Weak lensing reveals a tight connection
between dark matter halo mass and the
distribution of stellar mass in massive galaxies
Item Type Article
Authors Huang, Song; Leauthaud, Alexie; Hearin, Andrew; Behroozi,
Peter; Bradshaw, Christopher; Ardila, Felipe; Speagle, Joshua;
Tenneti, Ananth; Bundy, Kevin; Greene, Jenny; Sifón, Cristóbal;
Bahcall, Neta
Citation Song Huang, Alexie Leauthaud, Andrew Hearin, Peter Behroozi,
Christopher Bradshaw, Felipe Ardila, Joshua Speagle, Ananth
Tenneti, Kevin Bundy, Jenny Greene, Cristóbal Sifón, Neta
Bahcall, Weak lensing reveals a tight connection between dark
matter halo mass and the distribution of stellar mass in massive
galaxies, Monthly Notices of the Royal Astronomical Society,
Volume 492, Issue 3, March 2020, Pages 3685–3707, https://
doi.org/10.1093/mnras/stz3314
DOI 10.1093/mnras/stz3314
Publisher OXFORD UNIV PRESS
Journal MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
Rights Copyright © 2019 The Author(s). Published by Oxford University
Press on behalf of the Royal Astronomical Society.
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Version Final published version
MNRAS 492, 3685–3707 (2020) doi:10.1093/mnras/stz3314
Advance Access publication 2019 December 5
Weak lensing reveals a tight connection between dark matter halo mass
and the distribution of stellar mass in massive galaxies
Song Huang ,
1,2,8‹
Alexie Leauthaud ,
1
Andrew Hearin,
3
Peter Behroozi ,
4
Christopher Bradshaw,
1
Felipe Ardila ,
1
Joshua Speagle ,
5
Ananth Tenneti ,
6
Kevin Bundy,
7
Jenny Greene,
8
Crist
´
obal Sif
´
on
9
and Neta Bahcall
8
1
Department of Astronomy and Astrophysics, University of California Santa Cruz, 1156 High St., Santa Cruz, CA 95064, USA
2
Kavli-IPMU, The University of Tokyo Institutes for Advanced Study, the University of Tokyo (Kavli IPMU, WPI), Kashiwa 277-8583, Japan
3
Argonne National Laboratory, Argonne, IL 60439, USA
4
Department of Astronomy and Steward Observatory, University of Arizona, Tucson, AZ 85721, USA
5
Department of Astronomy, Harvard University, 60 Garden St, MS 46, Cambridge, MA 02138, USA
6
McWilliams Center for Cosmology, Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA
7
UCO/Lick Observatory, University of California, Santa Cruz, 1156 High Street, Santa Cruz, CA 95064, USA
8
Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08540, USA
9
Instituto de F
´
ısica, Pontificia Universidad Cat
´
olica de Valpara
´
ıso, Casilla 4059, Valpara
´
ıso, Chile
Accepted 2019 November 8. Received 2019 November 8; in original form 2018 November 1
ABSTRACT
Using deep images from the Hyper Suprime-Cam (HSC) survey and taking advantage of its
unprecedented weak lensing capabilities, we reveal a remarkably tight connection between
the stellar mass distribution of massive central galaxies and their host dark matter halo mass.
Massive galaxies with more extended stellar mass distributions tend to live in more massive
dark matter haloes. We explain this connection with a phenomenological model that assumes,
(1) a tight relation between the halo mass and the total stellar content in the halo, (2) that the
fraction of in situ and ex situ mass at r <10 kpc depends on halo mass. This model provides
an excellent description of the stellar mass functions (SMFs) of total stellar mass (M
max
) and
stellar mass within inner 10 kpc (M
10
) and also reproduces the HSC weak lensing signals of
massive galaxies with different stellar mass distributions. The best-fitting model shows that
halo mass varies significantly at fixed total stellar mass (as much as 0.4 dex) with a clear
dependence on M
10
. Our two-parameter M
max
–M
10
description provides a more accurate
picture of the galaxy–halo connection at the high-mass end than the simple stellar–halo mass
relation (SHMR) and opens a new window to connect the assembly history of haloes with
those of central galaxies. The model also predicts that the ex situ component dominates the
mass profiles of galaxies at r < 10 kpc for log M
≥ 11.7. The code used for this paper is
available online https://github.com/dr-guangtou/asap
Key words: galaxies: elliptical and lenticular, cD – galaxies: formation – galaxies: haloes –
galaxies: photometry – galaxies: structure.
