exhibit a clear retrograde net rotation, and are drawn from an MDF that peaks at [Fe/H] = −2.2, a factor
of four lower than that of the inner-halo population.
C10 used an expanded sample of calibration stars available from SDSS DR7, which included the SEGUE
sample, to refine and extend the results of C07. They derived velocity ellipsoids for the inner- and outer-halo
components of the Galaxy, as well as for the canonical thick-disk and the proposed metal-weak thick-disk
populations. C10 also considered the fractions of each component required to understand the nature of
the observed kinematic behavior of the stellar populations of the Galaxy as a function of distance from the
Galactic plane. Spatial density profiles for the inner- and outer-halo populations were inferred from a Jeans
Theorem analysis. The full set of calibration stars (including those outside the local volume) was used to
test for the expected changes in the observed stellar MDF with distance above the Galactic plane in situ,
due to the changing contributions from the underlying stellar populations.
Derivation of sufficiently accurate distances is a crucial required step in carrying out kinematic analyses
that make use of full space motions, as these involve distances, combined with radial velocities and proper
motions, in order to assemble the local velocity components of a sample. It is these distances that have been
called into question by S10. In the present paper, we show that many of their objections arise from their
incorrect adoption of a main-sequence absolute magnitude relationship from Ivezi´ c et al. (2008b; I08) that
does not apply for metal-poor halo stars near the main-sequence turnoff (TO), and which leads to assignments
of stellar distances that strongly disagree (a shorter scale by 10-18%) with those derived using the correct
relationship recommended by I08. A legitimate criticism by S10 relates to the luminosity classifications for
stars of intermediate gravity (as assigned spectroscopically) used by C07 and C10, which we demonstrate
below is easily corrected. We then consider a new kinematic analysis of likely outer-halo stars from C10,
and demonstrate that their original claim that the halo of the Milky Way requires at least a two-component
model (with the outer-halo component in net retrograde rotation and possessing a large velocity dispersion)
remains intact.
This paper is outlined as follows. In Section 2 we summarize the procedures used by C07 and C10 to
derive absolute magnitudes and distance estimates for their stars, which were based on those described by
Beers et al. (2000). A technique for the reassignment of (some) luminosity classifications for TO stars in the
original C10 sample is then developed and applied. In Section 3 we compare with absolute magnitudes and
distances derived by the approaches of I08 and An et al. 2011 (in preparation; A11) for stars spectroscopically
classified as likely dwarfs based on their derived surface gravities, as well as with those claimed by S10. We
demonstrate concordance between the distances for low-metallicity dwarf stars obtained by C10, I08, and
A11, and the apparent discordance of all three of these techniques with the results of S10. In Section 4
we reanalyze the kinematics of likely outer-halo stars from the C10 dwarf sample, as well as from the full
sample, including stars of dwarf, TO, and subgiant/giant luminosity classifications, and compare to the
results obtained from adoption of the I08, A11, and S10 distances. Additional tests for the presence of a
kinematically and/or chemically distinct outer halo in the C10 sample are discussed in Section 5. Section
6 presents a summary of further evidence in favor of a dual halo model for the Milky Way, based on other
data sets from SDSS and elsewhere. Our conclusions are given in Section 7.

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2.Procedures Used for Absolute Magnitude and Distance Estimates
2.1.As Employed by C07 and C10
The analyses of C07 and C10 made use of distance estimates for various luminosity classes as assigned
by the software pipeline employed by SDSS/SEGUE to estimate stellar atmospheric parameters based on
low-resolution (R ∼ 2000) spectroscopy and ugriz photometry. The SEGUE Stellar Parameter Pipeline
(SSPP) assigns distances for stars under the following assumed luminosity classes – D: dwarf, TO: main-
sequence turnoff, SG/G: subgiant and giant, FHB: Field Horizontal-Branch, and AGB: Asymptotic Giant
Branch.1Details of the development, calibration, and validation of the SSPP can be found in Lee et al.
(2008a,b), Allende Prieto et al. (2008), and Smolinski et al. (2011), to which we refer the interested reader.
The SSPP obtains estimates of stellar effective temperatures, Teff, with errors of determination on the
order of 150 K. The surface gravity estimates returned by the SSPP are accurate, for stars other than the
coolest giants, to on the order of 0.25 dex. Metallicity estimates for stars in the temperature range 4500 K
< Teff< 7000 K are accurate to on the order of 0.2 dex.
The SSPP distance estimates for various luminosity classes are based on a set of absolute magnitude
relationships (using absorption and reddening-corrected Johnson V magnitudes and B−V colors) calibrated
to Galactic globular and open clusters, as described by Beers et al. (2000; their Table 2). As demonstrated in
Beers et al., photometric distances estimated for their sample are in good agreement with distances derived
from accurate Hipparcos parallaxes. Even when confined to TO stars alone (with well-examined assignment
of stars into the TO class provided from previous work), the photometric distances using the Beers et al.
formulae are consistent with Hipparcos distances.
The samples used by C07 and C10 were selected from the calibration stars of SDSS/SEGUE, which cover
an apparent magnitude range of 15.5 < g0< 18.5. In those analyses, confinement to a local sample with
distances less than 4 kpc from the Sun corresponds to a g-band absolute magnitude fainter than Mg= 2.5,
i.e., the local sample is dominated by D and TO stars. This is in contrast to the sample considered by Beers
et al. (2000), which is dominated by SG/G stars.
