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Astronomy & Astrophysics manuscript no. main ©ESO 2022
January 4, 2022
Gas distribution from clusters to filaments in IllustrisTNG
C. Gouin1, 2? , S. Gallo1 , N. Aghanim1
1
Université Paris-Saclay, CNRS, Institut d’Astrophysique Spatiale, 91405, Orsay, France
2
School of Physics, Korea Institute for Advanced Study (KIAS), 85, Hoegiro, Dongdaemun-gu, Seoul, 02455, Republic
of Korea
January 4, 2022
ABSTRACT
arXiv:2201.00593v1 [astro-ph.CO] 3 Jan 2022
Matter distribution in the environment of galaxy clusters, from their cores to their connected cosmic filaments, must
be in principle related to the underlying cluster physics and it evolutionary state. We aim to investigate how radial and
azimuthal distribution of gas is affected by cluster environments, and how it can be related to cluster mass assembly
history.
Radial physical properties of gas (velocity, temperature, and density) is first analysed around 415 galaxy cluster environ-
ments from IllustrisTNG simulation at z = 0. Whereas hot plasma is virialised inside clusters (< R200 ), the dynamics
of warm hot inter-galactic medium (WHIM) can be separated in two regimes: accumulating and slowly infalling gas at
cluster peripheries (∼ R200 ) and fast infalling motions outside clusters (> 1.5R200 ).
The azimuthal distribution of dark matter (DM), hot and warm gas phases is secondly statistically probed by decom-
posing their 2-D distribution in harmonic space. Inside clusters, the azimuthal symmetries of DM and hot gas are well
tracing cluster structural properties, such as their center offsets, substructure fractions and elliptical shapes. Beyond
cluster virialised regions, we found that WHIM gas follows the azimuthal distribution of DM by tracing cosmic fila-
ment patterns. Azimuthal symmetries of hot and warm gas distribution is finally shown to be imprints of cluster mass
assembly history, by strongly correlating with the formation time, mass accretion rate, and dynamical state of clusters.
Azimuthal mode decomposition of 2-D gas distribution is a promising probe to assess the 3-D physical and dynamical
cluster properties up to their connected cosmic filaments.
Key words. Galaxies: cluster: general – Galaxies: cluster: intracluster medium – large-scale structure of Universe –
Methods: statistical – Methods: numerical
1. Introduction and geometry-based (Tempel et al. 2016; Pereyra et al.
2020; Bonnaire et al. 2020, 2021) filament-finder techniques.
Galaxy cluster environments are ideal laboratories to probe These cosmic web classification and detection methods are
both, the building up of massive structures, and the com- crucial to explore how cosmic web environment drives the
plex physics of baryons. These most massive gravitationally physical properties of it content: gas, galaxies, and DM.
bound objects of the Universe are located at the nodes of
the underlying large-scale cosmic web (de Lapparent et al. Focusing on the gas component, gas filaments in the
1986; Bond & Myers 1996) and they link a network of cosmic web are currently challenging to detect due to e.g.
cosmic filaments mainly composed of dark matter (DM), low X-ray emissivity, low signal to noise ratio, background
which constitutes the cosmic skeleton framework, along contamination, etc. Only few observations of cosmic gas
which baryons are flowing and collapsing. Under the ac- filaments have been reported, such as individual massive
tion of gravity, large-scale cosmic flows transport matter bridge of hot gas around or between clusters (Planck Col-
on cosmic large-scale structures from voids to sheets, and laboration et al. 2013; Eckert et al. 2015; Akamatsu et al.
then via elongated filaments into clusters (Zel’Dovich 1970). 2017; Nicastro et al. 2018; Bonjean et al. 2018), and statisti-
The anisotropic large-scale matter distribution and its asso- cally characterised by averaging gas filament profiles using
ciated accretion processes have been investigated both the- stacking techniques (Tanimura et al. 2019; de Graaff et al.
oretically and via N-body simulations (Pichon et al. 2010; 2019; Tanimura et al. 2020a,b). In order to interpret and
Codis et al. 2015; Shim et al. 2020), to establish a picture prepare upcoming observations of gas filaments, predictions
on the evolutionary and dynamical aspects of the cosmic of cosmic gas properties from state-of-art hydrodynamical
network (see e.g. Hahn 2016, for a review). Given the large cosmological simulations are essential. Martizzi et al. (2019)
diversity of filament types (in term of length and width, have shown that about 46% of baryons is supposed to be
see for example Cautun et al. 2014; Galárraga-Espinosa in the form of warm hot intergalactic medium (WHIM).
et al. 2020), different approaches have been developed to Majority of this warm gas phase is expected to be located
detect them, and lead to their own filament definition. One inside filamentary structures, and must account for 80% of
can cite topology-based (Sousbie 2011; Aragón-Calvo et al. the baryonic budget (Galárraga-Espinosa et al. 2021a,b).
2010a), hessian-based (Hahn et al. 2007; Cautun et al. 2013) It makes WHIM gas phase a powerful tracer of the cosmic
web, and should constitute a reservoir of baryons which
?
