A&A 626, A47 (2019)
https://doi.org/10.1051/0004-6361/201833771
Astronomy
&
Astrophysics
c ESO 2019
Galaxies lacking dark matter in the Illustris simulation?
M. Haslbauer1 , J. Dabringhausen2 , P. Kroupa1,2 , B. Javanmardi3,4 , and I. Banik1
1
2
3
4
Helmholtz Institut für Strahlen- und Kernphysik (HISKP), University of Bonn, Nussalle 14-16, 53121 Bonn, Germany
e-mail: mhaslbauer@astro.uni-bonn.de
Charles University, Faculty of Mathematics and Physics, Astronomical Institute, V Holešovivckách 2, 180 00 Praha 8,
Czech Republic
School of Astronomy, Institute for Research in Fundamental Sciences (IPM), PO Box 19395-5531 Tehran, Iran
LESIA, Paris Observatory, PSL University, CNRS, Sorbonne University, Univ. Paris Diderot, Paris Cité Sorbonne,
5 Place Jules Janssen, 92195 Meudon, France
Received 4 July 2018 / Accepted 22 April 2019
ABSTRACT
Context. Any viable cosmological model in which galaxies interact predicts the existence of primordial and tidal dwarf galaxies
(TDGs). In particular, in the standard model of cosmology (ΛCDM), according to the dual dwarf galaxy theorem, there must exist
both primordial dark matter-dominated and dark matter-free TDGs with different radii.
Aims. We study the frequency, evolution, and properties of TDGs in a ΛCDM cosmology.
Methods. We use the hydrodynamical cosmological Illustris-1 simulation to identify TDG candidates (TDGCs) and study their
present-day physical properties. The positions of galaxies in the radius–mass plane, depending on their nonbaryonic content, are
compared with observational data and other simulations. We also present movies on the formation of a few galaxies lacking dark
matter, confirming their tidal dwarf nature. Tidal dwarf galaxy candidates can however also be formed via other mechanisms, such as
from ram-pressure-stripped material or, speculatively, from cold-accreted gas.
Results. We find 97 TDGCs with Mstellar > 5 × 107 M at redshift z = 0, corresponding to a co-moving number density of
2.3 × 10−4 h3 cMpc−3 . The most massive TDGC has Mtotal = 3.1 × 109 M , comparable to that of the Large Magellanic Cloud.
Tidal dwarf galaxy candidates are phase-space-correlated, reach high metallicities, and are typically younger than dark matter-rich
dwarf galaxies.
Conclusions. We report for the first time the verification of the dual dwarf theorem in a self-consistent ΛCDM cosmological simulation. Simulated TDGCs and dark matter-dominated galaxies populate different regions in the radius–mass diagram in disagreement
with observations of early-type galaxies. The dark matter-poor galaxies formed in Illustris-1 have comparable radii to observed
dwarf galaxies and to TDGs formed in other galaxy-encounter simulations. In Illustris-1, only 0.17 percent of all selected galaxies
with Mstellar = 5 × 107 − 109 M are TDGCs or dark matter-poor dwarf galaxies. The occurrence of NGC 1052-DF2-type objects is
discussed.
Key words. Galaxy: evolution – Galaxy: formation – Galaxy: abundances – galaxies: dwarf – dark matter
1. Introduction
The current standard model of cosmology is based on
Einstein’s general relativity and requires the existence of
cold dark matter (CDM) and a cosmological constant (Λ) in
Einstein’s gravitational field equations. This ΛCDM model is
a much-used description of the large-scale structure of the
Universe, but fundamental problems, not only on galactic and
galaxy-group scales, remain unsolved (e.g., Kroupa et al. 2010;
Famaey & McGaugh 2012; Pawlowski et al. 2014; Kroupa 2012,
2015; Müller et al. 2018).
In the ΛCDM framework, the dual dwarf theorem has to be
valid, according to which primordial and tidal dwarf galaxies
(TDGs) must exist (Kroupa et al. 2010; Kroupa 2012). These
two types of dwarf galaxies are characterized by different formation scenarios and differ mainly by their amounts of nonbaryonic
dark matter.
Primordial galaxies are formed by the collapse of cold dark
matter particles into halos. These structures become gravitationally bound and their deep gravitational potentials act on the
?
Movies are available at https://www.aanda.org
baryonic matter, which streams and condenses into the halos.
Thus, each primordial galaxy has to be dark matter-dominated
(Bournaud & Duc 2006; Bournaud et al. 2008a; Ploeckinger
et al. 2018).
In the hierarchical ΛCDM cosmology, the formation of dwarf
galaxies can also be triggered by interactions of gas-rich galaxies. Galaxy encounters create tidal forces, which distort the galactic disk and cause the expulsion of gas and stars. The ejected
stars and gas form tidal tails and arms, which surround and
orbit around the host galaxy. Overdensities within tidal arms
collapse and grow continually in mass (Barnes & Hernquist 1992;
Bournaud & Duc 2006; Wetzstein et al. 2007; Bournaud et al.
2008b,a; Fouquet et al. 2012; Ploeckinger et al. 2014, 2015).
These substructures reach stellar masses between 106 M and
109 M and are called TDGs. The high velocity dispersion of dark
matter particles and the relatively shallow gravitational potential compared to their host galaxy prevent TDGs from capturing
a significant amount of dark matter (Barnes & Hernquist 1992;
Wetzstein et al. 2007; Bournaud et al. 2008b,a; Fouquet et al.
2012; Yang et al. 2014; Ploeckinger et al. 2018). Consequently,
TDGs are not dark matter-dominated (Kroupa 2012). The small
amount of dark matter also has implications for the survival time
Article published by EDP Sciences
A47, page 1 of 28
A&A 626, A47 (2019)
of TDGs. Since the dynamical friction force depends linearly on
the density of the surrounding matter field and on the square of
the mass of the dwarf galaxy, dark matter-dominated dwarf galaxies have a faster orbital decay with respect to their host galaxy
(Angus et al. 2011). Therefore, in spite of the vicinity of TDGs
to a larger host galaxy, it has been shown that especially lowmass TDGs have survival times comparable with the Hubble time
(Kroupa 1997; Recchi et al. 2007; Casas et al. 2012; Ploeckinger
et al. 2014, 2015). Observational constraints also show that TDGs
survive for many gigayears (Duc et al. 2014). Ram-pressure
stripping, interactions with their host galaxy, star formation, and
evolution can deplete the gas reservoir of TDGs over cosmic
time. Therefore, long-lived and gas-poor TDGs can potentially
resemble dwarf elliptical galaxies (dEs; Dabringhausen & Kroupa
2013), and models suggest that the Large and Small Magellanic
Clouds can also be TDGs (Fouquet et al. 2012). Estimates based
on the merger tree in the CDM cosmological model have shown
that TDGs can probably account for the observed number density of dEs (Okazaki & Taniguchi 2000). Because of the different formation scenarios, TDGs should typically be phase-spacecorrelated while primordial dwarfs should be spheroidally distributed in phase-space around their host (Kroupa et al. 2005;
Pawlowski et al. 2011; Kroupa 2012; Pawlowski 2018). In the
local Universe, phase-space correlations (a clustering of the direction of the orbital angular momentum vectors of dwarf galaxies)
are observed around the majority of the nearest (.4 Mpc) major
galaxies, namely M 31 (Metz et al. 2007; Ibata et al. 2013), the
Milky Way (Pawlowski & Kroupa 2013; Pawlowski 2018), and
Centaurus A (Müller et al. 2018). Observing the phase-space distribution of distant satellite galaxies is currently very difficult, but
a significant excess of observed co-rotating satellite pairs over
that expected in a ΛCDM universe has been found (Ibata et al.
2014). Disks of satellites thus appear to be the rule rather than
the exception. Phase-space-correlated satellite systems may however be destroyed if the host galaxy suffers another encounter.
The observed high incidence of disk-of-satellite systems thus
suggests that such encounters, let alone mergers, cannot be
frequent.
Several observations of interacting galaxies have confirmed
the existence of gaseous tidal tails, arms, and TDGs in the Universe (e.g., Mirabel et al. 1992; Duc et al. 2000, 2014; Mendes de
Oliveira et al. 2001; Weilbacher et al. 2002; Martínez-Delgado
et al. 2010; Kaviraj et al. 2012; Lee-Waddell et al. 2012). Since
primordial dwarf galaxies form in the dark matter halo while
TDGs form naked under their own self-gravity, the latter are
expected to have systematically smaller radii if dark matter exists
(Kroupa 2012). Dabringhausen & Kroupa (2013) studied the
position of early-type galaxies and ultra compact dwarf galaxies (UCDs) in the radius–mass plane. These latter authors conclude that no significant difference in the radius–mass plane
between observed dEs and observed TDGs can be found, which
is in conflict with the current standard model of cosmology.
However, the data they used are from different observations
(Bender et al. 1992, 1993; Ferrarese et al. 2006; Misgeld et al.
2008, 2009; Misgeld & Hilker 2011; Miralles-Caballero et al.
2012). Moreover, UCDs and globular clusters (GCs) are clearly
separated from dEs and TDGs in the radius–mass plane (Gilmore
et al. 2007; Dabringhausen & Kroupa 2013). Until now, no selfconsistent study exists of formation in a cosmological context
quantifying the expected differences between TDGs and primordial dwarf galaxies.
The recently observed ultra-diffuse galaxy NGC 1052-DF2
with a dark matter mass 400 times smaller than theoretically
expected based on an internal velocity dispersion of σintr =
A47, page 2 of 28
−1
3.2−3.2
+5.5 km s , seems to support the existence of dark matterfree galaxies in our Universe (van Dokkum et al. 2018a).
van Dokkum et al. (2018b) derived a revised internal velocity
−1
dispersion of σintr = 7.8−2.2
using ten GCs surround+5.2 km s
ing this galaxy. Danieli et al. (2019) measured a stellar veloc−1
ity dispersion of σstars = 8.5−3.1
with the Keck Cosmic
+2.3 km s
Web Imager (KCWI). The high relative velocity to the nearby
massive elliptical galaxy NGC 1052 underpins the theory that
this observed dark matter-lacking galaxy is indeed a TDG.
However, Martin et al. (2018) revised the internal velocity of
NGC 1052-DF2 to a 90 percent upper limit of 17.3 km s−1 corresponding to a mass-to-light ratio of M/LV < 8.1 Υ , consistent with many Local Group dwarf galaxies. Emsellem et al.
(2019) obtain M/LV in the range 3.5−3.9(±1.8) Υ using the
Jeans model if located at D = 20 Mpc. This result would be
close to the 2σ upper limit of the study from Martin et al. (2018).
The lack of dark matter and the unusual high luminosity of ten
globular cluster-like objects surrounding this galaxy only holds
if NGC 1052-DF2 is located at a distance of around 20 Mpc
(van Dokkum et al. 2018a). Danieli et al. (2019) confirmed that
DF2 is dark matter deficient and concluded that it is an outlier to dwarf galaxies of the Local Group. In contrast to that,
Trujillo et al. (2019) derived a revised distance to NGC 1052DF2 of D = 13.0 ± 0.4 Mpc based on five redshift-independent
measurements including the tip of the red giant branch and
the surface brightness fluctuation method. Thus, NGC 1052-DF2
would be a dwarf galaxy with an ordinary dark matter content
Mhalo /Mstellar > 20 and a normal globular cluster population.
Meanwhile, van Dokkum et al. (2019) reported that the dwarf
galaxy NGC 1052-DF4 also lacks dark matter and is found at a
distance of D = 20 Mpc.
In this paper we investigate dark matter-free galaxies in
the Illustris simulation, which is currently one of the most
advanced cosmological computations. We analyze their physical
properties and qualitatively estimate the probability of finding
NGC 1052-DF2-like galaxies in a ΛCDM Universe at redshift
z = 0 assuming that this observed ultra-diffuse galaxy is indeed
free of dark matter. High-resolution runs of modern cosmological hydrodynamical simulations such as EAGLE (McAlpine
et al. 2016) and Illustris (Vogelsberger et al. 2014a) allow
the analysis of TDGs in a self-consistent cosmological ΛCDM
framework. The formation of TDGs in the EAGLE simulation
has been studied by Ploeckinger et al. (2018). The formation
of TDGs in individual galaxy–galaxy encounters in the ΛCDM
context is well established (Wetzstein et al. 2007; Bournaud et al.
2008b,a).
The layout of the paper is as follows. In Sect. 2, we introduce the Illustris simulation and the selection criteria for dark
matter-free galaxies. Section 3 presents the results, in particular
we study different physical properties of dark matter-free galaxies and we plot the radius–mass relation. The results are compared with observational data. The evolution of dark matter-free
galaxies over cosmic time is shown. The results are discussed
in Sect. 4. We finally summarize and conclude with Sect. 5.
Throughout this paper co-moving distances are marked with the
prefix “c” (i.e., cpc, ckpc, cMpc). We note that at redshift z = 0,
the scale factor a(t) becomes unity and by definition proper and
co-moving distances become the same.
2. Methods
We use the cosmological hydrodynamical Illustris simulation to
study the evolution and physical properties of dark matter-free
galaxies. This section introduces the Illustris project by
M. Haslbauer et al.: Galaxies lacking dark matter in the Illustris simulation
describing the cosmological and numerical parameters and the
implemented physics of galaxy-formation models. The selection
criteria for primordial and TDG candidates (TDGCs) are stated.
Movies on the formation and evolution of TDGCs are attached
in the supplementary material.
2.1. Illustris simulation
The Illustris simulation project1 is a set of cosmological hydrodynamical and dark matter-only simulations at different resolutions performed with the moving-mesh code AREPO (Springel
2010). The simulations assume a flat ΛCDM cosmology based
on the Wilkinson Microwave Anisotropy Probe (WMAP)-9 measurements with the values of the cosmological parameters at the
present time being Ωm,0 = 0.2726, ΩΛ,0 = 0.7274, Ωb,0 = 0.0456,
σ8 = 0.809, ns = 0.963, and H0 = 100 h−1 km s−1 Mpc−1 with
h = 0.704 (Hinshaw et al. 2013). The main simulations cover a
co-moving volume of (75 h−1 cMpc)3 and start at redshift z = 127.
The evolution of dark matter particles, gas cells, passive gas tracers, stars and stellar wind particles, and supermassive black holes
(SMBHs) are followed up to redshift z = 0 (Nelson et al. 2015).
Dark matter halos are identified with the standard friends-offriends (FOF) algorithm (Davis et al. 1985) with a linking length
of 0.2 times the mean particle separation. The minimum particle
number of each halo is 32. Subhalos within halos are identified
with the Subfind algorithm (Springel et al. 2001; Dolag et al.
2009) and have a unique identification number (ID) within each
snapshot. The particle with the minimum gravitational potential
energy defines the spatial position of the subhalo (halo) within
the periodic box, and the total mass of a subhalo (halo) is defined
as the sum of the individual masses of particles (cells) connected to the subhalo (halo). The physical properties of FOF
and Subfind objects for each snapshot are listed in the group
catalogs, which can be downloaded from the Illustris webpage
(Vogelsberger et al. 2014a; Genel et al. 2014).
Throughout this paper, we use the highest-resolution run
(Illustris-1) with a dark matter mass resolution of 6.26 × 106 M
(the mass of one particle) and an initial baryonic mass resolution of 1.26 × 106 M (the mass of one particle). The gravitational softening lengths of dark matter and baryonic particles
are 1420 cpc and 710 cpc in co-moving length scale, respectively
(Vogelsberger et al. 2014b; Nelson et al. 2015).
Torrey et al. (2015) provide images for subhalos with
Mstellar > 1010 M at redshift z = 0, which are produced with the
radiative transfer code SUNRISE (Jonsson 2006; Jonsson et al.
2010). These galaxy PNG images and fits files can be downloaded with the web-based search tool Illustris Galaxy Observatory from the Illustris webpage2 .
In addition, the Illustris team supplies an online tool called
“The Illustris Explorer” which visualizes a slice with a depth
of 15 h−1 Mpc in projection of the Illustris-1 simulation box at
redshift z = 0. This deep zoom map interface allows one to visualize, for example, the gas temperatures and densities, the dark
matter densities, and the stellar luminosities in Johnson/SDSS
filters3 .
2.2. Galaxy-formation models
A detailed galaxy formation model for simulating astrophysical
processes is implemented in the Illustris simulation. The model
1
2
3
http://www.illustris-project.org
http://www.illustris-project.org/galaxy_obs/
http://www.illustris-project.org/explorer/
includes a stochastic star formation description in dense gas,
stellar evolution with mass loss and chemical enrichment, cooling and heating mechanisms of the ISM, AGN feedback, and
the growth and evolution of SMBHs. The implemented physical models and a comparison with observations can be found
in detail in Vogelsberger et al. (2013) and Torrey et al. (2014).
