# Dissipative Dark Substructure:
The Consequences of Atomic Dark Matter on Milky Way Analog Subhalos

Caleb Gemmell Department of Physics, University of Toronto, Toronto, Ontario
M5S 1A7, Canada  Sandip Roy Department of Physics, Princeton University,
Princeton, NJ 08544, USA  Xuejian Shen TAPIR, California Institute of
Technology, Pasadena, CA 91125, USA  Kavli Institute for Astrophysics and
Space Research, Massachusetts Institute of Technology, Cambridge, MA, 02139,
USA  David Curtin Department of Physics, University of Toronto, Toronto,
Ontario M5S 1A7, Canada  Mariangela Lisanti Department of Physics, Princeton
University, Princeton, NJ 08544, USA  Center for Computational Astrophysics,
Flatiron Institute, New York, NY 10010, USA  Norman Murray Canadian Institute
for Theoretical Astrophysics, University of Toronto, Toronto, ON M5S 3H8,
Canada  Philip F. Hopkins TAPIR, California Institute of Technology, Pasadena,
CA, 91125, USA

###### Abstract

Using cosmological hydrodynamical zoom-in simulations, we explore the
properties of subhalos in Milky Way analogs that contain a sub-component of
Atomic Dark Matter (ADM). ADM differs from Cold Dark Matter (CDM) due to the
presence of self interactions that lead to energy dissipation and bound-state
formation, analogous to Standard Model baryons. This model can arise in
complex dark sectors that are natural and theoretically-motivated extensions
to the Standard Model. The simulations used in this work were carried out
using GIZMO and utilize the FIRE-2 galaxy formation physics in the Standard
Model baryonic sector. For the parameter points we consider, the ADM gas cools
efficiently, allowing it to collapse to the center of subhalos. This increases
a subhalo’s central density and affects its orbit, with more subhalos
surviving small pericentric passages. The subset of subhalos that host visible
satellite galaxies have cuspier density profiles and smaller stellar-half-mass
radii relative to CDM. The entire population of dwarf galaxies produced in the
ADM simulations is much more compact than those seen in CDM simulations,
unable to reproduce the entire diversity of observed dwarf galaxy structures.
Additionally, we also identify a population of highly compact subhalos that
consist nearly entirely of ADM and form in the central region of the host,
where they can leave distinctive imprints in the baryonic disk. This work
presents the first detailed exploration of subhalo properties in a strongly
dissipative dark matter scenario, providing intuition for how other regions of
ADM parameter space, as well as other dark sector models, would impact
galactic-scale observables.

##  1 Introduction

The model of Cold Dark Matter (CDM) is theoretically minimal and has been
successful at describing the large-scale structure of the Universe (Aghanim et
al., 2020). Despite these successes, there are important reasons to explore
non-minimal interacting dark matter (DM) candidates. First, discrepancies
between observational data and CDM simulations have begun to appear at smaller
scales—see Bullock & Boylan-Kolchin (2017) for a review. While the addition of
baryons to CDM simulations can ameliorate some of the small-scale
disagreements (Governato et al., 2010; Garrison-Kimmel et al., 2019), these
simulations still fail to produce a population of compact dwarfs that have
been found in the Local Group (Santos-Santos et al., 2017; Jiang et al., 2019;
Garrison-Kimmel et al., 2019). This issue is also related to the _Diversity
Problem_ , as CDM (plus baryon) simulations are unable to reproduce the wide
variety of inner density slopes observed in observational data (Relatores et
al., 2019). Second, complex dark sectors with multiple particles and forces
are highly motivated from a particle theory point of view and can also
ameliorate the observed small-scale tensions, e.g., Tulin & Yu (2018). In
particular, they are a prediction of many scenarios that solve the Hierarchy
Problem, while being compatible with null results from Large Hadron Collider
searches. In this work, we study an interacting dark sector on galactic scales
that is motivated by both of these concerns.

In the past, most efforts to study non-minimal dark sectors have been limited
to DM candidates with simple elastic self interactions, e.g., Tulin & Yu
(2018). However, many implementations of complex dark sectors result in
inelastic scattering that dissipate energy (Ackerman et al., 2009; Arkani-
Hamed et al., 2009; Feng et al., 2009; Alves et al., 2010; Cline et al., 2014;
Schutz & Slatyer, 2015; Boddy et al., 2016; Foot & Vagnozzi, 2016; Agrawal et
al., 2017). The effect of dissipative DM on small-scale structure has only
recently begun to be explored in simulations (Huo et al., 2020; Shen et al.,
2021, 2022). While these initial efforts studied scenarios where dissipation
is a relatively small effect, a fraction of DM can easily be highly
dissipative without violating self-interaction bounds. To this end, we explore
Atomic Dark Matter (ADM) (Kaplan et al., 2010) as a case study of more
strongly dissipative models.

ADM is a useful benchmark model both due to its minimality and the fact that
it contains many of the most important features found in complex DM scenarios
predicted by theories like the Twin Higgs (Chacko et al., 2006; Barbieri et
al., 2016; Chacko et al., 2018). It has just a few ingredients: a dark proton
$p^{\prime}$ and a dark electron $e^{\prime}$ with masses
$m_{p^{\prime}}>m_{e^{\prime}}$ that are oppositely charged under a dark
electromagnetic force mediated by a dark photon $\gamma^{\prime}$ with
coupling $\alpha^{\prime}$. The ADM makes up a fraction
$f_{D}\equiv\Omega_{\mathrm{adm}}/\Omega_{\mathrm{dm}}$ of the DM density and
gives rise to a ‘dark CMB’ that is a factor $\xi\equiv
T_{\mathrm{cmb^{\prime}}}/T_{\mathrm{cmb}}<1$ colder than the normal CMB. In
the early universe, ADM produces dark acoustic oscillations in the power
spectrum, which can suppress structure formation at small scales111This small-
scale suppression will also result in a larger minimum halo mass (Boddy et
al., 2016), which could also be probed via the subhalo mass function. (Cyr-
Racine et al., 2014), but current cosmological constraints still allow ADM
fractions as large as $f_{D}\gtrsim\mathcal{O}(20\%)$ (Bansal et al., 2022a,
b). Subcomponents in this range could easily have very significant
astrophysical effects.

The structure of ADM on galactic scales has long been discussed, with some
suggesting the possibility of a ‘dark disk’ forming (Fan et al., 2013a, b;
McCullough & Randall, 2013; Randall & Scholtz, 2015; Schutz et al., 2018), or
collapsed dark gas fragments distributed throughout our Galactic halo
(Ghalsasi & McQuinn, 2018; Chang et al., 2019). Due to the complicated
dissipative and self-interacting dynamics of ADM, these discussions were based
on highly simplified analytical or semi-analytical treatments. A first-
principles approach was urgently needed, and this finally became possible
earlier this year, when the first cosmological hydrodynamical simulations of
ADM were presented (Roy et al., 2023).

These simulations, which include baryons, CDM, and a 6% fraction of ADM, focus
on a Milky-Way-like host halo and demonstrate the ability of ADM to form a
centrally-rotating dark disk for the two parameter points considered.
Alongside the dark ADM gas disks, these simulations also find large
populations of collapsed ADM clumps in a non-disk-like distribution, enhancing
the central structure of the host halo. Due to the increased central
densities, it is visible by eye that one of the ADM parameter points deforms
the Standard Model baryonic disk. Furthermore, both ADM scenarios appear to
enhance galactic rotation curves to the point of being incompatible with our
Milky Way (MW), but higher-resolution studies are required to make this
definitive. In general, a quantitative approach is needed to understand all of
the available predictions and hence extract astrophysical constraints on the
ADM parameter space, from these simulations.

In this paper, we use the simulations of Roy et al. (2023) to study the
effects of ADM on galactic substructure, explore how ADM affects visible
satellite galaxies, and understand whether such models can address some of the
small-scale structure problems. Our investigations not only define a detailed
analysis template for future simulation studies of ADM, they also demonstrate
that the two ADM parameter points simulated so far appear to be in significant
conflict with observational data and CDM expectations. We expect that the
intuition gained from these studies will apply to broader regions of ADM
parameter space, as well as other dissipative models more broadly.

The paper is organized as follows. Section 2 reviews the details of the
simulations studied in this work. In particular, Sec. 2.2 outlines the
methodology used to select the subhalos and satellite galaxies in the
simulated MW analogs. Section 3 analyses the properties of all DM subhalos,
while Sec. 4 focuses specifically on the visible satellite galaxies. We
conclude in Sec. 5. Appendices A–C summarize various cross checks on the
analysis methods.

##  2 Simulation Suite

This section briefly reviews the ADM simulations presented in Roy et al.
(2023), as well as the methodology for identifying and analyzing subhalos in
the simulated MW analogs.

###  2.1 Zoom-In Simulations

Simulation | Included Species | $\mathbf{\frac{\Omega_{\rm cdm}}{\Omega_{\rm m}}}$ | $\mathbf{\frac{{m_{\rm cdm}}}{{{\,\rm M_{\odot}}}}}$ | $\mathbf{\frac{\Omega_{\rm adm}}{\Omega_{\rm dm}}}$ | $\mathbf{\frac{m_{\rm adm}}{{\,\rm M_{\odot}}}}$ | $\mathbf{\frac{\Omega_{\rm b}}{\Omega_{\rm m}}}$ | $\mathbf{\frac{m_{\rm b}}{{\,\rm M_{\odot}}}}$ | $\boldsymbol{\frac{\alpha^{\prime}}{\alpha}}$ | $\mathbf{\frac{m_{p^{\prime}}}{m_{p}}}$ | $\mathbf{\frac{m_{e^{\prime}}}{m_{e}}}$ | $\mathbf{\frac{T_{\rm cmb^{\prime}}}{T_{\rm cmb}}}$
---|---|---|---|---|---|---|---|---|---|---|---
CDM | CDM+Bar. | 0.83 |  2.79$\times 10^{5}$ | 0 | - | 0.17 | $5.6\times 10^{4}$ | - | - | - | -
CDM-NF | CDM+Bar., no FB | 0.83 |  2.79$\times 10^{5}$ | 0 | - | 0.17 | $5.6\times 10^{4}$ | - | - | - | -
ADM-1 | CDM+ADM-1+Bar. | 0.78 |  2.62$\times 10^{5}$ | 0.06 |  1.67$\times 10^{4}$ | 0.17 | $5.6\times 10^{4}$ | $1/\sqrt{0.55}$ | $1.3$ | $0.55$ | 0.39
ADM-2 | CDM+ADM-2+Bar. | 0.78 |  2.62$\times 10^{5}$ | 0.06 |  1.67$\times 10^{4}$ | 0.17 | $5.6\times 10^{4}$ | $2.5$ | $1.3$ | $0.55$ | 0.39
|  |  |  |  |  |  |  |  |  |  |
Table 1:  Summary of the simulations from Roy et al. (2023) that are used in
this work. We compare two non-ADM simulations (with and without baryonic
feedback) to two with ADM. All maintain a total DM abundance of
$\Omega_{\mathrm{dm}}=0.83$. In ADM-inclusive simulations, ADM makes up 6% of
the DM. The symbols $m_{\mathrm{cdm}},m_{\mathrm{adm}}$, and $m_{\mathrm{b}}$
represent particle masses for various simulation components. ADM’s cooling
physics is defined by the dark fine-structure constant ($\alpha^{\prime}$),
dark proton mass ($m_{p^{\prime}}$), dark electron mass ($m_{e^{\prime}}$),
and dark CMB temperature $T_{\mathrm{cmb^{\prime}}}$ which we list relative to
the Standard Model values (unprimed quantities). A higher $\alpha^{\prime}$ in
ADM-2 leads to faster ADM cooling and a greater dark cut-off temperature due
to the increased dark binding energy. Thus, the dark gas cools more
efficiently in ADM-2 than in ADM-1, but predominantly at greater temperatures
($T\gtrsim 10^{5}K$).