E-mail: celinegouin@kias.re.kr could solve the so-called missing baryon problem (Cen &
Article number, page 1 of 15A&A proofs: manuscript no. main
Ostriker 1999; Davé et al. 2001). For these reasons, the Roncarelli et al. 2013; Ansarifard et al. 2020). However, the
gaseous component of the cosmic web is becoming the sub- azimuthal scatter method is sensitive to all kinds of devi-
ject of more and more studies, with the aim to construct ations arsing from the gas clumping, the cluster ellipticity,
a comprehensive picture of the baryonic physical processes and the large-scale anisotropic structures, without allowing
(heating, cooling, shocks, etc.) that gas undergoes during to identify individually these different features.
its transit from one cosmic environment to another (Gheller Here, we propose to use an alternative technique based
& Vazza 2019; Martizzi et al. 2019; Tuominen et al. 2021; on 2-D decomposition of matter distribution in harmonic
Zhu et al. 2021a). This interest on cosmic gas is further en- modes. This method has emerged to quantify separately
hanced by the prospect of future missions which will allow the different azimuthal symmetries inside a given aperture
us to explore the hidden cosmic gas with unprecedented centered on clusters. Such aperture multipole technique
accuracy in the coming years (Simionescu et al. 2021). has been developed for weak-lensing mass map applications
In this context, the outskirts of galaxy clusters consti- (Schneider & Bartelmann 1997), and succeeded in estimat-
tute unique regions, where cosmic filaments intersect and ing both, elliptical shape of clusters (see e.g. Clampitt &
are the most easily detectable due to larger density con- Jain 2016; Shin et al. 2018), and filamentary patterns at
trasts (as observed via galaxy distribution around clusters cluster outskirts (Dietrich et al. 2005; Mead et al. 2010;
Mahajan et al. 2018; Einasto et al. 2020; Malavasi et al. Gouin et al. 2017). Recently, Gouin et al. (2020) have ex-
2020; Gouin et al. 2020). Cosmic gas infalls from the large- tended the aperture multipole formalism to apply it to 2-D
scale cosmic web to clusters tunnelled by their connected fil- projected maps of galaxy distribution around clusters, and
aments. Due to the dissipative nature of the gas component, shown that azimuthal galaxy distribution evolves from the
it must undergo a large variety of complex physical mecha- elliptical cluster shape in the inner parts, up to harmonic fil-
nisms, such as accretion shocks (Shi et al. 2020; Zhang et al. amentary pattern at cluster outskirts. In the present work,
2021b), dynamical interaction with the hot gas inside clus- we will apply aperture multipole moment decomposition to
ters, gas disruption of infalling galaxies (Mostoghiu et al. gas distribution inside and around clusters. By separating
2021), turbulent motions (Rost et al. 2021), etc. One can gas in different main phases, we aim at highlighting which
cite Walker et al. (2019), for a complete review on gas clus- gas phase preferentially traces clusters shape and large-scale
ter outskirts. filamentary pattern. This method will be also used to dis-
In contrast, inside the gravitational potential wells of tinguish between the different features on azimuthal gas
clusters, the intra-cluster medium (ICM) is accumulating distribution such as the amount of substructures, the halo
mainly in the form of a hot plasma. In these central re- ellipticity, and the connected cosmic filaments. The gas az-
gions, gas is assumed to be at the hydrostatic equilibrium, imuthal symmetries will be finally probed to investigate if
and spherically distributed inside galaxy clusters. Never- the azimuthal gas distribution traces the cluster dynamics
theless, both observations and simulations have shown that and its accretion history.
clusters are not perfectly at the hydrostatic equilibrium due This paper is organized as follows. In Section 2, we de-
to turbulence and bulk motions which arise at cluster pe- scribe our sample of 415 simulated cluster extracted from
ripheries (see e.g. Angelinelli et al. 2020; Ansarifard et al. IllustriTNG simulation (Nelson et al. 2019), and their phys-
2020; Gianfagna et al. 2021). In order to probe the ther- ical properties. In Section 3, we start by investigating the
modynamical state of ICM, a powerful technique is to ex- properties of the gas as a function of the cluster-centric
plore the azimuthal gas distribution. Indeed, Chen et al. distance and cluster mass. This allows us to choose which
(2019) showed that the elliptical shape of ICM correlates gas phases and radial apertures are optimal choices to in-
with the amount of non-thermal pressure support, and can vestigate further spherical symmetry deviations of gas dis-
be related to the mass accretion history of clusters. It is tribution. In Section 4, we present the multipole moment
therefore crucial to accurately measure the anisotropy of formalism. We probe different azimuthal symmetries of hot
gas distribution from the ICM to cosmic web filaments, to gas and DM inside clusters, and show how they are related
better constrain relations between cosmic gas distribution to structural properties of cluster halo. In Section 5, the
and cluster evolution. average level of azimuthal symmetries of hot gas, WHIM
In order to assess deviations from spherical symmetry of and DM are estimated inside and outside clusters. These
gas distribution in clusters, different techniques have been deviations from circular symmetry are compared to cluster
developed, such as the asymmetry parameter (Schade et al. physical properties and to their recent mass assembly his-
1995), centroid shift (Mohr et al. 1993), light concentration tory. Finally, we discuss and summarize our conclusions in
ratio (Santos et al. 2008), Gaussian fit parameter (Cialone Section 6.