We point out that in the Illustris simulation the mass loading
and wind velocity are scaled with the local dark matter velocity dispersion (Vogelsberger et al. 2013). This is in contradiction with the standard view of cold dark matter theory, which
assumes weak interactions between nonbaryonic and baryonic
matter. With this recipe, more massive halos produce stronger
baryonic feedback.
2.3. Selection criteria for dark matter-containing and dark
matter-free stellar objects
We select two different kinds of stellar objects based on their
baryonic and dark matter masses. We identify subhalos with a
stellar mass Mstellar > 0 and a nonzero dark matter mass and refer
to them as dark matter-containing (DMC) stellar objects. Dark
matter-free (DMF) stellar objects are defined as subhalos with
a stellar mass Mstellar > 0 and a dark matter mass of Mdm = 0.
These selection criteria give us 304 302 DMC and 3484 DMF
stellar objects at redshift z = 0.
2.4. Selection criteria for DMC dwarf galaxies and TDG
candidates
The selection criteria stated above for DMF and DMC stellar
objects are independent of the environment. In fact, DMF and
DMC stellar objects can be substructures which are embedded
in the galactic disk of their host galaxies rather than real physical galaxies (Ploeckinger et al. 2018; Graus et al. 2018). Therefore we divide stellar objects based on the separation, s, to their
next host galaxy4 . A host galaxy is defined as the closest subhalo with Mstellar > 109 M and a stellar mass at least ten times
larger than the considered stellar object. A stellar object with a
separation to its host halo smaller than or equal to ten times the
stellar half-mass radius of the host (≤10 × Rhost
0.5 stellar ) is defined as
a substructure within a galaxy such as a massive GC or a numerical artifact. Dark matter-free or dark matter-containing stellar
objects beyond the distance criterion of 10 × Rhost
0.5 stellar and within
100×Rhost
are
identified
as
TDGCs
or
dark
matter-containing
0.5 stellar
dwarf galaxies (DMC DGs), respectively. We label these dark
matter-free objects explicitly as TDG “candidates” in order to
emphasis that apart from galactic interactions (tidal forces) such
objects can also be formed in other scenarios, such as for example ram-pressure disruption or perhaps cold accretion.
The minimum separation criterion is motivated by the fraction of the separation between the Milky Way (MW) galaxy
and the Large Magellanic Cloud (LMC; sMW−LMC ≈ 50 kpc,
Pietrzyński et al. 2013) to the 3D deprojected half-light radius
of the MW (RMW
0.5 light ≈ 4.8 kpc, Koda et al. 2015; Wolf et al.
2010). A maximum separation limit is used because the
catalog of observed early-type galaxies from Dabringhausen &
Fellhauer (2016) only includes dwarf galaxies which are found
in dense galactic regions. Ignoring this criterion the most distant
TDGC has a separation of 987 kpc to its host and was probably
expelled by a galaxy–galaxy interaction.
4
The separation, s, between two subhalos is defined as the distance
between the particles with the minimum gravitational potential energy
in each subhalo.
A47, page 3 of 28
number of TDGCs (sample A)
A&A 626, A47 (2019)
The different described samples and where they are described
are summarized in Table 3.
median 131 kpc
mean 165 kpc
8
2.5. Formation scenarios of TDGCs
6
4
2
0
0
200
400
Dcr [kpc]
600
Fig. 1. Distribution of the 3D distance-criterion parameter, Dcr (Eq. (1)),
for TDGCs of sample A at redshift z = 0. The dashed red and the
solid blue lines highlight the median and the mean of the distribution,
respectively.
Furthermore, we restrict our main analysis to TDGCs with
Mstellar > 5 × 107 M (hereafter TDGC sample A) and DMC
DGs within the 5 × 107 −109 M stellar mass regime. The minimum stellar mass ensures that these subhalos are resolved with
at least 50 stellar particles. Using these selection criteria we find
97 TDGCs corresponding to a co-moving number density of
2.3 × 10−4 h3 cMpc−3 at redshift z = 0.
In order to study the separation of TDGCs to their host galaxies we introduce the 3D distance-criterion parameter Dcr ,
Dcr ≡ sTDGC−host − 10 × Rhost
0.5 stellar ,
(1)
where sTDGC−host is the 3D separation between the TDGC and
its host galaxy, and Rhost
0.5 stellar is the stellar half-mass radius of the
host galaxy as already defined in the text above. The distribution of the Dcr parameter for TDGCs of sample A is shown in
Fig. 1. This plot and Table 1 point out that most of the TDGCs
are located in the vicinity of a larger galaxy, which is theoretically expected from the formation theory of TDGs. In contrast
to that, a significant number of DMC objects are also beyond
the chosen maximum separation limit of 100 × Rhost
0.5 stellar (i.e.,
Dcr,max = 90 × Rhost
)
as
summarized
in
Table
2.
DMC DGs
0.5 stellar
with less dark matter than baryonic mass are found mostly close
to their host galaxies suggesting that TDGCs can in principle
capture dark matter particles. About 0.35 percent of all galaxies with Mstellar = 5 × 107 −109 M and within the applied distance criteria are TDGCs or DM-poor DGs. This reduces to
0.17 percent when ignoring the maximum separation limit on
the samples.
The criteria applied here for TDGCs are independent of the
gas half-mass radius of the host galaxy, Rhost
0.5 gas , in contrast to
Ploeckinger et al. (2018). In particular, Ploeckinger et al. (2018)
consider TDG candidates with Mgas > 107 M and Mstellar >
2.26 × 105 M which are located beyond 2 × Rhost
0.5 gas and within
host
a proper radius of 200 kpc or <20 × R0.5 gas (i.e., smax = min
[200 kpc, 20 × Rhost
0.5 gas ]). The host galaxy is defined as a galaxy
9
with Mgas > 10 M or a galaxy that has a gas content at least
ten times higher than the considered TDGC. We therefore define
another sample, TDGCs sample B, which includes TDGCs with
Mgas > 5 × 107 M and at least one stellar particle (see Table 1).
A47, page 4 of 28
In order to confirm the tidal nature of TDGCs, we present a series
of snapshots of the formation and evolution of some DM-poor
DGs and TDGCs by plotting 2D histograms of the gas distribution at different time steps. The corresponding movies can be
found as supplementary material. TDGCs and DM-poor objects
are identified at redshift z = 0 and are then backtraced by following their individual stellar particle IDs found in the Subfind subhalos at different time steps (excepted are the subhalos of their
potentially host galaxies). The backtracing algorithm developed
here stops when stellar particles can no longer be detected in a
potential progenitor of the considered object.
First, we study in Fig. 2a the evolution of the host galaxy
with the identification number ID 404871 at redshift z = 0 (see
also Fig. A.1 and the movie “ID404871.mp4”) by following its
main progenitor branch (Rodriguez-Gomez et al. 2015). This
galaxy hosts a TDGC in a gaseous tidal arm, which was formed
by a close encounter with another massive galaxy around 1.6 Gyr
ago. A similar formation process of the TDGCs ID 78410 and
ID 74010 (both of sample A) is seen in Fig. 2b. A galaxy merger
at a lookback time of around 1.9 Gyr creates tidal debris. The
first stellar particles in the subhalos of both identified TDGCs
at z = 0 appear at about 0.1 Gyr (ID 74010) and 0.5 Gyr (ID
74810) after the merger, allowing us to estimate their ages to be
about 1.8 Gyr and 1.4 Gyr, respectively. At present, ID 74810
and ID 74010 have 63 and 200 stellar particles, respectively.
ID 74010 has similar properties to the observed NGC 1052-DF2
galaxy by van Dokkum et al. (2018a) (see also Sect. 3.2 and the
movies “ID73663.mp4” and “ID73663_zoom.mp4”). Figure 2c
shows the host galaxy ID 150872 with the TDGCs of sample B
IDs 151014, 151271, 151299, 151878, and 151132, which were
formed again through a galaxy–galaxy encounter around 1.9 Gyr
ago (see also the movie “ID150872.mp4”).
Finally, by tracing the host galaxy ID 138 back in time, a different formation process of dark matter-lacking subhalos compared to the above discussed examples can be observed in Fig. 2d
(see also Fig. A.1 and the movie “ID138.mp4”). At a lookback time .1 Gyr this galaxy undergoes ram-pressure stripping.
This is an example of how baryon-dominated dwarf galaxies can
form from material stripped from a host galaxy through rampressure (the “type B dwarfs” of Kroupa 2012 and “fireballs”
observed by Yoshida et al. 2008; Yagi et al. 2010). Recent observations have shown that enhanced star formation can appear
in the ram-pressure stripped tails of jellyfish galaxies (Vulcani
et al. 2018). The DMF subhalos around the host galaxy ID 138
have Mstellar > 5 × 107 M but are located within 10 × Rhost
0.5 stellar
and are defined as DMF substructures of their host and therefore are not counted as TDGCs in this work. This example
also demonstrates that we have applied a very stringent minimum separation criterion in order to avoid a misidentification
of DMF substructures. In other words, we expect to have several false negatives but accept this in order to minimize false
positives.
In Fig. 3 we address the gas, stellar, and dark matter mass
evolution of the objects discussed here. Each of these subhalos
has at most one dark matter particle at the time when their first
stellar particle was identified. Given the high velocity dispersion
of dark matter particles, their presence in the objects could simply be transients detected by the Subfind algorithm. Moreover,
the objects are always baryon-dominated.
M. Haslbauer et al.: Galaxies lacking dark matter in the Illustris simulation
Table 1. Number of TDGCs for different selection criteria identified at redshift z = 0.
TDGCs
Mgas [M ]
Sample A
Sample B
Sample C
≥0
>5 × 107
>5 × 107
∧
∧
∧
Mstellar [M ]
>5 × Rhost
0.5 stellar
>10 × Rhost
0.5 stellar
(10−50) × Rhost
0.5 stellar
(10−100) × Rhost
0.5 stellar
>5 × 107
>0
>5 × 107
119
987
15
98
575
10
76
317
9
97
416
10
Notes. TDGCs of our main samples have to fulfill the (10−100) × Rhost
0.5 stellar − distance criterion (last column, Eq. (1)) and have Mdm = 0.
Table 2. Number of DMC DGs for different selection criteria identified at redshift z = 0.
DMC DGs
Mdm /Mbaryonic
>5 × Rhost
0.5 stellar
>10 × Rhost
0.5 stellar
(10−50) × Rhost
0.5 stellar
(10−100) × Rhost
0.5 stellar
All
DM-rich
DM-poor
>0
≥1
<1
67 585
67 560
25
65 815
65 799
16
17 682
17 668
14
32 055
32 040
15
Notes. DMC DGs of our main samples have to fulfill the (10−100) × Rhost
0.5 stellar − distance criterion (last column).
Table 3. Different defined samples and where we discuss them.
Sample
Relevant sections/tables
DMC & DMF stellar objects
DMC & DMF substructures
TDGCs (sample A)
TDGCs (sample B)
DMC DGs
DM-rich DGs
DM-poor DGs
Sect. 2.3
Sect. 2.4
See Table 1
See Table 1
See Table 2
See Table 2
See Table 2
2.7. Dispersion- and rotation-dominated galaxies
Determining the morphology of simulated galaxies and the comparison thereof with observations is a nontrivial task. Here,
we use the κrot morphological parameter in order to separate
them in dispersion- and rotation-dominated systems, which was
already studied by Sales et al. (2012) and Rodriguez-Gomez
et al. (2017). The κrot parameter is defined as the fraction of the
rotational energy, Krot , to the kinetic energy, K, of all stellar particles in the considered subhalo. The morphological parameter,
κrot , is
Krot
1 X 1 ĥ · hi 2
κrot ≡
=
mi
,
(5)
K
K i 2
Ri
2.6. The orbital angular momentum of dwarf galaxies
The different formation scenarios of galaxies with and without
dark matter cause differences in their phase-space distributions.
In particular, TDGs can be significantly correlated in phase space
(Kroupa 2012; Ploeckinger et al. 2015). The specific orbital
angular momenta of dwarf galaxies with respect to their host
galaxies are calculated by,
Lorbit = (rDG − rhost ) × (uDG − uhost ),
(2)
where rDG , and rhost , and uDG , and uhost are the position
and velocity vectors of the dwarf galaxy and host galaxy,
respectively.
The degree of the phase-space correlation of a system with
more than two TDGCs or DMC DGs is then determined by
q
σorbit = var(lorbit, x ) + var(lorbit, y ) + var(lorbit, z ),
(3)
with var(lorbit,x ), var(lorbit,y ), and var(lorbit,z ) being the variances
of the x, y, and z components of the normalized specific orbital
angular momenta given by Eq. (2); for example,
var(lorbit, x ) =
N
1 X
(lorbit,x,i − l¯orbit,x )2 ,
N i=1
(4)
where N is the number of dwarf galaxies around a host galaxy
and l¯orbit,x is the mean of all x-components of the normalized
specific orbital angular momenta.
This method is independent of the coordinate system. In the
case of a purely spherical distribution of the angular momenta
the degree of the phase-space correlation becomes σorbit = 1.
where ĥ is a unit vector proportional to the total stellar angular momentum of the galactic system, hi is the specific angular
momentum vector, mi is the mass, and Ri is the projected radius
of the ith stellar particle. The positions and velocities of the stellar particles are calculated with respect to the center of mass of
the subhalo. According to Eq. (5), the κrot parameter can range
between 0 and 1 meaning that in the latter case all stellar particles move on circular orbits with respect to the total stellar angular momentum. Subhalos with κrot smaller or larger than 0.5 are
dispersion- or rotation-dominated systems, respectively. Images
of the most massive dispersion- and rotation-dominated Illustris
galaxies identified at redshift z = 0 are presented in Fig. 4. An
interesting discussion about the properties of the κrot morphological parameter for dynamical systems is found in Appendix A of
Rodriguez-Gomez et al. (2017).
3. Results
We present the physical properties of TDGCs and DMC DGs
and their positions in the radius-mass plane at redshift z = 0.
The results are compared with observational data from
Dabringhausen & Fellhauer (2016) and Mieske et al. (2008,
2013). The metallicities of TDGCs and DMC DGs are studied
in Appendix B. In addition, a discussion about the internal structures and kinematics of TDGCs including a σ-clipping scheme
as a 6D phase-space halo finder applied on gas-free Subfind
TDGCs of sample A can be found in Appendix C where the
gravitationally bound nature of these simulated objects is also
discussed.
A47, page 5 of 28
A&A 626, A47 (2019)
a)
t = 1.3 Gyr
0
−200
t = 0.33 Gyr
∆y [ckpc]
200
∆y [ckpc]
−200
c)
0
∆x [ckpc]
200 −200
t = 2.1 Gyr
0
∆x [ckpc]
−200
t = 1.3 Gyr
−200
t = 0.33 Gyr
200
−200
0
∆x [ckpc]
200 −200
200
t = 0.0 Gyr
−200
0
200
∆x [ckpc]
d)
−200
0
200
∆x [ckpc]
t = 1.8 Gyr
t = 1.4 Gyr
t = 1.1 Gyr
t = 0.78 Gyr
t = 0.46 Gyr
t = 0.0 Gyr
50
0
−50
50
0
−50
t = 0.0 Gyr
0
∆x [ckpc]
t = 1.6 Gyr
−200
t = 0.78 Gyr
0
t = 1.8 Gyr
0
∆y [ckpc]
200
t = 1.9 Gyr
−200
t = 1.8 Gyr
0
t = 2.1 Gyr
0
∆y [ckpc]
200
−200
200
200
0
t = 2.4 Gyr
−200
t = 0.0 Gyr
0
−200
b)
0
∆y [ckpc]
∆y [ckpc]
200
200
t = 0.78 Gyr
∆y [ckpc]
∆y [ckpc]
200
∆y [ckpc]
t = 1.8 Gyr
0
−200
∆y [ckpc]
t = 2.1 Gyr
∆y [ckpc]
∆y [ckpc]
200
50
0
−50
−50
0
50
∆x [ckpc]
−50
0
50
∆x [ckpc]
Fig. 2. Time evolution of the gas distribution weighted by the logarithm of the gas cell mass and with position relative to the subhalo center of host
galaxies. The TDGC and DM-poor objects identified at z = 0 are being backtraced by their individual stellar particle IDs and are highlighted in the
panels until stellar particles can no longer be found in their subhalo. The lookback time of the corresponding snapshot is given in the upper-right
corner of the panels. a) Host galaxy ID 404871 with the TDGC of sample B ID 404882 (red circle), DM-poor substructure ID 404873 (blue
square), and the subhalo ID 404879 (green down-pointing triangle) being identified at z = 0 (see also Fig. A.1 and the movie “ID404871.mp4”
in the supplementary information). The subhalo ID 404879 has Mstellar = 2.2 × 107 M and thus does not fulfill our criteria for a DM-poor DG
(see Table 2). A close encounter of two galaxies happens at a lookback time of about 1.6 Gyr creating a large extended tidal arm in which these
dark matter-lacking subhalos are identified. b) Host galaxy ID 73663 with the TDGCs ID 74010 (DF2-like; red circle) and ID 74810 (green downpointing triangle) being identified at z = 0 (both of sample A; see also Sect. 3.2 and the movies “ID73663.mp4” and “ID73663_zoom.mp4”).