Since the Beers et al. (2000) approach makes use of a non-SDSS photometric system, it is also necessary
to employ a color transformation from the SDSS system. Zhao & Newberg (2006) derived a transformation
obtained by making matches of SDSS stars with available Johnson magnitudes and colors from the HK
survey of Beers and colleagues (Beers et al. 1985, 1992), as well as additional photometry of the HK sample
stars obtained over the past decade (see, e.g., Beers et al. 2007, and references therein). They obtained:
V = g − 0.561(g − r) − 0.004
B − V = 0.916(g − r) + 0.187
Stars from the HK survey were used in order to specifically include stars with [Fe/H] < −1.0, which
pertain to most halo stars, although the results did not differ drastically from those of Fukugita et al. (1996)
that were based primarily on higher abundance stars. The color range of the matching stars sets the region
of applicability of the above transformation, which is −0.5 < g − r < 1.0. The choice of distance estimates
1The FHB and AGB classes do not pertain to the sample of calibration stars used by C07 and C10, and so are not discussed
further here.

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based on a non-SDSS photometric system was one of necessity at the time the SSPP was put into operation,
as there were no suitably calibrated fiducials based on SDSS photometry of Galactic clusters available, and
the isochrones that had been developed were rather primitive. These limitations no longer apply, and future
versions of the SSPP will employ alternative distance estimates based on improvements that have become
available in the past year.
It should be noted that the SSPP, by design, does not identify a preferred distance estimate, leaving
the choice of the appropriate luminosity classification to the user’s discretion. This choice is due, in part,
to the fact that the estimation of surface gravity by the SSPP has evolved with time, and may continue
to do so in the future. Hence, as many users will rely, at least at some level, on log g estimates for
making distance estimates based on luminosity classifications from available spectroscopic information, no
“approved” distance estimate is supplied by the SSPP.
For the purpose of the analyses carried out by C07 and C10, the following spectroscopically assigned
surface gravity intervals from the SSPP were used in the assignment of luminosity classifications:
• D: log g ≥ 4.0
• TO: 3.5 ≤ log g < 4.0
• SG/G: log g < 3.5
Estimates of log g carry errors, and one has to be concerned about the possible effects on any resulting
analyses based on their adoption. For the present, this is best assessed by consideration of inferences based
on samples of individual luminosity classes relative to the sample as a whole, which we discuss below.
Note that the above prescription for assignment of luminosity class does not take into account the
“known” evolutionary stage of a given star, as might be inferred from the location of a star in a color-
magnitude diagram expected to pertain to objects of a given age and metallicity. This uncertainly is of
particular concern for stars assigned to the TO class, since an alternative assignment to the D or SG/G
class could result in potentially large discrepancies in the adopted distance. This “defect” (actually a choice,
given that such knowledge is at best only partially constrained with present data, and in any case relies on
assumptions regarding the underlying stellar population one adopts) is one of the criticisms of the C07 and
C10 work levied by S10. However, it can be readily addressed, as described below.
As part of their analysis, I08 compared absolute magnitude estimates obtained by the Beers et al. (2000)
procedures with those used in their own analysis (which only applied to dwarfs). Pointing at the bottom
left panel of their Fig. 21, which examined the main-sequence comparisons of Galactic clusters between the
two studies, I08 concluded that “... the median offset of implied Mrevaluated in small bins of u − g and
g − r color is −0.07 mag, with an rms of 0.06 mag”. This satisfying level of agreement provided additional
reason to have faith in the distances for the majority of stars in the C10 sample upon which their kinematic
analysis was based. This agreement remains intact, as shown below.
2.2. A Refined Prescription for Luminosity Class Assignments
As pointed out above, refinements in luminosity class assignment require assumptions about the ages
and age distributions of the population(s) to which they will be applied. For the present discussion, which
turns on the nature of the stars associated by C07 and C10 with the inner- and outer-halo populations, it is

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reasonable to adopt a uniformly old age, with the unavoidable caveat that not all stars of these populations
may strictly adhere to this assumption.
We proceed as follows.
First, a set of theoretical log g vs. Teff diagrams is obtained, based on the Y2isochrones (Demarque
et al. 2004), for a population with age set to 12 Gyrs, metallicities in the range −3.0 ≤ [Fe/H] ≤ 0.0, and
with [α/Fe] set to 0.0 for solar metallicity, [α/Fe] = +0.3 for [Fe/H] ≤ −1.0, and using a linear scaling
between [Fe/H] = 0 and [Fe/H] = −1.0. We then obtain the effective temperatures at the position of the
main-sequence turnoff for each model, TMSTO, and assign a “critical temperature”, Tcrit, to be 250 K cooler
than TMSTO. The offset of 250 K was chosen since, in the region of the MSTO, this roughly corresponds to
the two-sigma accuracy of the estimated temperature from the SSPP, and provides a reasonable location for
the base of the subgiant branch for isochrones of old, low-metallicity populations. Our purpose is to define
a criterion such that a reassignment of luminosity classes can be considered for stars of intermediate gravity
(3.5 ≤ logg < 4.0) that are cooler than Tcrit.
A second-order polynomial is fit to the positions of the TMSTOvalues for each model:
TMSTO= 5572 − 519.3[Fe/H] − 44.3[Fe/H]2
(1)
The critical temperature is then simply set to Tcrit= TMSTO−250. This process is illustrated in Fig. 1. The
critical temperature is used in order to separate intermediate-gravity stars classified as TO by C07 and C10
into either bona-fide TO stars (those with Teff ≥ Tcrit) or into the D or SG/G classes (those with Teff <
Tcrit) according to their surface gravity estimates, as summarized in Table 1. Note that stars with original
luminosity classifications D and SG/G are not changed by this procedure.
