Content uploaded by Masashi Chiba
Author content
All content in this area was uploaded by Masashi Chiba on Dec 28, 2017
Content may be subject to copyright.
arXiv:1609.04346v2 [astro-ph.GA] 16 Sep 2016
Draft version September 19, 2016
Preprint typeset using L
A
T
E
X style emulateap j v. 5/2/11
A NEW MILKY WAY SATELLITE DISCOVERED IN THE SUBARU/HYPER SUPRIME-CAM SURVEY
Daisuke Homma1, Masashi Chiba1, Sakurako Okamoto2, Yutaka Komiyama3,4, Masayuki Tanaka3,
Mikito Tanaka1, Miho N. Ishigaki5, Masayuki Akiyama1, Nobuo Arimoto6,4, Jos´
e A. Garmilla7,
Robert H. Lupton7, Michael A. Strauss7, Hisanori Furusawa3, Satoshi Miyazaki3,4, Hitoshi Murayama5,
Atsushi J. Nishizawa8, Masahiro Takada5, Tomonori Usuda3,4, and Shiang-Yu Wang9
Draft version September 19, 2016
ABSTRACT
We report the discovery of a new ultra-faint dwarf satellite companion of the Milky Way based on
the early survey data from the Hyper Suprime-Cam Subaru Strategic Program. This new satellite,
Virgo I, which is located in the constellation of Virgo, has been identified as a statistically significant
(5.5σ) spatial overdensity of star-like objects with a well-defined main sequence and red giant branch
in their color-magnitude diagram. The significance of this overdensity increases to 10.8σwhen the
relevant isochrone filter is adopted for the search. Based on the distribution of the stars around the
likely main sequence turn-off at r∼24 mag, the distance to Virgo I is estimated as 87 kpc, and its
most likely absolute magnitude calculated from a Monte Carlo analysis is MV=−0.8±0.9 mag.
This stellar system has an extended spatial distribution with a half-light radius of 38+12
−11 pc, which
clearly distinguishes it from a globular cluster with comparable luminosity. Thus, Virgo I is one of the
faintest dwarf satellites known and is located beyond the reach of the Sloan Digital Sky Survey. This
demonstrates the power of this survey program to identify very faint dwarf satellites. This discovery
of Virgo I is based only on about 100 square degrees of data, thus a large number of faint dwarf
satellites are likely to exist in the outer halo of the Milky Way.
Subject headings: galaxies: dwarf — galaxies: individual (Virgo) — Local Group
1. INTRODUCTION
Dwarf spheroidal galaxies (dSphs) associated with the
Milky Way (MW) and Andromeda galaxies provide im-
portant constraints on the role of dark matter in galaxy
formation and evolution. Indeed, these faint stellar sys-
tems are largely dominated by dark matter with mass-
to-luminosity ratios of 10 to 1000 or even larger in fainter
systems, based on their stellar dynamics (Gilmore et al.
2007; Simon & Geha 2007). Thus, the basic properties
of dSphs, such as their total number and spatial distri-
butions inside a host halo like the MW, provide useful
constraints on dark matter on small scales, in particular
the nature and evolution of cold dark matter (CDM) in
a Λ dominated universe.
One of the tensions between theory and observation
is the missing satellite problem: the theory predicts a
much larger number of subhalos in a MW-like halo than
1Astronomical Institute, Tohoku University, Aoba-ku, Sendai
980-8578, Japan
E-mail: d.homma@astr.tohoku.ac.jp
2Shanghai Astronomical Observatory, 80 Nandan Road,
Shanghai 200030, China
3National Astronomical Observatory of Japan, 2-21-1 Osawa,
Mitaka, Tokyo 181-8588, Japan
4The Graduate University for Advanced Studies, Osawa 2-21-
1, Mitaka, Tokyo 181-8588, Japan
5Kavli Institute for the Physics and Mathematics of the Uni-
verse (WPI), The University of Tokyo, Kashiwa, Chiba 277-8583,
Japan
6Subaru Telescope, National Astronomical Observatory of
Japan, 650 North A’ohoku Place, Hilo, HI 96720, USA
7Princeton University Observatory, Peyton Hall, Princeton,
NJ 08544, USA
8Institute for Advanced Research, Nagoya University, Furo-
cho, Chikusa-ku, Nagoya 464-8602, Japan
9Institute of Astronomy and Astrophysics, Academia Sinica,
Taipei, 10617, Taiwan
the observed number of satellite galaxies (Klypin et al.