A galaxy merger occurs at a lookback time of around 1.9 Gyr. c) Host galaxy ID 150872 with the TDGCs of sample B ID 151014 (red circle),
ID 151271 (blue square), ID 151299 (black up-pointing triangle), ID 151878 (magenta diamond), and ID 151332 (green down-pointing triangle)
formed by an interaction around 1.9 Gyr ago (see the movie “ID150872.mp4”). d) Host galaxy ID 138 with the DMF substructures ID 878 (red
circle) and ID 1683 (green down-pointing triangle) being identified at z = 0 (see also Fig. A.1 and the movies “ID138.mp4”). These are not TDGs
because they form from gas ram-pressure stripped from the host ID 138. Ram-pressure stripping can be observed at a lookback time .1 Gyr.
A47, page 6 of 28
10
108
107
109
108
107
M [M ]
M [M ]
9
109
108
107
ID 1683
ID 878
ID 74010
gas
stars
dark matter
Table 4. Degree of the phase-space correlation, σorbit (Eq. (3)), for
TDGC samples and DMC DGs at redshift z = 0.
ID 74810
ID 404882
ID 404879
Sample
Counts
Mean
Median
TDGCs (sample A)
TDGCs (sample B)
DMC DGs
5
40
7810
0.52
0.22
0.73
0.54
0.15
0.82
Notes. Listed are the number of galactic systems with more than one
TDGC or DMC DG, the mean, and the median of the degree of the
phase-space correlation for each dwarf galaxy sample.
ID 404873
0.4
ID 151014
0.5 1.0 1.5
t [Gyr]
ID 151271
0.5 1.0 1.5
t [Gyr]
ID 151299
0.5 1.0 1.5
t [Gyr]
ID 151878
0.5 1.0 1.5
t [Gyr]
Fig. 3. Gas (green), stellar (red), and dark matter (black) mass evolution
of TDGCs and DM-poor objects shown in Fig. 2 starting from the first
time step at which the first stellar particles in their subhalos appeared.
Their ID numbers are given in the upper-right corner of the panels and
the discussed subhalos of each row belong to the same host galaxy. The
subhalo ID 404879 has Mstellar = 2.2 × 107 M , Mgas = 3.0 × 108 M ,
and Mdm = 6.3 × 106 M and is thus not included in the main sample of
DMC (-poor) DGs (see Table 2). The dashed and long-dashed horizontal
lines indicate the initial baryonic (1.26 × 106 M ) and dark matter mass
(6.26 × 106 M ) of a particle. The dark matter content is short lived and
is due to individual dark matter particles crossing the objects.
Subfind Image (SB99)
ID 0
Subfind Image (SB99)
ID 283832
fraction of dwarf galaxies
109
108
107
M [M ]
M [M ]
M. Haslbauer et al.: Galaxies lacking dark matter in the Illustris simulation
TDGCs (A)
TDGCs (B)
DMC DGs
0.3
0.2
0.1
0.0
0.0
0.2
0.4
σorbit
0.6
0.8
1.0
Fig. 5. Degree of the phase-space correlation, σorbit (Eq. (3)), for
TDGCs of sample A (red) and sample B (orange) and DMC DGs
(green). The histograms have a bin width of ∆σorbit = 0.05.
and the distributions of the degree of the phase-space correlation, σorbit , for TDGCs and DMC DGs are shown in Fig. 5. Tidal
dwarf galaxy candidates from sample B are significantly more
phase-space-correlated than DMC DGs. These results are discussed in Sect. 4.1.
3.2. NGC 1052-DF2-like galaxies in the Illustris-1 simulation
κrot = 0.28
FoV = 1 Mpc
κrot = 0.61
FoV = 220 kpc
Fig. 4. Examples of Subfind Starburst 99 (SB99) images of the most
massive dispersion- (left; ID 0, κrot = 0.28, Mstellar+gas = 2.9 × 1013 M ,
Mdm = 2.9 × 1014 M ) and most massive rotation-dominated (right; ID
283832, κrot = 0.61, Mstellar+gas = 4.9 × 1011 M , Mdm = 6.7 × 1012 M )
galaxy in the Illustris-1 simulation at redshift z = 0. The image field
of view (FoV) is ten times the stellar half-mass radius, R0.5 stellar , of
the shown galaxy. Credit: Illustris Galaxy Observatory http://www.
illustris-project.org/galaxy_obs/ [25.08.2018].
3.1. Phase-space correlation of TDGCs and DMC DGs
We quantify the degree of the phase-space correlation, σorbit
(Eq. (3)), for all galactic systems with more than one TDGC or
DMC DG. Considering all TDGCs with Mstellar > 5 × 107 M
(sample A) gives only five galactic systems that host more than
one such TDGC. Therefore, we determine the phase-space correlation for both samples A and B. The results are listed in Table 4
The ultra-diffuse galaxy NGC 1052-DF2 has Mstellar ≈ 2 ×
108 M with a dark matter mass 400 times smaller than theoretically predicted and has an effective radius along the major
axis of Re = 2.2 kpc, assuming it is at a distance of 20 Mpc
(van Dokkum et al. 2018a). Wolf et al. (2010) derived a scaling relation between the 2D projected half-light radius, Re , and
the 3D deprojected half-light radius, R0.5 light , for stellar systems.
These latter authors showed that the relation,
R0.5 light ≈
4
× Re ,
3
(6)
is accurate for most surface brightness profiles of spherical stellar systems with Sérsic indices in the range 0.10 ≤ n−1 ≤ 2.0 (see
Appendix B in Wolf et al. 2010). Applying this scaling relation
to the effective radius of NGC 1052-DF2 and taking into account
its axis ratio being 0.85 gives a 3D stellar half-light radius of
2.7 kpc.
Using the Illustris-1 simulation we found no single TDGC
fulfilling a minimum stellar mass criterion of 2 × 108 M and
a minimum stellar half-mass radius criterion of 2.7 kpc at the
same time. Choosing instead 20 percent reduced lower limits
A47, page 7 of 28
A&A 626, A47 (2019)
R0.5 stellar [kpc]
Mstellar [M ]
Number
Probability
wrt. sample A
Gas free
R0.5 stellar [kpc]
Mstellar [M ]
Number
Probability
wrt. sample A
TDGCs
TDGCs
TDGCs
≥2.7
≥2 × 108
0
0.0
≥0.8 × 2.7
≥0.8 × 2 × 108
1
1.0 × 10−2
≥0.6 × 2.7
≥0.6 × 2 × 108
6
6.2 × 10−2
TDGCs
≥2.7
≥2 × 108
0
0.0
TDGCs
≥0.8 × 2.7
≥0.8 × 2 × 108
0
0.0
TDGCs
≥0.6 × 2.7
≥0.6 × 2 × 108
5
5.2 × 10−2
number of TDGCs (sample A)
Table 5. Probability of finding a NGC 1052-DF2-like galaxy in the
Illustris-1 simulation at redshift z = 0.
of Mstellar = 0.8 × 2 × 10 M and R0.5 stellar = 0.8 × 2.7 kpc
gives only one TDGC at redshift z = 0 (ID 74010). The probability of finding such a NGC 1502-DF2-like galaxy among all
TDGCs of sample A is around 1.0 × 10−2 . In particular, this
TDGC has R0.5 stellar = 2.4 kpc, Mstellar = 1.9 × 108 M , Mgas =
1.5 × 109 M , and κrot = 0.46. The separation to its host galaxy
(ID 73679) is about 219 kpc, which is roughly consistent with
the observed NGC 1052-DF2 galaxy found in the vicinity of the
massive elliptical galaxy NGC 10525 . The simulated host galaxy
is dispersion-dominated and has Mstellar = 6.4 × 1010 M and
Mdm = 4.4 × 1011 M . Interestingly, this galaxy hosts a second
gas-rich TDGC (ID 74810) at 150 kpc. As seen in a series of
snapshots in Sect. 2.5 (see also the movies “ID73663.mp4” and
“ID73663_zoom.mp4”) these TDGCs were formed from the gas
expelled by tidal forces from massive interacting galaxies.
Summing up, there is no TDGC in the Illustris-1 simulations
at redshift z = 0 which has a stellar mass and a stellar-half mass
radius equal to or larger than the observed NGC 1052-DF2 at the
same time. However, relaxing the lower mass limits of the selection criteria by 20 and 40 percent yields one and six TDGCs,
respectively. But invoking the condition Mgas = 0 because
NGC 1052-DF2 is gas-free (Chowdhury 2019; Sardone
et
al.
2019) and choosing lower limits of Mstellar = 0.8 × 2 × 108 M
and R0.5 stellar = 0.8 × 2.7 kpc lead to no similar dwarf galaxies
existing in the Illustris-1 simulation. A parameter study of different selection criteria is given in Table 5. Regardless of the exact
definition, finding a NGC 1052-DF2-like galaxy at redshift z = 0
in the Illustris-1 simulation is extremely rare. This analysis does
not include a comparison of the peculiar velocity of the observed
NGC 1052-DF2 with simulated analogs.
However, the observed velocity dispersion is rather uncertain and allows for a significant dark matter content (Martin
et al. 2018). In addition, Trujillo et al. (2019) concluded that
5
8
The statistically expected 3D separation between the observed
NGC
1052 and NGC 1052-DF2 galaxies is about 100 kpc, which is
√
3/2 times its projected separation, assuming NGC 1052-DF2 is at
a distance from us comparable to that of NGC 1052 (20 Mpc, van
Dokkum et al. 2018a). However, this distance may be revised (Trujillo
et al. 2019).
A47, page 8 of 28
number of TDGCs (sample A)
10
8
6
4
2
0
7.0
Notes. The second part of the table only refers to gas-free NGC 1052DF2-like galaxies. The probabilities are calculated by dividing the number of selected TDGCs by the number of all TDGCs of sample A (97)
at redshift z = 0.
TDGCs (A)
12
7.5
8.0
8.5
9.0
log10 (Mstellar /[M ])
9.5
10.0
TDGCs (A)
12
10
8
6
4
2
0
7.0
7.5
8.0
8.5
9.0
log10 (Mtotal /[M ])
9.5
10.0
Fig. 6. Stellar mass, Mstellar , (top) and total mass, Mtotal , (bottom) distributions of TDGCs (sample A) at redshift z = 0. The dashed vertical line illustrates the minimum stellar mass criterion of 5 × 107 M .
The histograms have a bin width of log10 (∆Mstellar /[M ]) = 0.10 and
log10 (∆Mtotal /[M ]) = 0.10.
NGC 1052-DF2 is at a distance of 13.0 ± 0.4 Mpc from Earth
and is not an outlier to dwarf galaxies of the Local Group6 .
3.3. Physical properties of TDGCs and DMC DGs
Figure 6 shows the stellar (top) and total (bottom) mass distributions of TDGCs with Mstellar > 5 × 107 M (sample A). As
expected, TDGCs have typically small masses whereby the most
massive TDGC has Mtotal = 3.1×109 M . In high-resolution simulations of merging galaxies with dark matter, the most massive
TDGs have been reported to have baryonic masses in the range
of 108 M –109 M such that also the Large and Small Magellanic Clouds can be TDGs (Bournaud et al. 2008b,a; Fouquet
et al. 2012).
The applied selection criteria for TDGCs of sample A identify dwarf galaxies with low amounts of gas. In particular,
around 89 percent of all TDGCs are completely gas-free and
6
These calculations include only completely dark matter-free
galaxies. In a further analysis subhalos with the ratio Mhalo /Mstellar at
least 400 times lower than theoretically expected can be included. This
analysis would be an interesting extension to the present work.
M. Haslbauer et al.: Galaxies lacking dark matter in the Illustris simulation
0.25
fraction of dwarf galaxies
TDGCs (A)
TDGCs (B)
DMC DGs
0.20
0.15
0.10
0.05
0.00
0.0
2.5
5.0
7.5
10.0
lookback time [Gyr]
12.5
Fig. 7. Distribution of the age of the oldest stellar particles within dwarf
galaxies identified at redshift z = 0. The histograms have a bin width of
∆t = 0.2 Gyr. The statistics of the distributions shown here are listed in
Table 6.
also have no star formation. If we apply similar selection criteria for TDGCs as in the work of Ploeckinger et al. (2018)
(sample B), we obtain many more TDGCs than in sample A
(see Table 1)7 . This can be understood by the formation scenario of TDGCs, which are formed in gas-rich tidal tails expelled
from their host galaxies triggered by galactic interactions. The
median (mean) of the stellar mass of TDGCs belonging to sample B is about 1.7 (5.6) higher than the median (mean) of the
TDGCs from Ploeckinger et al. (2018). Furthermore, we report
a median (mean) of the gas mass that is 2.4 (1.6) times higher
than the sample of Ploeckinger et al. (2018). These discrepancies
could be caused by the different selection criteria for TDGCs
and the use of different cosmological simulations. Ploeckinger
et al. (2018) set a minimum gas mass limit of 107 M because
of the higher resolution of baryonic and dark matter particles
in the EAGLE simulations they used compared to the Illustris-1
run employed here. Moreover, Ploeckinger et al. (2018) select
TDGCs within z ≤ 2.0.
The age of dwarf galaxies is estimated here by the formation time of the oldest stellar particle within a subhalo identified at redshift z = 0. The derived age distribution of different
dwarf galaxy samples are studied in Fig. 7 and analyzed in more
detail in Table 6. The mean age of DM-rich DGs is 12.7 Gyr,
which is significantly higher than for DM-poor DGs (8.9 Gyr)
and TDGCs and underlines that DM-rich DGs are formed in
early stages of the Universe. The mean ages of the TDGCs of
samples A and B are 7.6 Gyr and 1.5 Gyr, respectively. Therefore TDGCs with a vanishing gas content are older objects,
which have already consumed or lost their gas reservoir via rampressure stripping and interactions.
The distribution of the κrot morphology parameter of TDGCs
(sample A) and DMC DGs is presented in Fig. 8, which states
that around 94 percent of all TDGCs with Mstellar > 5 × 107 M
(sample A) are dispersion-dominated (κrot < 0.5) at redshift z =
0. The high fraction of dispersion-dominated TDGCs is unexpected, because high-resolution simulations of galaxy encounters by Bournaud et al. (2008b,a) have shown that the most
7
Here, we refer to the TDGC sample B, which includes DMF stellar
host
objects beyond 10 × Rhost
0.5 stellar and within 100 × R0.5 stellar with Mgas >
7
5 × 10 M containing at least one stellar particle.
massive stellar TDGs in the mass range of 108 −109 M are dominated by rotation. However, the TDGs in their simulations are
young and gas-rich while most of the observed satellite galaxies
surrounding the MW are old and typically dispersion-dominated.
The simulations by Bournaud et al. (2008b,a) suggest that feedback processes such as SN explosions transform them into
gas-poor DGs which suffer from a loss of angular momentum. Therefore, TDGs can be transformed into dwarf spheroidal
satellite galaxies within a Hubble time (Metz & Kroupa 2007;
Dabringhausen & Kroupa 2013). The medians and means of the
distribution of the κrot parameter for simulated TDGCs (sample
A) and DMC DGs are almost the same (see Table 6). Nevertheless, calculating the κrot parameter for objects with a small number of stellar particles is insecure and the present results should
be treated with caution.
Finally, we study the 1D velocity dispersion of simulated
dwarf galaxies which is calculated by all particles (cells) belonging to the considered subhalo. The medians and means of the
1D velocity dispersion for different dwarf galaxy samples reveal
information about the properties of baryonic and dark matter particles. Dwarf galaxies with a small amount of dark matter have significantly lower velocity dispersions than dark matter-dominated
objects, as theoretically expected. The medians of the 1D velocity
dispersion of simulated TDGCs (sample A) and DM-poor DGs
are 7.8 km s−1 and 9.7 km s−1 , respectively. The intrinsic velocity dispersion of NGC 1052-DF2 derived by observing ten GCs is
−1
(van Dokkum et al. 2018b).