The luminosity class reassignment procedure described above affects a total of 4514 of the original 16920
accepted stars in the C10 sample (26%). The upper left panel of Fig. 2 shows the CMD for the original
assignments of C10, while the upper right panel is that obtained after the revised assignments have been
applied to this same sample. The gray dots are stars with [Fe/H] > −2.0, while the red dots are stars with
[Fe/H] < −2.0.2As can be appreciated from comparison of these two panels, stars that formerly fell into
regions of the CMD that might be considered astrophysically unlikely for an old, metal-poor population have
primarily moved into either the D or SG regions. The lower panels of Fig. 2 contrast the absolute magnitudes
of the revised and original C10 classifications (lower left) and the corresponding derived distances (lower
right).
Inspection of the upper left panel of Fig. 2 clearly shows the presence of the “spurious” TO stars in
the original C10 sample, most easily seen among the [Fe/H] < −2.0 stars as the plume extending from
roughly Mr= 3.7 to Mr= 4.7, over the color range 0.25 < g − i < 0.6. Comparison with the upper right
panel of this figure shows that most of these stars (51%) are reassigned to D status, with only some 10%
being reassigned to SG/G status (the remaining stars, 39%, retain their original luminosity classification of
TO). At low metallicity, [Fe/H] < −2.0, the fraction of reassigned TO stars to D status is 85%, while those
reassigned to SG/G status comprise 14%, and only a small fraction retain their TO classification. At higher
metallicities, [Fe/H] > −2.0, 44% of the TO stars are reassigned to D status, and only a small fraction are
reassigned to SG/G status. The remaining stars, 56%, retain their original luminosity classification of TO.
2We have made use of the corrected metallicity, [Fe/H]C, as described by C10, here and throughout the rest of this paper,
for the quoted metallicities.

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The lower left panel of Fig. 2 shows the difference in the assigned Mrabsolute magnitudes that arises
when one compares the revised C10 estimates with those of C10. For the TO stars that were reclassified as
D stars, and with [Fe/H] > −2.0, the revised C10 determinations are fainter by a median offset of 0.08 mags
(rms 0.36 mags) for 0.4 < g−i < 0.8, while the median offset of the revised C10 absolute magnitudes is 0.30
mags (rms 0.24 mags) fainter for bluer stars in the range g −i < 0.4. For the TO stars that were reclassified
as SG/G stars, and with [Fe/H] > −2.0, the revised C10 determinations are brighter by a median offset of
0.48 mags (rms 0.31 mags) for 0.4 < g −i < 0.8, while the median offset of revised C10 absolute magnitudes
is 0.44 mags (rms 0.22 mags) brighter for bluer stars in the range g − i < 0.4.
For the TO stars that were reclassified as D stars, and with [Fe/H] < −2.0, the revised C10 determina-
tions are fainter by a median offset of 0.97 mags (rms 0.43 mags) for 0.4 < g − i < 0.8, while the median
offset of revised C10 absolute magnitudes is 0.60 mags (rms 0.25 mags) fainter for bluer stars in the range
g −i < 0.4. For the TO stars that were reclassified as SG/G stars, and with [Fe/H] < −2.0, the revised C10
determinations are brighter by a median offset of 1.07 mags (rms 0.42 mags) for 0.4 < g −i < 0.8, while the
median offset of revised C10 absolute magnitudes is 0.63 mags (rms 0.24 mags) brighter for bluer stars in
the range g − i < 0.4.
The lower right panel of Fig. 2 shows the fractional difference in the derived distances between the
revised C10 and C10 scales. For TO stars that were reclassified as D stars, and with [Fe/H] > −2.0 and
0.4 < g − i < 0.8, the median offset of the revised C10 distances with respect to the C10 distances is 26%
(rms 9%). In the bluer range, g − i < 0.4, the offset increases to about 19% (rms 6%). Both are in the
direction that the revised C10 scale is shorter than the original C10 scale for the reclassified TO → D stars.
For TO stars that were reclassified as SG/G stars, and with [Fe/H] > −2.0 and 0.4 < g−i < 0.8, the median
offset of the revised C10 distances with respect to the C10 distances is 33% (rms 16%). In the bluer range,
g − i < 0.4, the offset decreases to about 25% (rms 11%). Both are in the direction that the revised C10
scale is longer than the original C10 scale for the reclassified TO → SG/G stars.
For TO stars that were reclassified as D stars, and with [Fe/H] < −2.0 and 0.4 < g−i < 0.8, the median
offset of the revised C10 distances with respect to the C10 distances is 36% (rms 14%). In the bluer range,
g−i < 0.4, the offset decreases to about 24% (rms 9%). Both are in the direction that the revised C10 scale
is shorter than the original C10 scale for the reclassified TO → D stars. For TO stars that were reclassified
as SG/G stars, and with [Fe/H] < −2.0 and 0.4 < g−i < 0.8, the median offset of the revised C10 distances
with respect to the C10 distances is 65% (rms 26%). In the bluer range, g − i < 0.4, the offset decreases to
about 34% (rms 14%). Both are in the direction that the revised C10 scale is longer than the original C10
scale for the reclassified TO → SG/G stars.
It is worth considering that our reclassification procedure assumes that many of the stars with spectro-
scopically assigned surface gravities in the range 3.75 ≤ logg < 4.0 (those significantly cooler than an inferred
old-population main-sequence turnoff) are indeed metal-poor dwarfs with slightly misestimated log g. This
is certainly a conservative assumption, and errs on the side of decreasing distances for actual TO or SG/G
stars to the much smaller values that would be derived if they are in fact main-sequence dwarfs. These fine
adjustments require further study and verification by high-resolution spectroscopic follow-up of a sample of
such stars, at a variety of metallicities and temperatures.