et al. 2018), etc., and the combination of these morpholog-
ical parameters (see e.g. De Luca et al. 2020). Recently, 2. Simulated cluster sample
Capalbo et al. (2021) have also proposed to infer clus-
ter morphology by modelling 2-D cluster gas maps with In this section, we present our sample of 415 simulated clus-
Zernike polynomials. These various techniques are power- ter environments, extracted from IllustrisTNG simulation
ful to quantify the degree of the cluster shape disturbance (Nelson et al. 2019), for which various physical and struc-
and are good proxies of cluster dynamical state. However, tural properties has been previously estimated in Gouin
they remain focused on clusters morphology, and on the et al. (2021).
analysis of gas distribution in the most inner part of clus-
ters (typically up to R500 ). Beyond the virial radius, the 2.1. Cluster environments from IllustrisTNG simulation
azimuthal scatter technique was proposed to quantify de-
partures from spherical symmetry in the radial profiles of The large cosmological magneto-hydrodynamical Illus-
gas properties (Vazza et al. 2011), and successfully traced trisTNG simulations (Nelson et al. 2019) provide the spa-
the thermodynamical state of the ICM (Eckert et al. 2012; tial and dynamical evolution of dark matter, gas, stars, and
Article number, page 2 of 15Gouin et al.: Gas distribution from clusters to filaments in IllustrisTNG
black holes on a moving-mesh code (Springel 2010), and following the definition of Cole & Lacey (1996).
assume cosmological parameters from the Planck 2015 re-
sults (Planck Collaboration et al. 2016). Considering the Structural properties. The structural properties of
series of IllustrisTNG simulation boxes, we focus here on clusters have been also estimated based on three different
IllustrisTNG300-1 at z = 0; the cubic box has a length parameters: the center offset Rof f , the subhalo fraction fsub
of 302.6Mpc and the mass resolution is about mDM = and the halo ellipticity , computed on the 3-D matter dis-
4.0 × 107 M /h. This large and high-resolution simula- tribution inside the virial radius Rvir of each cluster. First,
tion box is ideal to accurately describe matter distribution the center of mass offset is computed as the distance be-
around galaxy clusters up to their large scale environments tween the center of mass rcm and the density peak rc nor-
at z = 0. malised by the virial radius, such as
Our sample of galaxy clusters is based on the halo cata-
Rof f = |rcm − rc |/Rvir . (3)
log provided by IllustrisTNG and identified with a friends-
of-friends (FoF) algorithm (Davis et al. 1985). Notice that Secondly, the subhalo mass fraction represents the amount
the radial physical scale R200 of FoF halos is defined as the of mass contained in sub-clumps hosted inside a halo. It is
radius of a sphere centered on the halo which encloses a defined as the ratio between the sum of all subhalo masses
mass M200 and a density equals 200 times the critical den- (without taking into account the main subhalo) and the
sity of the Universe at z = 0. The IllustrisTNG simulations total halo mass Mtot , such as
provide also subhalo catalogues derived by the Subfind al- X
gorithm (Springel et al. 2001), which allow to quantify the fsub = Msub /Mtot . (4)
amount of substructures inside a given host halos. Starting
from the IllustrisTNG halo catalog at z = 0, we select all Thirdly, the shape of cluster halo is quantified by measuring
FoF halos with masses M200 > 5 × 1013 M /h which are the ellipticity of DM distribution in two (and three) dimen-
more distant than 5 R200 from the simulation box edges. sions. Following Suto et al. (2016), the fitted ellipsoid on
Our sample contains 415 clusters which can be divided in matter distribution is found by computing the eigenvalues
two distinct mass bins: the 266 massive groups with mass of the mass tensor of all DM particles, and by fixing the to-
M200 = [5 − 10] × 1013 M /h, and 149 galaxy clusters with tal mass enclosed in the ellipsoid equals to M200 . The two
M200 > 1 × 1014 M /h. Notice that if we do not distinguish (and three) dimensional ellipticity are
between galaxy groups and clusters, we otherwise refer to c−a c−a
the 415 most massive halos as our cluster sample. 2D = , 3D = , (5)
2(a + c) 2(a + b + c)
with a (≤ b) ≤ c the major, (intermediate,) and minor
2.2. Physical and structural properties axis vectors of the ellipsoid (Jing & Suto 2002). Fig. 4
We refer the reader to Gouin et al. (2021), for details on illustrates the ellipse modeled following this procedure in
the computation of physical and structural properties of the 2-D DM distribution of a given cluster.
