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The AGORA High-resolution Galaxy Simulations Comparison Project. V. Satellite
Galaxy Populations in a Cosmological Zoom-in Simulation of a Milky Way–Mass Halo
Minyong Jung
1,31
, Santi Roca-Fàbrega
2,3,30,31
, Ji-hoon Kim
1,4,30,31
, Anna Genina
5,30
, Loic Hausammann
6,7,30
,
Hyeonyong Kim
1,8,30
, Alessandro Lupi
9,10,30
, Kentaro Nagamine
11,12,13,30
, Johnny W. Powell
14,30
, Yves Revaz
7,30
,
Ikkoh Shimizu
15,30
, Héctor Velázquez
16,30
, Daniel Ceverino
17,18
, Joel R. Primack
19
, Thomas R. Quinn
20
, Clayton Strawn
19
,
Tom Abel
21,22,23
, Avishai Dekel
24
, Bili Dong
25
, Boon Kiat Oh
1,26
, and Romain Teyssier
27
The AGORA Collaboration
28,29
1
Center for Theoretical Physics, Department of Physics and Astronomy, Seoul National University, Seoul 08826, Republic of Korea; santi.roca_fabrega@fysik.lu.se
2
Lund Observatory, Department of Astronomy and Theoretical Physics, Lund University, Box 43, SE-221 00 Lund, Sweden; wispedia@snu.ac.kr
3
Departamento de Física de la Tierra y Astrofísica, Facultad de Ciencias Físicas, Plaza Ciencias, 1, 28040 Madrid, Spain; mornkr@snu.ac.kr
4
Seoul National University Astronomy Research Center, Seoul 08826, Republic of Korea
5
Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, D-85748, Garching, Germany
6
ITS High Performance Computing, Eidgenössische Technische Hochschule Zürich, 8092 Zürich, Switzerland
7
Institute of Physics, Laboratoire d’Astrophysique, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
8
Department of Aerospace Engineering, Seoul National University, Seoul 08826, Republic of Korea
9
DiSAT, Università degli Studi dellInsubria, via Valleggio 11, I-22100 Como, Italy
10
Dipartimento di Fisica “G. Occhialini”, Università degli Studi di Milano-Bicocca, I-20126 Milano, Italy
11
Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka, Osaka, 560-0043, Japan
12
Kavli IPMU (WPI), University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba, 277-8583, Japan
13
Department of Physics & Astronomy, University of Nevada Las Vegas, Las Vegas, NV 89154, USA
14
Department of Physics, Reed College, Portland, OR 97202, USA
15
Shikoku Gakuin University, 3-2-1 Bunkyocho, Zentsuji, Kagawa, 765-8505, Japan
16
Instituto de Astronomía, Universidad Nacional Autónoma de México, A.P. 70-264, 04510, Mexico, D.F., Mexico
17
Universidad Autónoma de Madrid, Ciudad Universitaria de Cantoblanco, E-28049 Madrid, Spain
18
CIAFF, Facultad de Ciencias, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
19
Department of Physics, University of California at Santa Cruz, Santa Cruz, CA 95064, USA
20
Department of Astronomy, University of Washington, Seattle, WA 98195, USA
21
Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, Stanford, CA 94305, USA
22
Department of Physics, Stanford University, Stanford, CA 94305, USA
23
SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
24
Center for Astrophysics and Planetary Science, Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel
25
Department of Physics, Center for Astrophysics and Space Sciences, University of California at San Diego, La Jolla, CA 92093, USA
26
Department of Physics, University of Connecticut, U-3046, Storrs, CT 06269, USA
27
Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544 USA
Received 2023 April 18; revised 2024 January 17; accepted 2024 January 29; published 2024 March 22
Abstract
We analyze and compare the satellite halo populations at z∼2 in the high-resolution cosmological zoom-in
simulations of a 10
12
M
e
target halo (z=0mass)carried out on eight widely used astrophysical simulation
codes (ART-I,ENZO,RAMSES,CHANGA,GADGET-3,GEAR,AREPO-T,andGIZMO)for the AGORA High-
resolution Galaxy Simulations Comparison Project. We use slightly different redshift epochs near z=2for
each code (hereafter “z∼2”)at which the eight simulations are in the same stage in the target halo’smerger
history. After identifying the matched pairs of halos between the CosmoRun simulations and the DMO
simulations, we discover that each CosmoRun halo tends to be less massive than its DMO counterpart. When
we consider only the halos containing stellar particles at z∼2, the number of satellite galaxies is significantly
fewer than that of dark matter halos in all participating AGORA simulations and is comparable to the number
of present-day satellites near the Milky Way or M31. The so-called “missing satellite problem”is fully
resolved across all participating codes simply by implementing the common baryonic physics adopted in
AGORA and the stellar feedback prescription commonly used in each code, with sufficient numerical
resolution (100 proper pc at z=2). We also compare other properties such as the stellar mass–halo mass
relation and the mass–metallicity relation. Our work highlights the value of comparison studies such as
The Astrophysical Journal, 964:123 (16pp), 2024 April 1 https://doi.org/10.3847/1538-4357/ad245b
© 2024. The Author(s). Published by the American Astronomical Society.
28
http://www.AGORAsimulations.org
29
The authors marked with
*
as code leaders contributed to the article by
leading the effort within each code group to perform and analyze simulations.
30
Code leaders.
31
Corresponding authors.
Original content from this work may be used under the terms
of the Creative Commons Attribution 4.0 licence. Any further
distribution of this work must maintain attribution to the author(s)and the title
of the work, journal citation and DOI.
1
AGORA, where outstanding problems in galaxy formation theory are studied simultaneously on multiple
numerical platforms.
Unified Astronomy Thesaurus concepts: Galaxy formation (595);Astronomical simulations (1857);Hydro-
dynamical simulations (767);Dwarf galaxies (416)
1. Introduction
Studied extensively by cosmologists, the Lambda cold dark
matter (ΛCDM)model is considered the standard model of Big
Bang cosmology, encompassing dark energy and dark matter.
However, there is a certain tension between theory and
observed galaxies, especially on a small scale (for reviews,
see, e.g., Bullock & Boylan-Kolchin 2017; Del Popolo & Le
Delliou 2017). For example, the observed number of dwarf
galaxies around the Local Group is significantly fewer than that
of the dark matter halos found in N-body simulations when
compared based on their circular velocity. This so-called
“missing satellite problem”is one of the long-standing
challenges of the contemporary ΛCDM model (Kauffmann
et al. 1993; Klypin et al. 1999; Moore et al. 1999; Benson et al.
2002). Reproducing satellite galaxies and small-scale sub-
structures in a simulation within the ΛCDM framework is a
nontrivial task because it requires high numerical resolution
and sophisticated baryonic physics.
The mismatch between the theory and the observation on a
small scale has motivated a great deal of theoretical modeling
such as the warm dark matter (e.g., Bode et al. 2001), fuzzy
dark matter (e.g., Hu et al. 2000), and self-interacting dark
matter (e.g., Spergel & Steinhardt 2000). By suppressing the
small-scale matter power spectrum in the early Universe and/or
stimulating halo disruptions at later times, these alternative
dark matter models have been shown to reduce the number of
subhalos around the Milky Way (MW)–mass halos (e.g.,
Dunstan et al. 2011; Nadler et al. 2021).
On the other hand, it is possible that baryonic processes could
suppress the formation of some dwarf galaxies or make them
difficult to observe, which could explain the missing satellite
problem (D’Onghia et al. 2010;Brooksetal.2013; Brooks &
Zolotov 2014;Sawalaetal.2016a;Wetzel&Hopkins2016;
Applebaum et al. 2021). In such cases, dark matter halos may still
exist but may not have formed visible dwarf galaxies due to the
effects of baryonic physics. This is a possible solution to the
missing satellite problem within the framework of the ΛCDM
paradigm. In addition, many authors have shown that low-mass
halos could be easily disrupted by baryon-induced physics such as
cosmic reionization, tidal stripping, ram pressure stripping, and
stellar feedback (Zhu et al. 2016;Simpsonetal.2018). In the Latte
simulations with the FIRE star formation and feedback model, the
dwarf galaxy population near the MW/M31-mass halo was found
to agree well with the observed population in the Local Group
(Wetzel & Hopkins 2016).Meanwhile,the“Mint”resolution DC
Justice League suite of MW-like zoom-in simulations showed that
the number of satellite galaxies matches the observed population of
the dwarf galaxies around MW-sized galaxies down to the
ultrafaint dwarf regime (UFD; Applebaum et al. 2021).Some
studies have also shown that ΛCDM simulations can reproduce the
radial distribution of MW satellites (Santos-Santos et al. 2018;
Garrison-Kimmel et al. 2019;Samueletal.2020).Moreover,the
number of observed faint galaxies has increased recently (for
reviews, see Simon 2019), which partially mitigates the missing
satellite problem. These findings suggest that the missing satellite
problem is very close to being solved. In fact, some researchers,
such as Kim et al. (2018)and Sales et al. (2022),arguethatthe
problem is resolved.