The dataset includes four cosmological hydrodynamical zoom-in simulations of
MW analogs. The matter component of the CDM and CDM-NF simulations is
comprised of CDM and baryons. Between the two, CDM includes baryonic stellar
feedback while CDM-NF does not. The remaining two simulations, denoted by
ADM-1 and ADM-2, contain CDM, baryons (with feedback), and ADM, a subcomponent
of the DM. Along with the specified ADM mass fraction
($\Omega_{\rm{adm}}/\Omega_{\rm{dm}}$), the ADM simulations are dependent on
three additional parameters: the dark fine-structure constant
($\alpha^{\prime}$), dark proton mass ($m_{p^{\prime}}$), and dark electron
mass ($m_{e^{\prime}}$). The main features of the simulation suite are
summarized in this section and Tab. 1; further details can be found in Roy et
al. (2023).

All simulations utilize the code GIZMO (Hopkins, 2015). The baryonic physics
adopts the prescription from the Feedback In Realistic Environments (FIRE)
project (Hopkins et al., 2014), specifically the “FIRE-2” version (Hopkins et
al., 2017a, b), including low-temperature gas cooling (Ferland et al., 1998;
Wiersma et al., 2009), heating from a meta-galactic radiation background
(Oñorbe et al., 2016; Faucher-Giguère, 2020) and stellar sources, star
formation, as well as explicit models for stellar and supernovae feedback
(Hopkins et al., 2014). The star formation criteria for baryonic gas include
reaching a critical density of $\sim 1000~{}\,{\rm cm}^{-3}$, hosting non-zero
molecular fractions (Krumholz & Gnedin, 2011), and becoming Jeans-unstable and
locally self-gravitating (Hopkins et al., 2013). For CDM-NF only, we remove
all forms of stellar, supernovae, and radiative feedback.

ADM is implemented in GIZMO as a separate gas species that is decoupled
hydrodynamically from the baryonic gas. The ADM cooling functions are
implemented as described in Roy et al. (2023) and Rosenberg & Fan (2017),
assuming no meta-galactic dark radiation background in the ADM sector except
for the dark Cosmic Microwave Background (CMB). The cooling functions assume
ionisation-recombination equilibrium for the ADM gas and do not include dark
molecular cooling (Ryan et al., 2022a). Dark molecular cooling is relevant for
simulating dense regions of ADM gas at scales below the current resolution of
the simulations.

There are several key features of ADM atomic cooling. At temperatures far
above the binding energy of the dark hydrogen
($B_{0}^{\prime}=\frac{1}{2}\alpha^{\prime 2}m_{e^{\prime}}c^{2}$),
Bremsstrahlung cooling is dominant and monotonically increases with
temperature. At temperatures closer to $B_{0}^{\prime}$, there is a prominent
collisional excitation cooling peak associated with non-zero neutral dark
hydrogen fractions. Lastly, there is a sharp cut-off in the atomic cooling
rates at temperatures significantly below $B_{0}^{\prime}$ where the dark gas
is neutral; we refer to this transition as the cut-off temperature. Greater
$B_{0}^{\prime}$ implies greater pressure support for dense, cold gas in the
center of halos. Because both $B_{0}^{\prime}$ and the cooling rate increase
with $\alpha^{\prime}$, the ADM gas in ADM-2 cools more efficiently than that
of ADM-1, but at greater temperatures ($T\gtrsim 10^{5}K$).

Once ADM gas cells become locally self-gravitating and Jeans-unstable, they
are turned into “clump” particles over the free-fall time scale. These clump
particles have the same mass as the ADM gas cell ($1.67\times 10^{4}{\,\rm
M_{\odot}}$) and represent collisionless objects at the resolution scale of
the simulation. This is due to the ADM gas cloud collapsing and fragmenting
into dark compact objects (Gurian et al., 2022) at scales smaller than we are
simulating, such as black holes or dark stars. Once formed, the clump
particles interact only gravitationally like the CDM particles.

The force softening for both the baryonic and ADM gas particles uses the
algorithm from Price & Monaghan (2007). The minimum gas softening is $h_{\rm
gas}=1.4\,{\rm pc}$ while the CDM force resolution of the simulations is
$h_{\rm dm}=40\,{\rm pc}$.

When considering the inner regions of substructure, we must verify that the
properties of the halo have converged and are resolution-independent. A
commonly used metric is the convergence radius criterion specified by Power et
al. (2003), mandating that the $N$-body relaxation time in DM-only
simulations, $t_{\rm relax}(r)$, is shorter than the age of the universe,
$t_{0}$. This is determined by the equation,

$\frac{t_{\rm{relax}}(r)}{t_{0}}=\frac{\sqrt{200}}{8}\frac{N}{\rm{ln}\>N}\bigg{(}\frac{\overline{\rho}(r)}{\rho_{\rm{crit}}}\bigg{)}^{-1/2}\,,$
(1)

where $N$ is the number of particles enclosed by $r$, $\overline{\rho}(r)$ is
the mean density enclosed by $r$, and $\rho_{\rm{crit}}$ is the critical
density of the universe. Hopkins et al. (2018) conducted an extensive study to
apply the convergence radius criterion to simulations with FIRE-2 baryonic
physics and found the DM to have converged for radii larger than
$r^{\rm{conv}}_{\rm{\scriptscriptstyle{DM}}}$, defined by the relation
$t_{\rm{relax}}(r^{\rm{conv}}_{\rm\scriptscriptstyle{DM}})=0.06\>t_{0}$. This
is approximately the radius that encloses 200 CDM particles. However, in the
same study, this was also shown to be a conservative estimate and that
simulations with baryons could be resolved to much smaller radii. The effect
of ADM on DM convergence is currently unknown, but the convergence of the ADM
structure theoretically should be much smaller as it is determined by the
minimum gas softening (1.4 pc) and not the CDM force resolution (40 pc). To
incorporate the effect of ADM on the convergence radii for all collisionless
DM in the ADM simulations, we calculate
$r^{\rm{conv}}_{\rm{\scriptscriptstyle{DM}}}$ using both CDM and ADM clump
particles. Thus, in the regime that ADM is able to cool and form dense regions
in the center of subhalos, $r^{\rm{conv}}_{\rm{\scriptscriptstyle{DM}}}$ is
much smaller than the CDM-only expectation, due to the high number of ADM
clumps at small radii. As a further check for convergence, we compare our
results with low-resolution simulations in Appendix A and comment on what
trends are resolution-independent.

The primary halo in the zoom-in area that forms the focus of this work is
m12i. It was selected from the standard FIRE-2 suite (Wetzel et al., 2022;
Hopkins et al., 2014) and has a CDM mass of $\sim 10^{12}{\,\rm M_{\odot}}$, a
stellar disk mass of $7.4\times 10^{10}{\,\rm M_{\odot}}$, as well as a stable
merger history for CDM below $z<1$ (Hopkins et al., 2017b). The publicly
released high-resolution m12i simulation (Wetzel et al., 2023a) is referred to
throughout this study as a cross-check against the CDM simulation, as it has
approximately a factor of eight better mass resolution
($m_{\rm{cdm}}=3.5\times 10^{4}{\,\rm M_{\odot}}$) than the CDM simulation.

The initial transfer functions for the baryons, CDM, and ADM particles are
calculated using a modified version of CLASS (Blas et al., 2011; Bansal et
al., 2022b, a), which accounts for the cosmological history of the ADM. MUSIC
(Hahn & Abel, 2011) is then used to generate the initial conditions at $z\sim
100$.

###  2.2 Subhalo Identification

To identify DM subhalos in our MW analogs, we use the ROCKSTAR 6D halo
finder.222Specifically, we use the adapted version of Wetzel & Garrison-Kimmel
(2020), found at https://bitbucket.org/awetzel/rockstar-galaxies/. In CDM-only
simulations, ROCKSTAR is run only on the DM particles for numerical stability
(Samuel et al., 2020). Equivalently, we run our analysis on the CDM particles
and collisionless ADM clumps within 300 kpc of the host’s center. The friends-
of-friends linking percentage in Rockstar is typically set to 70%, but for
this study, we conservatively increase it to 80%. This choice is inspired by
the fact that ADM can cool and fragment, potentially leading to substructure
forming at smaller scales in the ADM simulations. Increasing the linking
percentage ensures that the clustering algorithm is not dominated by the dense
regions of ADM clumps. However, the effect of changing this parameter is very
minor, see Appendix B. Once identified, subhalos are classified by
$R_{200,{\rm m}}$, the radius that encloses 200 times the mean matter density,
and $M_{200,{\rm m}}$, the total DM mass contained within this radius.

In CDM simulations, a cut is typically applied on particle numbers to ensure
that spurious subhalos comprising only a few simulation particles are not
considered. However, for the ADM simulations, the subhalos consist of both CDM
particles ($m_{\rm cdm}=2.62\times 10^{5}{\,\rm M_{\odot}}$) and ADM clumps of
mass $1.67\times 10^{4}{\,\rm M_{\odot}}$—an order-of-magnitude smaller than
the CDM particles. In these simulations, there may be subhalos where a small
number of CDM particles dominate the total mass of the subhalo. For example, a
subhalo of 2 CDM particles and 49 ADM clumps may pass a particle number cut,
$N>50$, but 39% of the subhalo’s mass/gravitational potential is determined by
the two CDM particles. To account for such scenarios, we assume that the
number cut in CDM-only simulations corresponds to requiring the relative
uncertainty on the halo’s mass to be below some threshold. Assuming that this
relative uncertainty scales as $N^{-p/2}$ in the small-number-limit, where $p$
is some _a priori_ unknown scaling constant, generalizing this threshold to
include ADM particles corresponds to adding the different particle species’
contribution in quadrature:

$\sigma=\Biggr{[}\bigg{(}\frac{f_{\rm{adm}}}{N_{\rm{adm}}^{p/2}}\bigg{)}^{2}+\bigg{(}\frac{f_{\rm{cdm}}}{N_{\rm{cdm}}^{p/2}}\bigg{)}^{2}\Biggr{]}^{1/2p}<\frac{1}{\sqrt{N_{\rm{cut}}}}\,,$
(2)

where $f_{\rm{adm}}$ ($f_{\rm{cdm}}$) is the subhalo ADM (CDM) mass fraction,
$N_{\rm{adm}}$ ($N_{\rm{cdm}}$) is the number of ADM (CDM) particles contained
within the subhalo, and $N_{\rm cut}$ is the number count that the halo must
satisfy. An overall exponential factor of $1/p$ is included to remove any
explicit $p$ dependence from the final threshold value.