1 INTRODUCTION
During the last decade, observations and hydrodynamic simulations
have significantly furthered our understanding of the formation and
assembly of massive galaxies in the nearby Universe. The observed
mass assembly (e.g. Lundgren et al. 2014; Ownsworth et al. 2014;
Vulcani et al. 2016; also see Bundy et al. 2017) and dramatic
structural evolution (e.g. van der Wel et al. 2014;Clauwensetal.
E-mail: shuang89@ucsc.edu
2017; Hill et al. 2017) support a ‘two-phase’ formation scenario of
massive galaxies (e.g. Oser et al. 2010, 2012; Rodriguez-Gomez
et al. 2016). According to this picture, intense dissipation at high-
redshift swiftly builds up the massive, compact ‘core’ of today’s
massive galaxies (e.g. van Dokkum et al. 2008; Damjanov et al.
2009;Toftetal.2014; van Dokkum et al. 2015; Wellons et al.
2016), including most of the in situ component: stars formed in
the main progenitor of the host dark matter halo (e.g. De Lucia &
Blaizot 2007; Genel et al. 2009). Supermassive galaxies, however,
are also expected to have a large ex situ component: stars that are
accreted from other haloes. After the quenching of star formation
C
2019 The Author(s)
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3686 S. Huang et al.
in massive galaxies, (e.g. Hopkins et al. 2008; Johansson, Naab &
Ostriker 2009; Conroy, van Dokkum & Kravtsov 2015), the gradual
accumulation of the ex situ component dominates the assembly
of massive galaxies and helps build-up extended stellar envelopes
(e.g. van Dokkum et al. 2008; Bezanson et al. 2009; Huang et al.
2013; Patel et al. 2013). More importantly, these two components
should show differences in their spatial distributions as a large
fraction of the ex situ component is expected to be deposited
at large radii (e.g. Hilz, Naab & Ostriker 2013; Oogi & Habe
2013). This suggests that the stellar mass distribution of massive
galaxies contains information about their assembly history. From
a cosmological perspective, to understand the assembly of massive
galaxies is to understand how they hierarchically grow with their
dark matter haloes (e.g. Wechsler & Tinker 2018 and the references
within). Recently, the basic understanding of the stellar–halo mass
relation (SHMR) has been established using various direct and
indirect methods (e.g. Hoekstra 2007;Moreetal.2011; Leauthaud
et al. 2012a; Behroozi, Wechsler & Conroy 2013b; Coupon et al.
2015; Zu & Mandelbaum 2015; van Uitert et al. 2016;Shanetal.
2017;Tinkeretal.2017; Kravtsov, Vikhlinin & Meshcheryakov
2018). At low redshift, the SHMR can be characterized by a power-
law relation at low masses, a characteristic pivot halo mass, and an
exponential rise at higher masses (Behroozi, Wechsler & Conroy
2013b; Rodr
´
ıguez-Puebla et al. 2017; Moster, Naab & White 2018).
Constraints on the SHMR have helped us gain insight into the
galaxy–halo connection, but an in-depth picture about how the
assembly of galaxies is tied to their dark matter haloes is still
lacking. At high-mass end, the situation is particularly true (e.g.
Tinker et al. 2017;Kravtsovetal.2018). First, challenges in
measuring the total stellar mass of massive elliptical galaxies with
extremely extended light profile (e.g. Bernardi et al. 2013, 2014,
2017;Kravtsovetal.2018; Pillepich et al. 2018b; Huang et al.
2018c) complicate constraints of the SHMR for massive galaxies.