Note that for construction of Figures 2-8, and for the distance-scale comparisons we carry out below, it
is useful to consider samples that explore the same local volumes. For simplicity, and for consistency with
C07 and C10, we have selected stars with revised C10 distance estimates that satisfy 7 < R < 10 kpc and
d < 4 kpc as our basis sample.

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2.3.Comparison Between Revised C10 and S10
The essence of the S10 complaint is that the distance scale utilized by C07 and C10 is too “long”, i.e.,
that we have artificially inflated the estimates of stellar distances through the combination of (1) the use of
misclassified TO stars (which they suggest could be D stars instead), and in particular, (2) the use of an
absolute magnitude scale for the D stars that assigns luminosities to main-sequence stars which displaces
them to larger-than-appropriate distances. We have shown above that the first issue is easily corrected for,
and that in any case it only applies to some 14% of the total calibration stars from C10, roughly 2300 stars.
Of these, 4% of the full sample (680 stars) possess the very low metalliticties (below [Fe/H] = −2.0) that
strongly influence the derived properties of a proposed outer-halo population. Thus, even if there might
be some impact, it is substantially diluted by the relatively small numbers of stars for which this concern
exists. In any case, we have applied the correction procedures described above, carried out the luminosity
classification changes for the cooler TO stars, and in the analysis below, refer to the modified sample as
the revised C10 sample. The second issue turns on whether or not one should put faith in our adopted
main-sequence absolute magnitude scale, which we address in detail below.
Fig. 3 shows the result of the comparison of the revised C10 determinations with those of S10. The
upper left panel of this figure shows the CMD for stars with spectroscopic assignments of D (logg ≥ 4.0),
with absolute magnitudes from the revised C10 sample. The upper right panel shows the corresponding
CMD obtained using the absolute magnitudes from S10 (Eqn. 3 below). Note that in the evaluation of both
relationships, the [Fe/H]Cfrom C10 was employed, although similar results are obtained when the adopted
metallicities from the SSPP ([Fe/H]A) are used. The stars are color-coded to indicate metallicities above
and below [Fe/H] = −2.0.
The lower left panel of Fig. 3 shows the difference in the assigned Mrabsolute magnitudes that arises
when one compares the revised C10 estimates with those of S10 for stars spectroscopically classified as D
stars (logg ≥ 4.0). For stars with [Fe/H] > −2.0, the revised C10 determinations are brighter by a median
offset of 0.38 mags (rms 0.19 mags) for 0.4 < g − i < 0.8, while the median offset of revised C10 absolute
magnitudes is 0.45 mags (rms 0.20 mags) brighter for bluer stars in the range g − i < 0.4. The offsets are
even larger for stars with [Fe/H] < −2.0. For the redder stars with 0.4 < g − i < 0.8, the median offset of
the revised C10 determinations compared with S10 is 0.45 mags (rms 0.16 mags) brighter; for bluer stars
with g − i < 0.4, the median offset is 0.52 mags (rms 0.18 mags) brighter.
The lower right panel of this figure shows the fractional difference in the derived distances between the
revised C10 and S10 scales. For stars with [Fe/H] > −2.0 and 0.4 < g − i < 0.8, the median offset of the
revised C10 distances with respect to the S10 distances is 19% (rms 10%). In the bluer range, g − i < 0.4,
the offset increases to about 23% (rms 11%). For stars with [Fe/H] < −2.0 and 0.4 < g−i < 0.8, the median
offset of the revised C10 distances with respect to the S10 distances is 23% (rms 10%). In the bluer range,
g − i < 0.4, the offset is 27% (rms 11%). All distance differences are in the sense that the revised C10 scale
is (as expected) longer than the S10 scale.
3.Absolute Magnitudes and Distances Based on Alternative Schemes
Since much of the discord between the conclusions reached by C10 and S10 arise from their adopted
absolute magnitudes and distances, we now consider two additional approaches for obtaining estimates of
these quantities. It is worth keeping in mind that these comparisons are only valid for stars that are
confidently assigned D status, for which we enforce the requirement that they have spectroscopic gravity

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estimates assigned by the SSPP of logg ≥ 4.0.
3.1.The Empirical Calibration of I08
We first consider the relationship adopted by I08, as summarized by their equation A7, used in con-
junction with the metallicity correction in their equations A2/A3. When combined into a single equation,
one obtains:
Mr(g − i,[Fe/H])=
−0.56 + 14.32x − 12.97x2
+6.127x3− 1.267x4+ 0.0967x5
−1.11[Fe/H] − 0.18[Fe/H]2, (2)
where x = (g − i). This was the recommended final photometric parallax relationship from I08, where it is
claimed to be valid (for main-sequence stars) over a wide color range (0.2 < g − i < 4.0).
S10 did not make use of the above equation, but rather, adopted an absolute magnitude relationship
taken from a previous stage of the I08 analysis, given there as equation A1, and applied a metallicity
correction from A2/A3 to obtain:
Mr(g − i,[Fe/H])=1.65 + 6.29x − 2.30x2
−1.11[Fe/H] − 0.18[Fe/H]2, (3)
where x = (g − i).
S10 argued that their adopted absolute magnitude determinations agreed better with their preferred
set of isochrones (the BaSTI isochrones: Pietrinferni et al. 2004, 2006), but in fact I08 did not expect
this relationship (which is from an early step in their development of the appropriate absolute magnitude
prediction) to perform well for bluer stars near the main-sequence turnoff. This is a crucial limitation, as the
calibration-star sample considered by C07 and C10 includes a considerable number of bluer objects – 19% of
the C10 sample, for example, have g−i < 0.4. The fraction becomes even larger at low metallicity – 31% for
[Fe/H]< −1.0, and 46% for [Fe/H]< −2.0. This relationship also does not take into account corrections for
differing ages of the underlying stellar populations that were applied by I08 in seeking a more generally useful
photometric parallax method. The combination of these two effects accounts for much of the discrepancy
cited by S10 in the absolute magnitudes (hence distances) used by the C07 and C10 studies.