The threshold $\sigma$ should recover the standard particle number cut,
$N>N_{\rm{cut}}$, in the limit where the halo contains only one particle type,
as well as the case where both particle types have the same mass. This
uniquely sets $p=1$ in Eq. (2), which also results in the cut being more
conservative than just $N>N_{\rm{cut}}$ for subhalos containing simulation
particles of different masses, which is sensible.

In this work, we set $N_{\rm{cut}}=50$. This corresponds to the halo mass in
the CDM simulation where the subhalo mass function begins to diverge from that
of the high-resolution m12i simulation, shown in Fig. C1. This establishes two
different mass thresholds. For the CDM and CDM-NF simulations, all subhalos
have masses larger than $50\times m_{\rm{cdm}}=1.4\times 10^{7}{\,\rm
M_{\odot}}$. For ADM-1 and ADM-2, all subhalos have masses larger than
$50\times m_{\rm{adm}}=8.4\times 10^{5}{\,\rm M_{\odot}}$. In Appendix C, we
compare our results to those using a larger threshold, $N>200$.

To identify visible satellite galaxies, we use HaloAnalysis (Wetzel &
Garrison-Kimmel, 2020) to associate stellar particles to DM subhalos
identified with Rockstar following the post-processing steps of Samuel et al.
(2020). For each subhalo, an initial position cut is applied so that we only
consider stellar particles within $0.8\times R_{\rm 200,m}$ of the subhalo’s
center, out to a maximum of 30 kpc. Additionally, the velocity of each star
particle relative to the subhalo must satisfy $v\leq 2\times
V_{\rm{circ}}^{\rm{max}}$ (maximum circular velocity) and $v\leq
2\times\sigma_{\rm v,dm}^{\rm 3D}$ (3D velocity dispersion of DM). Following
this step, an iterative cut is applied, keeping only stellar particles with
$r<1.5\times r_{90}$ (radius enclosing 90% of stellar particles in the
subhalo) and $v<2\times\sigma_{\rm v,*}^{\rm 3D}$ (3D velocity dispersion of
subhalo stellar particles), until the number of stellar particles converges at
the 1% level. Once baryon-containing subhalos are identified, we only include
subhalos with at least 10 stellar particles and an average stellar density
greater than $300{\,\rm M_{\odot}}$ kpc-3, which results in an overall stellar
mass cut, M${}_{*}>10^{5.5}{\,\rm M_{\odot}}$.

##  3 General Subhalo Properties

In the MW analogs for CDM, CDM-NF, ADM-1, and ADM-2, a total of 455, 388, 523,
and 264 subhalos, respectively, are identified. Of the subhalos in the ADM
simulations, 42% (13%) contain ADM clumps, in addition to CDM particles, for
ADM-1 (ADM-2). In Sec. 3.1–3.3, we present the subhalo mass and radial
distributions for each simulation, investigate the internal mass distribution
of the subhalos, and study the properties of their orbits around the host
halo. Key quantities include the subhalo density profiles, compactness, and
orbital parameters. The compactness is defined by $R_{200,{\rm m}}/R_{1/2}$,
where $R_{1/2}$ is the radius that encloses 50% of the subhalo’s total DM
mass. Finally, we briefly discuss ADM overdensities in the MW disk in Sec.
3.4.

###  3.1 Density Profiles

Figure 1: The subhalo mass function at $z=0$ for the CDM, CDM-NF, ADM-1, and
ADM-2 simulations. The shaded bands indicate the 1$\sigma$ Poissonian error
for the count in each bin. The vertical dashed-black line indicates the mass-
quality threshold for the CDM and CDM-NF simulations, $50\times m_{\rm
cdm}=1.4\times 10^{7}{\,\rm M_{\odot}}$, while the vertical dotted-black line
indicates the mass-quality threshold for the ADM-1 and ADM-2 simulations,
$50\times m_{\rm adm}=8.4\times 10^{5}{\,\rm M_{\odot}}$. The solid black is
the subhalo mass function obtained from the public FIRE-2 data for the m12i
simulation (Wetzel et al., 2023b). In the large mass bins
(M${}_{200,\rm{m}}>10^{9.5}{\,\rm M_{\odot}}$), the subhalo mass function for
CDM is the exact same as ADM-2 and, similarly, so is the subhalo mass function
for m12i for M${}_{200,\rm{m}}>10^{10}{\,\rm M_{\odot}}$. All simulations
except ADM-2 agree within the uncertainty for the highest mass bins, while
ADM-2 shows an obvious depletion across multiple mass bins. There is an
additional population of light ADM subhalos resolved below the CDM mass
threshold that consists nearly entirely of ADM clumps ($\sim 98\%$ ADM mass
fraction).

Figure 1 shows the subhalo mass function at $z=0$ for each simulation in the
suite: CDM (blue), CDM-NF (green), ADM-1 (orange), and ADM-2 (pink). The
shaded bands correspond to the 1$\sigma$ Poissonian error in counts for each
bin. For comparison, the solid black line shows the subhalo mass function
obtained from the public FIRE-2 data for the m12i simulation (Wetzel et al.,
2023b), for subhalos with $M_{200,\rm{m}}>1.4\times 10^{7}{\,\rm M_{\odot}}$,
which is the CDM mass threshold indicated by the black dashed line. The ADM
mass threshold is indicated by the black dotted line on the left edge of the
plot.

Figure 2:  Top: Median CDM density profiles across subhalos, per radial bin.
Colored bands indicate the 68% containment regions. Median and percentile
values are calculated for subhalos with halo masses in various ranges:
$10^{7.75}{\,\rm M_{\odot}}<M_{200,{\rm m}}\leq 10^{8.25}{\,\rm M_{\odot}}$
(left), $10^{8.25}{\,\rm M_{\odot}}<M_{200,{\rm m}}\leq 10^{9}{\,\rm
M_{\odot}}$ (middle), and $M_{200,{\rm m}}>10^{9}{\,\rm M_{\odot}}$ (right).
The dashed gray line depicts the largest convergence radius,
$r_{\rm{DM}}^{\rm{conv}}$, for each mass range. For
$r>r_{\rm{DM}}^{\rm{conv}}$, the CDM density profiles align for the lowest-
mass subhalos, but the ADM and CDM-NF profiles show an enhanced central
density for the more massive subhalos. Because CDM-NF has no baryonic
feedback, the subhalos are not cored relative to CDM, with adiabatic
contraction also contributing to the enhanced central density for the largest
mass range. The subhalos in the ADM simulation likely undergo dark adiabatic
contraction due to the cooling ADM gas. Bottom: Median ADM (clumps + gas)
density profiles across ADM-containing subhalos, per radial bin. The total DM
profiles for ADM are enhanced because the ADM gas cools and forms ADM clumps
at the center of a subhalo, which then contributes to the total DM density
profile.

Comparing simulations above the CDM mass threshold, the largest deviations are
in the lower mass bins, close to the threshold where resolution effects become
important. For heavier masses, there is good agreement within the count
distribution for all simulations except ADM-2, whose mass function is
suppressed across multiple bins. This behavior will be explained later in this
section. Below the CDM mass threshold, only the ADM simulations have some
resolved subhalos, due to the order-of-magnitude lighter ADM clump particles.
We emphasize this is not the complete subhalo mass function below the CDM mass
threshold, as a higher-resolution ADM simulation would also contain subhalos
with a majority of CDM particles down to these masses. Yet, the individual
subhalos consisting of the light ADM particles are themselves significant, as
we explore further below.

In Fig. 2, the subhalo radial DM density profiles are plotted for each
simulation; these profiles correspond to CDM (top row), as well as the ADM
clumps and gas (bottom row) for the ADM simulations. Each panel in the figure
corresponds to a different range in subhalo $M_{200,{\rm m}}$: from left to
right, $10^{7.75}$–$10^{8.25}~{}{\,\rm M_{\odot}}$,
$10^{8.25}$–$10^{9}~{}{\,\rm M_{\odot}}$, and $>10^{9}~{}{\,\rm M_{\odot}}$.
To obtain the profiles, each subhalo’s density is calculated in 10
logarithmically-spaced bins from 0.25 kpc to 12 kpc. The median density,
represented by the solid lines, is calculated for each radial bin across all
subhalos in that mass range and simulation. The shaded bands represent the 68%
containment in densities. Conservatively, the largest subhalo convergence
radius for each plot is indicated by the gray dashed line, which is always
from the CDM simulation.

Comparing the CDM density profiles for radii larger than
$r_{\rm{DM}}^{\rm{conv}}$, the profiles are consistent between simulations for
the smallest subhalo masses. For the intermediate subhalo masses, the profiles
start to deviate at radii just above $r_{\rm{DM}}^{\rm{conv}}$. There is a
possible enhancement in the ADM and CDM-NF simulations compared to CDM, but
the large spread in the subhalo density profiles from each simulation makes it
difficult to determine the significance of this. However, for the largest mass
subhalos, the deviations from CDM become more pronounced.

There are two conflating factors that may be causing the inner-density
enhancement in CDM-NF subhalos relative to CDM. Firstly, CDM-NF has no
baryonic feedback and thus its subhalos are not cored relative to those in
CDM, especially for the largest masses. Secondly, the CDM-NF subhaloes
typically have larger stellar-to-halo mass ratios ($M_{*}/M_{200,\rm{m}}\sim
0.1$) than those in CDM. While in CDM adiabatic contraction (Gnedin et al.,
2004; Chan et al., 2015) is not an influential effect for subhalos with
$M_{\rm 200,m}\lesssim 10^{9}{\,\rm M_{\odot}}$, the CDM-NF profiles in this
range can actually be enhanced due to the lack of feedback.

While we have discussed the CDM profile above the conservative limit
$r_{\rm{DM}}^{\rm{conv}}$, the ADM subhalos can be resolved down to smaller
radii due to the large number of ADM clumps that form and occupy their central
regions. For example, central enhancements are likely converged even within
$r\lesssim 0.3$ kpc for the most massive subhalos, as they contain an average
of $1.6\times 10^{4}$ ($2.7\times 10^{4}$) ADM clumps for ADM-1 (ADM-2).

For the intermediate-mass subhalos, the ADM-1 density profiles are enhanced
much like in CDM-NF. Even though the standard baryonic feedback is present in
the ADM-1 simulation, the cooling ADM gas is likely providing an additional
‘dark baryonic contraction’ effect that contracts the CDM profile, making it
cuspier than the CDM expectation. ADM-2 does not show the same enhancement,
likely because a smaller fraction (28%) of the subhalos contain ADM clumps
compared to ADM-1 (89%) in this mass range. This is due to the fact that the
cooling rate for ADM-2 only becomes efficient at higher temperatures/virial
masses due to its larger cut-off temperature compared to ADM-1, so the dark
adiabatic contraction has a smaller effect for the intermediate-mass subhalos.
This contraction in the CDM profiles was also noted in Roy et al. (2023). The
central CDM densities of the host galaxies ($<1$ kpc) for both ADM simulations
have a $\gtrsim 40\%$ enhancement compared to CDM.