Ideally, we would then expect the satellite galaxy populations to
be consistent regardless of the simulation code utilized. Never-
theless, due to differences in the inherent properties of the
simulations such as the adopted physics models and the
implementations of the gravity solver, discrepancies may arise
between codes (O’Shea et al. 2005; Heitmann et al. 2008).For
example, Elahi et al. (2016)studied subhalos and galaxies in a
galaxy cluster produced by multiple simulation codes and found
that in dark-matter-only (DMO)simulations, the population and
properties of subhalos show good agreements across code
platforms. Nevertheless, they also discovered that the codes
produced significantly different galaxy populations when baryonic
physics models were included. While they found both similarities
and disparities in the galaxy population, the comparison of dwarf
galaxy populations (M
halo
<10
10
M
e
)was not feasible due to the
limited resolution of their simulations. Indeed, there is an urgent
need for controlled comparisons of the dwarf galaxy populations
produced by different simulation codes. Such comparisons will be
essential to understand the robustness of the satellite galaxy
populations predicted in the simulations and how sensitive they are
with respect to the specific numerical methods and assumptions
adopted in the simulations.
The Assembling Galaxies of Resolved Anatomy (AGORA)
High-resolution Galaxy Simulations Comparison Project has
aimed at collectively raising the predictive power of numerical
galaxy formation simulations by comparing high-resolution
galaxy-scale calculations across multiple code platforms using a
DMO galaxy formation simulation (Kim et al. 2014, hereafter
Paper I), an idealized disk galaxy formation simulation (Kim et al.
2016, hereafter Paper II), and a fully cosmological zoom-in galaxy
formation simulation (Roca-Fàbrega et al. 2021,2024, hereafter
Papers III and IV). In this paper, we analyze the satellite halos
around the target MW-like halo in the AGORA “CosmoRun”
simulation suite introduced and studied in Papers III and IV.
Specifically, we compare the eight hydrodynamic CosmoRuns and
eight DMO simulations, all performed with the state-of-the-art
galaxy simulation codes widely used in the numerical galaxy
formation community, and study the populations of their satellite
halos and galaxies. We choose slightly different redshift epochs
near z=2 for each code in order to compare the runs at the same
dynamical stage in the target halo’s evolution history (see
Section 2.1 for details). We then compare the number of satellite
halos in CosmoRuns with its counterpart in the DMO simulations.
We also explore the consistency between the codes in other
properties of satellite galaxies, including the stellar mass–halo mass
relation as well as the mass–metallicity relation.
This paper is organized as follows. Section 2describes the
AGORA CosmoRun and the DMO simulation, as well as the
definition of a satellite halo. In Section 3, the satellite halo and
galaxy populations in the CosmoRuns are presented in
comparison with those in the DMO runs. In Section 4, based
on our results, we predict the satellite galaxy population at
z∼0 and test intercode convergence in other satellite proper-
ties. Finally, we conclude the paper in Section 5.
2
The Astrophysical Journal, 964:123 (16pp), 2024 April 1 Jung et al.
2. Methodology
2.1. The AGORA “CosmoRun”Simulation Suite
The CosmoRun described in Paper III is a suite of high-
resolution cosmological zoom-in simulations of an MW-mass halo
(10
12
M
e
at z=0)on multiple code platforms.
32
The simulations
analyzed herein started from a cosmological initial condition at
z=100 and reached z2. The adopted cosmological para-
meters are Ω
Λ
=0.728, Ω
matter
=0.272, Ω
DM
=0.227, σ
8
=
0.807, n
s
=0.961, and h=0.702. The code groups participat-
ing in this particular comparison encompass both particle-based
and mesh-based codes: ART-I,ENZO, and RAMSES are mesh-
based codes, whereas CHANGA,GADGET-3,GEAR,AREPO-T,
and GIZMO are particle-based codes.
33
Galaxy formation has
been studied using both approaches, each with its own
advantages and disadvantages. After a series of calibration
steps, all the codes in Paper III reached an overall agreement in
the stellar properties of the target halo and its mass assembly
history. The final CosmoRun suite includes common baryonic
physics modules in AGORA such as the GRACKLE radiative
gas cooling (Smith et al. 2017), cosmic ultraviolet background
radiation (Haardt & Madau 2012), and star formation, as well
as the code-dependent physics including—most notably—
stellar feedback prescriptions. Both code-independent and
code-dependent physics implemented in each code are
explained in great detail in Paper III (some in Paper II).We
update the two models from Paper III,ART-I and CHANGA,to
include weaker stellar feedback. In ART-I, we change the
condition for the minimum time step at high redshifts to
achieve better convergence in the halo growth history. We also
incorporate a new model using the AREPO code into our
analysis. We refer to this as AREPO-T, which represents the
AREPO code with thermal feedback. The differences between
the old and new ART-I and CHANGA models, as well as the
details of the AREPO-T model, are illustrated in Paper IV.
34
The gravitational force softening length for the particle-
based codes in the highest-resolution region is 800 comoving
pc until z=9 and 80 proper pc afterward. Meanwhile, the finest
cell size of the mesh-based codes is set to 163 comoving pc, or
12 additional refinement levels for a 128
3
root resolution in a
-
h60 comoving Mpc
13
(
)box. A cell is adaptively refined into
eight child cells on particle overdensities of 4. For details on
runtime parameters, we refer the reader to Paper III.
While all the AGORA CosmoRun simulations were
calibrated to produce similar stellar masses in the host halo
by z=4(see Section 5.4 and Figure 12 in Paper III),wefind
that the host halo in some codes’CosmoRun is at a different
stage in its dark matter accretion history from others’at z=2.
This is likely due to the intercode “timing discrepancy”(see
Section 5.3 in Paper Ifor more information). Because the halos
in different codes are at different evolutionary stages, the
satellite halo abundances are also different among the
CosmoRuns. To resolve this timing discrepancy, we have
created a merger tree for each code and selected an epoch near
z=2(hereafter called “z∼2”)for each code so that the target
halo is in the same stage in its merger history (for more
information, see Paper IV). The list of epochs for each code
used for the present paper is in Table 1. Snapshots of the
CosmoRun simulations at z∼2 are shown in Figure 1.
2.2. The DMO Simulations
In order to investigate the role of baryonic physics adopted
for AGORA in the satellite halo population, we have also
performed DMO simulations using the same zoom-in initial
condition generated with MUSIC (Hahn & Abel 2011)but with
no gas component. Accordingly, the mass of the dark matter
particles in the DMO runs is Ω
matter
/Ω
DM
=1.20 times heavier
than that in the CosmoRun. While Paper Ifound that the dark
matter properties and the satellite halo populations are nearly
identical across all participating codes in AGORA, there
remained a systematic discrepancy in the satellite halo
populations in the low-mass end. Therefore, we have employed
all eight codes in AGORA to run DMO simulations to check
their consistency.
35
Snapshots of these DMO runs z∼2 are
also included in Figure 1. The runtime parameters governing
the collisionless dynamics in the DMO runs are set to be
identical to those used for the CosmoRun.
2.3. Halo Finding
Halos in the CosmoRun and the DMO runs are identified
with the ROCKSTAR halo finder (Behroozi et al. 2013)using
only the highest-resolution dark matter particles (i.e., not stellar
or gas particles). We further narrow down the identified halos
to satellite halos using the following criteria: (i)it must reside
within 300 comoving kpc from the target host halo (100 proper
kpc at z=2; similar to the virial radius, R
vir
, of our host halo at
z=0), and (ii)it must be more massive than 10
7
h
−1
M
e
in dark
matter (equivalent to 45 dark matter particles in the DMO
runs).
36
We follow theBryan & Norman (1998)definition of
virial radius and mass.
For our analysis in Sections 3.4 and 4, we assign a stellar
particle to a halo following the process in Samuel et al. (2020).