σintr = 7.8+5.2
−2.2 km s
The stellar and gas metallicities of TDGCs belonging to sample A are shown and discussed in Appendix B and in Sect. 4.2,
respectively. The physical properties of different TDGCs and
DMC DGs samples at redshift z = 0 are summarized in Table 6.
The host halos of TDGCs (sample A) are studied in Fig. 9,
which shows the total host halo mass distribution of host halos
which contain at least one DMC DG (top; green) and/ or at
least one TDGC (top; red) at redshift z = 0. Most of the
TDGCs appear in host halos with a total halo mass range of
halo
Mtotal
≈ 1012 − 4.6 × 1014 M , but a small number of TDGCs
can also be found in the 7.8 × 107 − 2.7 × 108 M total halo mass
regime. In fact, 97 TDGCs belong to 42 different host halos and
halo
the most massive host halo (Mtotal
= 4.6 × 1014 M ) possesses
the highest number of TDGCs (nTDGCs = 12). Only a very small
number of TDGCs are found in low-mass host halos. The number of TDGCs per number of host halos within a given mass bin
is shown in Fig. 9 (bottom). The number of TDGCs per host halo
increases with the total host halo mass. The distribution is fitted
with an exponential function of the form,
halo
M
M halo
log10 Mtotal −c
total
ρ̃TDGCs log10
=a+b
,
(7)
M
with the fitting parameters
a = 0.331 ± 0.098,
b = 16.0 ± 4.5,
c
log10
= 13.832 ± 0.077,
M
halo
halo
where ρ̃TDGCs (log10 (Mtotal
))d log10 (Mtotal
) = d Ñ is the number
halo
of TDGCs per host halo with a mass in the range log10 (Mtotal
) to
halo
halo
log10 (Mtotal ) + d log10 (Mtotal ).
The higher probability for galactic interactions and mergers
in massive host halos can explain the increase of TDGCs per host
A47, page 9 of 28
A&A 626, A47 (2019)
Table 6. Physical properties of DMC DG and TDGC samples at redshift z = 0.
Properties
Sample
Mdm /Mbaryonic
Minimum
Maximum
Median
Mean
Mstellar [M ]
DMC DGs
DM-rich DGs
DM-poor DGs
TDGCs (A)
TDGCs (B)
TDGCs (C)
DMC DGs
DM-rich DGs
DM-poor DGs
TDGCs (A)
TDGCs (B)
TDGCs (C)
DMC DGs
DM-rich DGs
DM-poor DGs
TDGCs (A)
TDGCs (B)
TDGCs (C)
DMC DGs
DM-rich DGs
DM-poor DGs
TDGCs (A)
TDGCs (B)
TDGCs (C)
DMC DGs
DM-rich DGs
DM-poor DGs
TDGCs (A)
TDGCs (B)
TDGCs (C)
DMC DGs
DM-rich DGs
DM-poor DGs
TDGCs (A)
TDGCs (B)
TDGCs (C)
DMC DGs
DM-rich DGs
DM-poor DGs
TDGCs (A)
TDGCs (B)
TDGCs (C)
DMC DGs
DM-rich DGs
DM-poor DGs
TDGCs (A)
TDGCs (B)
TDGCs (C)
>0
≥1
<1
0
0
0
>0
≥1
<1
0
0
0
>0
≥1
<1
0
0
0
>0
≥1
<1
0
0
0
>0
≥1
<1
0
0
0
>0
≥1
<1
0
0
0
>0
≥1
<1
0
0
0
>0
≥1
<1
0
0
0
5.0 × 107
5.0 × 107
5.3 × 107
5.0 × 107
5.1 × 105
5.7 × 107
0.0
0.0
0.0
0.0
5.4 × 107
1.1 × 108
0.19
0.19
0.28
0.23
–
0.35
4.0
6.0
4.0
3.7
1.3
7.2
0.0
0.0
0.0
0.0
0.0
0.0028
0.00040
0.00040
0.0084
0.0089
0.0
0.0090
0.0
0.0
0.0
0.0
0.0
0.010
–
7.29
1.8
0.47
0.0
–
1.0 × 109
1.0 × 109
8.9 × 109
3.1 × 109
4.4 × 108
4.3 × 108
2.2 × 1010
2.2 × 1010
8.4 × 108
1.5 × 109
1.5 × 109
1.5 × 109
0.75
0.75
0.46
0.60
–
0.55
52
52
19
35
26
26
0.59
0.59
0.049
0.95
0.95
0.95
0.052
0.029
0.052
0.052
0.045
0.045
0.025
0.025
0.018
0.053
0.053
0.053
–
13.5
13.3
11.7
12.0
–
1.4 × 108
1.4 × 108
1.4 × 108
1.5 × 108
2.9 × 106
1.1 × 108
1.8 × 109
1.8 × 109
0.0
0.0
2.0 × 108
4.6 × 108
0.40
0.40
0.34
0.37
–
0.43
27
27
9.7
7.8
5.4
13
0.0031
0.0031
0.0
0.0
0.00066
0.20
0.0016
0.0016
0.028
0.019
0.0030
0.015
0.0018
0.0018
0.0
0.0
0.0033
0.022
–
12.8
9.2
8.0
1.0
–
2.4 × 108
2.4 × 108
3.6 × 108
3.1 × 108
1.0 × 107
1.6 × 108
2.6 × 109
2.6 × 109
1.0 × 108
6.2 × 107
2.5 × 108
5.9 × 108
0.42
0.42
0.35
0.38
–
0.44
26
26
10
9.6
5.8
14
0.013
0.013
0.0048
0.027
0.011
0.26
0.0021
0.0021
0.029
0.022
0.0047
0.021
0.0022
0.0022
0.0028
0.0030
0.0052
0.027
–
12.7
8.9
7.6
1.5
–
Mgas [M ]
κrot
vdisp [km s−1 ]
ψsfr [M yr−1 ]
Zstellar
Zgas
tage [Gyr]
Notes. Listed are the stellar mass, Mstellar , gas mass, Mgas , kinematical morphological parameter, κrot , 1D velocity dispersion of all the member
particles/cells, vdisp , star formation rate, ψsfr , and the stellar and gas mass-weighted average metallicities, Zstellar = (M>He /Mtot )stellar and Zgas =
(M>He /Mtot )gas , where M>He is the mass of all elements above Helium (only cells within twice the stellar half-mass radius are considered), and the
age, tage , of the oldest stellar particle within a dwarf galaxy identified at redshift z = 0. The metallicities of TDGCs are analyzed in more detail in
Appendix B.
halo with total host halo mass, consistent with these dark matterfree galaxies indeed being TDGs. This is qualitatively consistent
with the analysis by Okazaki & Taniguchi (2000).
A47, page 10 of 28
3.4. Radius-mass relation
According to the dual dwarf theorem, two types of dwarf galaxies must exist and they can be distinguished based on their
M. Haslbauer et al.: Galaxies lacking dark matter in the Illustris simulation
0.2
dispersiondominated
rotationdominated
0.1
0.20
0.15
0.10
0.05
0.0
0.0
0.2
0.4
κrot
0.6
0.8
0.00
1.0
Fig. 8. Distribution of the κrot morphological parameter for DMC DGs
(green) and TDGCs (red) with Mstellar > 5 × 107 M (sample A). DMC
DGs and TDGCs are divided into rotation- and dispersion-dominated
objects at κrot = 0.5 (dashed black line). The histograms have a bin
width of ∆κrot = 0.05.
stellar masses and radii (Kroupa et al. 2010; Kroupa 2012;
Dabringhausen & Kroupa 2013). In order to verify these predictions in the ΛCDM cosmological Illustris simulation, we show
first the positions of DMC and DMF stellar objects in the radius–
mass plane in Fig. 10. Due to the cell resolution of the Illustris1 simulation, a significant number of DMF stellar objects have
a stellar half-mass radius below the resolution limit and in this
sense are consistent with a radius equal to zero8 . These 1240
subhalos are removed from the diagram; they could be UCDs
(Hilker et al. 2007; Baumgardt & Mieske 2008). Dark matterfree and DMC stellar objects are clearly distributed differently
in the radius–mass diagram. In general, DMF stellar objects
have smaller stellar half-mass radii than most of the galaxies
with a nonzero dark matter component, confirming the prediction by Kroupa (2012). However, a few objects with a nonvanishing dark matter mass and with stellar masses between 107 M
and 1010 M can also be found in the region of DMF stellar
objects. The properties of these DMC stellar objects are discussed in Fig. 11, wherein the populations of dark matter-poor
and dark matter-rich DMC stellar objects in the radius–mass
plane are plotted. Most DMC stellar objects in the region of
DMF stellar objects have a dark matter-to-baryonic mass ratio
Mdm /Mbaryonic < 1 and are thus dark matter-poor.
Some of the stellar objects shown here are substructures with
a separation to their host galaxies smaller than 10 × Rhost
0.5 stellar
according to Tables 1 and 2. Therefore, we discuss the radius–
mass diagram for TDGCs of sample A9 and DMC DGs in
Fig. 12, which shows for the first time that the dual dwarf
theorem is valid in a self-consistent ΛCDM simulation. It is
worth noting that the independent simulations of galaxy-galaxy
encounters (in a dark matter Universe) by Fouquet et al. (2012)
of TDG formation show these to have radii consistent with the
DMF stellar objects and TDGCs in the Illustris simulation (upper
panel of Fig. 12).
8
halos of DMC DGs
halos of TDGCs (A)
0.25
fraction of halos
0.3
min
In the Illustris-1 simulation the smallest fiducial cell size rcell
is 48 pc
min
5
and the minimum mass mcell of a cell is 0.15 × 10 M (Vogelsberger
et al. 2014b).
9
In this section we only refer to TDGCs of sample A.
number of TDGCs (sample A) per halo
fraction of dwarf galaxies
0.30
DMC DGs
TDGCs (A)
5.0
7.5
10.0
12.5
halo
log10(Mtotal
/[M ])
15.0
exponential fit
8
6
4
2
0
8
10
12
halo
log10(Mtotal
/[M ])
14
halo
Fig. 9. Top: total host halo mass, Mtotal
, distribution of host halos in
which at least one DMC DG (green) is embedded is shown in green
and in which at least one TDGC of sample A is embedded is shown in
red for redshift z = 0. Bottom: distribution of the number of TDGCs
(sample A) per host halo at redshift z = 0. The histogram is fitted with
an exponential function (solid green line) given by Eq. (7). The fitting
parameters are listed in the text. The histograms have a bin width of
halo
log10 (∆Mtotal
/[M ]) = 0.25.
The Kolmogorov–Smirnov (KS) test is applied in Fig. 13 in
order to decipher whether or not DMC DGs and TDGCs follow the same stellar mass and stellar half-mass radius distribution. We only include simulated dwarf galaxies with stellar
masses between 5 × 107 M and 109 M . The lower mass limit
ensures that only well-resolved galaxies with a significant number of stellar particles are included in the statistical analysis. The
P-values for the stellar half-mass radii are <10−12 , which quantitatively confirms the dual dwarf theorem. Moreover, we find
only 15 DM-poor DGs that are possibly TDGs that captured dark
matter particles from their host galaxy. These DM-poor DGs typically reside in the radius–mass plot between the DMC DG and
TDGC branches. The probability of such a capture is very small
because of the high velocity dispersion of dark matter particles
and the shallow gravitational potential of TDGs, consistent with
the small number of such DM-poor DGs.
The simulated dispersion-dominated (κrot < 0.5) galaxies
formed in a ΛCDM framework are compared with observational
A47, page 11 of 28
A&A 626, A47 (2019)
norm. freq.
4
3
0.0
5.0
log10(Mstellar/[M ])
sim. DMF stellar objects
sim. TDGs (Fouquet et al. 2012)
NGC1052-DF2 (van Dokkum et al. 2018)
6
8
10
log10(Mstellar/[M ])
12
101
102
103
counts of sim. DMC stellar objects in bin
Fig. 10. Proper radius containing half of the stellar mass, R0.5 stellar , as a
function of the stellar mass, Mstellar , of simulated stellar objects at redshift z = 0. Blue bins are DMC and red dots are DMF stellar objects.
The stellar masses and the total half-mass radii of simulated TDGs by
Fouquet et al. (2012) are shown as black crosses. A few DMC stellar objects can also be found in the regions of DMF stellar objects.
The properties of these DMC stellar objects are studied in Fig. 11. The
dashed vertical and horizontal lines indicate the initial baryonic matter
mass of a particle (1.26 × 106 M ) and the smallest fiducial cell size
(48 pc) of the Illustris-1 run, respectively. Subhalos with a stellar halfmass radius below the cell resolution are not shown in the plots. The yellow star shows the position of NGC 1052-DF2 with Mstellar = 2×108 M
and a 3D deprojected half-light radius of 2.7 kpc (van Dokkum et al.
2018a).
data from Dabringhausen & Fellhauer (2016) (early type galaxies) and Mieske et al. (2008, 2013) (UCDs and GCs). The data
for UCDs and GCs only include dynamical masses but not stellar
masses. Therefore, we estimate the stellar mass by assuming a
constant stellar mass-to-light ratio of 2.5 M /LV in the V-band.
The 2D effective radii, Re , are converted into 3D deprojected
half-light radii, R0.5 light , by multiplying them by a factor of 4/3
(see Appendix B in Wolf et al. 2010).
The bottom panel of Fig. 12 demonstrates that UCDs and
GCs are separated from early-type galaxies in the radius–mass
diagram and are found below the spatial resolution limit of
the Illustris-1 run. The yellow star in the radius–mass diagram represents the ultra-diffuse galaxy NGC 1052-DF2, which
has Mstellar = 2 × 108 M and an effective radius along the
major axis of Re = 2.2 kpc (van Dokkum et al. 2018a) corresponding to a 3D deprojected half-light radius of 2.7 kpc.
Especially remarkable is the large effective radius of NGC 1052DF2 compared to the sample of observed early-type galaxies
from Dabringhausen & Fellhauer (2016). The median values of
simulated stellar half-mass radii and 3D deprojected half-light
radii of observed galaxies for different stellar mass ranges are
listed in Table 7 and are shown in Fig. 14. The median of simulated TDGCs is within the first and third quartiles of observed
half-light radii for galaxies with stellar masses between 108 M
and 1010 M . However, the observed galaxy NGC 1052-DF2 is
not within the first and third quartiles of simulated TDGCs and
DM-rich DGs.
A series of KS tests are performed to decipher whether or
not the stellar masses and radii of observed galaxies follow
the same distribution as simulated dwarf galaxies. The full
A47, page 12 of 28
log10(R0.5 stellar/[pc])
4.5
2
100
0.5
log10(R0.5 stellar/[pc])
log10(R0.5 stellar/[pc])
5
4.0
3.5
3.0
2.5
2.0
DM-rich stellar objects (Mdm/Mbaryonic ≥ 1)
DM-poor stellar objects (Mdm/Mbaryonic < 1)
NGC1052-DF2 (van Dokkum et al. 2018)
1.5
6
8
10
log10(Mstellar/[M ])
12
0
2
norm. freq.
Fig. 11. Proper radius containing half of the stellar mass, R0.5 stellar , as
a function of the stellar mass, Mstellar , of simulated DMC stellar objects
at redshift z = 0. Dark matter-containing stellar objects are separated
in dark matter-rich (Mdm /Mbaryonic ≥ 1; blue bins) and dark matterpoor (Mdm /Mbaryonic < 1; purple crosses) types. The yellow star shows
the position of NGC 1052-DF2 with Mstellar = 2 × 108 M and a 3D
deprojected half-light radius of 2.7 kpc (van Dokkum et al. 2018a). The
dashed vertical and horizontal lines indicate the initial baryonic matter
mass of a particle (1.26 × 106 M ) and the smallest fiducial cell size
(48 pc). Subhalos with a stellar half-mass radius below the cell resolution are not shown in the plots. The histograms are normalized such
that the total area is equal to 1.0 and such that they have bin widths of
log10 (∆Mstellar /[M ]) = 0.10 and log10 (∆R0.5 stellar /[pc]) = 0.10.
sample from Dabringhausen & Fellhauer (2016) is observationally biased, such that different types of galaxies can be over- or
under-represented resulting in an incorrect stellar mass function
of galaxies. In contrast to that, the sample from the Illustris
simulation includes all formed galaxies without any mass, luminosity, or radius restrictions except for the resolution limits.