Indeed, ADM-2 shows a similar central-density enhancement as ADM-1 for the
most massive subhalos, where a majority (73%) of its subhalos contain ADM
clumps, signifying the ADM gas is now able to cool and collapse efficiently.
For this mass range, 100% of ADM-1 subhalos contain ADM clumps with an average
total ADM clump mass of $\sim 10^{8.7}{\,\rm M_{\odot}}$, while 73% of ADM-2
subhalos contain ADM clumps with an average total ADM clump mass of $\sim
10^{8.9}{\,\rm M_{\odot}}$. These large central ADM clump densities also
contribute to the density profile enhancement in the centers of subhalos.

To summarize, the inner subhalo density profiles in CDM-NF can be enhanced
compared to those in CDM, which is to be expected as there is no baryonic
feedback to core the subhalos. Additionally, due to the subhalos forming with
large stellar-to-halo mass fractions, baryonic contraction could also enhance
the central densities. The ADM-containing subhalos in the ADM simulations also
have enhanced central DM densities compared to the CDM simulation. The ADM gas
then collapses into central ADM clumps, contributing to the total DM density
profile. Additionally, the cooling ADM gas back-reacts on the CDM particles,
resulting in a dark adiabatic contraction that leads to cuspier inner density
profiles. Between ADM-1 and ADM-2, ADM-1 is able to cool at smaller virial
masses, so this effect is present for a larger population of lighter subhalos
compared to ADM-2. However, at larger subhalo masses, ADM-2 cools more
efficiently, forming larger central ADM masses in the subhalos containing ADM.

Figure 3: Distributions of subhalo compactness, as defined by $R_{200,{\rm
m}}/R_{1/2}$, for CDM (blue), CDM-NF (green), ADM-1 (orange), and ADM-2 (pink)
simulations. Top: Plot of $R_{200,{\rm m}}/R_{1/2}$ versus halo mass,
$M_{200,{\rm m}}$. The vertical dashed black line represents the CDM mass
threshold, $50\times m_{\rm cdm}=1.4\times 10^{7}{\,\rm M_{\odot}}$, while the
vertical dotted black line represents the ADM mass threshold, $50\times m_{\rm
adm}=8.4\times 10^{5}{\,\rm M_{\odot}}$. The majority of subhalos have
$R_{200,{\rm m}}/R_{1/2}<15$, which we classify as ‘CDM-like’, as this
includes 99% of the CDM subhalos. There is also a large population of ADM
subhalos with $R_{200,{\rm m}}/R_{1/2}>15$, with compactness relatively
enhanced compared to the majority of CDM subhalos. These correspond to ADM
subhalos that contain a larger average mass fraction of ADM clumps in ADM-1
$(28\%)$ and ADM-2 $(36\%)$. The subhalos that are mostly comprised of ADM
clumps, which we refer to as ‘ADM-dominated,’ form even more compact subhalos
with $R_{200,{\rm m}}/R_{1/2}>150$. Bottom left: Plot of $R_{200,{\rm
m}}/R_{1/2}$ versus distance to host galaxy, $R_{\rm host}$. The subhalos with
enhanced compactness appear more likely to occupy the inner regions of the
galaxy. Additionally, the most compact subhalos are all found within 10 kpc of
the galactic center. Bottom right: Histogram of $R_{200,{\rm m}}/R_{1/2}$
values. All simulations peak in the ‘CDM-like’ region, but the ADM simulations
are peaked at slightly larger values of compactness and have more extensive
tails. The Enhanced-compactness region is mainly occupied by a second smaller
peak for CDM-NF and the extended tails of the ADM simulations. The ADM-
dominated region is mostly occupied by a second peak of ADM-1 subhalos.

###  3.2 Compactness

Next, we study the influence of ADM on a subhalo’s compactness, as quantified
by R${}_{200,\rm{m}}/$R1/2. Larger values of compactness signify that a
greater amount of a subhalo’s mass is concentrated in its central region. The
top panel of Fig. 3 shows how a subhalo’s compactness is related to its mass.
In this plot, there are three main regions populated by the subhalos. The
first region corresponds to $R_{200,{\rm m}}/R_{1/2}\lesssim 15$. This is
where the majority (99%) of subhalos in the CDM simulation (blue) are
clustered. A significant fraction of the subhalos in CDM-NF (green), ADM-1
(orange), and ADM-2 (pink) occupy this same region: 85%, 72%, and 90%,
respectively. Importantly, the majority of these subhalos do not contain any
ADM clumps in the ADM-1 (77%) and ADM-2 (95%) simulations. For this reason, we
classify these subhalos as ‘CDM-like.’

The second region corresponds to $R_{200,{\rm m}}/R_{1/2}$ in the $\sim
15$–150 range and is populated by a subset of subhalos in the CDM-NF (15%),
ADM-1 (21%), and ADM-2 (9%) simulations. We refer to these subhalos as
‘Enhanced compactness.’ The small fraction of CDM-NF subhalos in this region
is due to the fact that the lack of feedback leads to more concentrated
baryonic distributions, which in turn further concentrates the DM halo. Of the
subhalos from ADM-1 and ADM-2 in this region, a larger fraction contain ADM
clumps (88% and 74%, respectively) compared to those in the CDM-like region;
the average ADM mass fraction of these subhalos is 0.28 and 0.36,
respectively, compared to the vanishingly small fractions for the CDM-like
subhalos. In general, the more ADM is present in a subhalo, the more compact
the subhalo’s total DM distribution will be. Thus, the enhanced compactness
for the ADM subhalos is due to the additional contribution of ADM clumps in
their central regions, and also dark adiabatic contraction. Moreover, the fact
that the ADM-2 gas cools more efficiently in more massive subhalos explains
why the pink ADM-2 points in this region occur predominantly at larger masses
(M${}_{200,\rm{m}}>5\times 10^{8}{\,\rm M_{\odot}}$).

The last region in the top panel of Fig. 3 corresponds to a small fraction of
subhalos unique to ADM-1 (7%) and ADM-2 (2%). These subhalos are extremely
compact, with $R_{200,{\rm m}}/R_{1/2}\gtrsim 150$. The subhalos in both
simulations have a large average ADM clump mass fraction of $\sim 98\%$,
allowing them to be resolved at masses below the CDM threshold. We refer to
these subhalos as ‘ADM dominated’ and their origin is discussed in Sec. 3.4.

The bottom panel of Fig. 3 shows how a subhalo’s compactness is correlated
with its distance to the center of the host galaxy, $R_{\rm host}$. In
general, the more concentrated the subhalo, the closer it can be found to the
center of its host. For example, 22%, 43%, and 35% of subhalos below $R_{\rm
host}\sim 50$ kpc belong to the CDM-like, Enhanced-compactness, and ADM-
dominated populations, respectively. This is likely due to the fact that
subhalos with increased central densities are more likely to survive passages
close to the host center and thus occupy closer orbits (Errani et al., 2016),
which could explain why there are almost twice as many Enhanced-compactness
subhaloes within 50 kpc of the host as CDM-like subhalos. However, tidal
stripping of outer material on these close orbits could also contribute to the
increased compactness of these subhalos, thus it is unclear how much of the
enhancement in compactness is due to the increased central density due to ADM
/ lack of feedback or depletion of outer material due to tidal stripping. We
will disambiguate the relation between compactness and radial distance in Sec.
3.3 by studying the subhalo orbital parameters.

The population of extremely compact, ADM-dominated subhalos is mostly within
$\sim 10$ kpc of the galactic center, in the neighbourhood of the disk. This
suggests that these subhalos are not infalling into the MW-like host, but
instead form in the disk due to the fragmenting ADM gas, which we discuss in
Sec. 3.4.

###  3.3 Radial Distribution and Orbits

Figure 4: Cumulative distributions of subhalos at $z=0$. Results are shown for
the CDM (blue), CDM-NF (green), ADM-1 (orange), and ADM-2 (pink) simulations.
Shaded bands indicate the 1$\sigma$ Poissonian error in the count. The solid
black is the cumulative distribution obtained from the high-resolution (high
res.) public FIRE-2 data for the m12i simulation (Wetzel et al., 2023b). Top:
Cumulative number of subhalos within distance to host galaxy, Rhost. Both ADM
simulations contain a larger fraction of subhalos within the inner $\sim 125$
kpc of the galaxy, compared to the CDM-only simulations. The total number of
subhalos is enhanced in ADM-1, but depleted in ADM-2. Bottom: Cumulative
number of subhalos outside of distance to host galaxy, Rhost. There is good
agreement between m12i and CDM within uncertainty outside of $\sim 100$ kpc,
with ADM-1 also agreeing outside of $\sim 200$ kpc.

Figure 4 shows the cumulative radial distribution for subhalos within a given
radius and summarizes many of the trends previously discussed. The CDM
distribution (blue) has a similar shape to the high-resolution m12i
distribution (black), but fewer subhalos, which is suggestive of a resolution
effect. Indeed, if we increase the particle number cut to a larger mass ($\sim
200\times m_{\rm{cdm}}$, shown in Fig. C2), the two simulations agree within
the expected spread—thus, the difference in Fig. 4 is mostly due to low-mass
subhalos that are not resolved in CDM. Relative to CDM, the CDM-NF
distribution (green) has fewer total subhalos, but they are positioned closer
to the galactic center.

The radial distribution of subhalos in both ADM-1 and ADM-2 are quite
distinctive from the CDM case. Firstly, we note that ADM-1 shows a slight
total enhancement compared to CDM, while the ADM-2 simulation has a large
relative depletion in the total number of subhalos. This depletion was first
pointed out in Fig. 1 for $M_{200,\rm{m}}<10^{8.5}{\,\rm M_{\odot}}$, and we
will explore it later in this section. Secondly, the cumulative distributions
of both ADM simulations flatten in the range 125–200 kpc, a feature not
present in the CDM or CDM-NF distributions. This feature can also be thought
of as an enhancement in the fraction of subhalos at radii $\lesssim 125$ kpc.
Comparing the ratio $N(r<125~{}\text{kpc})/N(r<300~{}\text{kpc})$, we find
ADM-1 (0.47) and ADM-2 (0.42) have comparable values that are larger than
those for CDM (0.22) and CDM-NF (0.27).

Figure 5: Histograms of apocenters and pericenters for DM subhalos. Shaded
bands indicate 1$\sigma$ Poissonian errors for each bin. Top: Apocenter
distributions for each simulation with CDM-like subhalos ($R_{200,{\rm
m}}/R_{1/2}<15$) on the left and Enhanced-compactness subhalos
($15<R_{200,{\rm m}}/R_{1/2}<150$) on the right. The Enhanced-compactness
subhalos have much smaller apocenters, occupying orbits predominantly
$\lesssim 125$ kpc. Bottom: Pericenter distributions for each simulation with
CDM-like subhalos ($R_{200,{\rm m}}/R_{1/2}<15$) on the left and Enhanced-
compactness subhalos ($15<R_{200,{\rm m}}/R_{1/2}<150$) on the right. The
Enhanced-compactness subhalos again have a largely different distribution and
peak at much smaller values compared to the CDM-like subhalos, indicating
these subhalos have undergone close pericentric passages. The enhancement in
the lowest bin for pericenters $\lesssim 25$ kpc is not observed in CDM and
supports that this survival of close pericentric passages is possible due to
the large central densities found in the ADM subhalos.