We first identify all stellar particles located within 0.8R
vir
from
the halo, with their velocities relative to the halo less than twice
Table 1
The Redshift Epoch Selected for Each Code to Be Analyzed in This Paper
Code Redshift Epoch
CosmoRun DMO Run
ART-I 1.85 2.18
ENZO 2.29 2.15
RAMSES 2.21 2.12
CHANGA 2.08 2.09
GADGET-2/32.13 2.05
GEAR 1.88 1.87
AREPO-T 1.98 2.11
GIZMO 2.02 2.11
Note. At these epochs, the eight CosmoRuns are in the same stage in the target
halos’merger history. See Section 2.1 for details.
32
For publicly available data sets, visit http://www.AGORAsimulations.org
or http://flathub.flatironinstitute.org/agora.
33
We classify the SPH codes (CHANGA,GADGET-3,GEAR)and the arbitrary
Lagrangian–Eulerian codes (AREPO and GIZMO)as particle-based codes.
34
In the analysis presented in Section 4.1, we used the older ART-I model,
labeled as ART-I (old), which is described in Paper III, because the new model
has not reached z1. The results with both models are mostly consistent.
35
In terms of the gravity solver for collisionless components, GADGET-2
(latest version in 2011)and GADGET-3 (first introduced in Springel et al. 2008)
are identical for our purpose and will produce practically identical results in the
DMO runs.
36
Note that there are no velocity criteria or requirements when identifying
satellites. Therefore, some halos may be counted as satellites despite not being
gravitationally bound to the host halo.
3
The Astrophysical Journal, 964:123 (16pp), 2024 April 1 Jung et al.
the halo’s maximum circular velocity. We then calculate the
radius that encompasses 90% of the stellar particles (R
90
)and
the stellar velocity dispersion (σ
vel
). To further refine our
selection, we narrow down the stellar particle list to those
satisfying two more conditions: (1)they are located within
1.5 R
90
from the center of mass of the halo and stellar particles,
and (2)their velocities relative to the halo are less than 2σ
vel
.
We then iterate the analysis, recalculating R
90
and σ
vel
for
the selected member particles until they converge within 99%
of the previous values. We start from the most massive satellite
halos to lower ones, making sure not to reassign stellar
particles that have already been allocated. Finally, we define
satellite “galaxies”as those whose stellar masses are at least
6 times the approximate mass resolution of stellar particles
(i.e., M
star
>6m
gas,IC
=2.38 ×10
5
h
−1
M
e
; see Section 3.1 of
Paper III).
3. Results
3.1. Satellite Halo Populations at z∼2
Figure 2shows the dark matter surface density plots in a
(600 comoving kpc)
2
box, with the target host halo and the
satellite halos drawn in white circles (whose radii indicate half
the virial radii, 0.5R
vir
). One can already observe that the eight
Figure 1. The dark matter surface densities at z∼2(the exact redshift in each code in Table 1)for eight hydrodynamic “CosmoRun”simulations and eight DMO
simulations, projected through a 1.8 comoving Mpc thick slab, with the target host halo’s virial radius R
vir
drawn in a white circle. See Section 2for more information
on these simulations. Simulations performed by Santi Roca-Fàbrega (ART-I,RAMSES, and ART-I-DMO), Ji-hoon Kim (ENZO), Johnny Powell and Héctor Velázquez
(CHANGA and CHANGA-DMO), Kentaro Nagamine and Ikkoh Shimizu (GADGET-3), Loic Hausammann and Yves Revaz (GEAR and GEAR-DMO), Anna Genina
(AREPO-T and AREPO-DMO), Alessandro Lupi and Bili Dong (GIZMO), and Hyeonyong Kim (ENZO-DMO,RAMSES-DMO,GADGET-2-DMO, and GIZMO-DMO). Note
that the mean dark matter surface densities in DMO runs are Ω
matter
/Ω
DM
=1.20 times higher since they include the contribution from baryons. The high-resolution
versions of this figure and article are available at the Project website, http://www.AGORAsimulations.org/.
4
The Astrophysical Journal, 964:123 (16pp), 2024 April 1 Jung et al.
hydrodynamic CosmoRuns have produced similar numbers of
dark matter halos with similar R
vir
s for the host halo. Readers
can also see that the DMO runs clearly have more satellite
halos than the CosmoRuns.
To quantitatively study the differences in the participating
simulations, in Figure 3, we plot the cumulative number of
satellite halos at z∼2 in their dark matter mass, N
halo
(>M)
(left panels), and in radial distance from the host halo’s center,
N
halo
(<r)(right panels). It is worth noting several points.
1. First, we find that all eight hydrodynamic CosmoRuns
have fewer satellite halos than the DMO runs across all
halo masses and radii. In the halo mass function (left
panels of Figure 3), the numbers of satellite halos in all
CosmoRuns are systematically fewer than those in the
DMO runs by a factor of ∼2 for M
halo
(halo dark matter
mass)<10
8.5
h
−1
M
e
. To put it differently, the ratios of
the number of the CosmoRun satellite halos to that in the
DMO run (the mean number of halos in the eight DMO
runs)in each mass bin, N
halo
/〈N
halo,DMO
〉,is∼0.5
(bottom left panel).
2. Second, the ratio of the satellite halos’radial distribution
function in the CosmoRun to that in the DMO run,
N
halo
/〈N
halo,DMO
〉, tends to become small—often 0—in
the bin closest to the host halo’s center, r<
40 comoving kpc (bottom right panel of Figure 3). This
implies that the causes of the deficit—the effect of
baryonic physics, which we will explore in depth in
Section 3.2—have a stronger influence near the host
halo’s center. This is consistent with the findings of
Figure 2. The dark matter surface densities at z∼2 with the halos identified by the ROCKSTAR halo finder drawn in white circles whose radii indicate 0.5R
vir
. Only the
halos located within 300 comoving kpc from the host halo’s center and those more massive than 10
7
h
−1
M
e
in dark matter are drawn. Readers can readily see that the
DMO runs have more satellite halos than the CosmoRuns. See Section 3.1 for more information.
5
The Astrophysical Journal, 964:123 (16pp), 2024 April 1 Jung et al.
earlier studies (e.g., Brooks & Zolotov 2014; Wetzel &
Hopkins 2016; Garrison-Kimmel et al. 2017; Sawala
et al. 2017; Kelley et al. 2019).
3. The satellite halo populations in the eight DMO runs are
slightly different but are in general agreement with one
another in both mass and space (upper panels of Figure 3;
lines with a reduced stroke width and darker colors).
Among the DMO runs, no systematic difference exists
between the mesh-based and particle-based codes, a
result somewhat different from the earlier studies (e.g.,
O’Shea et al. 2005; Heitmann et al. 2008)or from our
findings in Paper I.
37
Instead, ENZO-DMO has a slightly
higher number of halos compared to the particle-based
codes, and RAMSES-DMO is in the middle of the pack of
particle-based codes. The numerical resolution in the
highest-resolution region of the CosmoRun—and, corre-
spondingly, our new DMO runs—is chosen to resolve the
interstellar medium and the star-forming regions in it
(i.e., 100 proper pc at all times between z=100 and 2).
The high resolution in our simulation suite might have
been sufficient for ENZO-DMO and RAMSES-DMO to
alleviate any discrepancy previously observed in the
satellite halo population between the particle-based and
mesh-based DMO runs. Note that ART-I-DMO seems to
have had a slightly harder time fully resolving the
outskirts of our target halo.
38
Even so, the difference is
not as severe as what was seen in the previous studies.
4. Two CosmoRuns, ART-I and ENZO, have smaller satellite
halo populations than the rest of the participating codes,
especially in the low-mass end (M
halo
<10
7.5
h
−1
M
e
)and
in the outskirts of the host halo (r>200 comoving kpc).
And the number of halos in the three mesh-based
CosmoRuns tends to be lower in the range of halo masses
M
halo
∼10
8.5
h
−1
M
e
and radial distances 100, 150
[]
comoving kpc. The intercode difference among the
CosmoRuns, which their counterpart DMO runs do not
exhibit, should be attributed to how the same (or similar)
baryonic physics are treated differently in the two
hydrodynamics approaches.
One of the most notable findings among the above is that all
hydrodynamic CosmoRuns have produced fewer satellite halos
than the DMO runs by z∼2 across all halo masses and radii.
We further study in Section 3.4 that the so-called “missing
satellite problem”(overabundance of satellite halos in simula-
tions; Kauffmann et al. 1993; Klypin et al. 1999; Moore et al.