1999; Moore et al. 1999). Solutions to this problem are
to consider other types of dark matter than CDM (e.g.,
Macci`o & Fontanot 2010) or to invoke baryonic physics
(e.g., Sawala et al. 2016). Another possibility is that
we have seen only a fraction of all the satellites asso-
ciated with the MW due to various observational bi-
ases (Tollerud et al. 2008). Motivated by this, a sys-
tematic search for new dSphs has been made based on
large survey programs, such as the Sloan Digital Sky
Survey (SDSS) (York et al. 2000) and the Dark Energy
Survey (DES) (Abbott et al. 2016). SDSS discovered
15 ultra-faint dwarf galaxies (UFDs) with MV>
∼−8
mag (e.g., Willman et al. 2005; Sakamoto & Hasegawa
2006; Belokurov et al. 2006), and DES recently reported
the discovery of many more candidate UFDs in the
south (e.g., Bechtol et al. 2015; Koposov et al. 2015;
Drlica-Wagner et al. 2015). These discoveries are consis-
tent with the work by Tollerud et al. (2008), anticipating
that there exists a large number of yet unidentified dwarf
satellites in the MW halo, especially in its outer parts.
This paper reports the discovery of a new faint dwarf
satellite in the MW, in the course of the Subaru Strategic
Program (SSP) using Hyper Suprime-Cam (HSC). HSC
is a new prime-focus camera on the Subaru telescope with
a 1.5 deg diameter field of view (Miyazaki et al. 2012),
which thus allows us to survey a large volume of the
MW halo out to a large distance from the Sun, where
a systematic search for new satellites has not yet been
undertaken.
2. DATA AND METHOD
The HSC-SSP is an ongoing optical imaging survey,
which consists of three layers with different combinations
of area and depth. Our search for new MW satellites is
2 Homma et al.
Fig. 1.— Left panel: the spatial distribution of the sources classified as stars with i < 24.5 mag and g−r < 1.0, covering one square
degree centered on the candidate overdensity of stars. The star counts are in bins of 0◦.05 ×0◦.05. Right panel: the plot for the sources
classified as galaxies with i < 24.5 mag and g−r < 1.0. Note that there is no overdensity at the center of this plot.
Fig. 2.— The spatial distribution of the stars around the overdensity (upper panels, where ∆αand ∆δare the relative offsets in celestial
coordinates) and their distribution in the g−rvs. rCMD (lower panels). Panel (a): spatial distribution of the sources classified as stars
with i < 24.5 mag and g−r < 1.0. Red circles denote annuli with radii = 2′, 6′, and 6′.33 from the center. There is an overdensity around
the field center with statistical significance of 5.5σ. Panel (b): the same as (a) but for the stars passing the isochrone filter shown in panel
(d). The statistical significance of the overdensity, 10.8σ, is higher than in panel (a). Panel (c): CMD for the stars at r < 2′, where the
error bars show a typical measurement error in color at each rmagnitude. Panel (d): the same as (c) but including an isochrone (red line)
for an old, metal-poor system [age of 13 Gyr and metallicity of [M/H]= −2.2 at a distance modulus of (m−M)0= 19.7 mag]. The shaded
area covers both the typical photometric error and likely intrinsic dispersion of the CMD in star clusters. Panel (e): the same as (c) but
for field stars at 6′< r < 6′.33, which has the same solid angle. Note the absence of a main sequence turn-off.
based on its Wide layer, aiming to observe ∼1400 deg2
in five photometric bands (g,r,i,z, and y), where the
target 5σpoint-source limiting magnitudes are (g,r,i,z,
y) = (26.5, 26.1, 25.9, 25.1, 24.4) mag. In this paper, we
A new satellite in the Milky Way 3
utilize the (g,r) data in the early HSC survey obtained
before 2015 November, covering ∼100 deg2in 5 fields
along the celestial equator. The HSC data are processed
with hscPipe v4.0.1, a branch of the Large Synoptic
Survey Telescope pipeline (Ivezic et al. 2008; Juric et al.