To further explore the subhalo radial distributions and this inner
enhancement, we now study some of the orbital parameters of the subhalos
across simulations. In Fig. 5, we plot distributions of the subhalo apocenters
(top row) and pericenters (bottom row). To calculate the apocenters, AGAMA
(Vasiliev, 2018) is used to construct an axisymmetric galactic potential from
the $z=0$ snapshot of each MW analog using a multipole expansion, which is
then used to calculate the apocenter for each constituent particle, with the
subhalo’s apocenter being the median of these values. The pericenters are
determined by tracking the innermost 20 constituent particles at $z=0$ to
earlier redshifts, to identify the snapshot at which their median
galactocentric distance to the host halo is smallest. To account for the
discrete timing of snapshots, AGAMA (Vasiliev, 2018) is again used to
construct an axisymmetric galactic potential at this earlier snapshot, from
which the constituent particles’ pericenters are calculated, with the
subhalo’s pericenter being the median value.

Considering the distributions in Fig. 5, the fraction of subhalos with close
orbits (R${}_{\rm apo}<125$ kpc) are 0.06, 0.11, 0.16, and 0.11 for CDM, CDM-
NF, ADM-1, and ADM-2, respectively. Of these subhalos, a large fraction are in
the Enhanced-compactness group: 0.15 (CDM), 0.83 (CDM-NF), 0.78 (ADM-1), and
0.54 (ADM-2). Thus, there is a larger percentage of subhalos with close orbits
(R${}_{\rm apo}<125$ kpc) in the CDM-NF and ADM simulations, mostly due to the
population of Enhanced-compactness subhalos. This contributes to the larger
numbers of subhalos at small radii found in the ADM and CDM-NF simulations at
$z=0$, relative to CDM.

However, the Enhanced-compactness subhalos cannot be the sole cause of the
distinctive plateau-like feature near $\sim$125 kpc in the ADM radial
distributions, as it would then also appear in CDM-NF. Given that it only
appears in the ADM simulations, it may be related to the dynamics and
formation of the ADM gas disk, which would affect the orbit of the subhalos.
This is supported by the fact the plateau-like feature only becomes apparent
at late times ($z\sim 0.2$) in both ADM simulations. We leave a more careful
study of the dark disk formation and its impact on the subhalo population to
future work.

The pericenter distributions in Fig. 5 show that the Enhanced-compactness
distributions are biased to much smaller pericenter values compared to the
CDM-like subhalos. In the smallest bin (R${}_{\rm peri}<20$ kpc), the count of
Enhanced-compactness (CDM-like) subhalos for each sim is 0 (12), 23 (11), 36
(19), and 6 (12) for CDM, CDM-NF, ADM-1, and ADM-2, respectively. In Garrison-
Kimmel et al. (2017), they found very few subhalos were able to survive to
$z=0$ with small pericenters due to the influence of the baryonic disk
potential. The increase in subhalos with small pericenters found in our
simulations, predominantly in the Enhanced-compactness group, supports the
fact that the concentrated inner densities of the subhalos increase their
chance of surviving close pericentric passages.

We now consider the depletion in the total number of subhalos found in ADM-2
relative to ADM-1. As previously shown in Fig. 1, this is mostly for masses
$\lesssim 10^{8.5}{\,\rm M_{\odot}}$. There are two effects likely
contributing to this observed depletion. First is the fact that the ADM-1
subhalos often have larger ADM mass fractions than those in ADM-2, which leads
to more compact halos that can survive closer orbits, as previously mentioned.
The second contributing factor has to do with the formation of a dark disk in
the host galaxy. While both ADM simulations form dark gas disks with
comparable densities, the ADM-1 disk extends out to radii $\sim 3$ kpc,
entirely encompassed by the baryonic disk. Comparatively, the ADM-2 disk
extends beyond the baryonic disk out to $\sim 14$ kpc. The additional tidal
field of a baryonic disk can cause subhalo depletion out to large distances
(Garrison-Kimmel et al., 2017; Silverman et al., 2022); presumably such an
effect would only be enhanced by the presence of a large dark disk. In light
of this, the ADM-2 disk is much more likely to disrupt the lighter ADM-2
subhalos (too light to have been cusped by ADM) that pass nearby, contributing
to their overall depletion relative to ADM-1.

To summarize, ADM appears to enhance the _fraction_ of subhalos within $\sim
125$ kpc of the host, with ADM cooling in subhalos creating cuspier profiles
that increase their likelihood of surviving small pericentric passages.
However, it is also possible that the dynamics of the ADM disk formation at
late times also causes an enhancement. Lastly, this can result in either an
enhancement or reduction in the total number of subhalos, depending on the
extent of the ADM gas disk that forms and the number / mass of subhalos
containing ADM clumps. The potential enhancement in the number of subhalos
with apocenters within 125 kpc of the galactic center also increases the
number of subhalos within the range of stellar streams ($R_{\rm host}\lesssim
50$ kpc), making ADM an interesting candidate for future stellar stream
surveys. Furthermore, since the subhalos in this region tend to be more
compact than the CDM expectation, the induced perturbations on the stellar
structure will be predictably different (Bonaca et al., 2018).

###  3.4 Subhalos in the Disk Plane

In this subsection, we briefly discuss the population of subhalos that are
found in the baryonic disk and its immediate vicinity. These subhalos are
primarily comprised of the ADM-dominated population (see Fig. 3) with
$R_{200,{\rm m}}/R_{1/2}\gtrsim 150$ and consist almost entirely of ADM
clumps. Because ADM clumps are an order-of-magnitude lighter than CDM
particles, these subhalos can be resolved down to $\sim 10^{6}{\,\rm
M_{\odot}}$.

Figure 6: Properties of visible satellite galaxies ($M_{*}\gtrsim
10^{5.5}{\,\rm M_{\odot}}$) within 300 kpc of their host at $z=0$. Shaded
bands indicate the 68% containment in the count. The black solid line depicts
the high-resolution (high res.) FIRE-2 m12i simulation. Left: Cumulative
number of galaxies above a given stellar mass. CDM-NF evidently over-produces
satellite galaxies, as well as making them too massive. For this reason, the
CDM-NF simulation will be suppressed for the rest of the paper. ADM-1 also has
a small enhancement in total number, specifically in the lower stellar mass
range. ADM-2, CDM, and the high-resolution m12i all show good agreement within
the observed spread. Right: Cumulative number of satellite galaxies within a
given galactocentric radius. The radial distribution for ADM-2, CDM, and the
high-resolution m12i all exhibit similar trends, while ADM-1 differs in having
a larger number of visible satellite galaxies across all host distances. CDM-
NF vastly overproduces satellite galaxies both in stellar mass and number.

The ADM clumps in these subhalos all formed at late times $(z\lesssim 2)$ and
within 10 kpc of the center of the galaxy. To characterize their orbits, we
use the orbital circularity, $\epsilon=j_{z}/j_{c}(E)$, defined as the ratio
of the $z$-component of a particle’s angular momentum to the angular momentum
of a particle with a circular orbit and the same energy (Abadi et al., 2003).
Of the ADM-dominated subhalos, 80% have thin-disk orbits ($\epsilon>0.8$) and
lie at heights $z<2$ kpc from the disk plane. Extending the circularity range
to thick-disk orbits ($\epsilon>0.2$), 93% of these subhalos are now included.
This strongly suggests that the ADM-dominated subhalos form near the disk
plane, likely from fragmentation of the ADM disk in the host’s central region.
Because ADM-2 has a larger cut-off temperature due to its higher binding
energy, its dark disk is more resistant to fragmentation, which explains why
it forms fewer ADM-dominated subhalos.

Because these subhalos lie within the disk region of MW-like galaxies and
consist primarily of ADM clumps, which are dark compact objects at our
simulations’ resolution level, their abundance could be constrained from
gravitational microlensing events (Winch et al., 2022), in addition to the
microlensing produced by the individual dark stars or ADM-sourced black holes.
Microlensing from extended structures has been considered and could be applied
to these compact subhalos (Croon et al., 2020). However, at the current
resolution, these disk subhalos have an average half-mass radius of 13 pc,
much larger than the maximum Einstein radius expected for surveys of stars in
the bulge (e.g., 0.02 pc), suggesting that these subhalos will provide weak to
no constraints when acting as lenses.

Additional constraints on these compact objects could come from interactions
with wide binaries (Bahcall et al., 1985; Monroy-Rodríguez & Allen, 2014),
where fly-by encounters with the dark compact objects inject energy into the
two-body system, increasing its semi-major axis or even completely disrupting
the system. Recent work has also used these observations to provide some
constraints on extended DM subhalos (Ramirez & Buckley, 2022), up to
$\mathcal{O}(1$ pc) scales. Again, probing such phenomena is beyond the
resolution of our current simulations, but this demonstrates that ADM-
dominated subhalos in the disk plane could lead to distinct observables and
emphasizes the importance of incorporating future improvements to ADM
simulations, such as dark molecular cooling (Ryan et al., 2022b) that will
allow one to resolve ADM clumps to smaller scales.

##  4 Visible Satellite Galaxies

This section explores the properties of the subset of subhalos with stellar
mass comparable to that of the MW’s dwarf galaxies. To this end, we now
require that each subhalo contain at least 10 stellar particles, which is
equivalent to a stellar mass cut of approximately $M_{*}\gtrsim 10^{5.5}{\,\rm
M_{\odot}}$, as outlined in Sec. 2.2. This respectively selects a total of 12,
105, 25, and 12 subhalos from CDM, CDM-NF, ADM-1, and ADM-2.

Figure 6 shows both the cumulative stellar mass (left panel) and radial
distribution (right panel) of visible satellite galaxies across the
simulations. There is good agreement (to within the observed spread) between
CDM and the high-resolution m12i for both mass and radial distributions. This
supports that the CDM simulation has converged for this range of satellite
galaxy masses. Unsurprisingly, the CDM-NF simulation overproduces satellite
galaxies both in stellar mass and number. We suppress showing CDM-NF in the
remaining figures for clarity, as it clearly diverges from a realistic MW
satellite population.