1999; Benson et al. 2002)could be easily resolved in all
participating codes simply by implementing the baryonic
physics adopted for AGORA in simulations with sufficient
numerical resolution (100 proper pc at z=2)by examining
the satellite galaxy populations around the target host halo. For
now, in Sections 3.2 and 3.3, we focus on the causes of the
Figure 3. The cumulative number of satellite halos at z∼2 in their dark matter mass, N
halo
(>M)(left), and in radial distance from the host halo’s center, N
halo
(<r)
(right). We distinguish mesh-based codes (solid lines)and particle-based codes (dashed lines)with different line styles and CosmoRuns and DMO runs with different
brightness. The bottom panels display the ratio of the number of CosmoRun satellite halos to that in the DMO run (the mean value of the eight DMO runs)in each
mass/radius bin. All hydrodynamic CosmoRuns have fewer satellite halos than the DMO runs do across all halo masses and radii. See Section 3.1 for more
information.
37
In Paper I, a systematic difference between particle-based and mesh-based
codes at the low-mass end was observed. It was because mesh-based codes tend
to have coarser force resolution as they attempt to resolve minute density
fluctuations in the outskirts of the target halo at high redshift, resulting in a
difference in the abundance of low-mass satellite halos. Note also that the
analysis in Paper Iwas carried out with the HOP halo finder, a different choice
from the ROCKSTAR halo finder for what is presented here, which could
produce different numbers of halos identified.
38
Note that runtime parameters are not chosen to match the refinement
structure between the CosmoRun and the DMO run. In a typical mesh-based
DMO run, cells are adaptively refined only by dark matter mass, whereas in a
CosmoRun, they are refined not only by dark matter mass but also by baryon
mass and others. As a result, ART-I and ART-I-DMO may have different
refinement structure, especially in the outskirts of the target halo.
6
The Astrophysical Journal, 964:123 (16pp), 2024 April 1 Jung et al.
differences seen in Figure 3between the satellite halos in the
CosmoRuns and in the DMO runs.
3.2. Evolution of Satellite Halo Populations
We now study the halo populations at multiple epochs from
z=15 to ∼2 to understand and discriminate various causes that
have affected the satellite halo populations. Figure 4shows
the evolution of the number of satellite halos in two different
mass bins, 10
7
h
−1
M
e
<M
halo
<10
8
h
−1
M
e
(left panels)and
M
halo
>10
8
h
−1
M
e
(right panels). Readers can notice that the
hydrodynamic CosmoRun simulations and the DMO runs
show systematic differences in both mass bins at nearly all
redshifts. In the left panels of Figure 4, one may spot the
systematic disagreements between the DMO runs, the group of
particle-based CosmoRuns, and the group of mesh-based
CosmoRuns, already at z=15. From z=8 to 4, the number
of halos in the CosmoRuns barely grows in both mass bins,
while those in the DMO runs increase steadily. The number of
halos in the CosmoRuns in the higher-mass bin (right panels;
M
halo
>10
8
h
−1
M
e
)remain approximately constant from z=3
to ∼2, whereas those in the DMO runs continue to increase. In
the meantime, just as in Figure 3, there exists disagreement
between the particle-based codes (colored dashed lines in
the top panels of Figure 4)and the mesh-based codes (colored
solid lines), especially in the lower-mass bin (top left panel;
10
7
h
−1
M
e
<M
halo
<10
8
h
−1
M
e
).
Now we investigate various causes for these differences
in time.
1. As early as z=12, the CosmoRuns tend to have fewer
halos than the DMO runs, even before the cosmic
reionization begins or the extragalactic ultraviolet back-
ground radiation is turned on in GRACKLE.
39
It is
especially true in the higher-mass bin (right panels;
M
halo
>10
8
h
−1
M
e
).Atz∼15, smaller dark matter halos
have difficulties keeping baryons because the density
fluctuation of gas is smoother than that of dark matter on
small scales (Gnedin & Hui 1998). Thus, these smaller
Figure 4. The evolution of the number of satellite halos across cosmic time for two different dark matter mass bins, 10
7
h
−1
M
e
<M
halo
<10
8
h
−1
M
e
(left)and
M
halo
>10
8
h
−1
M
e
(right). We only count halos that reside within 300 comoving kpc from the target host halo. The top panels highlight the CosmoRuns with the
DMO runs shown at reduced opacity, while the bottom panels emphasize the DMO runs with the CosmoRuns at reduced opacity. All hydrodynamic CosmoRuns have
fewer satellite halos than the DMO runs do in both mass bins at nearly all redshifts. The mesh-based CosmoRuns tend to host slightly fewer lower-mass satellite halos
than the particle-based CosmoRuns do at most redshifts (top left panel). See Section 3.2 for more information.
39
We set the GRACKLE parameters UVbackground_redshift_on =15
and UVbackground_redshift_fullon =15.
7
The Astrophysical Journal, 964:123 (16pp), 2024 April 1 Jung et al.
halos have a smaller enclosed baryon mass than the
cosmic average (O’Leary & McQuinn 2012). This leads
to lower halo masses in the CosmoRuns at z=15 and
therefore fewer halos in Figure 4. From z=15 to 8, the
difference between the CosmoRuns and the DMO runs
persists in both mass bins.
2. Again as early as z=12, one can observe a discrepancy in
the CosmoRuns between particle-based codes and mesh-
based codes in the lower-mass bin (top left panel;
10
7
h
−1
M
e
<M
halo
<10
8
h
−1
M
e
). Particle-based codes
show a tendency to have more halos than mesh-based codes
until z∼6, when RAMSES begins to behave like particle-
based codes. It is well documented that the particle-based
codes may produce more satellite halos due to the so-called
“gas–dark matter particle coupling”in the early Universe
(Yoshida et al. 2003;O’Leary & McQuinn 2012).Whena
gas particle is close to a nearby dark matter particle, the gas
particle could be captured in the dark matter particle’s
potential well. This gas particle now obtains an artificial
velocity that follows that of the dark matter particle, resulting
in an increased power on small scales. Even a minute gas–
dark matter two-particle coupling could be a source of
numerically driven fluctuation, particularly in the early
Universe, that is nearly homogeneous. While this artifact
may be alleviated with adaptive gravitational softening, the
particle-based codes in the AGORA CosmoRun suite
adopted a fixed gravitational softening length (see
Section 2), prone to overproduction of satellite halos.
40
On
the other hand, some DMO runs in mesh-based codes
may have coarser force resolution at high redshift as they
attempt to resolve small density fluctuations in the
outskirts of the target halo (O’Shea et al. 2005; Heitmann
et al. 2008), leading to smaller numbers of halos in, e.g.,
ART-I-DMO and RAMSES-DMO.
3. From z=8 to 4, reionization plays an important role in
suppressing the growth of satellite halos in the CosmoRun
(see Section 2and Paper III), when other local baryonic
physics mechanisms are yet to become effective. The
extragalactic photoionizing background radiation heats and
removes the gas prior to infall and efficiently inhibits the
growth of halos at z8(Sawala et al. 2015; Qin et al.
2017).
41
Reionization is relatively more effective on the
low-mass halos (<-
v20 km s ;
circ,max 1Sawala et al.
2015; Zhu et al. 2016).
4. At later times, other baryonic effects enhance the depletion
of substructures when compared to the DMO counterparts.
Gasinlow-masshalosisremovedbyrampressurestripping
before the infall, along with the extragalactic radiation field.
Tidal stripping in the steep gravitational potential of the host
halo becomes important now and significantly affects the
satellite halo population, especially in the intermediate-
mass range (<<
--
v
2
0 km s 35 km s
;
1circ,max 1D’Onghia
et al. 2010;Brooksetal.2013; Brooks & Zolotov 2014;
Sawala et al. 2016b,2017;Zhuetal.2016;Garrison-
Kimmeletal.2017; Kelley et al. 2019). However, tidal
disruption induced by the stellar bulge and disk in
cosmological simulations could be overestimated due to
insufficient resolution (see Webb & Bovy 2020; Green et al.
2022). Stellar feedback such as supernovae also expels the
gas and impedes the halos’mass growths (Brooks et al.
2013;Munshietal.2013; Velliscig et al. 2014; Schaller et al.
2015; Fitts et al. 2017). These late-time baryonic processes
can explain the widening gap between the CosmoRuns and
the DMO runs at z4inboththeleftandrightpanelsof
Figure 4.
In summary, we find that baryonic processes cause all
hydrodynamic CosmoRun simulations to have fewer satellite
halos than the DMO runs at nearly all redshifts. While baryonic
physics left only indirect signatures in the halos’growth
histories of dark matter masses (M
halo
), in Section 3.4, we will
see its more direct impact on the halos’stellar components.