2015) calibrated against PanSTARRS1 photometry and
astrometry (Schlafly et al. 2012; Tonry et al. 2012;
Magnier et al. 2013).
We use the extendedness parameter from the pipeline
to select point sources. This parameter is computed from
the ratio between PSF and cmodel fluxes, which are mea-
sured by fitting PSF models and two-component PSF-
convolved galaxy models to the source profile, respec-
tively (Abazajian et al. 2004). When the ratio between
these fluxes is larger than 0.985, a source is classified as
a point source. We use the parameter measured in the
i-band, in which the seeing is typically the best of our
five filters with a median of about 0′′.6. In particular,
the i-band seeing for the region around our new-found
satellite is about 0′′ .5. In order to characterize the com-
pleteness and contamination of our star/galaxy classifi-
cation, we stack the COSMOS data (COSMOS is one of
our UltraDeep fields, where we have many exposures) to
the depth of the Wide survey and compare our classifi-
cation against the HST/ACS data from Leauthaud et al.
(2007). We find that the completeness, defined here as
the fraction of objects that are classified as stars by ACS,
and correctly classified as stars by HSC, is above 90% at
i < 22.5, and drops to ∼50% at i= 24.5. On the other
hand, contamination, which is defined as the fraction of
HSC-classified stars which are classified as galaxies by
ACS, is close to zero at i < 23, but increases to ∼50%
at i= 24.5. Based on this test, we choose to use the
extendedness parameter down to i= 24.5 to select stars
in this work10. We further apply a g−r < 1.0 cut to
eliminate numerous M-type disk stars.
In order to search for the signature of new satellites,
we count stars in 0◦.05 ×0◦.05 bins in right ascension
and declination, with an overlap of 0◦.025 in each di-
rection, where 0◦.05 corresponds to a typical half-light
diameter (∼80 pc) of an ultra-faint dwarf at a dis-
tance of 90 kpc. We then calculate the mean density
and its dispersion over all cells for each of the Wide layer
fields to search for any spatial overdensities of stars (e.g.,
Koposov et al. 2008; Walsh et al. 2009). The deviation
from the mean density has close to a Gaussian distribu-
tion. We have found one stellar overdensity with 5.5σ
in one of the Wide layer fields. The standard devia-
tion is estimated separately for each survey field (cover-
ing typically 20 to 30 deg2); each field is at different
Galactic coordinates. This overdensity is centered at
(α, δ) = (180◦.04,−0◦.68). As Figure 1 shows, there is
no corresponding overdensity in extended objects (galax-
ies)11.
10 Another method for star/galaxy classification by combining
the colors of the sources (Garmilla et al. in prep.) has also been
applied and we have confirmed that the main results of this work
remain unchanged. The full description for the analysis of the
data based on this alternative scheme will be presented in a future
paper.
11 Another high-sigma overdensity (6.8σ) of the sources with
extendedness = 0 has been identified in the survey region, but
this appears an artefact related to scattered light from a nearby
bright star.
In Figure 2(a), we plot the spatial distribution of the
stars around this overdensity, which shows a localized
concentration of stars within a circle of radius 2′. To
get further insights into this overdensity, in Figure 2(c),
we plot the (g−r, r) color-magnitude diagram (CMD)
of stars within the 2′radius circle shown in Figure 2(a).
This CMD shows signatures of main sequence (MS) stars
near its turn off (MSTO) as well as stars on the red
giant branch (RGB), whereas these features disappear
when we plot stars at 6′< r < 6′.33 with the same
solid angle, i.e. likely field stars outside the overdensity,
as shown in Figure 2(e). To investigate the distribu-
tion of the overdensity in the CMD further, we adopt
a fiducial locus of stars in a typical ultra-faint dwarf
galaxy based on a PARSEC isochrone (Bressan et al.