More importantly, this simple scaling relation does not provide the
full picture; specifically, it does not describe whether or not the
internal structure (i.e. the way in which stellar mass is distributed
in massive galaxies) is tied to the assembly history of their dark
matter haloes. At high-stellar mass (M
) end, the scatter of halo
mass at fixed stellar mass is of order 0.3–0.4 dex (e.g. Tinker et al.
2017). In this paper, we seek to explain how similarly massive
galaxies can live in haloes with very different mass and assembly
histories, by looking for signatures of this assembly process in
the stellar mass profiles of massive galaxies. In previous work
(Huang et al. 2018a,c, Paper I and Paper II hereafter), we map
the stellar mass distributions of massive galaxies at 0.3 ≤ z<0.5 to
>100 kpc individually using deep images from the Hyper Suprime-
Cam (HSC; Miyazaki et al. 2012) Subaru Strategic Program (SSP,
hereafter ‘HSC survey’; Aihara et al. 2017a,b). With the help of
deep images and the redMaPPer cluster catalogue (e.g. Rozo &
Rykoff 2014; Rykoff et al. 2014), we find evidence that the surface
stellar mass density profiles (μ
) of massive central galaxies depend
on dark matter halo mass: centrals galaxies in more massive haloes
tend to have more extended stellar mass distributions (also see:
Charlton et al. 2017; Yoon, Im & Kim 2017) and less mass in the
inner 10 kpc (M
10
).
Here, we seek to directly confirm this dependence and char-
acterize this relation using the galaxy–galaxy weak lensing (‘g–
g lensing’) method (e.g. Mandelbaum et al. 2006a, b; Leauthaud
et al. 2012a; Coupon et al. 2015; Leauthaud et al. 2017) that probes
the dark matter halo mass distribution by measuring the coherent
shape distortion of background galaxies. Instead of relying on a
cluster catalogue, the unprecedented g–g lensing capability of the
HSC survey (e.g. Mandelbaum et al. 2018; Medezinski et al. 2018;
Miyatake et al. 2018) allows us to map the halo mass trend across
a 2D plane described by the M
10
and stellar mass within the largest
aperture that is allowed by the depth of the image (M
max
) and build
an empirical model for galaxy–halo connection at high-mass end.
This paper is organized as follows. We briefly summarize the
sample selection and data reduction processes in Section 2. Please
refer to Paper I for more technical details. Section 3 describes
the weak lensing methodology, and the measurements of aperture
M
and μ
profiles are discussed in Section 4. In Section 5, we
introduce an empirical model to describe the relation between
dark matter halo mass and the distribution of stellar mass within
super massive galaxies. The results from our best-fit model are
presented in Section 6 and discussed in Section 7. Our summary
and conclusions are presented in Section 8.
We use galactic extinction corrected (Schlafly & Finkbeiner
2011) AB magnitudes (Oke & Gunn 1983). For cosmology, we
assume H
0
= 70 km s
−1
Mpc
−1
,
m
= 0.3, and
= 0.7. Stellar
mass (M
) is derived using a Chabrier initial mass function (IMF;
Chabrier 2003). And we use the virial mass for dark matter halo
mass (M
vir
) as defined in Bryan & Norman 1998.
2 DATA AND SAMPLE SELECTION
2.1 SSP S16A data
In this work, we use the WIDE layer of the internal data release
S16A of the HSC SSP, an ambitious imaging survey using the new
prime focus camera on the 8.2-m Subaru telescope. These data
are reduced by
HSCPIPE 4.0.2, a specially tailored version of the
Large Synoptic Survey Telescope (LSST) pipeline (e.g. Axelrod
et al. 2010;Juri
´
cetal.2015), modified for HSC (Bosch et al.
2017). The coadd images are ∼3–4 mag deeper than SDSS (Sloan
Digital Sky Survey; e.g. Abazajian et al. 2009;Aiharaetal.2011;
Alam et al. 2015), with a pixel scale of 0
.
168. The seeing in the
i band has a mean full width at half maximum (FWHM) of 0.
58.