Therefore, we choose a statistically fair subsample from the catalog by Dabringhausen & Fellhauer (2016), which includes all
galaxies of the Fornax, the Hydra, and the Centaurus cluster catalogs with Mstellar > 5 × 107 M . These catalogs include dwarf
galaxies as well as large galaxies such that these catalogs sample the observed galaxy luminosity and stellar mass function of
galaxies over a wide range.
Since galaxy cluster surveys almost always include the central parts of the clusters where the massive galaxies tend to
gather, dwarf galaxies can be under-represented in the observational sample. In order to remove this bias towards high stellar
masses for observed galaxies we restrict the KS test to dwarfs
with stellar masses between 5 × 107 M and 109 M as shown in
Fig. 15. We find that the stellar mass distribution for all simulated
DMC DGs and TDGCs fits the observed stellar mass distribution
with a P-value of 0.260 and 0.766, respectively. The P-value for
the stellar half-mass radius distribution for DMC DGs is <10−12 ,
which means that it is virtually impossible that the simulated
and observed radii can be described with the same distribution
function. In contrast to that, the P-value obtained by comparing
the stellar half-mass radius distributions of the observed dwarf
M. Haslbauer et al.: Galaxies lacking dark matter in the Illustris simulation
Fig. 12. Top: proper radius containing half of the stellar mass, R0.5 stellar , as a function of the stellar mass, Mstellar , of simulated stellar objects
at redshift z = 0. Blue bins are DMC stellar objects, green dots are DM-rich DGs (Mdm /Mbaryonic ≥ 1), magenta squares are DM-poor DGs
(Mdm /Mbaryonic < 1), and red triangles are TDGCs. The stellar masses and the total half-mass radii of simulated TDGs by Fouquet et al. (2012)
are shown as black crosses. Pink circles are simulated TDGCs identified in the EAGLE simulations by Ploeckinger et al. (2018). Bottom: masses
and radii of the simulated stellar objects compared with the 3D deprojected half-light radii of observed galaxies. The colors here refer to the same
objects as in the top panel, but only dispersion-dominated (κrot < 0.5) TDGCs and DMC DGs are shown. Gray circles are early-type galaxies
from faint dwarf spheroidals to giant ellipticals taken from Dabringhausen & Fellhauer (2016). Orange diamonds are ultra compact dwarf galaxies
(UCDs) and globular clusters (GCs) taken from Mieske et al. (2008, 2013). The stellar masses of UCDs and GCs are calculated by assuming a
constant stellar mass-to-light ratio in the V-band of 2.5 M /LV . The yellow star shows the position in the radius–mass plane of the ultra-diffuse
galaxy NGC 1052-DF2, which has Mstellar = 2 × 108 M and a 3D deprojected half-light radius of 2.7 kpc (van Dokkum et al. 2018a). The dashed
vertical and horizontal lines indicate the initial baryonic matter mass of a particle (1.26 × 106 M ) and the smallest fiducial cell size (48 pc).
Subhalos with a stellar half-mass radius below the cell resolution are not shown in the plots. The KS-test is applied for dwarf galaxies with stellar
masses between 5 × 107 M and 109 M marked by the two solid vertical black lines.
A47, page 13 of 28
A&A 626, A47 (2019)
cumulative probability
Comparison of dwarf galaxies in the Illustris simulation
with 5 × 107 M < Mstellar < 109 M
1.0
TDGCs
DMC DGs
TDGCs
DMC DGs
0.5
d = 0.994
P < 1 × 10−12
d = 0.104
P = 0.261
cumulative probability
0.0
1.0
TDGCs, κrot < 0.5
DMC DGs, κrot < 0.5
TDGCs, κrot < 0.5
DMC DGs, κrot < 0.5
0.5
d = 0.967
P < 1 × 10−12
0.0
103
104
R0.5 stellar [pc]
105
d = 0.104
P = 0.279
108
109
Mstellar [M ]
Fig. 13. KS test for all and dispersion-dominated (κrot < 0.5) simulated
DMC DGs (green) and TDGCs (red) in the 5 × 107 −109 M stellar mass
regime at redshift z = 0.
galaxies with simulated TDGCs is 0.209. This means that if the
treatment of baryonic physics in the Illustris-1 simulations is a
reasonable approximation of reality, then the observed (real) dE
galaxies ought to be TDGs. This conclusion was reached independently by Okazaki & Taniguchi (2000).
Pillepich et al. (2018) compared the galaxy sizes in the Illustris simulation and in the Illustris TNG (The Next Generation)
simulation10,11 . These latter authors concluded that the TNG
simulation produces stellar half-mass radii two times smaller
than in the Illustris simulation for galaxies Mstellar < 1010 M ,
which is caused by a modification of the treatment of galactic
winds. Although the new galaxy physics model improves the
simulated galaxy sizes, a mismatch between stellar half-mass
radii is still present in Illustris TNG. Therefore, we not only compare the observed radius distribution with the radius distributions
directly from the Illustris simulation, but also with the distributions that follow when every radius is divided by two. The
P-values of the KS test in Fig. 15 (red and green thin lines) for
galaxies that are twice as compact as the original Illustris data are
<10−12 for both DMC DGs and TDGCs. Interestingly, simulated
TDGCs become more compact than the observed ones when
their radii are divided by two. However, since the Illustris TNG
data are not yet publicly available, we do not know at present
whether the dark matter-poor and dark matter-free galaxies are
indeed also more compact in the Illustris TNG simulation than in
the Illustris simulation. Here we assume that all galaxies in the
Illustris TNG simulation are more compact than in the Illustris
simulation by a factor of two. Nevertheless, the vast majority of
the simulated galaxies (i.e., the dark matter-dominated galaxies)
would still have radii that are too large to be consistent with the
observed radius distribution.
10
http://www.tng-project.org
The data of the TNG simulation project are not yet public available
[02.06.2018].
11
A47, page 14 of 28
Summarizing, the observations do not clearly show different
populations of galaxies based on their masses and radii, which
was already reported by Dabringhausen & Kroupa (2013) using
a sample they consider to be TDGs (TDG candidates) as discussed in their Sect. 2.2.1. This is in disagreement with the Illustris simulation, which predicts two populations of dwarf galaxies
in the radius–mass plane. The possible implications of this for
ΛCDM cosmology are discussed in Sect. 4.3.
3.5. Evolution of the number density of TDGCs across
cosmic time
Figure 16 shows the evolution in the co-moving number
density, nTDGCs , of simulated TDGCs (sample A) over cosmic
time. These TDGCs with Mstellar > 5 × 107 M are identified
by the searching algorithm for the first time at redshift z = 4.7
and therefore appear 0.752 Gyr later than DMC stellar objects
with a stellar mass of at least 5 × 107 M . This may indicate
that the formation of TDGCs is triggered by the encounters
of DMC galaxies once these DMC galaxies have grown sufficiently in mass through mergers to spawn TDGCs above a
stellar mass threshold of 5 × 107 M . Less-massive TDGCs are
most likely formed earlier, but cannot be resolved in the Illustris simulation. The number density of TDGCs increases up
to redshift z = 1.4, where a global maximum of nTDGCs (z =
1.4) = 8.2 × 10−4 h3 cMpc−3 is reached. Later on, the number
density of TDGCs decreases in time. Since galaxies at higher
redshifts were more gas-rich, metal-poor, and more dynamically active, TDGCs are formed efficiently through galaxy
interactions resulting in an increase of the co-moving number
density with decreasing redshift.
4. Discussion
In this section we discuss the properties of TDGCs and DMC
DGs in the Illustris simulation. The dual dwarf theorem and its
implications for ΛCDM cosmology are considered.
4.1. Formation and evolution of TDGCs
The highest-resolution run of the Illustris suite allows us to study
the formation and evolution of TDGCs. We consider that baryonic substructures may be spurious objects or fragments within
a galaxy and that TDGCs may be formed out of the gas of a
disk galaxy during galactic interactions. Mergers of rotationally
supported galaxies in dark matter halos occur in the Illustris
simulation. Previous work has shown that TDGs form in such
encounters (Barnes & Hernquist 1992; Bournaud & Duc 2006;
Wetzstein et al. 2007; Fouquet et al. 2012; Yang et al. 2014) and
thus it can be expected that they would also form in the selfconsistent cosmological Illustris simulation. The verification of
this theory would require following the merger tree of all TDGCs
over cosmic time. However, none of the TDGCs at redshift z = 0
are included in the merger trees provided by the Illustris team
(Rodriguez-Gomez et al. 2015) and backtracing all TDGCs by
their particle data is very resource consuming. Therefore we
have shown for some TDGCs that these subhalos have indeed
been formed due to tidal forces caused by galactic interactions
(see Sect. 2.5, Appendix A, and the movies in the supplementary
information).
Tidal dwarf galaxies lack dark matter due to the physics of
their formation. We point out that apart from galactic interactions, efficient cooling processes provided by the implemented
M. Haslbauer et al.: Galaxies lacking dark matter in the Illustris simulation
Table 7. Medians of simulated stellar half-mass radii, R0.5 stellar , for dispersion-dominated (κrot < 0.5) DMC stellar objects, DMC DGs, and TDGCs
samples for different stellar mass ranges.
Sample
Mdm /Mbaryonic
Mstellar [M ]:
107 −108
108 −109
109 −1010
1010 −1011
1011 −1012
DMC stellar objects
DM-rich stellar objects
DM-poor stellar objects
DMC DGs
DM-rich DGs
DM-poor DGs
TDGCs
Observed
>0
≥1
<1
>0
≥1
<1
0
–
hR0.5 stellar i [pc]:
4342
4346
1903
4633
4635
2667
1657
969
5770
5779
1681
582
5826
2185
1125
1339
7232
7246
1687
–
–
–
773
1988
8213
8235
3994
–
–
–
–
3930
11 697
11 717
3445
–
–
–
–
8315
hR0.5 light i [pc]:
Notes. The medians of the 3D deprojected half-light radii, R0.5 light , of observed early type galaxies for different stellar mass ranges are given in the
last row (Dabringhausen & Fellhauer 2016). The statistical properties of simulated and observed galaxies are visualized in Fig. 14.
Comparison of simulated and observed dwarf galaxies
with 5 × 107 M < Mstellar < 109 M
NGC1052-DF2 (van Dokkum et al. 2018)
16000
14000
sim. DM-poor DGs (Mdm /Mbaryonic < 1)
sim. DM-rich stellar objects (Mdm /Mbaryonic ≥ 1)
12000
R0.5 stellar [pc]
cumulative probability
obs. early types (Dabringhausen & Fellhauer 2016)
simulated TDGCs
sim. DM-rich DGs (Mdm /Mbaryonic ≥ 1)
sim. DM-poor stellar objects (Mdm /Mbaryonic < 1)
10000
8000
2000
7
8
9
10
log10(Mstellar/[M ])
11
12
Fig. 14. Median, first, and third quartile of simulated stellar half-mass
radii, R0.5 stellar , of dispersion-dominated (κrot < 0.5) objects and 3D
deprojected half-light radii, R0.5 light , of observed early type galaxies for
different stellar mass bins (107 −108 M , 108 −109 M , 109 −1010 M ,
1010 −1011 M , and 1011 −1012 M ). Blue right triangles are DM-rich
stellar objects, purple crosses are DM-poor stellar objects, green dots
are DM-rich DGs, magenta squares are DM-poor DGs, and red triangles are TDGCs (see Table 3). Gray open circles are observed
early-type galaxies taken from Dabringhausen & Fellhauer (2016). The
yellow star shows the position of NGC 1052-DF2 with Mstellar = 2 ×
108 M and a 3D deprojected half-light radius of 2.7 kpc (van Dokkum
et al. 2018a). The medians of simulated and observed galaxies for different mass ranges are listed in Table 7.
galaxy-formation models of the Illustris simulation can also
artificially trigger the formation of DMF stellar objects. Jeans
instabilities depend on the mass and temperature of the
molecular gas cloud. The collapse of a cloud is supported by
an increase of the mass (at a given temperature) or a decrease
of the temperature (at a given mass) (Jeans 1902; Coles &
Lucchin 2003). Efficient cooling of great baryonic matter accumulations allows for the collapse of these structures without
the need for high amounts of nonbaryonic matter. Cold accretion of gas clumps onto halos might also perhaps produce such
DMF objects. The agreement of the properties of the TDGCs
cumulative probability
4000
obs. galaxies
TDGCs, κrot < 0.5
b a
0.5
0.0
6000
0
1.0
obs. galaxies
TDGCs, κrot < 0.5
1.0
da = 0.147
db = 0.674
Pa = 0.209
Pb < 1 × 10−12
d = 0.0925
P = 0.766
obs. galaxies
DMC DGs, κrot < 0.5
obs. galaxies
DMC DGs, κrot < 0.5
b a
0.5
0.0
da = 1.000
db = 0.907
Pa < 1 × 10−12
Pb < 1 × 10−12
103
104
R0.5 stellar [pc]
105
d = 0.0928
P = 0.260
108
109
Mstellar [M ]
Fig. 15. KS test for observed late-type galaxies (gray) and dispersiondominated (κrot < 0.5) simulated (red, green) DGs with stellar masses
between 5 × 107 M and 109 M . The thick lines and the displayed da and Pa -values refer to the real stellar half-mass radius distribution of the
Illustris-1 simulation. The thin lines and the db - and Pb -values refer to a
distribution in which all radii in the Illustris-1 simulation are divided by
two (see text). The observational data are a subset of the catalog from
Dabringhausen & Fellhauer (2016) including all galaxies from the Fornax, Hydra, and Centaurus cluster catalog with stellar masses between
5 × 107 M and 109 M .
formed in Illustris-1 with independent work reporting the formation of TDGs (Barnes & Hernquist 1992; Bournaud & Duc
2006; Wetzstein et al. 2007; Fouquet et al. 2012; Yang et al.
2014; Ploeckinger et al. 2018), the shown formation scenarios in
Sect. 2.5, and the applied 6D phase-space halo finder on selected
TDGCs (see Appendix C) all together suggest that the TDGCs
formed in Illustris-1 are physical.
By extracting the formation time of the oldest stellar particle
within a dwarf galaxy identified at redshift z = 0, we have shown
that TDGCs and DM-poor DGs are typically younger than
DM-rich DGs. This underlines that DM-rich DGs are formed
A47, page 15 of 28
A&A 626, A47 (2019)
0.0
0.2
redshift z
0.4 0.6 0.81.0
2.0
4.0 12.0
nTDGCs [h3 cMpc−3]
8.0E-04
6.0E-04
4.0E-04
2.0E-04
0.0E+00
0
5
10
lookback time [Gyr]
Fig. 16. Time evolution of the co-moving number density of TDGCs,
nTDGCs , identified with the same selection criteria as for sample A. The
x-axis shows the lookback time in gigayears (i.e., 0 Gyr corresponds to
the present time) and redshift z.
in the early universe in contrast to TDGCs as expected from
their different formation scenarios, since TDGs are being formed
from the expelled gas from massive galaxies triggered by galactic encounters and interactions. Furthermore, gas-rich TDGCs
are typically younger than gas-free TDGCs.
We have shown that TDGCs with Mgas > 5 × 107 M and
with at least one stellar particle (sample B) are typically more
phase-space-correlated than DMC DGs. TDGCs with Mstellar >
5×107 M (sample A) are less phase-space-correlated than sample B but are still more so than DMC DGs. The difference is
qualitatively consistent with sample A (gas-poor TDGCs) being
older than sample B (gas-rich TDGCs). Gas-poor TDGs would
have been stripped of their gas or would have consumed it and
their orbits are likely perturbed due to later mergers of the hosting galaxy which are likely to destroy phase-space-correlated
populations in the dark matter-based cosmological models (see
also Kroupa 2015). However, the small number of galactic systems of sample A hosting more than one TDGC requires further
study of this issue in order to produce any statistically robust
conclusions about their phase-space correlation (see Sect. 3.1).
In a more detailed analysis we also have to investigate if and how
an initial phase-space correlation is affected by further galactic encounters and mergers. In the local Universe a large if not
dominant fraction of the dwarf galaxies surrounding the MW,
M 31, and NGC 5128 (Centaurus A) are significantly phasespace-correlated (Kroupa et al. 2005; Metz & Kroupa 2007;
Ibata et al. 2013, 2014; Pawlowski & Kroupa 2013; Müller et al.
2018; Pawlowski 2018). This observed ubiquitous occurrence of
disks or planes of satellites (Ibata et al. 2014; Pawlowski 2018)
may thus imply an absence of such encounters in the real Universe.