2012), in which we assume an age of 13 Gyr and metal-
licity of z= 0.0001 ([M/H]= −2.2). We first derive this
isochrone in the SDSS filter system and then convert to
the HSC filter system using the following formula cali-
brated from both filter curves and spectral atlas of stars
(Gunn & Stryker 1983), g=gSDSS −a(gSDSS −rSDSS)−b
and r=rSDSS −c(rSDSS −iSDSS)−d, where (a, b, c, d) =
(0.074,0.011,0.004,0.001) and the subscript SDSS de-
notes the SDSS system. This isochrone, at the assumed
distance modulus of (m−M)0= 19.7 mag as determined
below, is shown in Figure 2(d), which does a good job of
tracing the distributions of MSTO and RGB stars. To
test the statistical significance of the overdensity along
this isochrone, we set the selection filter defined by the
CMD envelope [shaded region in Figure 2(d)], which con-
sists of the above isochrone, 1σ(g−r) color measurement
error as a function of r-band magnitude, and a typical
color dispersion of about ±0.05 mag at the location of the
RGB arising from a metallicity dispersion of ±0.7 dex for
dSph stars. By passing this filter over the stars in the
relevant region, we derive an overdensity that peaks at a
distance modulus of 19.7 mag at a statistical significance
of 10.8σ, much higher than without the filter. Figure 2(b)
shows the distribution of the stars that pass this filter,
revealing a higher overdensity contrast than Figure 2(a).
This suggests that the overdensity we have found here
is indeed an old stellar system, either a globular cluster
or dwarf galaxy. Hereafter we refer to this system as
Virgo I12. The stars selected by this isochrone filter lie
along a clear stellar sequence even in a 2-color (g−r,
r−i) diagram. We note that the statistical significance
of this overdensity before (after) passing this isochrone
filter remains basically unchanged when we adopt differ-
ent magnitude limits for the sample: 5.6σ(10.3σ) for
i < 24 mag and 4.8σ(9.6σ) for i < 25 mag.
3. PROPERTIES OF STELLAR POPULATION
We estimate the basic structural properties of
Virgo I. For this purpose, we adopt six parameters
(α0, δ0, θ, ǫ, rh, N∗): (α0, δ0) for the celestial coordinates
of the centroid of the overdensity, θfor its position angle
from north to east, ǫfor the ellipticity, rhfor the half-
light radius, and N∗for the number of stars belonging
to the overdensity. The maximum likelihood method of
Martin et al. (2008) is applied to the stars within a circle
12 This is not to be confused with the so-called Virgo overdensity,
which is closer at ∼6 to 20 kpc and covering a much larger volume
(Juric et al. 2008).
4 Homma et al.
TABLE 1
Properties of Virgo I
ParameteraValue
Coordinates (J2000) 12h00m09s.6, −0◦40′48′′
Galactic Coordinates (l, b) 276◦.94, 59◦.58
Position angle +51+18
−40 deg
Ellipticity 0.44+0.14
−0.17
AV0.066 mag
(m−M)019.7+0.3
−0.2mag
Heliocentric distance 87+13
−8kpc
Half light radius, rh1′.5±0′.4 or 38+12
−11 pc
Mtot,V −0.8±0.9 mag
aIntegrated magnitudes are corrected for
the mean Galactic foreground extinction, AV
(Schlafly & Finkbeiner 2011).
Fig. 3.— Density profile of the stars in Virgo I that pass the
isochrone filter shown in Figure 2(b), in elliptical annuli as a func-
tion of mean radius, where the uncertainties are derived assuming
Poisson statistics. The line shows a fitted exponential profile with
rh= 1′.5.
of radius 20′passing the isochrone filter; the results are
summarized in Table 1.
Figure 3 shows the radial profile of the stars passing
the isochrone filter [Figure 2(b)] by computing the av-
erage density within elliptical annuli. The overplotted
line corresponds to the best-fit exponential profile with
a half-light radius of rh= 1′.5 or 38 pc. This spatial
size is larger than the typical size of MW globular clus-
ters but is consistent with the scale of dwarf satellites as
examined below.
The total absolute magnitude of Virgo I, MV, is esti-
mated by summing the luminosities of the stars within
the half-light radius, rh, and then doubling the summed
luminosity (e.g., Sakamoto & Hasegawa 2006). For the
transformation from (g , r) to V, we adopt the formula in
Jordi et al. (2006) calibrated for metal-poor Population
II, which are appropriate for stars in ultra-faint dwarf
galaxies. Assuming that the distance to this stellar sys-
tem is 87 kpc or (m−M)0= 19.7 mag, we obtain MV=
−0.17 mag for rh= 1′.5. This value varies when we
adopt different half-light radii or different distance mod-
uli within their 1σuncertainties. We find MV= +0.08
mag if we adopt rh= 1′.1 and (m−M)0= 19.5 mag and
MV=−1.87 mag for rh= 1′.9 and and (m−M)0= 20.0
mag. The latter case yields a much brighter MVdue to
the inclusion of a bright RGB star inside the aperture.