3.3. How Baryonic Physics Affects Each Individual Halo
Until now, we have mainly focused on the population of
satellite halos and how it changes with the inclusion of
baryonic physics. To investigate how each individual halo is
actually affected by the baryonic processes, we now match and
compare halos in hydrodynamic simulations (e.g., ENZO
CosmoRun)to their counterparts in the DMO simulation
(e.g., ENZO-DMO run). The matching process is adapted from
Schaller et al. (2015)and Lovell et al. (2022). For every
satellite halo in, e.g., ENZO CosmoRun, we first identify the 40
dark matter particles that are closest to the halo’s center. Since
the particle IDs are shared by the ENZO and ENZO-DMO runs,
we can locate these 40 particles in the ENZO-DMO run. Then we
search for a halo containing 50% or more of these counterpart
particles. Finally, by carrying out the same procedure in
reverse, another link is obtained—i.e., first find the 40 most
bound particles in the ENZO-DMO run and then locate these
particles in the ENZO CosmoRun. A pair of halos that are
bijectively mapped (bidirectionally connected)between the two
simulations are considered as a “matched”pair. Particle IDs are
identically assigned in the initial conditions of CHANGA,
GAGDET-3,GEAR,AREPO-T,GIZMO, and their DMO counter-
parts, so we can similarly find matched pairs in between the
two codes. But because particle IDs in ART-I,RAMSES, and
their DMO counterpart simulations are not identically assigned
in their initial conditions, halos in these two simulations need to
be matched with a different method based on the distribution of
dark matter particles at z=100 (see Appendix for details).
We conjecture that various baryonic processes have slowed
down the growth of halos in hydrodynamic simulations
compared to their DMO counterparts. To test this hypothesis,
in Figure 5, we plot the ratio of the dark matter mass of an
individual halo in the CosmoRun to that of its matched DMO
counterpart (M
halo
/M
DMO
). A few observations to note are as
follows.
1. In all eight CosmoRuns matched to their respective DMO
counterpart, the ratio M
halo
/M
DMO
is on average less than
Ω
DM
/Ω
matter
=0.83 (marked with solid horizontal lines
in Figure 5), where Ω
matter
=0.272 and Ω
DM
=0.227 (see
Section 2.1). If the halo in the CosmoRun had followed
an identical mass growth history as that of its DMO
counterpart, the dark matter mass of the CosmoRun
40
A new type of cosmological initial condition generated with a higher-order
Lagrangian perturbation theory may provide another solution to this problem
(Michaux et al. 2021). It will enable us to start our simulation at z;15, much
later than z=100 as in the CosmoRun, bypassing the gas–dark matter coupling
problem at high redshift entirely.
41
It is worth reminding readers that, in DMO runs, the mass of the gas is
included in the dark matter component, effectively making Ω
matter
=
0.272 =Ω
DM
(see Section 2.2). Therefore, while the gas experiences
hydrodynamic forces such as reionizing radiation and may “evaporate”in the
CosmoRun, the gas mass contributes in whole to the growth of the halo in the
DMO run.
8
The Astrophysical Journal, 964:123 (16pp), 2024 April 1 Jung et al.
halo, M
halo
, should have been M
DMO
×Ω
DM
/Ω
matter
=
0.83 M
DMO
. The fact that the ratio lies below 0.83 means
that the halos have smaller masses and smaller virial radii
in all hydrodynamic simulations when compared with
their DMO counterparts. Although the halos originated
from the same patch in the initial condition, the ones
under the influence of baryonic physics did not grow as
much in mass as their DMO counterparts did.
2. The baryonic effects are present at all redshifts, slightly
more so at later times (i.e., the M
halo
/M
DMO
ratio is
smaller at z∼2 than at z=12). The baryonic effects are
the combination of early- and late-time processes, such as
reionization inhibiting the growth of small satellite halos
with shallow gravitational wells, and the host halo’s tidal
field stripping the halos of existing gas, as discussed in
Section 3.2.
3. Among the CosmoRuns, the mesh-based codes tend to
have lower M
halo
/M
DMO
values than the particle-based
codes do in general, especially at low-mass end. The
discrepancy between the two code groups is considerable
already at z=12, which is in line with the overabundance
of satellite halos in particle-based codes discussed in
Section 3.2. Furthermore, consistent with the patterns
observed in Figures 3and 4,ART-I and ENZO have
smaller ratios compared to the other codes.
It should be noted that only a small fraction of halos are
matched with their DMO counterparts in the low-mass end
(M
DMO
10
8
h
−1
M
e
). Figure 6illustrates the fraction of halos
whose counterparts in the DMO simulations are identified at
z∼2, averaged over all eight CosmoRuns. Since our halo
matching process is more demanding for halos with fewer
member particles, the “match fraction”is lower for low-mass
halos. This suggests that the low-mass matched halos are likely
biased toward the ones with quiescent accretion histories and
without major mergers or disruptions in the past, potentially
resulting in an overestimated M
halo
/M
DMO
ratio. Readers may
also find it interesting that massive satellite halos (M
DMO
10
9
h
−1
M
e
)have disappeared between z=7 and 4 (second and
third panels from the right in Figure 5). According to the
accretion history of the host halo, multiple mergers occur
between z=7 and 4, which explains the disappearance of the
massive satellites by z=4.
To summarize, we have shown that each individual halo
tends to have a slower mass accretion history until z∼2 in the
CosmoRun than in its counterpart DMO run. The discrepancy
can be explained by early- and late-time baryonic physics that
slows down the growth of satellite halos.
Figure 5. The ratio of the dark matter mass of an individual halo in the CosmoRun to that of its DMO counterpart (M
halo
/M
DMO
). Each symbol represents a
CosmoRun–DMO run pair at four different epochs, from z=12 to ∼2. A thick solid line is the median value in each mass bin for each CosmoRun. The solid
horizontal line denotes Ω
DM
/Ω
matter
=0.83. In all CosmoRuns we analyzed, the median value of M
halo
/M
DMO
is less than 0.83. This means that the halos originated
from the same patch in the initial condition, but under the influence of baryonic physics, they did not grow as much in mass as their DMO counterparts did. See
Section 3.3 for more information.
Figure 6. The fraction of halos whose counterparts in the DMO simulations are
identified at z∼2, averaged over all eight CosmoRuns. Error bars indicate one
standard deviation. The “match fraction”is lower for low-mass halos because
the matching criterion is more demanding for them. It implies that the low-mass
matched halos are likely biased toward the ones with quiescent accretion
histories. See Section 3.3 for more information.
9
The Astrophysical Journal, 964:123 (16pp), 2024 April 1 Jung et al.
3.4. Satellite Galaxy Populations at z∼2
In Section 3.1, we have demonstrated that all hydrodynamic
CosmoRun simulations produce fewer satellite halos around
our host halo than the DMO runs do across all satellite masses
and radii. To verify that this finding naturally leads to the
baryonic solution to the “missing satellite problem”(see
Section 3.1)that is independent of the numerical platform
utilized, in this section, we examine the satellite galaxy
populations around the target host halo. Here we define
“galaxies”as satellite halos that contain stellar particles (see
Section 2.3 for more information).
In Figure 7, we plot the cumulative number of satellite
galaxies at z∼2 in their stellar mass, N
galaxy
(>M)(left), and
in their three-dimensional stellar velocity dispersion,
N
galaxy
(>σ
vel
)(right). In both panels, we restrict the satellite
galaxies to those with M
star
>6m
gas,IC
=2.38 ×10
5
h
−1
M
e
(see Section 2.3). Several notable points are as follows.
1. By comparing with the mass function of satellite halos,
N
halo
, in Figure 3or with the gray dotted line in the right
panel of Figure 7denoting the average number of satellite
halos in all CosmoRuns, one can readily see that the
number of satellite galaxies is significantly fewer than
that of satellite halos in all participating CosmoRuns.
While baryonic physics left indirect signatures in the
halos’growth histories of dark matter masses in
Sections 3.1 and 3.2, we can now see its more direct
impact on the halos’stellar components. All the baryonic
processes discussed in Section 3.2—such as cosmic
reionization, tidal stripping, ram pressure stripping, and
stellar feedback—act efficiently to halt or impede the
stellar mass growth inside the halo (Bullock et al. 2001;
Revaz & Jablonka 2018). For example, gas in a low-mass
halo with a shallow potential well is removed by ram
pressure stripping before its infall to the host halo and by
stellar feedback as supernovae explode. Further, these
processes can interact; for example, supernova feedback
can expel gas from halos, which is then more easily
removed by ram pressure stripping. As a result, gas is
depleted in most low-mass satellite halos in the
CosmoRuns, which end up with few stellar particles.