our cluster sample. Here, we summarise the definitions and
computation procedures of the different estimated parame- Dynamical state. In order to investigate the dynam-
ters. ical state of clusters, the so-called relaxedness parameter
Mass assembly history. In order to probe the mass χDS has been computed following the definition of Haggar
assembly history of clusters, the time evolution of clus- et al. (2020),
ter mass M200 (z) has been computed using the available v
u 3
merger tree of subhalos computed by SubLink algorithm χDS = u 2 . (6)
2 η−1 2
t
(see Rodriguez-Gomez et al. 2015, for details on merger ∆r fsub
0.07 + 0.1 + 0.15
tree computation in Illustris). Two distinct proxies of the
mass assembly history of clusters have been estimated: the This equation is a quadratic average of three dynamical
formation redshift zf orm and the mass accretion rate Γ. and structural proxies, with η the ratio between the kinetic
These two parameters provide complementary information energy and the gravitational potential energy. Groups and
to quantify cluster mass assembly history, by probing the clusters with χDS ≥ 1 are supposed to be dynamically
accretion phase, and the birth of a object according to its relaxed, whereas dynamically perturbed systems have a
mass growth. First, the accretion rate is the ratio between relaxedness value such as χDS < 1 (see e.g. Kuchner
the halo mass at z = 0 and the mass of its main progenitor et al. 2020). Notice that recently, Zhang et al. (2021a)
at a given z (according the definition of Diemer et al. 2013): have extended the above relation to a new threshold-free
function to classify cluster dynamical states.
∆log(M200m )
Γ≡ . (1) Connectivity. The connectivity, K, defines the number
∆log(a)
of cosmic filaments which connect to clusters. In practice,
This parameter allows us to quantify the accretion phase it is computed by counting the number of filaments which
of a given halo between two time steps, chosen to be z = intersect a sphere of 1.5 R200 radius around the each clus-
0 and 0.5 (which corresponds to the expected relaxation ter centers (similarly to Darragh-Ford et al. 2019; Sarron
timescales of halos, according to Power et al. 2012; Diemer et al. 2019; Kraljic et al. 2020). In the present study, the
& Kravtsov 2014; More et al. 2015). Secondly, the formation filamentary pattern in the whole simulation box is detected
redshift is the time at which the mass of the main progenitor based on a cosmic-web skeleton constructed from the Graph
halo is equal to half its mass at the present time: model of the algorithm T-ReX (Bonnaire et al. 2020) and
M200 (zform ) applied on the 3-D subhalos distribution of the simulation
= 1/2 , (2) (as explained in Gouin et al. 2021).
M200 (z = 0)
Article number, page 3 of 15A&A proofs: manuscript no. main
3. Radial gas distribution in cluster environments We now probe the detail radial profile of the different gas
phases as a function of cluster-centric distance. Similarly
We introduce in this section key features of the gas proper- to Galárraga-Espinosa et al. (2021a), we defined the mass
ties as a function of the cluster radial distance. We consider fraction of a given gas phase such as:
all the gas cells contained around our 415 halo samples up to
5×R200 (labeled as PartType0 in IllustrisTNG). We focus ρgas
i (r)
ψigas (r) = gas , (7)
here on two thermodynamical properties: the temperature ρT OT (r)
T (computed under the assumption of perfect monoatomic with r is the 3-D radial distance to the cluster center,
gas, as in Galárraga-Espinosa et al. 2021a) and the nH ρgas gas
hydrogen number density which is a direct tracer of the i (r) the radial density of the i gas phase, and ρT OT (r)
the radial density of the total gas. The radial density of gas
total gas density (directly pre-computed in IllustrisTNG). is computed by summing the mass of gas cells contained
We refer to, Martizzi et al. (2019) for an accurate descrip- in spherical shells from a radius rk−1 to rk , following the
tion of gas properties in the different cosmic web environ- above equation:
ments (voids, walls, filaments, and nodes), and Galárraga-
Espinosa et al. (2021a) for a complete study of gas ther-
PNk
j mj
modynamics inside cosmic filaments; two studies of cosmic gas
ρ (rk ) = , (8)
gas using the IllustrisTNG simulation. In our case, we focus 4/3π(rk3 − rk−1
3 )
on the particular case of transition from infalling gas along with Nk is the number of gas cells j contained in a spherical
filaments to the captured gas inside cluster gravitational shell with radius from rk−1 to rk centered on the halo.
potential wells. Following Eq. 8 and 7, we have computed the mass frac-
tion of the five gas phases around each halo of our cluster
sample. The mean radial profile of gas phases is presented in
3.1. The gas phases Fig. 2, by averaging over our all halo sample, only consider-
ing galaxy clusters (M200 > 1014 M /h) and only consider-
One commonly used way to characterise gas types is to ing galaxy groups (M200 = [5−10]×1013 M /h) respectively
probe its distribution in a temperature-density diagram, as in top, middle and bottom panels. Figure 2 shows that the
it allows to artificially separate the gas in different phases hot gas phase is strongly dominating the interior of all halos
(see e.g. Cen & Ostriker 2006). The temperature and den- (top panel). As expected the gas must be strongly heated
sity of gas is commonly separated in five gas phases which inside the deep gravitational potential wells of clusters, and
are related to different environments and physical processes: thus appears in the form of a hot plasma. Beyond the clus-
the diffuse intergalactic medium (Diffuse IGM), the warm- ter region, the fraction of hot gas decreases, such that the
hot intergalactic medium (WHIM), the warm circumgalac- gas becomes colder and less dense: WHIM gas phase. The
tic medium (WCGM), the halo gas and the hot gas (see warm diffuse gas starts to dominate at distances larger than
e.g. Martizzi et al. 2019, for a detailed description of each ∼ 0.9R200 on average.