Shot noise due to the small number of stars in Virgo I
is a significant additional source of uncertainty in MV.
We quantify this and other sources of error using a Monte
Carlo method similar to that described in Martin et al.
(2008) to determine the most likely value of MVand its
uncertainty. As summarized in Table 1 for Virgo I, we
have derived N∗= 19 ±5 at i < 24.5 mag, the dis-
tance modulus of (m−M)0= 19.7+0.3
−0.2mag, and we
use a stellar population model with an age of 13 Gyr
and metallicity of [M/H]= −2.2. Based on these infor-
mation, we generate 104realizations of CMDs for three
different initial mass functions (IMFs); Salpeter, Kroupa,
and Chabrier (lognormal) (Salpeter 1995; Kroupa 2002;
Chabrier 2001). We then derive the luminosity of the
stars for each CMD at i < 24.5 mag, taking into account
the completeness of the observed stars with HSC. Based
on this Monte Carlo simulation, we obtain the expected
values of MVas MV=−0.82±0.95, MV=−0.81±0.91,
and MV=−0.83 ±0.92, for Salpeter, Kroupa, and
Chabrier IMFs, respectively. Thus, the values of MV
for these different IMF models are consistent each other,
summarized as MV=−0.8±0.9 mag, and are within
the 1σuncertainty of MVdetermined above by directly
counting the observed member stars.
We note that the above models suggest the ratio be-
tween the number of RGB+HB and that of MSTO stars
is about 0.2, whereas the observed ratio is about 0.4.
This discrepancy by a factor of 2 can be understood
when we consider the contamination of some field RGBs
and/or incompleteness of faint MSTO stars.
4. DISCUSSION
To assess if Virgo I identified here is indeed a new
MW dwarf satellite galaxy, we compare its size quan-
tified by rhwith globular clusters with comparable lu-
minosity, in the range of MV∼+0.10 to −1.72 mag.
In Figure 4(a), we plot the relation between MVand rh
for the MW globular clusters (dots) taken from Harris
(1996), and dwarf galaxies in the MW (filled squares) and
M31 (open squares) from McConnachie (2012), the re-
cent DES work (Bechtol et al. 2015; Koposov et al. 2015;
Drlica-Wagner et al. 2015), and other recent discover-
ies (Laevens et al. 2014; Kim et al. 2015; Kim & Jerjen
2015; Laevens et al. 2015a,b). The red star with error
bars shows Virgo I detected in this work.
As is clear from the figure, the current stellar system
is systematically larger than MW globular clusters with
comparable MVand is located along the locus of the MW
and M31 dwarf galaxies. This is the case even if we adopt
the brighter estimate of MV=−1.72 mag by consider-
ing the 1σuncertainty in MV. Thus, the overdensity of
the stars we have found here is a candidate ultra-faint
dwarf galaxy. This is also supported from its non-zero
ellipticity of ǫ= 0.44+0.14
−0.17, which is more similar to those
of dwarf galaxies than globular clusters.
A new satellite in the Milky Way 5
Fig. 4.— (a) The relation between MVand rhfor stellar
systems. Dots denote globular clusters in the MW taken from
Harris (1996). Filled and open squares denote the MW and M31
dSphs, respectively, taken from McConnachie (2012), the recent
DES work for new ultra-faint MW dSphs (Bechtol et al. 2015;
Koposov et al. 2015; Drlica-Wagner et al. 2015), and other recent
discoveries (Laevens et al. 2014; Kim et al. 2015; Kim & Jerjen
2015; Laevens et al. 2015a,b). The red star with error bars cor-
responds to the overdensity described in this paper, Virgo I, which
lies within the locus defined by dSphs. (b) The relation between
MVand heliocentric distance for the systems shown in panel (a).