2. The thick black solid and dashed lines in both panels of
Figure 7indicate the present-day satellites around the
MW and M31, respectively (McConnachie 2012).
42,43
Although readers should be cautioned that we are
comparing two data sets at different epochs, one can
observe that the satellite galaxy populations in the
CosmoRuns at z∼2 are largely consistent with those of
the MW and M31 at z=0 in their stellar masses and
velocity dispersions. For more on how we attempt to
compare the satellite galaxy populations at z∼0, see
Section 4.1 and Figure 8.
3. The agreement among the satellite galaxy populations of
the eight CosmoRuns is better in the right panel
(N
galaxy
(>σ
vel
)in stellar velocity dispersion)than in
the left panel (N
galaxy
(>M)in stellar mass). This is
because the velocity dispersion serves as a better and
Figure 7. The cumulative number of satellite galaxies at z∼2 in their stellar mass, N
galaxy
(>M)(left), and three-dimensional stellar velocity dispersion,
N
galaxy
(>σ
vel
)(right).Wedefine galaxies as satellite halos that contain stellar particles. The number of satellite galaxies is significantly lower than that of satellite
halos in all eight CosmoRuns. Readers may compare N
galaxy
with N
halo
(in Figure 3)or with the gray dotted line in the right panel denoting the average number of
satellite halos in all CosmoRuns (plotted with their dark matter velocity dispersion). The thick black solid and dashed lines in both panels indicate the known present-
day satellites around the MW and M31, respectively, which of course are lower limits to the true numbers. See Section 3.4 for more information.
42
The latest compilation in 2021 can be found in https://www.cadc-ccda.hia-
iha.nrc-cnrc.gc.ca/en/community/nearby/. For the stellar velocity dispersion
of M33, however, we followed Quirk et al. (2022). To estimate the stellar mass
of galaxies, we assume a mass-to-light ratio of 1. Recent observations find
more satellite galaxies in the Local Group, yielding 50−60 satellites around the
MW. However, most of these newly discovered galaxies are UFDs, which are
fainter than M
V
=−7.7 (or L=10
5
L
e
; Simon 2019). Therefore, these newly
discovered UFDs are beyond the scope of the present study owing to the
limited numerical resolution.
43
The three-dimensional stellar velocity dispersions, σ
vel
, of the MW and M31
satellite galaxies are estimated by the line-of-sight stellar velocity dispersions
multiplied by 3. The number of satellite galaxies around M31 shown in the
two panels of Figure 7differs slightly due to the lack of stellar velocity
information for two satellites. That is, among the 19 observed satellites around
M31, 16 have available stellar velocity information.
10
The Astrophysical Journal, 964:123 (16pp), 2024 April 1 Jung et al.
more useful proxy for the dynamical mass of a system, as
it reflects the gravitational impact of the underlying dark
matter halo (not just the stellar component of a galaxy).
While the difference in the satellite galaxy population
among the CosmoRuns is more pronounced when
considering their stellar mass, there remains a good
overall agreement. In Section 4.2, we further investigate
the relationship between the dark matter mass and stellar
mass of the satellite halos.
To sum up, we have found that the number of satellite
galaxies is significantly lower than that of dark matter halos
in all CosmoRun simulations and is comparable to the
number of present-day satellites near the MW or M31. The
so-called “missing satellite problem”is resolved in all
participating codes simply by implementing the baryonic
physics adopted for AGORA in simulations with sufficient
numerical resolution (100 proper pc at z=2). We argue
that various baryonic processes make the CosmoRuns have
far fewer satellite galaxies than the satellite dark matter halos
in the DMO runs. Future studies tracing the star formation
history and the trajectory of each halo will tell us which
baryonic mechanism acts most prominently and when.
4. Discussion
4.1. Predicting Satellite Galaxy Populations at Lower Redshifts
In Section 3, we choose to study the satellite halo
populations at z∼2 because not all the AGORA CosmoRuns
have yet reached z=0. This approach, of course, has
limitations, as the majority of satellite halos at z∼2 are likely
to undergo mergers or be disrupted by z=0. Here we describe
what form of satellite galaxy populations we expect to see at
lower redshifts.
In the DMO simulations, the number of satellite halos tends
to increase over time, which may lead one to conclude that a
higher satellite halo abundance is expected at z∼0 than at
z∼2. However, as illustrated in Section 3.2, baryonic physics
may disrupt halos, considerably reducing the number of
satellite halos in the hydrodynamic simulations at lower
redshift. And particularly because the AGORA CosmoRun
adopted an initial condition of a halo with a quiescent merger
history after z=2, the number of newly accreted satellite halos
may be small after z=2. Therefore, we expect that the satellite
galaxy population in the CosmoRuns would not change
dramatically from z∼2toz∼0.
In order to verify this, in Figure 8, we plot the satellite halo
population at z=0.3 as a function of stellar mass and stellar
velocity dispersion for the five codes that reached the epoch
already.
44
The numbers of satellite galaxies at z=0.3 for these
codes are either only a factor of 2 larger than those at z∼2or
almost identical (as in the case of ENZO and AREPO-T).
However, the intercode differences have greatly increased. For
instance, ENZO and AREPO-T have no satellite galaxies with
M
star
>10
7
h
−1
M
e
at that epoch, while GADGET-3 and GEAR
each have six satellite galaxies exceeding that stellar mass.
Compared by three-dimensional stellar velocity dispersion,
ENZO has no satellite galaxies with σ
vel
>40 km s
−1
, while
GEAR has five satellite galaxies exceeding that velocity
dispersion. Despite these differences, the results still align well
with the observed satellite galaxy populations for the MW and
M31, except that ENZO shows a slightly lower population in
both stellar mass and velocity dispersion, and AREPO-T exhibits
a reduction in stellar mass. We conclude that our findings in
Section 3for z∼2 will likely also hold at z∼0.
Figure 8. The cumulative number of satellite galaxies at z=0.3 in their stellar mass, N
galaxy
(>M)(left), and three-dimensional stellar velocity dispersion,
N
galaxy
(>σ
vel
)(right), for the ART-I (old),ENZO,GADGET-3, and GEAR CosmoRuns. The gray area represents the minimum and maximum values of the cumulative
number of satellite galaxies at z∼2 from those codes. The numbers of satellite galaxies at z=0.3 are only a factor of 2 larger than those at z∼2, or almost identical
in abundance in some codes. As the latest ART-I CosmoRun has not reached z=0.3, we use the older model for the ART-I code, denoted as ART-I (old), which is
represented in Paper III. See Section 4.1 for more information.
44
ART-I (old)in Figure 8represents the older ART-I model used in Paper III.
The satellite galaxy population at z∼2 is almost identical between the two
models. However, the older model, ART-I (old), exhibits a more severe
intercode timing discrepancy.
11
The Astrophysical Journal, 964:123 (16pp), 2024 April 1 Jung et al.
4.2. Testing Intercode Convergence in Satellite Properties: The
Stellar Mass–Halo Mass Relation and the Mass–Metallicity
Relation
We now explore the interplatform convergence in satellite
properties among the CosmoRuns by studying the two relations
that probe the baryonic physics: the stellar mass–halo mass
relation and the mass–metallicity relation. This allows us to
verify the realism of the AGORA baryonic physics in the
CosmoRun.
First, in the left panel of Figure 9, we show the stellar mass–
halo mass relation at z∼2 of the satellite galaxies identified in
Sections 2.3 and 3.4. For the completeness of our analysis, in
the right panel of Figure 9, we also draw the same plot using
the field galaxies found in our simulations. This is possible
thanks to the sufficiently large zoom-in region around the host
halo that contains 20−30 field galaxies at z∼2.
45
One may
notice that, on average, the dark matter halos of field galaxies
are about 2.5 times more massive than the dark matter halos of
satellite galaxies for a given luminosity. The satellites’halo
masses do not grow after their infall to the host, or rather,
decrease due to tidal stripping. In the meantime, their stellar
masses continue to grow (Gunnet al. 1972; Behroozi et al.
2019). Thus, satellite galaxies tend to have more stellar masses
at a given halo mass than field galaxies do.