The upper left panel of Fig. 4 shows the CMD for stars with spectroscopic assignments of D (logg ≥ 4.0),
with absolute magnitudes assigned by the relationship adopted by S10 (Eqn. 3 above). The upper right
panel shows the corresponding CMD obtained using the absolute magnitudes from Eqn. 2 above, which is the
recommended relationship from I08. Note that in the evaluation of both relationships above, the [Fe/H]C
from C10 was employed, although similar results are obtained when either the photometric metallicity
estimates from I08 or the adopted metallicity from the SSPP ([Fe/H]A) are used. The stars are color-coded
to indicate metallicities above and below [Fe/H] = −2.0. Note, however, that since both procedures adopted
the same metallicity correction scheme, there are no differences in their behavior over different intervals of
[Fe/H].

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The lower left panel of Fig. 4 shows the difference in the assigned Mrabsolute magnitudes that arises
when one compares the adopted S10 and I08 relationships. For stars with 0.4 < g − i < 0.8, the median
offset is 0.23 mags, with the S10 assignments being fainter. The difference for bluer stars with g − i < 0.4
range from ∼ 0.23 mags fainter at the red end of this interval to roughly 1.0 mags fainter at the blue end
(median difference of 0.48 mags).
The lower right panel of this figure shows the fractional difference in the derived distances between S10
and I08. For redder stars with 0.4 < g − i < 0.8, the difference amounts to no more than about 15% at the
blue end of this range (median offset of 10%), but for the bluer stars with g−i < 0.4 the difference increases
from ∼ 15% up to roughly 40%, with a median offset of 20%. All distance differences are in the sense that
the S10 scale is shorter than the I08 scale.
3.2. The Calibrated Isochrone Approach
Distances to individual stars can also be estimated using a set of stellar isochrones, once they have been
properly calibrated against the observed colors and magnitudes of stars with known distances and ages. For
the present exercise, we follow the prescription in An et al. (2009b) to derive distances to individual stars
employing stellar isochrones with empirical corrections on the colors (An et al. 2009a). This calibration
was based on photometry from An et al. (2008) for a number of open and globular clusters, including M67
([Fe/H] = 0.0) and M92 ([Fe/H] = −2.4), which provides metallicity-dependent color corrections in ugriz
over the metallicity range under consideration. A full description of the isochrone calibration can be found
in A11.
After correcting the photometry for dust extinction, we performed model fits over the full parameter
space (with metallicity range −3.0 ≤ [Fe/H] ≤ +0.4). We included griz photometry and the key SSPP
atmospheric parameters ([Fe/H], log g , Teff) in the model fits, and found a best-fitting model by searching
for a minimum χ2of the fit. Note that, for consistency with the other approaches, the corrected metallicity
[Fe/H]Cwas employed. We assumed minimum errors in the photometry of 0.01 mags for gri and 0.02 mags
for z, and took conservative errors of 0.3 dex for [Fe/H], 160 K for Teff, and 0.4 dex for log g, as characteristic
errors in each of these parameters (including possible systematic scale differences between the SSPP and
the models). The lower limit of [Fe/H] in the models is −3.0, so we assumed [Fe/H] = −3.0 for any stars
with metallicity less than this value. This choice has a negligible impact on distance estimation, since the
isochrones are insensitive to a change in the atmospheric abundances for [Fe/H] < −3.0. An age of 12 Gyr
is assumed for [Fe/H] < −1.0, while 4 Gyr is taken for [Fe/H] > −0.3, with a linearly interpolated value for
metallicities between the two boundaries. Solutions for distances were dropped from further consideration in
cases where either the fitting process did not converge, or if the final reduced χ2of a converged fit exceeded
1.2.
Unlike the original approach described by An et al. (2009b), the calibrated isochrones actually reach into
the main-sequence turnoff region, thus distance estimates are available for both TO and SG stars, in addition
to D stars, albeit with lower accuracy in the distance estimates. For the purpose of our present comparisons
we only accepted stars with spectroscopic assignments of surface gravity logg ≥ 4.0. An inter-comparison of
results from various color indices indicates that the internal error in the distance modulus is ∼ 0.1 mag; an
additional ∼ 0.1 mag error is expected from the errors in age, [Fe/H], [α/Fe], and adopted E(B − V ). This
suggests that the associated distance-modulus error is ∼ 0.1−0.2 mags for individual stars. As was the case
for the I08 approach, the effects of binarity are more difficult to quantify, and are not included in this error

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estimate (see An et al. 2007).
The upper left panel of Fig. 5 shows the CMD obtained using the absolute magnitudes from equation A1
of I08 as adopted by S10. The upper right panel shows the CMD for stars with spectroscopic assignments as
D (logg ≥ 4.0), with absolute magnitudes assigned by the calibrated isochrone procedure of A11. Note that
in the evaluation of both relationships above, the [Fe/H]Cused by C10 was employed, although similar results
are obtained when either the photometric metallicity estimates or the adopted metallicity from the SSPP
([Fe/H]A) were used. The stars are color-coded to indicate metallicities above and below [Fe/H]= −2.0. As
is clear from inspection of the upper right panel, the A11 procedure assigns roughly half of the spectroscopic
D stars into SG/G classifications, with correspondingly brighter absolute magnitudes near Mr∼ 3.