4.2. Gas masses and star formation rates of TDGCs
TDGCs are likely formed out of the stellar and gas reservoir
of their host galaxies. We have shown that the amount of gas
depends strongly on the applied selection criteria. Our main sample (sample A) includes 97 TDGCs with Mstellar > 5 × 107 M ,
such that around 89 percent are completely gas-free suggesting
that a significant fraction of TDGCs have already converted their
A47, page 16 of 28
gas content to stars. The large fraction of gas-free TDGCs has a
direct consequence on the star formation rate such that 90 percent have no star formation. However, when we apply selection criteria similar to Ploeckinger et al. (2018) we find a larger
number of TDGCs (sample B, see Table 1). These are young and
gas-rich TDGCs which have recently formed out of the gaseous
disk of their host galaxies (see Sects. 2.5 and 3.3).
TDGCs and DM-poor DGs (Mdm /Mbaryonic < 1) are
often more metal-rich and younger than DM-rich DGs
(Mdm /Mbaryonic ≥ 1). This is consistent with the formation theory of TDGs and underlines that TDGs can also capture at
least a small amount of dark matter particles (see Appendix B).
By back-tracing the particle identification numbers, one can
decipher whether or not a TDGC in the Illustris simulation
can indeed capture dark matter particles. Such events must be
extremely rare given the weak gravitational potential of TDGCs,
but it may be interesting to study this in the future. Indications of such a capture can be seen in Fig. 3 in Sect. 2.5, but
it is likely that these dark matter particles identified by the Subfind algorithm are just individual particles crossing the object.
Nevertheless, the small number of DMC DGs with a darkto-baryonic matter fraction smaller than one and their similar
physical properties to TDGCs indicate that such DM-poor DGs
are TDGs.
4.3. Radius–mass relation
According to the dual dwarf theorem, two different types of
dwarf galaxies should exist in the mass range between about
106 M and 1010 M (Kroupa 2012; Dabringhausen & Kroupa
2013). Although observed dEs and TDGs are indistinguishable
in the radius–mass plane (Dabringhausen & Kroupa 2013), simulated TDGCs are clearly separated by being smaller than DMC
DGs. By showing that TDGCs and DM-poor DGs are more
compact than DM-rich DGs in the stellar mass range between
5 × 107 M and 109 M we have verified the dual dwarf theorem for the first time in a self-consistent ΛCDM simulation.
The KS test underlines a statistically highly significant difference between the stellar-half mass distribution of TDGCs
and DMC DGs. The P-value of the KS test is <10−12 . These
results are consistent with the formation scenario of TDGs in the
ΛCDM framework, which are understood to be formed naked
without the help of a dark matter potential and ought to be
therefore more compact than primordial dwarfs (Kroupa 2012).
It is noteworthy that the observed physical stellar half-light
radii more closely resemble simulated stellar half-mass radii of
dark matter-free and -poor galaxies rather than of dark matterdominated galaxies in the stellar mass regime of 5 × 107 M
and 109 M (Dabringhausen & Kroupa 2013; Duc et al. 2014).
Comparing the stellar half-mass radius distributions of
dispersion-dominated TDGCs and DMC DGs from the Illustris1 simulation with observed early-type galaxies gives a P-value
of 0.209 and <10−12 , respectively. The radii of TDGCs formed
in the Illustris-1 simulation are confirmed by the independent
simulations of Fouquet et al. (2012). The fact that the radius
of TDGCs and DM-poor galaxies in Illustris-1 agree with the
observed dE galaxies suggests that the latter are TDGs, as also
concluded by Okazaki & Taniguchi (2000) based on different
arguments.
The first results from the new Illustris TNG simulation
have shown that a modification of the galactic wind model
reduces the stellar half-mass radii by a factor of two for galaxies with Mstellar < 1010 M (Pillepich et al. 2018). Nevertheless, we have shown in the present paper that even these current
M. Haslbauer et al.: Galaxies lacking dark matter in the Illustris simulation
state-of-the-art cosmological hydrodynamical simulations cannot reproduce the observed galaxy sizes (see Sect. 3.4).
A further consistency test of the ΛCDM cosmology
would be to study the positions on the baryonic TullyFisher relation (BTFR) of simulated dark matter-poor and
dark matter-dominated galaxies. Dark matter-poor galaxies (i.e.,
TDGs) are thus expected to lie above the BTFR by having
smaller rotation speeds than DMC galaxies of the same baryonic
mass. The apparent absence of observed dwarf galaxies, some of
which must be TDGs that lie above the BTFR, may pose a serious challenge for dark matter cosmology (Kroupa 2012; Flores
et al. 2016). This issue could be directly tested with confirmed
old TDGs settled down to virial equilibrium as is likely with
the observed TDGs identified by Duc et al. (2014). Observations
show a very tight power-law correlation between the baryonic
mass and the circular velocity for galaxies with baryonic masses
between 107 M and 5 × 1011 M (McGaugh 2012; Lelli et al.
2016). However, a proper analysis requires the extraction of each
model galaxy and the fitting of its rotation curve, meaning that
this line of investigation needs to be postponed to a detailed analysis of the rotation curves of galaxies in the Illustris and EAGLE
simulations.
5. Conclusion
We studied the physical properties of dwarf galaxies lacking dark
matter in the ΛCDM Illustris simulation. In particular, we identified 3484 stellar objects without any dark matter in the simulation volume of (75 h−1 cMpc)3 at redshift z = 0. After applying
a minimum mass criterion, we separated them into substructures
and TDGCs based on their separation to their host galaxies (see
Sect. 2.4). The minimum stellar mass of our main sample (sample A) is set to 5 × 107 M and includes 97 TDGCs corresponding to a co-moving number density of 2.3 × 10−4 h3 cMpc−3 in
the Illustris-1 simulation. These galaxies have total masses up to
3.1 × 109 M , which is comparable to the mass of the LMC.
Fouquet et al. (2012) suggest that the observed Magellanic
Clouds could be TDGs (see Sect. 3.3). We present movies of
the formation scenarios of TDGCs confirming their tidal dwarf
nature. In particular, TDGCs are formed through galactic interactions and in the ram-pressure-stripped gas clouds of the host
galaxy (see Sect. 2.5, Appendix A and the movies in the supplementary information). However, TDGCs may conceivably also
be formed in other scenarios such as cold accretion of gas clumps
onto halos (see also Sect. 4.1) which has not been addressed in
this work, and has also never been reported to actually occur.
Dwarf galaxies lacking dark matter are mostly found in massive halos, in the vicinity of a massive galaxy, and are typically
younger than DM-rich DGs. These results support the theory that
these objects are TDGs formed through galactic interactions and
mergers (see Sects. 2.4 and 3.3). TDGCs and DMC DGs with a
small dark matter mass are often metal-rich (see Appendix B),
which indicates that these satellite galaxies are possibly TDGs
formed from a chemically enriched host galaxy (Recchi et al.
2015). Almost all of the TDGCs of sample A are gas depleted
and dispersion-dominated, which suggest that these are older
TDGs which could have already lost their gas content by feedback processes and suffered from an angular momentum loss.
The density distribution of four selected massive TDGCs can be
described by a Plummer model and an exponential profile (see
Figs. C.2 and C.8).
Analyzing the orbital angular momenta of TDGCs which
have a minimum gas mass of 5 × 107 M and at least one
stellar particle (sample B) yields that these objects are signif-
icantly phase-space-correlated as observed in the Local Group
(Kroupa et al. 2005; Pawlowski 2018) and Centaurus A (Müller
et al. 2018). Moreover, simulated TDGCs are significantly more
phase-space-correlated than DMC DGs (see Sect. 3.1).
Throughout the paper we have identified TDGCs based on
the Subfind algorithm, which is a position-space subhalo finder.
We also apply a 2σ-clipping scheme as a 6D phase-space halo
finder to the surroundings of gas-free Subfind TDGCs of sample
A and we show that 92 percent of these objects are gravitationally self-bound by including the velocity-space information of
stellar particles (see Appendix C).
We quantified the probability of finding a NGC 1052-DF2like galaxy in the Illustris-1 simulation at redshift z = 0. While
finding a few similar galaxies (Table 5), there is also a nondetection of gas-free TDGCs with Mstellar ≥ 0.8 × 2 × 108 M
and R0.5 stellar ≥ 0.8 × 2.7 kpc. Thus, such dwarf galaxies appear
to be extremely rare in the Illustris-1 simulation. However, we
note that this analysis does not consider the peculiar velocity of
the observed NGC 1052-DF2 dwarf galaxy (see Sect. 3.2).
We reported for the first time that the dual dwarf theorem is
fulfilled in the self-consistent ΛCDM cosmological Illustris-1
simulation. TDGCs and DM-poor DGs populate regions in the
radius–mass plane that are different from those populated by DMrich DGs. In the stellar mass range between 5×107 M and 109 M
galaxies which are dark matter-poor have smaller stellar halfmass radii than dark matter-dominated galaxies as predicted by
Kroupa (2012). In particular, the KS test showed that the probability that simulated TDGCs and DMC DGs follow the same stellar
half-mass radius distributions is less than 10−12 . The independent
simulations by Fouquet et al. (2012) lead to TDGs which have
radii in agreement with those of TDGCs in the Illustris simulation. However, the work of Dabringhausen & Kroupa (2013) has
shown that observed TDGs occupy the same region in the radius–
mass diagram as elliptical dwarf galaxies. This region agrees with
our model TDGCs, causing a major conflict with ΛCDM cosmology, because based on Illustris-1 some splitting is expected
for galaxies with such different origins (see Sect. 3.4). However,
we note that only 0.17 percent of all galaxies with Mstellar =
5 × 107 −109 M are TDGCs or DM-poor DGs in the Illustris-1
simulation.
It is therefore essentially important to conduct dedicated
dwarf galaxy surveys (such as Merritt et al. 2016; Javanmardi
et al. 2016) to find dwarf galaxies which are lacking dark matter, as this would confirm the dual dwarf galaxy theorem (it
would be established that dwarfs with and without dark matter do
exist in the real Universe), thus supporting ΛCDM cosmology.
van Dokkum et al. (2018a, 2019) have indeed found two candidates for such dwarf galaxies in the group of NGC 1052 (i.e.,
NGC 1052-DF2 and -DF4). However, the different positions of
the Illustris TDGCs and DMC DGs in the radius–mass plane are
in significant tension with the fact that there is only one population of observed dwarf galaxies. That the TDGCs in Illustris-1
have radii in agreement with the observed radii of dE galaxies
suggests that the latter are TDGs, as also concluded independently by Okazaki & Taniguchi (2000).
Acknowledgements. We thank the anonymous referee for her/his constructive comments and suggested improvements. IB is supported by
an Alexander von Humboldt research fellowship. We thank the DAADOstpartnerschaftsprogramm für 2018 at the University of Bonn for funding
exchange visits between Charles University in Prague and Bonn University. We
would like to thank the staff of the Illustris project, especially Dylan Nelson and
Vicente Rodriguez-Gomez, for providing the Illustris data, the κrot morphology
parameter, example scripts, and useful suggestions. We thank Paul Torrey for
explanations about the Illustris Galaxy Observatory.
A47, page 17 of 28
A&A 626, A47 (2019)
References
Angus, G. W., Diaferio, A., & Kroupa, P. 2011, MNRAS, 416, 1401
Barnes, J. E., & Hernquist, L. 1992, Nature, 360, 715
Baumgardt, H., & Mieske, S. 2008, MNRAS, 391, 942
Bender, R., Burstein, D., & Faber, S. M. 1992, ApJ, 399, 462
Bender, R., Burstein, D., & Faber, S. M. 1993, ApJ, 411, 153
Binggeli, B., Sandage, A., & Tarenghi, M. 1984, AJ, 89, 64
Bournaud, F., & Duc, P.-A. 2006, A&A, 456, 481
Bournaud, F., Duc, P.-A., & Emsellem, E. 2008a, MNRAS, 389, L8
Bournaud, F., Bois, M., Emsellem, E., & Duc, P.-A. 2008b, Astron. Nachr., 329,
1025
Casas, R. A., Arias, V., Peña Ramírez, K., & Kroupa, P. 2012, MNRAS, 424,
1941
Chowdhury, A. 2019, MNRAS, 482, L99
Coles, P., & Lucchin, F. 2003, Cosmology: The Origin and Evolution of Cosmic
Structure (John Wiley & Sons)
Dabringhausen, J., & Fellhauer, M. 2016, MNRAS, 460, 4492
Dabringhausen, J., & Kroupa, P. 2013, MNRAS, 429, 1858
Danieli, S., van Dokkum, P., Conroy, C., Abraham, R., & Romanowsky, A. J.
2019, ApJ, 874, L12
Davis, M., Efstathiou, G., Frenk, C. S., & White, S. D. M. 1985, ApJ, 292,
371
Dolag, K., Borgani, S., Murante, G., & Springel, V. 2009, MNRAS, 399, 497
Duc, P.-A., Brinks, E., Springel, V., et al. 2000, AJ, 120, 1238
Duc, P.-A., Paudel, S., McDermid, R. M., et al. 2014, MNRAS, 440, 1458
Emsellem, E., van der Burg, R. F. J., Fensch, J., et al. 2019, A&A, 625, A76
Famaey, B., & McGaugh, S. S. 2012, Liv. Rev. Relativ., 15, 10
Ferrarese, L., Côté, P., Jordán, A., et al. 2006, ApJS, 164, 334
Flores, H., Hammer, F., Fouquet, S., et al. 2016, MNRAS, 457, L14
Fouquet, S., Hammer, F., Yang, Y., Puech, M., & Flores, H. 2012, MNRAS, 427,
1769
Genel, S., Vogelsberger, M., Springel, V., et al. 2014, MNRAS, 445, 175
Gilmore, G., Wilkinson, M. I., Wyse, R. F. G., et al. 2007, ApJ, 663, 948
Graus, A. S., Bullock, J. S., Boylan-Kolchin, M., & Nierenberg, A. M. 2018,
MNRAS, 480, 1322
Heggie, D., & Hut, P. 2003, The Gravitational Million-body Problem: A
Multidisciplinary Approach to Star Cluster Dynamics (IOP Publishing)
Hilker, M., Baumgardt, H., Infante, L., et al. 2007, A&A, 463, 119
Hinshaw, G., Larson, D., Komatsu, E., et al. 2013, ApJS, 208, 19
Ibata, R. A., Lewis, G. F., Conn, A. R., et al. 2013, Nature, 493, 62
Ibata, N. G., Ibata, R. A., Famaey, B., & Lewis, G. F. 2014, Nature, 511, 563
Javanmardi, B., Martinez-Delgado, D., Kroupa, P., et al. 2016, A&A, 588,
A89
Jeans, J. H. 1902, Trans. R. Soc. London Ser. A, 199, 1
Jonsson, P. 2006, MNRAS, 372, 2
Jonsson, P., Groves, B. A., & Cox, T. J. 2010, MNRAS, 403, 17
Kaviraj, S., Darg, D., Lintott, C., Schawinski, K., & Silk, J. 2012, MNRAS, 419,
70
Knebe, A., Knollmann, S. R., Muldrew, S. I., et al. 2011, MNRAS, 415, 2293
Koda, J., Yagi, M., Yamanoi, H., & Komiyama, Y. 2015, ApJ, 807, L2
Kroupa, P. 1997, New Astron., 2, 139
Kroupa, P. 2008, in The Cambridge N-Body Lectures, eds. S. J. Aarseth, C. A.