Different simulation codes display varied behaviors, but
there is also evidence of remarkable convergence. To begin,
intercode differences in the mass–metallicity relation are
evident. ART-I,RAMSES, and GEAR show a relatively large
M
star
/M
halo
value, while the ratios for ENZO and GIZMO are
slightly smaller than those of other codes. This trend reflects
what was already discovered in the satellite galaxy populations
(left panel of Figure 7).CHANGA also shows a large M
star
/M
halo
for the satellite galaxies, which could arise from the insufficient
number of satellite galaxies. The field galaxies in CHANGA
exhibit a relation consistent with other codes (right panel of
Figure 9).
However, despite these initial differences, the overall picture
reveals convergence. The differences in stellar mass–halo mass
relations are within 1 dex for the field galaxies across all
CosmoRuns with no visible systematic discrepancy between
mesh-based and particle-based codes. The common baryonic
physics adopted in AGORA and the stellar feedback prescrip-
tion typically used in each code group (calibrated to produce a
similar stellar mass at z=4)are responsible for this
convergence, particularly because the simulations are per-
formed with sufficient resolution (100 proper pc at z=2).
We then compare our result with previous studies. The thick
gray dotted, dashed, and dotted–dashed lines represent the
relation for dwarf galaxies at z=0 in the FIRE-2, Auriga, and
DC Justice League simulations (Hopkins et al. 2018; Grand
et al. 2021; Munshi et al. 2021, respectively).
46,47
The blue
shaded region represents the relation inferred from MW
satellites (Nadler et al. 2020). The thin black and gray solid
lines are for the semiempirical models at 2 <z<2.5 with
extrapolation to dwarf-sized galaxies (Legrand et al. 2019;
Girelli et al. 2020, respectively). The stellar masses in the
AGORA CosmoRuns are on average ∼0.5 dex higher than the
Figure 9. The stellar mass–halo mass relation of the satellite (left)and field (right)galaxies at z∼2. The y-axis indicates the mean value of the stellar masses in each
mass bin. The thick gray dotted, dashed, and dotted–dashed lines are for dwarf galaxies in other zoom-in simulations at z=0(FIRE-2, Auriga, and DC Justice
League, respectively; Hopkins et al. 2018; Grand et al. 2021; Munshi et al. 2021), while the thin black and gray solid lines without markers are semiempirical models
for 2 <z<2.5 with extrapolation to low-mass galaxies (Legrand et al. 2019; Girelli et al. 2020). The relationship with a 68% confidence interval, as constrained by
Nadler et al. (2020)using MW satellites, is represented in the blue shaded region. All CosmoRuns produce similar relations with no systematic discrepancy between
mesh-based codes and particle-based codes. See Section 4.2 for more information.
45
In contrast to the satellite halos defined in Section 2.3,wedefine field halos
using the following criteria: (i)afield halo must reside beyond 300 comoving
kpc of our target host halo (or 100 proper kpc at z=2; a value similar to the
virial radius of our host halo at z=0),(ii)it must be more massive than
10
7
h
−1
M
e
in dark matter, and (iii)it must not have a parent halo in the
ROCKSTAR halo catalog (i.e., satellites of other halos are excluded). And after
assigning stellar particles to these halos using the method described in
Section 2.3, we plot only the field galaxies whose stellar masses are heavier
than 6m
gas,IC
=2.38 ×10
5
h
−1
M
e
, just as in Section 3.4.
46
These lines represent both satellite and field galaxies in both panels. In
contrast to the previous studies listed here that employ the total halo mass, the
halo mass M
halo
in the present paper specifically refers to the mass of dark
matter in the halo. However, as the majority of mass in satellite galaxies is dark
matter, this slight difference in the mass definition does not significantly affect
Figure 9.
47
Hopkins et al. (2023)show that the latest FIRE model, FIRE-3, predicts a
stellar mass up to a factor of 10 higher compared to the FIRE-2 model for
dwarf galaxies with M
peak
≈10
9
M
e
. For the dwarf galaxies with stellar masses
10
6
–10
7
M
e
, in contrast, there is little difference in galaxy stellar masses
(Hopkins et al. 2023).
12
The Astrophysical Journal, 964:123 (16pp), 2024 April 1 Jung et al.
empirical predictions but are largely consistent with the
previous simulation studies at z=0. The intercode scatters in
the low-mass halos (M
halo
10
9
h
−1
M
e
)are due to the
complex interplay between baryonic physics and the different
merger history of the halos, which cannot easily be reproduced
by abundance matching in the empirical models (Revaz &
Jablonka 2018).
48
The galaxy–halo connection seen in Figure 9
indicates not only the robustness and reproducibility of the
participating simulations but also the realism of the AGORA
CosmoRun baryonic physics.
Second, in Figure 10, we present the mass–metallicity
relation at z∼2 for the satellite and field galaxies. Stellar
masses and metallicities are used to draw the plots in the top
panels, while stellar masses and gas metallicities are used in
the bottom panels. For the bottom panels, we assign a gas
parcel (cell or particle)to a halo if it is within 0.15R
vir
from the
halo’s center. Only galaxies whose gas mass is greater than
3 times the approximate mass resolution of stellar particles,
3m
gas,IC
=1.19 ×10
5
h
−1
M
e
(see Section 3.1 of Paper III), are
included in the bottom panels of Figure 10.
We note that there exists a small but systematic difference
between the mesh-based and particle-based codes. Some mesh-
based codes, ART-I and RAMSES, tend to show higher stellar
metallicities than the particle-based codes do for the satellite
galaxies (left panels in Figure 10), and a similar trend exists for
the field galaxies, too (right panels). However, the differences
between codes are mitigated on the high stellar mass end,
M
star
10
8
M
e
, where the mean values of the relation converge
within ∼0.5 dex for the field galaxies (right panels). Since our
careful calibration of stellar feedback for the CosmoRun has
yielded similar star formation histories across the participating
codes (see Papers III and IV for detailed discussion), the
difference in metallicities is most likely due to the difference in
the metal transportation scheme each simulation has adopted.
We have already reported a systematic discrepancy in the metal
distribution between the two hydrodynamics approaches in the
isolated galaxy comparison (Paper II). And Shin et al. (2021)
quantified the difference in metal distribution caused by
different metal diffusion schemes and different numerical
resolutions (especially in galactic halos). We will further
investigate the circumgalactic and intergalactic media of the
Figure 10. The mass–metallicity relation of the satellite (left)and field (right)galaxies at z∼2 using stellar (top)and gas (bottom)metallicity. The y-axis indicates the
mean value of the stellar metallicities in each mass bin. A systematic difference exists between mesh-based codes (solid lines)and particle-based codes (dashed lines).
For comparison, the thick gray (red)dotted line represents the stellar mass–stellar (gas)metallicity relation at z=2 that best fits the field galaxies in the FIRE-2
simulation (Ma et al. 2016), while the thick gray (brown)dotted–dashed line represents the same relation at z=2 in the TNG50 simulation (Nelson et al. 2019;
Pillepich et al. 2019). We also include the observed mass–metallicity relation of dwarf galaxies in the Local Group, represented by gray crosses with error bars (top
panels; Sanati et al. 2023), as well as the mass–metallicity relation observed by JWST in a z∼2 galaxy cluster field, shown as a thick light blue line (bottom panels; Li
et al. 2023). See Section 4.2 for more information.
48
In Figure 9, some codes do not reach the highest dark matter mass bin,
indicating an absence of satellite halos in that range. Similarly, some codes do
not reach the lowest dark matter mass bin because there is no halo with a
sufficient number of stellar particles in that mass range.
13
The Astrophysical Journal, 964:123 (16pp), 2024 April 1 Jung et al.
CosmoRuns, providing clues to the origin of the discrepancy in
their metal content.
Comparing the results with previous studies, the best fitto
the FIRE-2 simulations sits right in the middle of our eight
simulations (thick dotted lines; Ma et al. 2016), while that to
the TNG50 simulation sits ∼1.0 dex higher in metallicity than
our CosmoRuns do (thick dotted–dashed lines; Nelson et al.
2019; Pillepich et al. 2019). Additionally, we include the
observed mass–metallicity relation of present-day dwarf
galaxies in the Local Group (gray crosses with error bars;
Sanati et al. 2023)and the median value of the relation for 29
galaxies in a galaxy cluster field at z∼2(thick light blue line;
JWST; Li et al. 2023).