The lower left panel of Fig. 5 shows the difference in the assigned Mrabsolute magnitudes that arises
when one compares the adopted S10 and A11 relationships for stars spectroscopically classified as D stars.
For the purpose of this exercise we focus on the stars to which the A11 procedure assigns dwarf status, with
absolute magnitudes Mr> 4.0. For stars with [Fe/H] > −2.0, the S10 determinations are fainter than those
of A11 by a median offset of 0.10 mags (rms 0.09 mags) for 0.4 < g − i < 0.8, while they are fainter by up
to 0.7 mags (median offset of 0.31 mags, rms 0.15 mags) for the bluer stars with g −i < 0.4. The offsets are
significantly larger for stars with [Fe/H] < −2.0. For the redder stars with 0.4 < g − i < 0.8, the median
offset of the S10 determinations compared with A11 is 0.24 mags (rms 0.06 mags) fainter; for bluer stars
with g − i < 0.4, the median offset is 0.41 mags (rms 0.15 mags) fainter.
The lower right panel of this figure shows the fractional difference in the derived distances between S10
and A11 scales. For stars with [Fe/H] > −2.0 and 0.4 < g − i < 0.8, the median offset of the S10 distances
with respect to the A11 distances is only about 4% (rms 4%). In the bluer range, g − i < 0.4, the median
offset increases to about 13% (rms 6%). For stars with [Fe/H] < −2.0 and 0.4 < g − i < 0.8, the median
offset of the S10 distances with respect to the A11 distances increases to 10% (rms 3%). In the bluer range,
g−i < 0.4, the median offset increases to about 17% (rms 6%). All distance differences are in the sense that
the S10 scale is shorter than the A11 scale.
3.3.Comparison with the C10 Dwarfs
We now compare the C10 sample, with revised TO classifications, with the calculations of I08 (Fig. 6)
and with those of A11 (Fig. 7). As can be appreciated by inspection of these figures, the absolute magnitude
scale for the revised C10 sample agrees well with those from both I08 and A11 (in the latter case, one can
only consider the stars considered dwarfs by the A11 procedure; see below).
The lower left panel of Fig. 6 shows the difference in the assigned Mrabsolute magnitudes that arises
when one compares the revised C10 estimates with those of I08 for stars spectroscopically classified as D
stars. For stars with [Fe/H] > −2.0, the revised C10 determinations are brighter by a median offset of 0.21
mags (rms 0.16 mags) for 0.4 < g − i < 0.8, while the median offset of revised C10 absolute magnitudes is
0.14 mags (rms 0.27 mags) brighter for bluer stars in the range g−i < 0.4. The offsets are of similar size for
stars with [Fe/H] < −2.0. For the redder stars with 0.4 < g − i < 0.8, the median offset of the revised C10
determinations compared with I08 is 0.23 mags (rms 0.15 mags) brighter; for bluer stars, the median offset
is 0.13 mags (rms 0.14 mags) brighter.
The lower right panel of this figure shows the fractional difference in the derived distances between the
revised C10 and I08 scales. For stars with [Fe/H] > −2.0 and 0.4 < g − i < 0.8, the median offset of the

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revised C10 distances with respect to the I08 distances is 10% (rms 9%). In the bluer range, g − i < 0.4,
the median offset is about 6% (rms 7%). For stars with [Fe/H] < −2.0 and 0.4 < g − i < 0.8, the median
offset of the revised C10 distances with respect to the I08 distances is 11% (rms 8%). In the bluer range,
g − i < 0.4, the median offset is 6% (rms 6%). All distance differences are in the sense that the revised C10
scale is longer than the I08 scale.
Turning to Fig. 7, if we focus on the stars that are assigned dwarf status by the A11 procedure (we
accomplish this by only comparing stars with derived Mr> 4.0), the agreement between the revised C10
estimates of absolute magnitude and distance is only slightly worse, with respect to A11, than with respect
to I08.
The lower left panel of Fig. 7 shows the difference in the assigned Mrabsolute magnitudes that arises
when one compares the revised C10 estimates with those of A11, for stars spectroscopically classified as D.
For stars with [Fe/H] > −2.0, the revised C10 determinations are brighter by a median offset of 0.31 mags
(rms 0.18 mags) for 0.4 < g − i < 0.8, while the median offset of revised C10 absolute magnitudes is 0.17
mags (rms 0.15 mags) brighter for bluer stars in the range g − i < 0.4. The offsets are smaller for stars
with [Fe/H] < −2.0. For the redder stars with 0.4 < g − i < 0.8, the median offset of the revised C10
determinations compared with I08 is 0.21 mags (rms 0.14 mags) brighter; for bluer stars with g − i < 0.4,
the median offset is 0.15 mags (rms 0.12 mags) brighter.
The lower right panel of this figure shows the fractional difference in the derived distances between the
revised C10 and A11 scales. For stars with [Fe/H] > −2.0 and 0.4 < g − i < 0.8, the median offset of the
revised C10 distances with respect to the A11 distances is 15% (rms 10%). In the bluer range, g − i < 0.4,
the median offset decreases to about 8% (rms 8%). For stars with [Fe/H] < −2.0 and 0.4 < g − i < 0.8,
the median offset of the revised C10 distances with respect to the I08 distances is 10% (rms 7%). In the
bluer range, g −i < 0.4, the median offset is 7% (rms 6%). All distance differences are in the sense that the
revised C10 scale is longer than the A11 scale.
3.4. Comparison Between A11 and I08
For completeness, Fig. 8 shows the comparison between the isocohrone fitting procedure of A11 and the
calculations of I08.