Tout, & R. A. Mardling (Berlin Springer Verlag), Lect. Notes Phys., 760, 181
Kroupa, P. 2012, PASA, 29, 395
Kroupa, P. 2015, Can. J. Phys., 93, 169
Kroupa, P., Theis, C., & Boily, C. M. 2005, A&A, 431, 517
Kroupa, P., Famaey, B., de Boer, K. S., et al. 2010, A&A, 523, A32
Lee-Waddell, K., Spekkens, K., Haynes, M. P., et al. 2012, MNRAS, 427,
2314
Lelli, F., McGaugh, S. S., & Schombert, J. M. 2016, ApJ, 816, L14
A47, page 18 of 28
Martin, N. F., Collins, M. L. M., Longeard, N., & Tollerud, E. 2018, ApJ, 859,
L5
Martínez-Delgado, D., Gabany, R. J., Crawford, K., et al. 2010, AJ, 140, 962
McAlpine, S., Helly, J. C., Schaller, M., et al. 2016, Astron. Comput., 15, 72
McGaugh, S. S. 2012, AJ, 143, 40
Mendes de Oliveira, C., Plana, H., Amram, P., Balkowski, C., & Bolte, M. 2001,
AJ, 121, 2524
Merritt, A., van Dokkum, P., Danieli, S., et al. 2016, ApJ, 833, 168
Metz, M., & Kroupa, P. 2007, MNRAS, 376, 387
Metz, M., Kroupa, P., & Jerjen, H. 2007, MNRAS, 374, 1125
Mieske, S., Hilker, M., Jordán, A., et al. 2008, A&A, 487, 921
Mieske, S., Frank, M. J., Baumgardt, H., et al. 2013, A&A, 558, A14
Mirabel, I. F., Dottori, H., & Lutz, D. 1992, A&A, 256, L19
Miralles-Caballero, D., Colina, L., & Arribas, S. 2012, A&A, 538, A61
Misgeld, I., & Hilker, M. 2011, MNRAS, 414, 3699
Misgeld, I., Mieske, S., & Hilker, M. 2008, A&A, 486, 697
Misgeld, I., Hilker, M., & Mieske, S. 2009, A&A, 496, 683
Müller, O., Pawlowski, M. S., Jerjen, H., & Lelli, F. 2018, Science, 359, 534
Nelson, D., Pillepich, A., Genel, S., et al. 2015, Astron. Comput., 13, 12
Okazaki, T., & Taniguchi, Y. 2000, ApJ, 543, 149
Pawlowski, M. S. 2018, Mod. Phys. Lett. A, 33, 1830004
Pawlowski, M. S., & Kroupa, P. 2013, MNRAS, 435, 2116
Pawlowski, M. S., Kroupa, P., & de Boer, K. S. 2011, A&A, 532, A118
Pawlowski, M. S., Famaey, B., Jerjen, H., et al. 2014, MNRAS, 442, 2362
Pietrzyński, G., Graczyk, D., Gieren, W., et al. 2013, Nature, 495, 76
Pillepich, A., Springel, V., Nelson, D., et al. 2018, MNRAS, 473, 4077
Ploeckinger, S., Hensler, G., Recchi, S., Mitchell, N., & Kroupa, P. 2014,
MNRAS, 437, 3980
Ploeckinger, S., Recchi, S., Hensler, G., & Kroupa, P. 2015, MNRAS, 447, 2512
Ploeckinger, S., Sharma, K., Schaye, J., et al. 2018, MNRAS, 474, 580
Recchi, S., Theis, C., Kroupa, P., & Hensler, G. 2007, A&A, 470, L5
Recchi, S., Kroupa, P., & Ploeckinger, S. 2015, MNRAS, 450, 2367
Rodriguez-Gomez, V., Genel, S., Vogelsberger, M., et al. 2015, MNRAS, 449,
49
Rodriguez-Gomez, V., Sales, L. V., Genel, S., et al. 2017, MNRAS, 467, 3083
Sales, L. V., Navarro, J. F., Theuns, T., et al. 2012, MNRAS, 423, 1544
Sardone, A., Pisano, D. J., Burke-Spolaor, S., Mascoop, J. L., & Pol, N. 2019,
ApJ, 871, L31
Springel, V. 2010, MNRAS, 401, 791
Springel, V., White, S. D. M., Tormen, G., & Kauffmann, G. 2001, MNRAS,
328, 726
Torrey, P., Vogelsberger, M., Genel, S., et al. 2014, MNRAS, 438, 1985
Torrey, P., Snyder, G. F., Vogelsberger, M., et al. 2015, MNRAS, 447, 2753
Trujillo, I., Beasley, M. A., Borlaff, A., et al. 2019, MNRAS, 733
van Dokkum, P., Danieli, S., Cohen, Y., et al. 2018a, Nature, 555, 629
van Dokkum, P., Cohen, Y., Danieli, S., et al. 2018b, Res. Notes Am. Astron.
Soc., 2, 54
van Dokkum, P., Danieli, S., Abraham, R., Conroy, C., & Romanowsky, A. J.
2019, ApJ, 874, L5
Vogelsberger, M., Genel, S., Sijacki, D., et al. 2013, MNRAS, 436, 3031
Vogelsberger, M., Genel, S., Springel, V., et al. 2014a, MNRAS, 444, 1518
Vogelsberger, M., Genel, S., Springel, V., et al. 2014b, Nature, 509, 177
Vulcani, B., Poggianti, B. M., Gullieuszik, M., et al. 2018, ApJ, 866, L25
Weilbacher, P. M., Fritze-v. Alvensleben, U., Duc, P. A., & Fricke, K. J. 2002,
ApJ, 579, L79
Wetzstein, M., Naab, T., & Burkert, A. 2007, MNRAS, 375, 805
Wolf, J., Martinez, G. D., Bullock, J. S., et al. 2010, MNRAS, 406, 1220
Yagi, M., Yoshida, M., Komiyama, Y., et al. 2010, AJ, 140, 1814
Yang, Y., Hammer, F., Fouquet, S., et al. 2014, MNRAS, 442, 2419
Yoshida, M., Yagi, M., Komiyama, Y., et al. 2008, ApJ, 688, 918
Zjupa, J., & Springel, V. 2017, MNRAS, 466, 1625
M. Haslbauer et al.: Galaxies lacking dark matter in the Illustris simulation
Appendix A: Stellar luminosities and gas densities
of TDGCs and their host galaxies
Using the Illustris Explorer online tool12 , we visualize in
Fig. A.1 the projected gas densities and stellar luminosities of
stellar luminosities
64 kpc
3
TDGCs and DM-poor objects of the studied host galaxies ID
138 and ID 404871 in Sect. 2.5 at redshift z = 0. The identification number and physical parameters of the stellar objects shown
in Fig. A.1 are listed in Table A.1.
gas densities
2
64 kpc
3
2
1
1
host, ID 404871
DMC galaxy (1), ID 404872
DM-poor substructure (2), ID 404873
TDGCs (3), sample B, ID 404882
host, ID 404871
DMC galaxy (1), ID 404872
DM-poor substructure (2), ID 404873
TDGCs (3), sample B, ID 404882
stellar luminosities
gas density
1
1
2
host, ID 138
DMF substructure (1), sample A, ID 878
DMF substructure (2), sample A, ID 1683
2
host, ID 138
DMF substructure (1), sample A, ID 878
DMF substructure (2), sample A, ID 1683
67 kpc
67 kpc
Fig. A.1. Projected stellar luminosity (left panels) and gas density (right panels) of the environment of the host galaxy ID 404871 (top panels)
and ID 138 (bottom panels) at redshift z = 0. Top panels: stellar objects (1)–(3) close to ID 404871 (the white circle marks the host galaxy) are
explained in the figure legend. Bottom panels: stellar objects (1) and (2) are identified as DMF substructures of the host galaxy ID 138 (the white
circle as above). The luminous galaxy in the lower-right corner is a foreground galaxy, which has a 3D separation of 1626 kpc to the galaxy ID
138. Credits: http://www.illustris-project.org/explorer/ [13.08.2018].
Table A.1. Properties of the discussed and depicted stellar objects identified at redshift z = 0 and shown in Fig. A.1.
Galaxy (ID)
Host (ID)
Mstellar [M ]
Mgas [M ]
Mdm /Mbaryonic
κrot
shost [kpc]
shost /Rhost
0.5 stellar
b
Lorbit
878
1683
404872
404873
404879
404882
138
138
404871
404871
404871
404871
6.7 × 107
5.7 × 107
1.1 × 109
8.0 × 106
2.2 × 107
1.7 × 107
1.4 × 109
5.6 × 108
2.1 × 109
1.8 × 109
3.0 × 108
2.5 × 108
0.0
0.0
4.5
0.020
0.019
0.0
0.47
0.39
0.66
0.39
0.37
0.41
94
49
115
157
182
193
9.7
5.1
7.0
9.5
11
12
(+0.812, −0.0896, +0.576)
(+0.936, −0.0479, +0.350)
(−0.712, +0.225, +0.665)
(+0.0415, −0.0105, −0.994)
(+0.0831, −0.0204, −0.996)
(−0.0283, −0.158, −0.987)
Notes. Listed are the identification number of the stellar object, the identification number of its host galaxy, the stellar mass, Mstellar , gas mass,
Mgas , the fraction of dark matter-to-baryonic matter, Mdm /(Mgas + Mstellar ) = Mdm /Mbaryonic , the morphological parameter, κrot , the 3D separation
between the stellar object and its host galaxy, shost , the fraction of this separation to the stellar half-mass radius of the host galaxy, shost /Rhost
0.5 stellar ,
b
and the normalized specific orbital angular momentum, Lorbit (Eq. (2)).
12
http://www.illustris-project.org/explorer/
A47, page 19 of 28
A&A 626, A47 (2019)
Appendix B: Gas and stellar metallicity of TDGCs
and DMC DGs
Appendix C: Internal structures and kinematics of
TDGCs
Fig. C.1. Relation between the potential and kinetic energy for all
TDGCs of sample A. The colorbar presents the stellar mass, Mstellar , of
the TDGCs. The black solid lines highlight the condition for virial equilibrium, i.e., where the virial ratio becomes q = 1 (see Eq. (C.1)). All
objects above the black dashed line are gravitationally bound (q < 2).
In the following we discuss the internal structures and kinematics of TDGCs, which includes an analysis of their energy contents, density and dispersion distributions, and rotation curves.
Different halo finders running on the same simulation can provide different results (Knebe et al. 2011). Therefore a σ-clipping
procedure as a 6D phase-space halo finder is applied to the surroundings of the Subfind TDGCs to examine whether or not
these objects are gravitationally bound by including their particle velocity data.
Fig. B.1. Stellar (top) and gas (bottom) mass-weighted average metallicity, Zstellar and Zgas , respectively, in dependence of the stellar mass,
Mstellar , and gas mass, Mgas . The stellar and gas mass-weighted average
metallicities, Zstellar and Zgas , are defined by Eq. (B.1). Blue bins are
DMC stellar objects, green dots are DM-rich DGs (Mdm /Mbaryonic ≥ 1),
magenta squares are DM-poor DGs (Mdm /Mbaryonic < 1), and red triangles are TDGCs of sample A.
Figure B.1 shows the stellar and gas metallicity in dependence
of the stellar and gas mass, respectively, for DMC stellar objects,
DMC DGs, and TDGCs (sample A). The stellar and gas massweighted average metallicities are defined as
M
>He
,
Zstellar ≡
Mtot stellar
M
>He
Zgas ≡
,
(B.1)
Mtot gas
where Mtot is the total mass and M>He is the mass of all elements
above Helium (He)13 . DM-poor DGs and TDGCs are often significantly more metal-rich than DM-rich DGs, which is consistent with these galaxies being TDGs formed from chemically
enriched host galaxies in the Illustris model (Recchi et al. 2015).
Dark matter-containing stellar objects in the region of TDGCs
and DM-poor DGs in Fig. B.1 (top) are typically metal-enriched
substructures of massive subhalos. Therefore, DM-poor DGs can
have captured dark matter particles.
13
Only cells within twice the stellar half-mass radius are considered.
A47, page 20 of 28
C.1. Virial equilibrium of TDGCs
The kinetic energy (including the thermal energy of the gas),
Ekin , and the potential energy, Epot , of subhalos at redshift z =
0 are taken from a supplementary catalog prepared by Zjupa
& Springel (2017) in which the energies of the subhalos are
calculated by the particles identified by the Subfind algorithm
(Springel et al. 2001).
All identified Subfind TDGCs of sample A and sample B
fulfill the condition |Epot | > |Ekin |, which demonstrates that
these subhalos are gravitationally bound. Here the virial ratio
is defined by
q≡
2 × Ekin
,
Epot
(C.1)
such that for a self-gravitating object virial equilibrium is
achieved if q = 1 and the object is gravitationally bound if q < 2.
Figure C.1 shows that TDGCs of sample A only slightly deviate
from virial equilibrium for larger stellar masses or smaller stellar half-mass radii in the sense that they become dominated by
potential energy (q < 1). The mean and the standard deviation
of the virial ratio of all TDGCs of sample A is 0.85 and 0.18,
respectively. Therefore, the condition for virial equilibrium lies
roughly within the 1σ range of the virial ratio distribution. The
statistics of the virial ratio for different dwarf galaxy samples are
given in Table C.1.
M. Haslbauer et al.: Galaxies lacking dark matter in the Illustris simulation
Table C.1. Virial ratio, q (Eq. (C.1)), for TDGC samples and DMC DGs
at redshift z = 0 as resulting from the Subfind algorithm.
Sample
Mean
Median
Std.
16th−84th percentile
TDGCs (sample A)
TDGCs (sample B)
DM-poor DGs
DM-rich DGs
0.85
0.59
0.95
1.0
0.82
0.58
0.92
1.0
0.18
0.25
0.28
0.080
0.69−0.97
0.34−0.86
0.73−1.2
0.98−1.1
Notes. Listed are the mean, the median, the standard deviation (std.),
and the 16th−84th percentile of the virial ratio, q, for dwarf galaxies.
C.2. Density distribution, velocity distribution, and rotation
curves of TDGCs
In Fig. C.2 we study the internal structure of four massive gasfree TDGCs of sample A which are among the most deviant
ones from virial equilibrium (i.e., with q = 0.60−0.70) by fitting
their density distributions with a Plummer model and an exponential function. The 3D density profile for a Plummer model
(e.g., Heggie & Hut 2003; Kroupa et al. 2008) is given by
3Mtot
r2 −5/2
ρP (r) =
1
+
,
(C.2)
a2P
4πa3P
where Mtot is the total mass of the object and aP is the Plummer
radius which is related to the half-mass radius, R0.5 total , by
aP ≈ 1.3R0.5 total .
(C.3)
The exponential function describes the observed dwarf satellite galaxies well (Binggeli et al. 1984) and has the form,
ρe (r) = ρe,0 exp(−r/rd ),
(C.4)
where ρe,0 is the central density and rd is the scale radius. Both
fitting functions can reasonably describe the density profile of
the shown TDGCs, that is, their total masses derived from the
fits are comparable to the total masses obtained from the Subfind
algorithm. The half-mass radius calculated from the Plummer fit
for all the four TDGCs is smaller than the radii given by the Subfind algorithm. The fitting parameters and their uncertainties and
a quantitative comparison with the total mass and half-mass radii
obtained from the Subfind algorithm are labeled in the panels of
Fig. C.2. These demonstrate that even the density distributions of
simulated TDGCs which are not fully in virial equilibrium follow a profile which is expected from observed dwarf galaxies.
The internal kinematics of the above discussed gas-free
TDGCs are analyzed in Figs. C.3 and C.4 in which their rotation curves and the 3D velocity dispersion (top panels) are plotted. By assuming that the mass distribution of these TDGCs is
spherical we can calculate the circularity velocity by
r
GMtot (< r)
,
(C.5)
vc (r) =
r
where G is the gravitational constant and Mtot (<r) is the total mass
within the radius r. The rotation curves of TDGCs decline for
larger radii because of the absence of dark matter particles. The 3D
velocity dispersion for the TDGCs with the ID 372, ID 487, and ID
593 increases with increasing radii up until reaching a maximum
value, which could indicate that their stellar mass grew during formation inside-out. In order to address this formation theory, we
plot in Figs. C.3 and C.4 (bottom panels) the mean and the standard deviation as error bars of the stellar particle age in dependence of the distance to the center of the TDGC. The age gradient
is almost zero across the whole galaxy, which does not confirm an
inside-out formation scenario of these TDGCs.
C.3. Mass-weighted σ-clipping (outlier-rejection)
Throughout this study the analysis relies on the Subfind algorithm,
which is a position-space subhalo finder (Springel et al. 2001).
We apply a mass-weighted σ-clipping scheme in the 6D phasespace as an outlier-rejection method in order to cross-check if the
TDGCs identified by the Subfind algorithm are indeed gravitationally bound objects. For simplicity we only analyze TDGCs
that are gas-free according to the Subfind algorithm (i.e., 86 out
of 97 TDGCs of sample A), such that the σ-clipping procedure is
only applied to the stellar particles within the Illustris-1 box14 .