49
Both of these observations show
∼0.5 dex higher metallicity than the satellite galaxies in the
CosmoRuns do. Considering that the metallicity of dwarf
galaxies tends to increase from z=2to0(by ∼0.4 dex in the
FIRE-2 simulations), this difference between the CosmoRuns
and Local Group dwarfs may be less pronounced at z=0. The
mass–metallicity relation seen in Figure 10 is an important test
of the realism of the feedback prescriptions used in the
CosmoRuns. While all CosmoRuns at z∼2 reproduce the
stellar masses of satellite galaxies similar to that of the MW and
M31, the differences in their metallicities indicate that the
baryon physics models implemented in the CosmoRuns have
limitations.
5. Conclusion
We have studied the satellite halo populations near z=2in
the high-resolution cosmological zoom-in simulations carried
out on eight widely used astrophysical simulation codes (ART-I,
ENZO,RAMSES,CHANGA,GADGET-3,GEAR,AREPO-T, and
GIZMO)for the AGORA High-resolution Galaxy Simulations
Comparison Project. We use different redshift epochs near
z=2 for each code (“z∼2”)at which the eight CosmoRuns are
in the same evolutionary stage in the target halo’s merger
history in order to alleviate the timing discrepancy. Our key
results are as follows.
1. All hydrodynamic CosmoRuns have fewer satellite halos
than the DMO runs at z∼2 across all halo masses. The
number of satellite halos in all CosmoRuns is lower than
that in the DMO runs by a factor of ∼2 for M
halo
<
10
8.5
h
−1
M
e
(Section 3.1).
2. The difference between CosmoRuns and DMO runs
exists as early as z=12. The discrepancies in the early
Universe can be explained by the “gas–dark matter
particle coupling”in the particle-based codes and/or by
the coarse force resolution in the mesh-based codes in the
outskirts of the target halo. Other late-time baryonic
effects such as reionization, tidal stripping, ram pressure
stripping, and stellar feedback enhance the depletion of
substructures when compared to the DMO counterparts
(Sections 3.2 and 3.3).
3. When we consider only the halos containing stellar
particles at z∼2, the number of satellite galaxies is
significantly lower than that of dark matter halos in all
participating AGORA simulations. The populations of
satellite galaxies in all eight CosmoRuns are indeed
comparable to that of present-day satellites near the MW
or M31 in their stellar masses and three-dimensional
stellar velocity dispersions. This finding is in line with
previous studies (Section 3.4; see also Brooks &
Zolotov 2014; Sawala et al. 2016a; Wetzel & Hop-
kins 2016; Applebaum et al. 2021).
4. Using the five CosmoRuns that reached z=0.3, we also
show that the number of satellite galaxies at z=0.3 is
expected to be only a factor of 2 larger than that at
z∼2. Thus, our conclusion that the number of satellite
galaxies is significantly lower than that of satellite halos
will likely also hold at z∼0(Section 4.1).
5. We also find small but systematic differences in other
galaxy properties such as the stellar mass–halo mass
relation and the mass–metallicity relation. ART-I,
RAMSES, and GEAR show a relatively large M
star
/M
halo
value, while the ratios for ENZO and GIZMO are slightly
smaller than those of the other codes. Similarly, ART-I
and RAMSES exhibit a relatively large mass–metallicity
relation (Section 4.2). We observe the differences in the
metallicities between CosmoRuns and the observations,
which indicate that the baryon physics models imple-
mented in the CosmoRuns have limitations.
Overall, it is notable that the so-called “missing satellite
problem”is fully and easily resolved across all participating
codes simply by implementing the common baryonic physics
adopted in AGORA and the stellar feedback prescription
commonly used in each code group with sufficient numerical
resolution (100 proper pc at z=2). We have demonstrated
that the baryonic solution to the decade-old problem in the
ΛCDM model is effective in all eight AGORA participating
codes at z∼2. Because the results of our numerical experiment
are reproduced by one another through the AGORA frame-
work, the solution is independent of the numerical platform
adopted—excluding the possibility that it is an artifact of any
one particular numerical implementation. Note that the stellar
feedback prescriptions in the CosmoRun suite were calibrated
to produce similar stellar masses in the host halo by z=4(see
Section 5.4 in Paper III), which remains true to z∼2(see
Paper IV), but they were never specifically aimed at or
designed to suppress the satellite galaxy population.
Acknowledgments
We thank all of our colleagues participating in the AGORA
Project for their collaborative spirit, which has enabled the
Collaboration to remain strong as a platform to foster and
launch multiple science-oriented comparison efforts. We
particularly thank Oscar Agertz, Kirk Barrow, Oliver Hahn,
Desika Narayanan, Eun-jin Shin, Britton Smith, Ben Tufeld,
and Matthew Turk for their insightful comments during the
work presented in this paper and Yongseok Jo and Seungjae
Lee for their helpful feedback on the earlier version of this
manuscript. We are also grateful to Volker Springel for making
the GADGET-2 code public and for providing the original
versions of GADGET-3 to be used in the AGORA Project. This
research used resources of the National Energy Research
Scientific Computing Center, a DOE Office of Science User
Facility supported by the Office of Science of the U.S.
Department of Energy under contract No. DE-AC02-
05CH11231. J.-H.K. acknowledges support by the Samsung
Science and Technology Foundation under project No. SSTF-
BA1802-04. His work was also supported by the National
Research Foundation of Korea (NRF)grant funded by the
49
We adopt =+ -ZZlog 12 log O H 9.0
gas
() ()(Ma et al. 2016).
14
The Astrophysical Journal, 964:123 (16pp), 2024 April 1 Jung et al.
Korea government (MSIT)(Nos. 2022M3K3A1093827 and
2023R1A2C1003244). His work was also supported by the
National Institute of Supercomputing and Networking, Korea
Institute of Science and Technology Information, with super-
computing resources, including technical support (grants KSC-
2020-CRE-0219, KSC-2021-CRE-0442, and KSC-2022-CRE-
0355). The publicly available ENZO and yt codes used in this
work are the products of collaborative efforts by many
independent scientists from numerous institutions around the
world. Their commitment to open science has helped make this
work possible.
Appendix
Halo Matching Process between ART-I/Ramses and ART-
I-DMO/Ramses-DMO
To investigate how each individual halo is affected by the
baryonic processes, in Section 3.3, we match and compare
halos in hydrodynamic simulations (e.g., ENZO CosmoRun)to
their counterparts in the DMO simulation (e.g., ENZO-DMO
run). But because particle IDs in RAMSES and RAMSES-DMO
(or ART-I and ART-I-DMO)are not identically assigned in their
initial conditions, we need to employ a method different from
what is described in Section 3.3 to match the halos between
these two simulations. Here we introduce an alternative
approach to find a pair of matched halos between two
simulations that only share the initial condition but not their
particle IDs. The idea is that we find a pair of halos originating
from the same dark matter patch at a nearly homogenous early
Universe. First, we choose 40 particles closest to a target halo’s
center in, e.g., RAMSES CosmoRun at z∼2. We trace each
dark matter particle in a halo back in time and find its position
at z=100 (the initial condition). Now, for each of the 40
particles in the RAMSES run, a particle in the RAMSES-DMO run
is randomly assigned. For each pair of particles, we can
compute the distances between them at z=100. Among the 40
edges, we sum up the 20 smallest distances. A group of
particles with the smallest distance sum is chosen in the
RAMSES-DMO initial condition, and we trace them forward in
time to find a “matched”halo at z∼2. Finally, by carrying out
the same procedure in reverse, another link is obtained—i.e.,
first find the 40 most bound particles in the RAMSES-DMO run
and then locate their counterpart particles in the RAMSES
CosmoRun. A pair of halos that are bijectively mapped
(bidirectionally connected)in between the two simulations
are considered as a “matched”pair.
ORCID iDs
Minyong Jung https://orcid.org/0000-0002-9144-1383
Santi Roca-Fàbrega https://orcid.org/0000-0002-
6299-152X
Ji-hoon Kim https://orcid.org/0000-0003-4464-1160
Hyeonyong Kim https://orcid.org/0000-0002-7820-2281
Kentaro Nagamine https://orcid.org/0000-0001-7457-8487
Johnny W. Powell https://orcid.org/0000-0002-3764-2395
Daniel Ceverino https://orcid.org/0000-0002-8680-248X
Joel R. Primack https://orcid.org/0000-0001-5091-5098
Clayton Strawn https://orcid.org/0000-0001-9695-4017
Tom Abel https://orcid.org/0000-0002-5969-1251
Avishai Dekel https://orcid.org/0000-0003-4174-0374
Boon Kiat Oh https://orcid.org/0000-0003-4597-6739
Romain Teyssier https://orcid.org/0000-0001-7689-0933
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