Please refer to Aihara et al. (2017a,b) for more details about the
survey design and the data products. The general performance
of
HSCPIPE is validated using a synthetic object pipeline SYNPIPE
(e.g. Huang et al. 2018b; code available on github at this link
https://github.com/lsst/synpipe). In addition to the full-colour and
full-depth cuts, regions that are affected by bright stars are also
masked out Coupon et al. (2017). The HSC collaboration compiles
the spectroscopic redshifts (spec-z hereafter) of HSC galaxies from
a series of available spectroscopic surveys, which is the main source
of spec-z in this work. We also include additional spec-z from
the most recent data release of the Galaxy And Mass Assembly
(GAMA) survey (Driver et al. 2009, 2011; Liske et al. 2015;Baldry
et al. 2018) which significantly overlaps with HSC coverage in
their G02, G09, G12, and G15 regions and greatly improve the
spec-z completeness of our massive galaxy sample. The HSC
collaboration also provides photometric redshift (photo-z hereafter)
measurements using the point spread function (PSF)-matched five-
band fluxes within 1
.
5 apertures and six different algorithms. Here,
we use the spec-z sample and the photo-z measurements based on
the Flexible Regression over Associated Neighbours with Kernel
dEnsity estimatioN for Redshifts (FRANKEN-Z; Speagle et al.
2019) algorithm. Please refer to Tanaka et al. (2018) for details
about photo-z catalogues.
For our weak lensing measurements, we make use of the first-year
shear catalogue described in detail by Mandelbaum et al. (2018).
Currently, we use the re-Gaussianization algorithm (Hirata & Seljak
MNRAS 492, 3685–3707 (2020)
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Halo mass and stellar mass profiles 3687
2003) to measure galaxy shapes on i-band coadd images. Please
see Mandelbaum et al. (2017, 2018) for more details about our
shape measurements and their calibration. Our shape catalogue also
excludes a small fraction of the survey area that has a problematic
PSF model. The resulting survey area is the full-depth full-colour
region for weak lensing analysis (WLFDFC) region, which covers
∼137 deg
2
in all five bands (grizy) to the required imaging depth
(5σ point source detection limit of 26.0 mag). For our g–g lensing
measurements, we also use a random catalogue that contains a half
million objects and covers the WLFDFC area (e.g. Coupon et al.
2017; Singh et al. 2017).
2.2 Sample selection
Our sample selection is very similar to Huang et al. (2018a, c; Paper I
and Paper II hereafter). We select all galaxies with i
CModel
< =22.0
mag and useful five-band cModel photometry in the WLFDFC
area. Instead of only using galaxies with spec-z’s however, we now
assign a best redshift (z
best
) to each object: We adopt the spec-z
when it is available; for others, we use the photo-z measurements
from FRANKEN-Z as z
best
. We select all galaxies within 0.19 <
z
best
< 0.51, where redshift evolution is not a serious concern
and the volume is large enough (1.03 × 10
8
Mpc
3
) to ensure a
large sample of massive galaxies. The performance of FRANKEN-
Z at this redshift and magnitude range is unbiased and reliable
with respect to the training sample. The typical 1σ uncertainty
is ∼7 per cent with a median bias of about −0.3 per cent and
typical outlier fraction of 11–19 per cent in this redshift range.
Compared with the spec-zonly sample, adding in the photo-z’s
greatly improves the M
completeness of our sample but does
not alter any of our key results. We perform five-band spectral
energy distribution (SED) fitting using the cModel photometry to
derive the average mass-to-light ratio (M
/L
) of galaxies and initial
estimates of M
(M
cmod
). The SED fitting procedure is identical to
the one used in Paper I. In short, we use iSEDFit (Moustakas
et al. 2013)tomeasureM
/L
ratios and k-corrections, assuming
the Chabrier (2003) IMF and using the Flexible Stellar Population
Synthesis models (FSPS; v2.4; Conroy & Gunn 2010a, b). Please
refer to Paper I for more details. Based on the SED fitting results,
we select galaxies with log
10
(M
, cmodel
/M
) > 10.8 as the initial
sample of massive galaxies. Typical uncertainty of M
cmod
is around
0.05–0.1 dex. We further measure the μ
profiles of these galaxies
and aperture M
within different radii (see Section 4.1).