The lower left panel of Fig. 8 shows the difference in the assigned Mr absolute magnitudes between
the A11 and I08 estimates, for stars spectroscopically classified as D (and with Mr> 4.0, in order to only
compare the stars considered as dwarfs by the A11 procedure). For stars with [Fe/H] > −2.0, the A11
determinations are fainter by a median offset of 0.10 mags (rms 0.08 mags) for 0.4 < g − i < 0.8, while
the median offset is 0.12 mags (rms 0.08 mags) fainter for bluer stars in the range g − i < 0.4. The offsets
are smaller for stars with [Fe/H] < −2.0. For the redder stars with 0.4 < g − i < 0.8, the median offset
of the A11 determinations compared with I08 is 0.06 mags (rms 0.06 mags) brighter; for bluer stars with
g − i < 0.4, the median offset is 0.10 mags (rms 0.08 mags) fainter.
The lower right panel of this figure shows the fractional difference in the derived distances between the
A11 and I08 calculations. For stars with [Fe/H] > −2.0 and 0.4 < g − i < 0.8, the median offset of the
A11 distances with respect to the I08 distances is 5% (rms 4%). In the bluer range, g − i < 0.4, the offset
is also about 5% (rms 4%). For stars with [Fe/H] < −2.0 and 0.4 < g − i < 0.8, the median offset of the
A11 distances with respect to the I08 distances is 3% (rms 3%). In the bluer range, g − i < 0.4, the offset

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is similar, about 4% (rms 4%). The distance differences are in the sense that, for the redder stars, the A11
scale is longer than that of I08, while for the bluer stars, the A11 scale is shorter than that of I08.
If we restrict our attention to the stars with [Fe/H] < −2.0, the ones that matter the most for inferences
concerning an outer-halo population, we conclude from the above analysis that the I08 and A11 distance
scales are compatible with one another (maximum offsets of around 5%), while the revised C10 distance
scale differs (in the sense of being longer) than both the I08 and A11 scales by no more than about 10%
(better for stars near the main-sequence turnoff, around 6-7%). By contrast, the S10 scale differs (in the
sense of being shorter) with respect to the I08 scale by between 10% and 18% (independent of metallicity;
worse for stars near the main-sequence turnoff), and similarly, between 10% and 17% (worse for stars near
the main-sequence turnoff) with respect to the A11 scale. Although it is presently unknown which of these
distance scales is closer to “ground truth”, the greater disagreement of the S10 scale (in particular close to
the main-sequence turnoff), not only with respect to the revised C10 scale, but also with respect to those
of I08 and A11, suggests that it is the S10 scale that should be considered suspect, rather than the revised
C10 scale.
4.A Reanalysis of Kinematics for Likely Outer-Halo Stars
We now reconsider a limited kinematic analysis for a local sample of the SDSS DR7 calibration stars
following the procedures described by C10, making use of the four different sets of distance assignments
discussed above for calculation of the full space motions. In order to provide a fair comparison, we apply the
same local volume constraints (7 < R < 10 kpc and d < 4 kpc) to the various samples, but use the values
of R and d that would be obtained for each of the different distance scales. This has the obvious result that
different numbers of stars will enter into each sample. In order to maximize the contribution from proposed
outer-halo stars, we choose to only include stars with [Fe/H] ≤ −2.0. Our purpose is to test the robustness
of the retrograde signature that was criticized by S10, which is most evident at low metallicity.
Fig. 9 shows histograms of Vφ for the stars spectroscopically classified as type D in the revised C10
sample, for all ranges of Zmax (the maximum value of the distance above or below the Galactic plane
reached by a given star during its orbit). The red lines shown in each panel are the two components of a
model obtained by the R-Mix procedure (http://www.math.mcmaster.ca/peter/mix/mix.html) employed
by C10, which the interested reader is referred to for additional details. As can be appreciated from inspection
of this figure, all four of the distance calibrations we consider lead to distributions of Vφ that include
asymmetric tails, which would not be expected to arise for a single-component halo. Naturally, the suggested
components and significance of the splits vary from sample to sample; Table 2 summarizes these results.
Column (1) lists the sample under consideration (recall that the samples differ only in their adopted distances
as described above). Columns (2) and (3) list the inferred means and dispersions (and their errors) of an
assumed Gaussian population for the first component of a two-component fit to the observed distribution of
Vφ, based on the R-Mix procedure. Columns (4) and (5) list the same quantities for the second component
(where required). Column (6) is the p-value of the fits to a one-component model.
The first section of Table 2 concerns the parameters of the R-Mix fits, for D stars only, associated with
Fig. 9. Note that the number of dwarfs listed in the revised C10 sample is more than twice that in the other
samples; this is the result of the inclusion of the reclassified TO → D described above (including a subset of
the stars with 3.75 ≤ logg < 4.00). In the other samples, only the stars with logg ≥ 4.0 are included. From
inspection of the table, the suggested splits from R-Mix all include a retrograde and a prograde component,

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and are highly statistically significant (in the sense that a one-component fit is strongly rejected). This even
includes the S10 sample, although one can see that the formal derived velocity for the first component is less
retrograde than found for the other samples.
Fig. 10 shows the result of a similar analysis for the four different sets of distance calibrations, but
restricted to only include stars with derived estimates of Zmax> 5 kpc. The samples of spectroscopically
classified D stars on orbits that reach beyond 5 kpc from the disk plane is much smaller than considered
for all ranges of Zmax, but the fraction of likely outer-halo stars included by this cut on Zmax should be
increased.
Inspection of Fig. 10 reveals some interesting differences. While the revised C10 sample (which is
considerably larger than the other samples) shown in the upper left panel exhibits a clear asymmetric tail
extending to negative Vφ, the tails of the I08 and A11 samples are weaker than previously, but located at
larger negative values of Vφ. We judge this to be primarily the result of the smaller numbers of stars included.