Comparing stellar masses, $\log_{10}(M_{*}/{\,\rm M_{\odot}})$, of the
satellite galaxies, the median and 68% containment values for ADM-1
($6.44_{-0.71}^{+0.99}$), ADM-2 ($6.88_{-0.65}^{+0.74}$) and CDM
($6.05_{-0.30}^{+0.97}$) are all consistent within the observed spread, the
only difference being that ADM-1 appears to overproduce specifically lighter
satellites with M${}_{*}<10^{6}{\,\rm M_{\odot}}$. In general, satellite
galaxy formation is enhanced in ADM simulations. For example, ADM-1 has
roughly twice as many visible satellites as CDM, even though it only produces
20% more subhalos overall. ADM-2 forms 60% of the number of subhalos compared
to CDM, but still has a comparable number of visible satellites. The visible
satellites in both simulations are part of the Enhanced-compactness population
(see Fig. 3), with the majority of visible satellites in ADM-1 (84%) and ADM-2
(100%) having $R_{200,\rm{m}}/R_{1/2}\gtrsim 15$. Comparatively, the maximum
compactness for visible CDM satellites is 11. This is an important point to
emphasize: Because ADM increases the central potentials of subhalos, the ADM-
containing subhalos are more likely to trap Standard Model baryons and form
visible satellite galaxies. For the case of ADM-2, only 16% of subhalos
contain ADM, but it is only this subset that go on to host satellite galaxies.

Figure 7: Inner DM density slope, $\alpha$, averaged over
$(1.5$–$2.5\%)\times\rm{r}_{\rm vir}$, as a function of the stellar mass
fraction, $M_{*}/M_{200,\rm{m}}$, at $z=0$. The ADM points are shaded to
indicate the total ADM clump mass contained in each subhalo. The gray band
shows the density slope from FIRE-2 CDM simulations, taken from Lazar et al.
(2020). While only a few CDM satellite galaxies are resolved at these inner
radii, most ADM satellites are. The inner regions ($r<0.5$ kpc) of these ADM
satellites are dominated by the collapsed ADM clumps and form extremely cuspy
slopes, with median values $\alpha\sim-2.6$.

To quantify this enhancement in the central density profile, we plot the slope
of the density profile, $\alpha$, at small radii. Specifically, we fit the
density to a power law, $\rho(r)\propto r^{\alpha}$, for radii in the range
$(1.5$–$2.5\%)\times\rm{r}_{\rm vir}$, where $r_{\rm vir}$ is the virial
radius. Only satellite galaxies with $r_{\rm{DM}}^{\rm{conv}}<1.5\%\times$rvir
are included. Note that this excludes the majority of CDM satellite galaxies.
The results for the CDM subhalos are shown by the blue circles in Fig. 7. For
comparison, the gray band shows the best-fit model for the FIRE-2 feedback
physics, as obtained in Lazar et al. (2020).333Note that Lazar et al. (2020)
uses a smaller radial range $(1$–$2\%)\times\rm{r}_{\rm vir}$. We increase the
range to ensure a subset of the CDM satellites have converged at $1.5\%$ rvir,
but we find that it makes little difference for the ADM slopes in this
range—both their median values decrease slightly from $\alpha=-2.7$ to $-2.6$
when increasing the range. The overall trend is similar to the distributions
for MaGICC (Di Cintio et al., 2014) and NIHAO (Tollet et al., 2016), although
the slope distributions are not the same in detail.

Figure 8: Total DM compactness, R${}_{200,\rm{m}}/$R1/2, as a function of a
visible satellite galaxy’s orbital pericenter, $R_{\rm peri}$. The ADM data
points are shaded to indicate the total ADM clump mass contained in each
subhalo. The results show a trend of increasing compactness as a subhalo’s
pericenter decreases. Specifically, a large fraction of ADM subhalos reach
smaller pericenters compared to their CDM counterparts.

The CDM satellites lie on the band from Lazar et al. (2020) and have slopes
with $\alpha\sim-1$, but we cannot make any strong statements with only two
data points. The visible satellites in the ADM simulations largely differ from
the CDM expectation. The profiles are cuspier than NFW, with median $\alpha$
values of $-2.6^{+0.4}_{-0.2}$ for ADM-1 and $-2.6^{+0.3}_{-0.6}$ for ADM-2.
(The lower/upper ranges denote 68% containment.) This is because the ADM
clumps mainly occupy a subhalo’s central-most region, with an average of 69%
contained within $2.5\%\times r_{\rm vir}$ across all ADM satellite galaxies.
Thus, for the parameter points considered in these ADM simulations, visible
satellites are typically all produced with significant inner cusps, rather
than with a diversity of inner slopes.

The spatial distribution of visible satellites is a consequence of the
individual orbits of its members. A relevant relation to consider is thus the
pericentric distances for the visible satellites and how they correlate with
compactness. The pericenters are calculated using the same methodology
described in Sec. 3.3 using the stellar particles contained in the satellite
galaxy.

Figure 8 shows the relationship between a visible satellite’s pericenter and
its compactness. As mentioned earlier, the visible satellites in ADM-1 and
ADM-2 are typically more compact than those in CDM, but they also have smaller
pericenters, as shown by the median and 68% containment values for ADM-1
($27.2^{+58.3}_{-17.4}$ kpc) and ADM-2 ($23.9^{+29.2}_{-11.8}$ kpc) compared
to CDM ($65.9^{+113.2}_{-27.3}$ kpc). This pattern is suggestive of a
survivorship bias, where satellites with large central densities are those
that survive passages with small pericenters. As mentioned previously, cuspy
profiles are more resistant to tidal stripping than cored profiles (Errani et
al., 2016), which supports this interpretation.

Figure 9: Stellar-half-mass radius, $r_{1/2,*}$, versus stellar mass, $M_{*}$,
for the visible satellite galaxies in each simulation, with the ADM points
shaded to indicate the total ADM clump mass contained in each subhalo. On
average, both ADM simulations form more compact satellites compared to the CDM
simulation, but with a larger distribution of radii.

We now inspect whether the increased compactness of the DM subhalos in ADM-1
and ADM-2 affects the spatial distribution of their stars. Figure 9 plots the
relationship of stellar-half-mass radius, $r_{1/2,*}$, the radius that
encloses 50% of the galaxy’s stellar mass, with $M_{*}$. We require that
$r_{1/2,*}$ be larger than $r^{\rm{conv}}_{\rm{DM}}$ for each satellite galaxy
to be confident the DM distribution has converged. The baryons, however, are
susceptible to further resolution effects such as an artificially enhanced
‘bursty’ star formation rate (Hopkins et al., 2018), which can puff up
satellite galaxies. These effects are discussed in Appendix A, where we
compare to lower-resolution runs to check the validity of our results and find
that the qualitative trends are robust, even if the quantitative values may
shift. In general, the ADM galaxies have more compact stellar distributions,
with smaller $r_{1/2,*}$ values for ADM-1 ($0.75^{+3.57}_{-0.43}$ kpc) and
ADM-2 ($0.49^{+0.60}_{-0.25}$ kpc) compared to CDM ($1.92^{+0.19}_{-0.29}$
kpc). The range in the ADM-1 values has a small overlap with CDM as it
produces some puffier outlier satellite galaxies. These satellites are also
interesting to highlight as they indicate that while ADM-1 is routinely
producing subhalos with very cuspy inner slopes, it is still possible to
produce a diversity of baryonic structure, such as these diffuse galaxies with
relatively large $r_{1/2,*}$ values.

Figure 10: Vmax versus rmax for the visible satellite galaxies. The values
correspond to the maximum velocity of the rotation curve and the radial
position of this peak. The black points show the corresponding data for the
Milky Way dwarf spheroidals, as obtained in Kaplinghat et al. (2019), assuming
an NFW DM profile. The ADM points are shaded to indicate the total ADM clump
mass contained in each subhalo, which is strongly correlated with the
resulting Vmax for the ADM satellite galaxies. We observe a clear distinction
between the ADM and CDM satellites, which agree relatively well with the
observed Milky Way dwarf spheroidals.

All of this informs what may be the most distinguishing, and perhaps most
robust, characteristics displayed by visible satellites with ADM compared to
CDM-only. Figure 10 shows the (rmax,Vmax) values for the satellite galaxies
across simulations, where (r${}_{\mathrm{max}},$Vmax) defines the maximum of
its circular velocity curve. Again, we ensure that
r${}_{\rm{max}}>r^{\rm{conv}}_{\rm{DM}}$ for each satellite galaxy, which
results in one ADM-1 satellite galaxy being excluded. Because the subhalos in
ADM-1 and ADM-2 have increased central densities, their Vmax values are
enhanced compared to those from the CDM simulation and occur at smaller radii.
The (r${}_{\rm max},$Vmax) values for CDM correspond to
$(3.69_{-2.04}^{+3.22}~{}\text{kpc},22.44_{-7.88}^{+8.74}~{}\text{km/s})$,
while the ADM-1 and ADM-2 simulations have ($0.22_{-0.09}^{+0.16}$ kpc,
$62.32_{-26.83}^{+34.84}$ km/s) and ($0.24_{-0.15}^{+0.23}$ kpc,
$74.00_{-22.35}^{+28.93}$ km/s). This leads to a large separation between CDM
and both ADM simulations in the r${}_{\rm max}-$Vmax plane. By eye, the two
ADM simulations do not produce a population of CDM-like satellite galaxies.
There also appears to be a correlation with Vmax and the total ADM mass
enclosed within the subhalo, depicted by the shading of ADM parameter points.
This correlation is seemingly stronger than the dependence on the specific
cooling physics, as ADM-1 and ADM-2 have similar distributions.

Overlaid on the plot are r${}_{\rm max}-$Vmax values for bright dwarf
spheroidals (dSph), originally presented in Kaplinghat et al. (2019). In their
work, they use Jeans analysis to infer projected line-of-sight velocities and
perform a Bayesian fit to the observed dSph data assuming an NFW profile for
the DM, which is in good agreement with the CDM simulation. Because an NFW
profile is assumed when performing the Bayesian fit to the data, and the ADM
subhalos favor a cuspier density profile, the data points are best compared to
the CDM simulation. To directly compare the ADM simulation to data, one would
have to implement a Bayesian fit assuming some parameterised ADM density
profile.

As discussed in Appendix A, the qualitative discrepancy between ADM and CDM
satellites is quite resolution robust. Resolution-dependent effects tend to
puff up satellite galaxies, counteracting the density enhancement provided by
the ADM. Therefore any qualitative changes higher-resolution runs might cause
will only increase this separation between the ADM and CDM satellites. We can
therefore claim with some confidence that both ADM simulations only form
highly compact satellite galaxies that do not resemble the satellite
population we observe in the MW.

##  5 Conclusions

Compared to CDM simulations, we find that our two simulations with a 6% ADM
subcomponent cause large deviations in the properties of DM substructure,
demonstrating that even small ADM fractions can significantly affect galactic
dynamics. The various differences can all be traced back to the fact that the
ADM gas is able to cool and collapse in the center of subhalos, leading to
enhanced central densities and more compact halos overall. This is realized by
the ADM gas itself cooling and collapsing to clumps in the central region, as
well as the gas dragging the CDM inward via dark baryonic contraction. This
increased central density makes subhalos more resistant to tidal disruption,
allowing them to survive small pericentric passages and occupy orbits at
smaller radii, which is potentially causing an increase in the fraction of
subhalos in the inner regions of the host galaxy.