The heliocentric distance to Virgo I is D= 87+13
−8kpc,
where the error estimate is derived from the range of
the distance yielding the 1σdecrease in the statistical
significance of Virgo I after passing the isochrone filter
[defined in Figure 2(d)] from its peak value of 10.8σ.
This distance is beyond the reach of previous surveys for
MW dwarfs with comparable luminosity. This is demon-
strated in Figure 4, which shows the relation between
MVand Dfor the MW and M31 dwarfs as well as the
MW globular clusters.
5. CONCLUSIONS
We have identified a new ultra-faint dwarf satellite of
the MW, Virgo I, in the constellation of Virgo. The
satellite is located at a heliocentric distance of 87 kpc
and its absolute magnitude in the Vband is estimated
as MV=−0.8±0.9 mag, which is comparable to or
fainter than that of the faintest dwarf satellite, Segue 1.
The half-light radius of Virgo I is estimated to be ∼38
pc, significantly larger than globular clusters with the
same luminosity, suggesting that it is a dwarf galaxy. To
set further constraints on Virgo I, follow-up spectroscopic
studies of bright RGB stars will be useful to investigate
their membership and to determine the chemical and dy-
namical properties in this dwarf satellite.
Virgo I is located beyond the reach of the SDSS: its lim-
iting magnitude of r= 22.2 implies that the completeness
radius beyond which a faint dwarf galaxy like Virgo I will
not be detected (Tollerud et al. 2008) is 28 kpc. With
Subaru/HSC, this completeness radius for Virgo I is es-
timated as 89 kpc, if we adopt the limiting i-band magni-
tude of 24.5 mag combined with a typical (r−i) color of
≃0.2. Thus, Virgo I with D= 87+13
−8kpc is located just
at the edge where Subaru/HSC can reach. We therefore
expect the presence of yet unidentified faint satellites in
the outer parts of the MW halo as the HSC survey con-
tinues. Deep imaging surveys for these faint and distant
satellites are indeed important to get further insights into
their true number and thus the nature of dark matter on
small scales.
We thank the referee for his/her helpful comments and
suggestions. This work is supported in part by JSPS
Grant-in-Aid for Scientific Research (B) (No. 25287062)
and MEXT Grant-in-Aid for Scientific Research on In-
novative Areas (No. 15H05889).
The Hyper Suprime-Cam (HSC) collaboration includes
the astronomical communities of Japan and Taiwan, and
Princeton University. The HSC instrumentation and
software were developed by the National Astronomical
Observatory of Japan (NAOJ), the Kavli Institute for
the Physics and Mathematics of the Universe (Kavli
IPMU), the University of Tokyo, the High Energy Ac-
celerator Research Organization (KEK), the Academia
Sinica Institute for Astronomy and Astrophysics in Tai-
wan (ASIAA), and Princeton University. Funding was
contributed by the FIRST program from Japanese Cab-
inet Office, the Ministry of Education, Culture, Sports,
Science and Technology (MEXT), the Japan Society for
the Promotion of Science (JSPS), Japan Science and
Technology Agency (JST), the Toray Science Founda-
tion, NAOJ, Kavli IPMU, KEK, ASIAA, and Princeton
University. This paper makes use of software developed
for the Large Synoptic Survey Telescope. We thank the
LSST Project for making their code freely available. The
Pan-STARRS1 (PS1) Surveys have been made possible
through contributions of the Institute for Astronomy, the
University of Hawaii, the Pan-STARRS Project Office,
the Max-Planck Society and its participating institutes,
the Max Planck Institute for Astronomy and the Max
Planck Institute for Extraterrestrial Physics, The Johns
Hopkins University, Durham University, the University
of Edinburgh, Queen’s University Belfast, the Harvard-
Smithsonian Center for Astrophysics, the Las Cumbres
Observatory Global Telescope Network Incorporated, the
National Central University of Taiwan, the Space Tele-
scope Science Institute, the National Aeronautics and
Space Administration under Grant No. NNX08AR22G
issued through the Planetary Science Division of the
NASA Science Mission Directorate, the National Science
Foundation under Grant No.AST-1238877, the Univer-
sity of Maryland, and Eotvos Lorand University (ELTE).
6 Homma et al.
REFERENCES
Abazajian, K., Adelman-McCarthy, J. K., Ag¨ueros, M. A., et al.