phase). However, we can see that the transition radius from hot
In Fig. 1, we show the stacked gas distribution in to WHIM gas phase strongly differs for galaxy clusters and
temperature-density diagrams of the 415 galaxy cluster galaxy groups (middle and bottom panel). To illustrate this,
environments, by separating it in five bins of cluster- we highlight the radius for which hot gas phase is no longer
centric distance from 0 to 5 R200 . We have normalised dominant in gray vertical lines in Fig. 2. The hot plasma
the radial aperture centered on clusters by R200 to easily extends up to 1.2R200 inside galaxy clusters, whereas it is
stack gas distribution of different clusters with different only dominant up to ∼ 0.6R200 for galaxy groups. In addi-
masses (without mixing their physical radial scale). Fig- tion, the hot gas mass fraction inside 1 R200 is about 93%
ure 1 illustrates the distribution of gas in the different for galaxy clusters, whereas it is only 68% for the galaxy
temperature-density phases as a function of cluster radial groups. Whereas hot plasma is largely extended and rep-
distance. Inside clusters (R < 1R200 ), gas is mainly in resents almost all of the gas inside galaxy clusters, gas in
the form of hot plasma at high temperature, T > 107 K. galaxy groups is a mixture of hot and warm dense gas.
Increasing the distance from the cluster centers, from 1 The bottom panel of Fig. 2 shows that the transition
to 3 R200 , we can see that most of the gas is at lower from hot to WHIM gas phase is different in galaxy groups
temperature (in the range of 105 < T [K] < 107 ) and at because it implies a third gas phase: the warm circum-
lower density (in the range of nH < 104 cm−3 ). The gas galactic medium. The WCGM gas phase has a similar tem-
is transiting from hot dense plasma to diffuse warm gas, perature than the WHIM but is denser (see Fig. 1). The
in the so-called phase: warm-hot intergalactic medium. shallower gravitational potential of galaxy groups is not
At larger distances from cluster center (> 3R200 ), the deep enough to heat the gas up to 107 K beyond the core re-
distribution of the gas in temperature-density diagrams gion (> 0.6×R200 ). At larger distance, the gas temperature
appears distributed in the different phases: cold diffuse decreases first, with the gas transiting to the warm dense
(IGM), cold dense (halo gas), warm diffuse (WHIM), warm phase (WCGM), and then density decreases at 0.8R200 ,
dense (WCGM) and hot gas. This temperature-density transforming the gas in diffuse and warm phase (WHIM).
distribution is quite similar to the expected distribution According to Martizzi et al. (2019), WCGM gas phase must
of overall cosmic gas in the universe at z = 0 (see figure be created by shock heating and feedback of massive galax-
2 of Galárraga-Espinosa et al. 2021a, which considered all ies, and located mostly at the vicinity of massive galaxies
gas cells in the simulation box). Therefore, it suggests that and inside galaxy groups. We confirm here that, WCGM
beyond radial distances larger that 3R200 the influence of phase is one of the dominant phases inside galaxy groups
cluster environments is no more significant. accounting for 23% of the mass within R < R200 , with a
peak contribution at around 0.7R200 .
Article number, page 4 of 15Gouin et al.: Gas distribution from clusters to filaments in IllustrisTNG
0 < R[R200] < 1 1 < R[R200] < 2 2 < R[R200] < 3 3 < R[R200] < 4 4 < R[R200] < 5 10 2
9
8
Probability density
7 Hot Gas 10 3
log(T[K])
6
5 WHIM WCGM 10 4
4
3 Diffuse IGM Halo Gas 10 5
6 4 2 6 4 2 6 4 2 6 4 2 6 4 2
log(nH[cm 3]) log(nH[cm 3]) log(nH[cm 3]) log(nH[cm 3]) log(nH[cm 3])
Fig. 1. Stacked temperature-density diagrams for all gas cells around galaxy clusters and groups in IllustrisTNG, considering
different radial apertures from cluster central regions R[R200 ] < 1 up to 4 < R[R200 ] < 5
HM small fraction of hot gas is expected to be in the form of
WHIM small massive clumps located in cosmic filaments (Zhuravl-
0.75 WCGM eva et al. 2013; Angelinelli et al. 2021). Far from the group
Diffuse IGM
Gas halo and cluster centers (> 3 R200 ), the warm diffuse gas remains
gas fraction
0.50 415 groups & clusters
the dominated phase. Indeed, WHIM gas is supposed to be
M200 > 5 × 1013M /h the dominant phase in the Universe with a mass fraction of
around 46% according to Martizzi et al. (2019). Notice that
0.25
in our case, at distances of 5 × R200 , the mass fraction of
WHIM is quite high with a value of 70%. This is coherent
0.00 with the findings of Galárraga-Espinosa et al. (2021a), who
shown that WHIM gas phase slowly decreases up to 20M pc
0.75 away from the spine of denser filaments. We can thus expect
similar behaviour for radial WHIM fraction profile around
gas fraction
clusters.