3 GALAXY–GALAXY WEAK LENSING
METHODOLOGY
Galaxy–galaxy lensing measures the coherent shape distortion of
background galaxies around foreground lens galaxies. Please refer
to Mandelbaum et al. (2018) for a detailed description of the
construction of our shear catalogue. A detailed description of our
method for computing is presented in Speagle et al. 2019).
Our methodology is briefly summarized below. The HSC shape
catalogue includes a per-galaxy optimal weight defined as
w
i
=
1
e
2
rms
+ σ
2
e,i
, (1)
where σ
e, i
is the shape measurement error per source galaxy and
e
rms
is the intrinsic shape noise.
We follow the methodology outlined in Singh et al. (2017)to
measure the excess surface mass density (hereafter )profilesof
lens galaxies. Using this method, we measure as:
LR
(r) =
Ls
w
Ls
γ
(ls)
t
(Ls)
crit
Ls
w
Ls
−
Rs
w
Rs
γ
(Rs)
t
(Rs)
crit
Rs
w
Rs
, (2)
whereweuseL for a real-lens galaxy and R for random point. The
superscript or subscript Ls indicates measurement for lens–source
pair, while Rs means the measurement for random-source pair. γ is
the tangential shear, w is the weight, and
crit
is the critical surface
density defined as:
crit
=
c
2
4πG
D
A
(z
s
)
D
A
(z
l
)D
A
(z
l
,z
s
)(1 + z
l
)
2
, (3)
where D
A
(z
L
), D
A
(z
s
), and D
A
z
L
, z
s
are the angular diameter
distances to lens (random), source, and between them, respectively.
We use 11 radial bins uniformly spaced in log-space from 200 kpc
to 10 Mpc (physical units are assumed). The redshift distribution
of random points is matched to the lens sample. The subtraction
of signal around random positions helps remove overestimated
jackknife errors (e.g. Clampitt et al. 2017; Shirasaki et al. 2017)
and accounts for non-negligible coherent additive bias of the shear
measurements (e.g. Takada & Hu 2013). This method has been
adopted by the Dark Energy Survey (DES; e.g. Prat et al. 2017)
and the Kilo-Degree Survey (KiDS; e.g. Amon et al. 2018). We
selected source galaxies based on the following criteria. First, a
set of photo-z quality cuts are applied to the sample; these are the
basic cuts that are described in Speagle et al. 2019). For each
lens, we further require z
s
− z
L
≥ 0.1 and z
s
>z
L
+ σ
s, 68
,where
σ
s, 68
is the 1σ confidence interval of the source photo-z. Errors are
estimated via jackknife resampling. We divide the S16A WLFDFC
footprint into 41 roughly equal-area jackknife regions with regular
shapes. In practice, the effective number of jackknife regions varies,
depending on the specific subsample of lenses. Typically N
JK
> 30.
The diagonal errors for are then estimated as:
Va r
Jk
(
) =
N
Jk
− 1
N
Jk
N
Jk
i=1
(
i
− )
2
, (4)
where N
Jk
is the number of jackknife regions,
i
is the profile
in each region, and
is the mean profile among all jackknife
regions.
We measure the stacked profiles of massive galaxies using
a pure Python g–g lensing pipeline designed for the HSC survey:
dsigma (available here: https://github.com/dr-guangtou/dsigma).
Please refer to Speagle et al. 2019) for more technical details of
dsigma and the g–g lensing measurements.
4 MEASUREMENTS
4.1 μ
profiles and aperture stellar masses
We measure 1D surface brightness profiles on the HSC i-band
images which typically have the best imaging conditions. We use
the Ellipse task from IRAF package after fixing the shape of
the isophote and adaptively masking out all neighbouring objects
based on their brightness and distance to the target. The 1D surface
brightness profile is based on the median flux of unmasked pixels
along each isophote after 3σ -clipping the pixels twice.
1
Since we
limit the sample at z>0.2, the angular sizes of these galaxies make
1
We use projected 2D stellar mass maps from hydrosimulation to show
that our profiles are robust against the impact of unmasked flux from other
objects (Ardilla et al. in preparation).
MNRAS 492, 3685–3707 (2020)
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