The increased subhalo compactness affects a range of properties for visible
satellite galaxies in the ADM simulations. Compared to satellites in CDM
simulations, they have cuspier inner slopes and smaller stellar-half-mass
radii. Thus, ADM is able to produce more compact satellites due to its
efficient cooling, but these satellites fail to produce the full diversity of
inner slopes observed in data, see Fig. 7. In fact, for the parameter points
in our simulations, satellites with ADM were completely distinct from the CDM-
only expectation in the $(r_{\mathrm{max}},V_{\mathrm{max}})$-plane, see Fig.
10. This robustly extends the conclusions of Roy et al. (2023), in particular
the exclusion of ADM-1, which does not disrupt the Standard Model gas disk in
the central host galaxy as obviously as ADM-2.

Additionally, we highlighted the ability of ADM to form DM subhalos not
through cosmic overdensities but through fragmentation of the ADM gas disk.
While future work is needed, these highly concentrated dark objects could
prove to be a promising supplementary source of constraints from microlensing
and wide binary surveys.

These results motivate a more extensive systematic investigation of dwarf
galaxy properties in the presence of an ADM sub-component. This will determine
the ranges of parameters for which ADM is excluded due to its impact on
galactic dynamics, as well as the ADM parameters that are compatible with
observations. Such a study would place new and powerful constraints on the ADM
parameter space, likely with far greater sensitivity than purely cosmological
probes (Bansal et al., 2022a). An even more exciting possibility would be the
discovery of ADM using current or future observation data of satellite
galaxies, aided by the detailed understanding of its effects that these future
studies would provide. This may also settle the question of whether the more
compact satellite galaxies produced by an ADM subcomponent could ultimately
address the diversity problem.

While we are only at the start of assembling a detailed and general
understanding of ADM in our Galaxy, the initial studies already demonstrate
that dissipative DM interactions can have significant impacts on galactic-
scale physics. The implications of these findings extend beyond this specific
case study of ADM, as they demonstrate that non-trivial dark sectors leave
stark imprints on the formation and dynamics of galaxies. This motivates
deeper study of a broader range of dark-sector scenarios along with the
corresponding astrophysical tests needed to successfully probe them.

##  6 Acknowledgments

We would like to thank Arpit Arora, Ting Li, Tri Nguyen, Xiaowei Ou, Nondh
Panithanpaisal, Robyn Sanderson, and Nora Shipp for helpful discussions during
the completion of this project. The research of DC and CG was supported in
part by Discovery Grants from the Natural Sciences and Engineering Research
Council of Canada and the Canada Research Chair program. The research of DC
was also supported by the Alfred P. Sloan Foundation, the Ontario Early
Researcher Award, and the University of Toronto McLean Award. The work of CG
was also supported by the University of Toronto Connaught International
Scholarship, McDonald Institute Graduate Student Exchange program, and the
Canada First Research Excellence Fund. ML is supported by the Department of
Energy (DOE) under Award Number DE-SC0007968, as well as the Simons
Investigator in Physics Award. This work was performed in part at the Aspen
Center for Physics, which is supported by National Science Foundation grant
PHY-2210452. The work presented in this paper was performed on computational
resources managed and supported by Princeton Research Computing. This research
also made extensive use of the publicly available codes IPython (Pérez &
Granger, 2007), matplotlib (Hunter, 2007), Rockstar (Behroozi et al., 2012),
Jupyter (Kluyver et al., 2016), AGAMA (Vasiliev, 2018), HaloAnalysis (Wetzel &
Garrison-Kimmel, 2020), NumPy (Harris et al., 2020), SciPy (Virtanen et al.,
2020), and gizmo-analysis (Wetzel et al., 2020).

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This appendix discusses several systematic uncertainties relevant for the
analysis in the main body and their impact on the primary conclusions of the
work. In particular, the choice of particle resolution, friends-of-friends
linking percentage, and subhalo threshold criteria are discussed.

##  Appendix A Resolution Effects on Visible Satellites

The properties of low-mass satellite galaxies can be resolution-dependent,
with the dark matter (DM) and stellar content being ‘puffed up’ to larger
sizes (Shen et al., 2022). For example, Fitts et al. (2019) found that
increasing the baryon mass resolution from $4000{\,\rm M_{\odot}}$ to
$62.5{\,\rm M_{\odot}}$ resulted in their r1/2,∗ values shrinking by half in a
study of the isolated dwarf, m10b. Ludlow et al. (2023) also found that lower-
resolution simulations could cause DM particles to spuriously heat stellar
matter, leading to satellite galaxies with larger sizes and characteristic
velocities when compared to higher-resolution simulations.

Here, we explore how the main-text results concerning visible satellite
galaxies depend on resolution. In particular, we compare to results from a
CDM, ADM-1, and ADM-2 simulation that are run at _lower_ resolution to the
primary simulations in the paper. The relevant particle masses for the low-
resolution simulations are provided in Tab. A1.

Simulation | Included Species | $\mathbf{\frac{\Omega_{\rm cdm}}{\Omega_{\rm m}}}$ | $\mathbf{\frac{{m_{\rm cdm}}}{{{\,\rm M_{\odot}}}}}$ | $\mathbf{\frac{\Omega_{\rm adm}}{\Omega_{\rm dm}}}$ | $\mathbf{\frac{m_{\rm adm}}{{\,\rm M_{\odot}}}}$ | $\mathbf{\frac{\Omega_{\rm b}}{\Omega_{\rm m}}}$ | $\mathbf{\frac{m_{\rm b}}{{\,\rm M_{\odot}}}}$ | $\boldsymbol{\frac{\alpha^{\prime}}{\alpha}}$ | $\mathbf{\frac{m_{p^{\prime}}}{m_{p}}}$ | $\mathbf{\frac{m_{e^{\prime}}}{m_{e}}}$ | $\mathbf{\frac{T_{\rm cmb^{\prime}}}{T_{\rm cmb}}}$
---|---|---|---|---|---|---|---|---|---|---|---
CDM (LOW RES) | CDM+Bar. | 0.83 |  2.25$\times 10^{6}$ | 0 | - | 0.17 | $4.0\times 10^{5}$ | - | - | - | -
ADM-1 (LOW RES) | CDM+ADM-1+Bar. | 0.78 |  2.12$\times 10^{6}$ | 0.06 |  1.35$\times 10^{5}$ | 0.17 | $3.9\times 10^{5}$ | $1/\sqrt{0.55}$ | $1.3$ | $0.55$ | 0.39
ADM-2 (LOW RES) | CDM+ADM-2+Bar. | 0.78 |  2.12$\times 10^{6}$ | 0.06 |  1.35$\times 10^{5}$ | 0.17 | $3.9\times 10^{5}$ | $2.5$ | $1.3$ | $0.55$ | 0.39
|  |  |  |  |  |  |  |  |  |  |
Table A1:  Similar to Tab. 1, except listing the properties for the low-
resolution versions of each simulation.

Figure A1 shows the relationship between the stellar mass fraction
($M_{*}/M_{200,\rm{m}}$) and the inner slope of the DM density profile. The
left panel shows the same simulations as Fig. 7, while the right panel shows
the corresponding result for the lower-resolution simulations. The increased
baryon particle mass in the lower-resolution simulation results in a larger
stellar mass cut as we require each satellite galaxy to contain at least 10
baryon particles in the lower-resolution simulations. We implement a larger
stellar mass cut, $M_{*}>10^{6.6}{\,\rm M_{\odot}}$, for both panels to
directly compare the results. Again, we require all subhalos to satisfy the
convergence criterion, $r_{\rm{DM}}^{\rm{conv}}<1.5\%\times$rvir, which
excludes all CDM satellite galaxies in the lower-resolution simulation. With
the increased stellar mass cut, the equivalent values for the higher-
resolution simulations are $-2.59_{-0.41}^{+0.26}$ (ADM-1) and
$-2.45_{-0.22}^{+0.20}$ (ADM-2). In the lower-resolution simulations, there is
still a population of resolved ADM satellites with median slopes and 68%
containment values of $-2.32_{-0.27}^{+0.28}$ (ADM-1) and
$-2.29_{-0.30}^{+0.25}$ (ADM-2). The median values for the pairs of
simulations agree within the observed scatter even though the qualitative
values do shift. Overall the observation that the ADM satellites form cuspier
density profiles to the trends expected from CDM with baryonic feedback is
robust.

Figure A1: The left panel uses the same simulations as Fig. 7, but with a
larger stellar mass cut, $M_{*}>10^{6.6}{\,\rm M_{\odot}}$, and the right
panel is its lower-resolution counterpart with the same stellar mass cut. All
subhalos plotted satisfy the convergence criterion,
$r_{\rm{DM}}^{\rm{conv}}<1.5\%\times$rvir, excluding more of the lower-
resolution satellite galaxies. The resolved ADM satellites have a similar
distribution of inner slopes, agreeing within the observed scatter.

Figure A2 shows the relationship between pericenter and compactness for each
satellite galaxy. The left panel shows the same simulations as Fig. 7, but
with an increased stellar mass cut ($M_{*}>10^{6.6}{\,\rm M_{\odot}}$), while
the right panel shows the corresponding result for the lower-resolution
simulations. We see the same trends, even more evident in the lower-resolution
ADM simulations, of a correlation between a satellite galaxy’s compactness and
pericenter. The higher-resolution simulations with the new mass cut have
pericenters $76.1_{-19.5}^{+140.5}$ kpc (CDM), $28.1_{-14.8}^{+50.3}$ kpc
(ADM-1), and $34.4_{-10.6}^{+24.5}$ kpc (ADM-2) and compactness
$5.52_{-1.21}^{+0.13}$ (CDM), $18.5_{-6.26}^{+49.6}$ (ADM-1), and
$25.2_{-12.1}^{+4.84}$ (ADM-2). The lower-resolution simulations have median
pericenters with 68% containment of $77.3_{-22.7}^{+110}$ kpc (CDM),
$41.4_{-25.0}^{+41.2}$ kpc (ADM-1), and $32.8_{-14.3}^{+37.6}$ kpc (ADM-2) and
compactness $4.51_{-0.66}^{+2.93}$ (CDM), $14.0_{-4.43}^{+15.3}$ (ADM-1), and
$21.4_{-9.09}^{+9.78}$ (ADM-2). Again, these median values agree within the
observed scatter.

Figure A2: The left panel uses the same simulations as Fig. 8, but with a
larger stellar mass cut, $M_{*}>10^{6.6}{\,\rm M_{\odot}}$, and the right
panel is its lower-resolution counterpart with the same stellar mass cut. We
find the same trend in both plots, with a general correlation between a
satellite galaxy’s compactness and its pericenter.

Figure A3 shows the relationship between stellar mass and stellar-half-mass
radius. The left panel shows the same results as Fig. 9, but with an increased
stellar mass cut ($M_{*}>10^{6.6}{\,\rm M_{\odot}}$), while the right panel
shows the corresponding result for the lower-resolution simulations. With the
larger stellar mass cut, the median and 68% containment values for $r_{1/2,*}$
in the higher-resolution CDM, ADM-1, and ADM-2 are now $2.00_{-0.04}^{+0.24}$
kpc, $0.75_{-0.49}^{+8.71}$ kpc, and $0.42_{-0.16}^{+0.61}$ kpc, respectively.
The corresponding values for the lower-resolution simulations are
$5.24_{-1.06}^{+1.12}$ kpc, $1.14_{-0.35}^{+1.09}$ kpc, and
$1.36_{-1.03}^{+0.42}$ kpc. There is a clear shift in the median values,
beyond the observed scatter. The shift is in the expected direction, with
half-light radii increasing for the lower-resolution runs. Importantly, the
trend that the ADM simulations form more compact satellite galaxies compared
to CDM is still present at lower resolution, suggesting that the qualitative
trend is robust.