0.50 149 clusters We can finally notice that, far from cluster centers at
M200 > 1 × 1014M /h around 2.5 R200 , the WHIM gas phase starts to decrease in
0.25 favor of diffuse IGM. It relates to the presence of cold dif-
fuse gas in galaxies. The increase of diffuse IGM at around
2R200 from cluster centers, is in agreement with results from
0.00
Mostoghiu et al. (2021), who show that cold gas in infalling
galaxies is completely depleted at 1.7R200 from cluster cen-
0.75 ters (see also Arthur et al. 2019; Singh et al. 2020; Zhu
et al. 2021a; Song et al. 2021, on the impact of filaments
gas fraction
0.50 and cluster environments on the depletion of cold gas in
266 groups
infalling galaxies).
M200 = [5 10] × 1013M /h
0.25
3.2. The gas dynamics
0.00 Beyond the temperature-density gas phases, it is also a
0 1 2 3 4 5
R/R200 prime of importance to probe gas motions to investigate
their infall from large-scale environment to clusters. The
Fig. 2. Mean gas mass fraction profiles (see Eq. 7) of the dynamics of the gas is explored in phase-space coordinates
five different gas phases around all halos in our sample (top),
(velocity, position) following the definitions presented by
only galaxy clusters (middle) and only galaxy groups (bot-
tom). The radial boundary at which the hot gas phase is no Oman et al. (2013). Considering the 3-D vector position r
longer dominant is shown by gray vertical lines, and is about and 3-D vector velocity v of each gas cell, we can identify
RHOT ∼ 0.91, 1.20 and 0.61 for the all groups and clusters, only all gas cells by their 6-D coordinates (rx , ry , rz , vx , vy , vz ).
clusters, and only groups respectively. As the same, each cluster is characterised by its central
position rc , and its 3-D velocity vc (the halo velocity is
computed as the sum of the mass-weighted velocities of all
particles/cells in the halo, pre-computed by IllustrisTNG
Outside groups and clusters, typically beyond distance collaboration). Considering these phase-space coordinates,
& 1 R200 , the WHIM gas phase largely dominates, and we can define the radial velocity of each gas cell, relative to
tends to smoothly peak at around 2 R200 . These radial dis- their associated host cluster environment, such as:
tances are typically the infalling regions around clusters
where gas is expected to be located inside cosmic filamen- v3D = sgn((r − rc ).(v − vc ))|v − vc | . (9)
tary pattern connected to clusters (see e.g. Eckert et al.
2015, for a observational evidence). In this regions, the frac- Note that the sign of v3D allows to distinguish between the
tion of hot gas remains still non-negligible, with about 13% infalling gas (v3D < 0) and the outgoing gas (v3D > 0)
of the total mass of gas from 1 to 3 R200 . In fact, this around a given cluster. In order to stack gas radial velocity
Article number, page 5 of 15A&A proofs: manuscript no. main
All gas Hot gas WHIM
6 0.0007
415 groups & clusters
4
2
0.0006
3D
0
V3D/
2
4
0.0005
66
149 clusters- M200 > 1 × 1014M /h
4
Probability density
2 0.0004
3D
0
V3D/
2 0.0003
4
66
266 groups - 5 < M200 < 10 × 1013M /h 0.0002
4
2
3D
0 0.0001
V3D/
2
4
6 0.0000
0.0 1.0 2.0 3.0 4.0 0.0 1.0 2.0 3.0 4.0 0.0 1.0 2.0 3.0 4.0
R/R200 R/R200 R/R200
Fig. 3. Stacked phase-space diagrams for all gas cells (left panels), only hot gas (middle panels), and warm-hot inter-galactic
medium (right panels). All groups and clusters are considered in top panels, only galaxy clusters (with M200 > 1014 M /h) in the
middle panels, and only galaxy groups (with M200 = [5 − 10] × 1013 M /h) in bottom panels.
for all cluster environments, we normalize it by the overall outside clusters (identically to Mostoghiu et al. 2019; Da-
velocity dispersion σ3D , such as it is the root-mean-square cunha et al. 2021, for galaxy distribution). In more details,
of the radial gas velocity v3D within R200 of each cluster. we see that the virialised gas inside clusters (R < R200 )
The velocity-position diagram is commonly used to is the hot gas phase, as shown in top middle panel. This
probe the infall of galaxies into clusters (Dacunha et al. hot plasma is virialised, i.e. there is an equal balance be-
2021). We can consider typically three different dynamical tween inflow and outflow motions with low velocity values
regimes in the velocity-position diagram: (i) infalling ma- −2.5σ < vHM < 2.5σ. Focusing on the WHIM gas phase in
terial with v3D < 0 and R > R200 , (ii) backsplash material top right panel, we can distinguish two distinct dynamical
with v3D > 0 and R > R200 , and (iii) virialized material in- behaviors. At cluster peripheries, from ∼ 1 to ∼ 2 R200 , the
side clusters with R < R200 characterised by shell crossing WHIM gas is a combination of slowly infalling and back-
caustics in velocity-position diagrams. In this frame, galax- splash gas (−2σ < vW HIM < 2σ). In contrast to hot gas,
ies start their infall far from cluster center and increase the WHIM inflow and outflow motions are not balanced
their velocity as they approach the cluster. When they are and infalling gas is a significantly dominant. This means
close to the cluster, they first infall and then move away that this WHIM gas is accumulating at cluster peripheries,
from the cluster (to form the backsplash population), and by slowly infalling inside clusters and with a minor fraction
then they transit between infall and backsplash, until they which is ejected outside clusters. Beyond the cluster pe-
are captured by the gravitational potential wells of cluster, ripheries, at distances from 1.5 to 5R200 , the WHIM gas is
forming the virialised population (R < R200 ) (see figure 2 also rapidly infalling on clusters with high velocity values,
of Arthur et al. 2019, for a schematic view of phase-space typically −5σ < vW HIM < −2σ < v3D . According to Rost
plane). et al. (2021), gas is entering into clusters with turbulent
motions. This might explain that WHIM gas phase is accu-
In Fig. 3, we present phase-space diagram for gas in clus- mulated and ejected at cluster peripheries (∼ 1R200 ). More-
ter environments. They are obtained by stacking all gas cells over, Rost et al. (2021) have also shown that gas is preferen-
(left panels), only hot gas (middle panels), and only WHIM tially infalling from filaments. Therefore, one can suppose
gas (in right panels) for the 415 halo sample (top pan- that fast infalling WHIM (R > R200 and vW HIM < −2σ)
els), only the 149 galaxy clusters with M200 > 1014 M /h must be inside cosmic filaments whereas the WHIM back-
(middle panels), and only the galaxy groups with M200 = splash material (∼ R200 and vW HIM > 0) should leave the
[5 − 10] × 1013 M /h (bottom panels). In the top left panel, cluster centre outside filaments.