The σ-clipping scheme for a single gas-free TDGC which
was originally identified by the Subfind algorithm works as follows: In the first step, we load the center and the stellar halfmass radius of the considered TDGC provided by the Subfind
algorithm. Secondly, we extract all stellar particles within a
sphere centered at the position of the considered TDGCs with a
radius of 20 times the stellar half-mass radius. Subsequently, the
σ-clipping procedure starts by calculating the stellar center-ofmass position and velocity in the first iteration by
PN
mi ri
rcom ≡ i=1
,
M
(C.6)
PN
mi ui
,
ucom ≡ i=1
M
where N is the number of all selected stellar particles within the
sphere, mi is the mass, ri is the position vector, ui is the velocity
vector of the ith stellar particle, and M is the mass of all selected
stellar particles. Each of the selected stellar particles has to fulfill
the following two conditions
r2rel,i ≡ (ri − rcom )2 < η2 σ2r ,
u2rel,i ≡ (ui − ucom )2 < η2 σ2v ,
(C.7)
where η is the σ-threshold, and σr and σv are the standard deviations in position and velocity space given by
PN
mi (ri − rcom )2
σ2r = i
,
M
(C.8)
PN
2
i mi (ui − ucom )
2
σv =
,
M
whereby σr and σv are set to be zero in the first iteration. The
stellar particles which do not fulfill the condition C.7 are rejected
and the center-of-mass position and velocity are re-calculated
for the accepted stellar particles (see Eq. (C.6), where N and
M refer to only the accepted stellar particles). This procedure is
iteratively repeated until the algorithm converges such that the
following three conditions are fulfilled
|r − rold |2
< δ2 ,
σ2r
|u − uold |2
< δ2 ,
σ2v
σ 2
v
− 1 < δ2 ,
σold
v
(C.9)
14
The Illustris-1 simulation box includes 18203 dark matter particles
and 18203 gas tracer particles (gas cells and stellar particles). Therefore
operating on the gas cells and dark matter particles would be extremely
storage consuming such that we focus here purely on the stellar particles.
A47, page 21 of 28
A&A 626, A47 (2019)
gas-free TDGCs of sample A
100
ρ [M pc−3]
10−1
ID 372
Subfind: q=0.70
Mtot = 3.1 × 109 M
R0.5 total = 716 pc
Mtot = 2.0 × 109 M
R0.5 total = 881 pc
Exponential function:
Exponential function:
−3
10−2
ρe,0 = (3.579 ± 0.070) M pc
rd = (384 ± 11) pc
10−3
Plummer model:
MP,tot = (39.0 ± 1.2) × 108 M
10−4
ID 487
Subfind: q=0.64
ρe,0 = (1.603 ± 0.037) M pc−3
rd = (408 ± 13) pc
Plummer model:
MP,tot = (21.3 ± 1.5) × 108 M
aP = (686.2 ± 8.2) pc, R0.5 total ≈ 528 pc
aP = (735 ± 20) pc, R0.5 total ≈ 565 pc
Plummer fit (Eq. C.2)
Exponential fit (Eq. C.4)
10
−5
100
ID 59553
Subfind: q=0.64
Mtot = 1.5 × 109 M
R0.5 total = 744 pc
Mtot = 2.4 × 109 M
R0.5 total = 843 pc
Exponential function:
Exponential function:
10−2
ρe,0 = (1.83 ± 0.19) M pc−3
rd = (395 ± 56) pc
ρe,0 = (2.301 ± 0.050) M pc−3
rd = (381 ± 14) pc
10−3
Plummer model:
MP,tot = (18.0 ± 4.5) × 108 M
Plummer model:
MP,tot = (23.75 ± 0.79) × 108 M
10−1
ρ [M pc−3]
ID 593
Subfind: q=0.60
10
−4
aP = (650 ± 63) pc, R0.5 total ≈ 500 pc
10−5
102
aP = (672.6 ± 8.7) pc, R0.5 total ≈ 517 pc
103
102
103
r [pc]
r [pc]
Fig. C.2. Radial density distributions of four selected gas-free TDGCs of sample A (IDs 372, 487, 593, and 59553) fitted with a Plummer model
(green; Eq. (C.2)) and an exponential function (red; Eq. (C.4)). The radial bins have a width of 100 pc. The identification number, ID, their
corresponding virial ratios, q (Eq. (C.1)), their total masses and stellar half-mass radii obtained from the Subfind algorithm, and their fitting
parameters are given in the panels. According to the particles identified by the Subfind algorithm, the TDGCs shown here are not fully in virial
equilibrium. The rotation curves and 3D velocity dispersion of the TDGCs discussed here are shown in Fig. C.3 and Fig. C.4.
where δ is the convergence threshold and σold
v is the velocity
dispersion of the previous iteration. We chose for the following
analysis a σ-threshold of η = 2 or η = 3 and a convergence
threshold of δ = 0.01.
Finally, the virial ratio is calculated using the stellar particles
accepted by the σ-clipping scheme. The kinetic and potential
energy are given, respectively, by
N
1X
Ekin =
mi (ui − ucom )2 ,
(C.10)
2 i=1
A47, page 22 of 28
Epot = −
N X
N
X
Gmi m j
r2
i=1 j=i+1 i, j
2
+ baryonic
,
(C.11)
where N is the number of all accepted stellar particles based
on the σ-clipping scheme, G is the gravitational constant, and
baryonic is the softening length, for which we assume for simplicity a fixed value of 710 pc corresponding to the resolution of
gravitational dynamics in Illustris-1.
Figure C.5 and Table C.2 compare the virial ratio of
gas-free TDGCs of sample A calculated by the Subfind and
M. Haslbauer et al.: Galaxies lacking dark matter in the Illustris simulation
σ3D [km s−1]
80
rotation curve
rotation curve
60
ID 372, q=0.64
σ3D [km s−1]
100
60
40
20
ID 487, q=0.70
40
20
0
102
r [pc]
102
103
ID 372, q=0.64
9.7
r [pc]
103
ID 487, q=0.70
t̄age [Gyr]
t̄age [Gyr]
7.6
7.4
9.6
9.5
7.2
9.4
7.0
102
r [pc]
103
102
r [pc]
103
Fig. C.3. Rotation curves and radial 3D velocity dispersion distributions (top), and the radial distribution of stellar particle ages (bottom) of gasfree TDGCs of sample A with the ID 372 and ID 487. The radial bins have a width of 100 pc. The error bars in the bottom panels correspond to the
standard deviation of the stellar particle age within a radial bin. The identification number, ID, and their corresponding virial ratios, q (Eq. (C.1)),
are given in the panels. The radial density distributions of the TDGCs discussed here are shown in Fig. C.2.
σ-clipping algorithms. As expected, the percentage of gravitationally bound objects depends on the σ-threshold. Choosing
η = 2 in the σ-clipping scheme we find that 92 percent of our
gas-free TDGCs of sample A identified by the Subfind algorithm
fulfill |Epot | > |Ekin | and are thus also gravitationally bound when
they become selected by a 6D phase-space halo finder. Objects
that are not gravitationally bound have q > 2. In Fig. C.6 we
illustrate for three TDGCs the σ-clipping scheme by plotting
selected and accepted stellar particles in a position–velocity diagram and compare them with the particle distribution obtained
by the Subfind algorithm. The TDGCs ID 372 (top panels) and
ID 2275 (panels in the second row) are examples that are also
gravitationally bound objects according to a σ-clipping scheme
with η = 2. Despite the unusual appearance in the right panel
of ID 2275 the velocity–radius distribution of accepted particles is rather similar to the distribution of the Subfind particles.
The σ-clipping algorithm calculates the center-of-mass position
and velocity by using the accepted stellar particles resulting in
a shift in the velocity-position diagram (see ID 2275 in the left
panel in the second row of Fig. C.6). The TDGC ID 53625 is
an example which is gravitationally bound according to the Subfind algorithm (q = 0.78), but cannot be identified as a gravitationally bound object by using the σ-clipping scheme as a 6D
phase-space halo finder, that is, the virial ratio calculated by all
accepted stellar particles is q = 1387 and thus |Ekin | |Epot |.
The Subfind TDGCs which are not gravitationally bound according to the σ-clipping scheme typically have lower stellar masses
in the range of 5.6 × 107 −1.4 × 108 M and their positions in the
radius–mass diagram are highlighted in Fig. C.7.
We also compare the Subfind algorithm and σ-clipping
scheme with a σ-threshold of η = 2 for the density distribution of the TDGCs discussed in Fig. C.2. In Fig. C.8 the
density distributions of the TDGCs are fitted with a Plummer
model (see Eq. (C.2)) and the fitting parameters are qualitatively compared in the figure panels. The two different halo
finders (i.e., 3D position-space and 6D phase-space algorithms)
give these TDGCs approximately the same density distributions
as those pointed out by the fitting parameters of the Plummer
model.
Summarizing, a small number of TDGCs identified with the
Subfind algorithm are not confirmed by a σ-clipping scheme as
gravitationally self-bound objects. These TDGCs might either
not be real or cannot be identified as bound objects given the
limitations of the σ-clipping scheme. Therefore, the frequency
of Subfind TDGCs is ≈10 percent too high and this does not
affect our results significantly.
A47, page 23 of 28
A&A 626, A47 (2019)
80
rotation curve
60
σ3D [km s−1]
σ3D [km s−1]
ID 593, q=0.60
40
20
60
rotation curve
ID 59553, q=0.64
40
20
0
102
103
102
103
r [pc]
10.2
r [pc]
ID 59553, q=0.64
ID 593, q=0.60
9.6
t̄age [Gyr]
t̄age [Gyr]
10.1
10.0
9.4
9.2
9.9
9.8
9.0
10
2
10
102
3
103
r [pc]
r [pc]
Fig. C.4. As in Fig. C.3 but for gas-free TDGCs of sample A with the ID 593 and ID 59553. The radial density distributions of the here discussed
TDGCs are shown in Fig. C.2.
Table C.2. Virial ratio, q (Eq. (C.1)), for gas-free TDGCs of sample A calculated by the stellar particles identified by the Subfind and σ-clipping
algorithms.
Algorithm
#
# of |Epot | > |Ekin |
Mean
Median
Std.
16th−84th percentile
Subfind (Zjupa & Springel 2017)
2σ-clipping (+fixed softening length)
3σ-clipping (+fixed softening length)
86
86
86
86 (100 percent)
79 (92 percent)
61 (71 percent)
0.85
0.88
0.95
0.83
0.88
0.87
0.19
0.12
0.28
0.69−0.97
0.76−1.0
0.76−1.0
Notes. Listed are the number of gas-free TDGCs of sample A, the number of gas-free TDGCs which fulfill |Epot | > |Ekin |, the mean, the median,
the standard deviation (std.), and the 16th−84th percentile percentile of the virial ratio, q, for gas-free TDGCs with |Epot | > |Ekin |, i.e., with q < 2.
A47, page 24 of 28
M. Haslbauer et al.: Galaxies lacking dark matter in the Illustris simulation
gas-free TDGCs of sample A
|Epot| [1010 M km2 s−2]
105
104
Subfind (Zjupa & Springel 2017)
σ-clipping (η = 3, δ = 0.01)
σ-clipping (η = 2, δ = 0.01)
103
102
101
100
10−1
100
102
104
|2 × Ekin| [1010 M km2 s−2]
Fig. C.5. Relation between the potential and kinetic energy for gas-free
TDGCs of sample A calculated by the Subfind and σ-clipping (η = 2,
3; δ = 0.01) algorithms. The black solid line highlights the condition
for virial equilibrium, i.e., where the virial ratio becomes q = 1 (see
Eq. (C.1)). All objects above the black dashed line are gravitationally
bound (q < 2) . The kinetic and potential energy for the Subfind algorithm are taken form Zjupa & Springel (2017) and the calculation for
the potential energy using particles identified by σ-clipping assumes a
fixed softening length in Eq. (C.11).
A47, page 25 of 28
A&A 626, A47 (2019)
Subfind, ID 372, q=0.64
100
10−1
20 × R0.5 stellar
ID 372
101
|~rrel| [kpc]
|~rrel| [kpc]
101
q=0.72
100
10−1
10−2 0
10
101
102
|~vrel| [km s−1]
10−2 0
10
103
101
101
q=0.93
|~rrel| [kpc]
|~rrel| [kpc]
101
100
10−1
100
10−1 0
10
101
|~vrel| [km s−1]
103
20 × R0.5 stellar
ID 2275
Subfind, ID 2275, q=0.85
102
|~vrel| [km s−1]
101
ID 53625
Subfind, ID 53625, q=0.64
102
|~vrel| [km s−1]
103
20 × R0.5 stellar
|~rrel| [kpc]
|~rrel| [kpc]
101 q=1387
100
100
10−1
102
101
|~vrel| [km s−1]
Subfind, ID 53625, q=0.64
20
20
103
all selected stellar particles
all accepted stellar particles
σ-clipping (η = 2, δ = 0.01)
10
yrel [kpc]
yrel [kpc]
10
ID 53625
q=1387
|~vrel| [km s−1]
0
0
−10
−10
−20
−20
−20
0
xrel [kpc]
20
−20
0
xrel [kpc]
20
Fig. C.6. Top three panels: modulus of the position and velocity vectors with respect to the center-of-mass for stellar particles (see Eq. (C.7)). Blue
dots are stellar particles identified by the Subfind algorithm (left panels), red dots are all selected stellar particles within a sphere with radius 20
times the stellar half-mass radius (highlighted by the dashed solid black line; right panels) and centered around the considered Subfind TDGCs,
and green dots are all stellar particles which become accepted by the σ-clipping algorithm with η = 2 and δ = 0.01 (right panels). Bottom:
projected stellar particle distribution with positions relative to the center-of-mass for ID 53625. For the σ-clipping, the center-of-mass position
and velocity change in each iteration and also for the final accepted stellar particles (see text).
A47, page 26 of 28
M. Haslbauer et al.: Galaxies lacking dark matter in the Illustris simulation
log10(R0.5 stellar/[pc])
5
4
3
sim. DM-rich DGs
sim. DM-poor DGs
sim. gas-free Subfind TDGCs (confirmed by 2σ-clipping)
2
sim. gas-free Subfind TDGCs (not confirmed by 2σ-clipping)
NGC1052-DF2 (van Dokkum et al. 2018)
1
100
6
8
10
log10(Mstellar/[M ])
12
101
102
103
counts of sim. DMC stellar objects in bin
Fig. C.7. As in Fig. 12 (top) but for gas-free TDGCs analyzed by a σclipping scheme (η = 2, δ = 0.01). Red triangles are gas-free TDGCs
confirmed by 2σ-clipping and black crosses are gas-free TDGCs which
are according to 2σ-clipping not gravitationally bound objects.
A47, page 27 of 28
A&A 626, A47 (2019)
Comparison of the Subfind and 2σ-clipping algorithms applied on gas-free TDGCs of sample A
ID 372
100
ID 487
ρ [M pc−3]
10−1
10−2
10−3
10
−4
Subfind+Plummer: q=0.64
Subfind+Plummer: q=0.70
MP,tot = (39.0 ± 1.2) × 108 M
aP = (686.2 ± 8.2) pc, R0.5 total ≈ 528 pc
MP,tot = (21.3 ± 1.5) × 108 M
aP = (735 ± 20) pc, R0.5 total ≈ 565 pc
2σ-clipping+Plummer: q=0.72
2σ-clipping+Plummer: q=0.79
MP,tot = (53.7 ± 6.7) × 108 M
MP,tot = (21.7 ± 2.7) × 108 M
aP = (796 ± 39) pc, R0.5 total ≈ 612 pc
aP = (711 ± 34) pc, R0.5 total ≈ 547 pc
Subfind & Plummer fit (Eq. C.2)
2σ-clipping & Plummer fit (Eq. C.2)
10−5
ID 593
100
ID 59553
ρ [M pc−3]
10−1
Subfind+Plummer: q=0.60
10−2
10−3
10
−4
Subfind+Plummer: q=0.64
8
MP,tot = (18.0 ± 4.5) × 10 M
aP = (650 ± 63) pc, R0.5 total ≈ 500 pc
MP,tot = (23.75 ± 0.79) × 108 M
aP = (672.6 ± 8.7) pc, R0.5 total ≈ 517 pc
2σ-clipping+Plummer: q=0.70
2σ-clipping+Plummer: q=0.75
MP,tot = (17.8 ± 3.1) × 108 M
MP,tot = (25.5 ± 1.9) × 108 M
aP = (636 ± 44) pc, R0.5 total ≈ 489 pc
10−5
102
103
r [pc]
aP = (649 ± 19) pc, R0.5 total ≈ 499 pc
102
103
r [pc]
Fig. C.8. Radial density distributions of four selected gas-free TDGCs of sample A (IDs 372, 487, 593, and 59553) calculated by the particles
identified by the Subfind (blue) and σ-clipping (η = 2 and δ = 0.01; red) algorithms and fitted with a Plummer model (Eq. (C.2)). The radial bins
have a width of 100 pc. The identification number, ID, their corresponding virial ratios, q (Eq. (C.1)), and their fitting parameters are given in the
panels. The kinetic and potential energy for the Subfind algorithm are taken form Zjupa & Springel (2017) and the calculation for the potential
energy using particles identified by σ-clipping assumes a fixed softening length in Eq. (C.11). We note that q is computed solely for the particles
selected using Subfind or 2σ-clipping.
A47, page 28 of 28