2004, AJ, 128, 502
Abbott, T., Abdalla, F. B., Allam, S., et al. 2016, MNRAS, in
press (arXiv:1601.00329)
Bechtol, K., Drlica-Wagner, A., Balbinot, E., et al. ApJ, 807, 50
Belokurov, V., Zucker, D. B., Evans, N. W., et al. 2006, ApJ, 647,
L11
Bressan, A., Marigo, P., Girardi, L., et al. 2012, MNRAS, 427, 127
Chabrier, G., 2001, ApJ, 554, 1274
Drlica-Wagner, A., Bechtol, K., Rykoff, E. S., et al. 2015, ApJ,
813, 109
Gilmore, G., Wilkinson, M. I., Wyse, R. F. G., et al. 2007, ApJ,
663, 948
Gunn, J. E., & Stryker, L. L., 1983, ApJS, 52, 121
Harris, W. E. 1996, AJ, 112, 1487
Ivezic, Z., Axelrod, T., Brandt, W. N., et al. 2008, AJ, 176, 1
Jordi, K., Grebel, E. K., Ammon, K. 2006, ˚a, 460, 339
Juric, M., Ivezic, Z., Brooks, A., et al. 2008, ApJ, 673, 864
Juric, M., Kantor, J., Lim, K.-T., et al. 2015, ArXiv e-prints,
arXiv:1512.07914
Kim, D., Jerjen, H., Milone, A. P. et al. 2015, ApJ, 803, 63
Kim, D., & Jerjen, H. 2015, ApJ, 808, L39
Klypin, A., Kravtsov, A. V., Valenzuela, O., & Prada, F. 1999,
ApJ, 522, 82
Koposov, S., Belokurov, V., Evans, N. W., et al. 2008, ApJ, 686,
279
Koposov, S. E., Belokurov, V., Torrealba, G., & Evans, N. W.
2015, ApJ, 805, 130
Kroupa, P., 2002, Science, 295, 82
Laevens, B. P. M., Martin, N. F., Sesar, B., et al. 2014, ApJ, 786,
L3
Laevens, B. P. M., Martin, N. F., Ibata, R. A. et al. 2015a, ApJ,
802, L18
Laevens, B. P. M., Martin, N. F., Bernard, E. J. et al. 2015b,
ApJ, 813, L44
Leauthaud, A., Massey, R., Kneib, J.-P., et al. 2007, ApJS, 172,
219
Macci`o, A. V., & Fontanot, F. 2010, MNRAS, 404, L16
Magnier, E. A., Schlafly, E., Finkbeiner, D., et al. 2013, ApJS,
205, 20
Martin, N. F., de Jong, J. T. A., & Rix, H.-W. 2008, ApJ, 684,
1075
McConnachie, A. W., 2012, AJ, 144, 4
Miyazaki, S., Komiyama, Y., Nakata, H., et al. 2012, Proc. SPIE,
8446, 84460Z
Moore, B., Ghigna, S., Governato, F., Lake, G., Quinn, T., &
Stadel, J. 1999, ApJ, 524, L19
Sakamoto, T., & Hasegawa, T. 2006, ApJ, 653, L29
Salpeter, E. E. 1955, ApJ, 121, 161
Sawala, T., Frenk, C. S., & Fattahi, A., et al. 2016, MNRAS, 457,
1931
Schlafly, E. F., & Finkbeiner, D. P. 2011, ApJ, 737, 103
Schlafly, E. F., Finkbeiner, D. P., Juri´c, M., et al. 2012, ApJ, 756,
158
Schlegel, D. J., Finkbeiner, D. P., & Davis, M. 1998, ApJ, 500,
525
Simon, J. D., & Geha, M. 2007, ApJ, 670, 313
Tollerud, E. J., Bullock, J. S., Strigari, L. E., & Willman, B.
2008, ApJ, 688, 277
Tonry, J. L., Stubbs, C. W., Lykke, K. R., et al. 2012, ApJ, 750,
99
Walsh, S. M., Willman, B., & Jerjen, H. 2009, AJ, 137, 45
Willman, B., Blanton, M. R., West, A. A., et al. 2005, AJ, 129,
2692
York, D. G., Adelman, J., Anderson, J. E., Jr., et al. 2000, AJ,
120, 1579