the stacked phase-space diagram of all gas cells in all cluster
environments shows the three dynamical regimes: virialised Regarding the halo mass dependency we can compare
gas inside clusters, infalling gas with high infalling veloc- middle and bottom panels showing clusters and groups of
ity, and splashback gas component with positive velocity galaxies, respectively. Focusing on all gas cells, there are
Article number, page 6 of 15Gouin et al.: Gas distribution from clusters to filaments in IllustrisTNG
not significant differences between clusters and groups. solid lines, and the errorbars are the errors on the mean
However considering hot and WHIM gas phases separately, computing by bootstrap re-sampling, (iii) the number of
we can see that galaxy groups and clusters have differ- objects used to compute the average in each bin (of x-axis)
ent dynamical behaviors. The hot gas is more spatially is written on the top of the figures in gray, (iv) the Spear-
extended inside galaxy clusters compared to groups, as al- man’s Rank correlation coefficient ρsp (X, βm ) is written on
ready found in the radial gas phase profile (Fig. 2).Also, we the figure, with X the cluster property and βm the multi-
can notice that only galaxy clusters present residual hot gas polar ratio at the multipole order m as defined below. The
distribution beyond R200 . This small fraction of infalling p-value of correlation coefficient remains lower than 10−3
hot gas must be associated with dense clumps of matter for each plots.
inside cosmic filaments as proposed by Angelinelli et al.
(2021). Regarding the WHIM velocity-position diagram,
we can see that warm gas dynamics is different for groups 4.1. Formalism of multipole moments Qm
and clusters. Whereas the WHIM gas phase is mostly in The aperture multipole moments of 2-D density field was
the form of fast infalling gas (high velocity and low velocity first introduced by Schneider & Bartelmann (1997) for weak
dispersion) outside galaxy clusters, WHIM gas around lensing map application. It consists in a multipole decompo-
groups is strongly accumulating at their outskirts (with sition of a surface density in harmonics modes m, integrated
large scatter in velocity, and backsplashing motion from 1 over a given radial aperture, such as:
to 2 R200 ). This suggests that WHIM gas phase is mostly
inside filaments at cluster peripheries, whereas WHIM gas
Z Rmax Z 2π
around groups is infalling and ejected at cluster peripheries. Qm (∆R) = R dR dφ eimφ Σ(R, φ) , (10)
Rmin 0
Radial gas properties summary where Σ(R, φ) is the 2-D matter distribution in polar coor-
We conclude that the hot gas is the dominant phase dinates centered on the cluster center. The 2-D radial aper-
inside cluster halos (R < R200 ), mostly governed by low ture ∆R = (Rmax , Rmin ) is also centered on the cluster
velocity dispersion of well-balanced inflow and outflow mo- center with Rmin and Rmax the radii delimitating the cir-
tions (|vHM | . 2.5σ). In contrast, outside groups and clus- cular shell. For illustration, we show the different azimuthal
ters (R > R200 ) the gas is mainly in the form of warm symmetries quantified by the multipole moments Qm in Fig
diffuse gas. The WHIM gas phase outside halos can be sep- A.1 with monopole (m = 0), dipole (m = 1), quadrupole
arated in two distinct dynamical regimes, accumulating gas (m = 2), etc. Using the multipolar expansion of 2-D mat-
slowly infalling from ∼ 1 to ∼ 2 R200 , and fast infalling gas ter distribution around galaxy clusters, this technique suc-
at distances larger than 1.5 R200 . Cluster peripheries are ceeded in highlighting both the elliptical shape of clusters
thus crucial places to probe the transition between hot and (see e.g. Clampitt & Jain 2016; Shin et al. 2018), and fila-
warm gas, and to probe the complex dynamics of infalling mentary patterns at cluster outskirts (Dietrich et al. 2005;
WHIM gas. In fact, this is in these regions that gas is ex- Mead et al. 2010; Gouin et al. 2017; Codis et al. 2017) from
pected to flow from filaments into clusters, with turbulent 2-D projected DM distribution.