Figure A3: The left panel uses the same simulations as Fig. 9, but with a
larger stellar mass cut, $M_{*}>10^{6.6}{\,\rm M_{\odot}}$, and the right
panel is its lower-resolution counterpart with the same stellar mass cut.
Lowering the resolution tends to increase r1/2,∗ for a given $M_{*}$. However,
the general trend of ADM satellite galaxies having smaller half-light radii
compared to CDM subhalos is still present.

Figure A4 demonstrates how lowering the resolution impacts the
r${}_{\rm{max}}-$Vmax distributions. With the larger stellar mass cut, the
CDM, ADM-1, and ADM-2 simulations have the following median and 68%
containment for ($r_{\rm{max}}$,$V_{\rm{max}}$): ($7.46_{-1.00}^{+1.99}$ kpc,
$36.01_{-4.94}^{+0.98}$ km/s), ($0.18_{-0.05}^{+0.16}$ kpc,
$94.41_{-20.25}^{+3.82}$ km/s), and ($0.21_{-0.11}^{+0.07}$ kpc,
$99.01_{-28.46}^{+11.66}$ km/s). For the lower-resolution simulations, CDM,
ADM-1, and ADM-2 have median and 68% containment for (rmax,Vmax):
($8.97_{-3.39}^{+0.51}$ kpc$,30.86_{-9.95}^{+13.19}$ km/s),
($0.76_{-0.25}^{+0.20}$ kpc$,51.29_{-18.89}^{+15.55}$ km/s), and
($0.37_{-0.12}^{+0.17}$ kpc$,55.31_{-7.21}^{+52.17}$ km/s). While the CDM
values agree within the observed scatter, the values for both ADM simulations
shift to smaller rmax and larger Vmax values as the resolution is increased.
The qualitative trend that there is a clear separation between the CDM and ADM
satellite galaxies in the r${}_{\rm max}-$Vmax plane is present at both
resolutions. Additionally, since known resolution-dependent effects ‘puff up’
satellite galaxies if satellite galaxies are not converged, increasing the
resolution should only further increase central densities, resulting in even
smaller rmax values and also larger $V_{\rm max}$ values. Thus higher-
resolution simulations should not ameliorate this discrepancy between CDM and
ADM satellite galaxies, making this qualitative trend of ADM having increased
relative circular velocity profiles robust.

Figure A4: The left panel uses the same simulations as Fig. 10, but with a
larger stellar mass cut, $M_{*}>10^{6.6}{\,\rm M_{\odot}}$, and the right
panel is its lower-resolution counterpart with the same stellar mass cut. The
CDM distribution is roughly consistent between both panels while and still
exhibit the same trend discussed in the body of the paper.

##  Appendix B Friends-of-Friends Linking Percentage

ROCKSTAR (Behroozi et al., 2012) is a 6D halo finder that works through
hierarchical refinement of friends-of-friends (FOF) groups. The FOF algorithm
works by linking particles directly to other particles (friends) within a
specified linking length, $l$, and then indirectly through any particles
linked to its friends (friends-of-friends), forming a group. This algorithm is
implemented in ROCKSTAR via the following steps. Initially, 3D FOF groups are
established in position space from simulation particles, using a fixed linking
length for easy parallelization. These groups are then individually normalized
in 6D phase space by dividing particle positions and velocities by the group’s
position and velocity dispersions. For each of these normalized groups, a 6D
linking length is adaptively chosen such that a certain percentage of
particles in the group are part of a subgroup. This percentage is what is
referred to as the “FOF linking percentage.” This process is repeated,
identifying deeper substructure at each iteration, until subgroups are
identified with some minimum number ($\sim$10) of particles. ‘Seed halos’ are
placed at these groups and simulation particles are assigned hierarchically to
the closest seed halo in phase space. Lastly, any unbound particles are
removed. These are the subhalos identified by ROCKSTAR and that we study in
this work.

The FOF linking percentage determines the number of particles that must be
within another particle’s linking radius at each iterative step. Because
several simulations in our suite contain both CDM and ADM particles with
different masses, we considered using a customised ROCKSTAR that adaptively
increases the linking length until a percentage of total mass of the group is
linked, rather than the number of particles. This implementation was tested
and there was no difference to the identified subhalo populations using the
standard version of ROCKSTAR.

The default FOF linking percentage used in ROCKSTAR for CDM simulations is
70%. Since ADM clumps mostly occupy central regions of subhalos in large
numbers, one may worry that by only requiring 70% of particles to be linked at
each subgroup, the identified subhalos will be biased towards these dense,
high-occupation regions. In the main body, we conservatively increased the FOF
linking percentage to 80% to increase the number of potential subgroups we
identify. In this appendix, we test the differences that arise due to changes
to the FOF linking length.

Figure B1 shows how the subhalo mass and radial distributions for the CDM,
CDM-NF, ADM-1, and ADM-2 simulations vary when changing the FOF linking
percentage. The solid line corresponds to a linking percentage of 80% (used in
the main body), while the bands bracket the range of values obtained when it
is decreased to 70% (Behroozi et al., 2012) or increased to 90% (maximally
computationally efficient value). There are small quantitative changes based
on the linking fraction choice, with CDM-NF having the largest variation. The
overall trends—such as the plateau $\sim 125$ kpc in the ADM-1 and ADM-2
radial distributions—are robust, however. Additionally, increasing the linking
percentage to 90% does not result in a large increase of subhalos, confirming
that most substructure is already identified at 80% linking percentage.

Figure B1: Mass (left) and radial (right) distributions for subhalos within
300 kpc of the host halo at $z=0$, similar to Fig. 1 and 4. In both panels,
the solid line indicates the result for 80% linking percentage, corresponding
to the results shown in the body of the paper. The colored bands indicate the
range of values when the linking percentage is decreased to 70% (Behroozi et
al., 2012) or increased to 90% (maximally computationally efficient value).

Figure B2 also compares the mass and radial distributions for visible
satellite galaxies using different linking percentages. Again, there is little
qualitative change in the distributions, and the CDM simulation shows almost
no variation across the range considered.

Figure B2: Mass (left) and radial (right) distributions of visible satellite
galaxies within 300 kpc of the host halo at $z=0$, similar to Fig. 6. In both
panels, the solid line indicates the result for 80% linking percentage,
corresponding to the results shown in the body of the paper. The colored bands
indicate the range of values when the linking percentage is decreased to 70%
(Behroozi et al., 2012) or increased to 90% (maximum computationally efficient
value).

##  Appendix C Subhalo Threshold Criteria

In the body of the paper, a value $N_{\rm{cut}}=50$ is used to set the mass-
weighted threshold. This value is chosen as it corresponds approximately to
the number of particles in the CDM simulation where the subhalo mass function
turns over at low masses, diverging from the the high-resolution m12i
simulation, shown in Fig. C1. Here, we test the effect of increasing this
threshold to $N_{\rm{cut}}=200$. Note that all the visible satellite galaxies
across all simulations studied satisfy this cut, so the results in Sec. 4
remain unchanged by default.

Figure C1: The mass function at $z=0$ for subhalos within 300 kpc of the host
galaxy in the CDM and high-resolution m12i (Wetzel et al., 2023b) simulations,
with no cuts applied. The shaded bands indicate the 1$\sigma$ Poisson error
for the count in each bin. The vertical dashed black line indicates $50\times
m_{\rm cdm}=1.4\times 10^{7}{\,\rm M_{\odot}}$, and the dotted black line
indicates $200\times m_{\rm cdm}=5.6\times 10^{7}{\,\rm M_{\odot}}$. Figure
C2: Cumulative number of subhalos within a given distance to the host center,
at $z=0$, with a larger mass-weighted threshold ($N_{\rm{cut}}=200$). Results
are shown for the CDM (blue), CDM-NF (green), ADM-1 (orange), and ADM-2 (pink)
simulations. Shaded bands indicate the 1$\sigma$ Poisson error in the count.
The solid black is the cumulative distribution obtained from the high-
resolution (high res.) public FIRE-2 data for the m12i simulation (Wetzel et
al., 2023b), with a mass cut $M_{200,\rm{m}}>200\times m_{\rm cdm}=5.6\times
10^{7}{\,\rm M_{\odot}}$. Compared to Fig. 4, there is better agreement
between CDM and m12i simulations, suggesting the discrepancy in the body of
the paper is mainly due to low-mass subhalos. Both ADM simulations still
contain a larger fraction of subhalos within the inner $\sim 125$ kpc of the
galaxy compared to the CDM-only simulations. The total number of subhalos is
still enhanced in ADM-1, but only slightly depleted in ADM-2.

Figure C2 shows the radial distribution of subhalos subject to
$N_{\rm{cut}}=200$; all previously identified trends remain, except with
better agreement between the CDM and m12i simulations. The ADM-1 simulation
still exhibits a relative enhancement compared to the others, while the total
number of subhalos in ADM-2 is suppressed. Moreover, the plateau feature in
both ADM simulations is present from 125–200 kpc, as observed previously.

Figure C3: Distributions of subhalo compactness, as defined by $R_{200,{\rm
m}}/R_{1/2}$, for CDM (blue), CDM-NF (green), ADM-1 (orange), and ADM-2 (pink)
simulations. Subhalos satisfy an increased mass-weighted threshold with
$N_{\rm{cut}}=200$. Top: Plot of $R_{200,{\rm m}}/R_{1/2}$ versus halo mass,
$M_{200,{\rm m}}$. The vertical dashed black line represents the CDM mass
threshold, $200\times m_{\rm cdm}=5.6\times 10^{7}{\,\rm M_{\odot}}$, while
the vertical dotted black line represents the ADM mass threshold, $200\times
m_{\rm adm}=3.4\times 10^{6}{\,\rm M_{\odot}}$. All the previously identified
and discussed groupings of subhalos are present, albeit less populated. Bottom
left: Plot of $R_{200,{\rm m}}/R_{1/2}$ versus distance to host galaxy,
$R_{\rm host}$. All trends discussed in the body of the paper are also visible
even with the increased prticle number cut. Bottom right: Histogram of
$R_{200,{\rm m}}/R_{1/2}$ values, all simulations peak in the ‘CDM-like’
region, but the ADM simulations peak at slightly larger values. The Enhanced-
compactness region is mainly occupied by the extended tails of the ADM aand
CDM-NF distributions. The ADM-dominated region is then mostly occupied by a
small peak of ADM-1 subhalos.

Figure C3 shows the compactness of all the DM subhalos. Due to the stronger
quality cut, the overall population of subhalos is smaller, but the
qualitative trends identified in the body of the paper are still present. In
particular, the three groups of subhalos are still present. Thus, the main
conclusions regarding ADM influence on subhalo compactness are still
applicable.