Of particular interest is the lower right panel, which shows the result for the S10 sample. As can be seen,
if one were to accept the S10 absolute magnitude scale and corresponding distances, one would indeed be
driven to interpret at least this cut on the data as well-represented by a single component, which was the
essence of the argument presented by S10.
The second section of Table 2 concerns the parameters of the R-Mix fits, for D stars only, associated
with Fig. 10. From inspection of the table, the suggested splits from R-Mix include a retrograde and a
prograde component for the revised C10 sample, the I08 sample, and the A11 sample, all of which are
highly statistically significant, but not for the S10 sample, which only allows for a marginally prograde one-
component fit. It is revealing that the inferred prograde velocities for the second components have dropped
considerably from the case that considered all values of Zmax. The split of the A11 sample to include a
highly retrograde, low dispersion, component, is presumably driven by small number statistics.
Finally, we consider a similar set of analyses for the full revised C10 sample, including the D, TO, and
SG/G classifications and their associated distances and derived space motions. Fig. 11 shows the results of
this exercise for both the full range of Zmax(left panel) and the case where only stars with Zmax> 5 kpc are
considered. Inspection reveals the clear presence of an asymmetric tail towards negative Vφin both cases,
which we associate with the outer-halo component, as also concluded by C07 and C10.
The last two sections of Table 2 apply to the samples shown in Fig. 11. As can be seen from inspection
of this table, the mean velocity of the retrograde component is rather similar to that obtained by C07 and
C10, albeit with a slightly larger formal error. The dispersions of the components are also similar to those
obtained previously. A one-component halo is strongly rejected in both cases.
In all of the above, it should be recalled that the final results given by C10 for the parameters of the
various suggested populations were derived with a custom maximum-likelihood procedure, not from the
R-Mix procedure described above. Hence, small differences are expected in the final derived values.

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5.Additional Tests for the Presence of a Kinematically and/or
Chemically Distinct Outer Halo
The limited kinematic analysis carried out above is already strong evidence for the need of more than
a single-component halo for the Milky Way, and provides insight as to why a dual halo interpretation halo
was not supported by S10, when using their adopted absolute magnitude scale. Nevertheless, additional
tests of a complex halo model that are not strongly influenced by the adopted distance scale (other than
for sample selection) are useful to carry out. In this section we consider four such pieces of evidence – (1)
The origin of the retrograde signature from the revised C10 D classifications as well as for the full set of D,
TO, and SG/G classifications, (2) Changes in the as-observed MDF of the revised C10 sample (including
stars without measured proper motions and located outside the local samples considered in the kinematic
analysis), (3) The observed distribution of Galactocentric radial velocities for the well-selected sample of
Blue Horizontal-Branch (BHB) stars from SDSS DR8 discussed by Xue et al. (2011), and (4) Changes in
the as-observed MDF of the BHB sample over different cuts in Galactocentric distance.
5.1. Additional Evidence (1):
The Origin of the Retrograde Signature
It is useful to ask if the single-halo hypothesis, e.g., a halo as described by the best-fit kinematic model
from Bond et al. (2010) (and argued to be valid by S10) can be rejected even without making use of the
analysis of full space motions. The gist of the difficulty with the single-halo hypothesis is the fact that the
derived rotational velocity distribution is asymmetric for stars with low [Fe/H] (this asymmetry is already
present for stars with [Fe/H] < −1.5, and becomes even stronger for stars with [Fe/H] < −2.0).
The fraction of low-metallicity stars with high retrograde motions (Vφ< −200 km s−1) in the SDSS/SEGUE
DR7 calibration-star sample is significantly larger than those with high prograde motions. For stars with
[Fe/H] < −1.5 (and exploring Zmax > 0 kpc) the fraction of stars with high retrograde motions is 9%,
compared with 4% of stars with high prograde motions (Vφ> 200 km s−1). For stars with [Fe/H] < −2.0,
the fractions are 13% highly retrograde compared with 5% highly prograde. For orbits reaching to larger
distances from the Galactic plane, Zmax> 5 kpc, the asymmetry is even stronger (as expected), 16% com-
pared with 5% for [Fe/H] < −1.5, and 20% compared with 6% at [Fe/H] < −2.0. This asymmetric behavior
is present even when only dwarfs are considered (Fig. 9, Fig. 10), which alleviates concerns about potential
systematic distance errors associated with the other stellar classifications.
Belief in the reality of the derived asymmetry in the rotation velocities leads naturally to several impor-
tant questions. For example, “Are stars in the highly retrograde subsample different in any other measured
property than the rest of sample?,” and “Why do they possess such large inferred retrograde velocities?.”
Fig. 12 demonstrates that the distributions of g apparent magnitudes and g − i colors are very similar
for the full sample and the retrograde subsample (the large red squares highlight the subsample of stars
with highly retrograde motion, Vφ< −200 km s−1). Their distance distributions are also similar (median
distances of D stars are both ∼ 2.1 kpc; median distances of the D, TO, and SG/G stars are both ∼ 2.5
kpc). Since these are the quantities which, by and large, drive the spectroscopic target selection, it is unlikely
that spectroscopic selection effects are important in this context. The apparent structure in this figure (the
discontinuity at g = 17) is simply the transition between the two categories of calibration stars in the sample.
The spectrophotometric calibration stars cover the apparent magnitude range 15.5 < g < 17.0, and satisfy
the color ranges 0.6 < u − g < 1.2; 0.0 < g − r < 0.6. The telluric calibration stars cover the same color