motions (Rost et al. 2021; Vallés-Pérez et al. 2021), and In order to assess the relative weight of one azimuthal
where accretion shocks might arise (Shi et al. 2020; Zhang symmetry traced by the order m relatively to the circular
et al. 2020, 2021b; Zhu et al. 2021b). Following these find- one, we define the multipolar ratio βm such as
ings on the radial gas properties, we focus in the rest of the
paper our exploration of the azimuthal gas distribution in |Qm |
βm = , (11)
cluster environment concentrating on two main gas phases |Q0 |
in two different radial apertures: hot medium up to 1 R200
and WHIM from 1 to 2R200 . with |Qm | the modulus of the aperture multipole moment
at the order m. By decomposing surface mass density
in harmonic expansion terms, Schneider & Weiss (1991)
4. Azimuthal distribution as a proxy of structural have shown that |Q m|
|Q0 | −→ 1/2 for a matter distribution
properties of clusters Σ(θ) ∝ cos(2θm). Therefore, the value of multipolar ratio
βm varies between 0 and 1/2, such that βm = 0 for a circular
In this section, we define the aperture multipole formal- matter distribution and βm = 1/2 for a matter distribution
ism, and use this technique on gas azimuthal distribution describing the azimuthal symmetry at the order m (see also
to statistically highlight angular-dependent features in com- Vallés-Pérez et al. 2020, for a similar definition).
parison to the "reference" DM distribution. This technique Here, we aim at probing different aspherical features
focuses on 2-D spatial distribution, and has thus the ad- from the dipolar signature traced by m = 1, to large har-
vantage of being easily applicable on observational data monic orders (small angular scale patterns) up to m = 9.
as was done on weak lensing maps (Dietrich et al. 2005) Indeed, Gouin et al. (2020) showed that azimuthal mat-
and on projected photometric galaxy distribution (Gouin ter distribution away from the cluster centers can be de-
et al. 2020). The azimuthal symmetries of gas and DM are scribed by the sum of multipolar moments from m = 1 to
explored as a function of cluster structural properties (de- m ∼ 9, tracing multi-angular scale filamentary patterns.
fined in Sect. 2), to probe if they are good tracers of the We present in appendix Fig. A.2 the evolution of the differ-
structural features of cluster halos. ent multipolar ratio βm as a function of radial distance for
In this section and the next one, a general colour m = 1 to 9. As expected, the multipolar ratio increase with
and style code is used in the plots such as: (i) Hot gas, the radial distances, similarly to the more commonly used
WHIM, and dark matter are respectively in red, orange azimuthal scatter technique (Eckert et al. 2015). Indeed,
and blue/black colors, (ii) the mean profiles are shown by anisotropy of matter distribution is expected to increase
Article number, page 7 of 15A&A proofs: manuscript no. main
Fig. 4. Illustration of the dark matter (left), hot gas (middle) and WHIM (right) 2-D projected distribution up to 5R200 of one
simulated galaxy cluster. The cyan ellipse on dark matter traces the ellipticity of the DM halo (2D
DM ) as discussed in 2.
with the radial distance from halo center, as also detailed mass. We find that the dipolar symmetry of DM and hot gas
in Despali et al. (2017) for the ellipticity term. traces well the center offset of clusters, with a correlation
From the equations 10 and 11, we have computed the coefficient between β1 and Rof f is larger than ρSP > 0.5.
multipolar ratio βm for m from 1 to 9, in both (hot and Notice that, as expected by taking into account larger mass
WHIM) gas and DM distribution for each cluster. We have distribution up to 2 R200 we increase the correlation be-
projected matter distribution enclosed inside sphere of ra- tween dipolar ratio β1 and center offset.
dius R3D = 5R200 centered on each clusters considering the The top right panel shows the level of quadrupolar
three different projection axes (along x-, y- and z- axis) of symmetry (with m = 2) as a function of the 2-D ellip-
the simulation box. Therefore, the cluster sample increases ticity of DM halo. In agreement with the previous stud-
from 415 clusters to 1245 2-D projected maps of cluster ies (Clampitt & Jain 2016; Shin et al. 2018), we confirm
mass distribution. In Fig. 4, we show an example of the that the quadrupolar decomposition of DM density field
DM, the hot medium and the WHIM 2-D projected distri- is strongly correlated with the elliptical shapes of halos
bution around a simulated cluster. As discussed in Sect. 3, with ρSP ∼ 0.8. Notice that increasing the radial aper-
the hot gas is mostly located inside the cluster halo (typi- ture above R200 does not drastically increase the correla-
cally < R200 ), whereas WHIM traces the infalling gas out- tion coefficient, suggesting that the halo shape information
side cluster. In the following, we will thus focus on the hot is mostly contained inside R200 . We also found a good cor-
medium to explore the gas inside clusters, and the WHIM relation between the quadrupolar symmetry of hot gas and
to probe the gas filamentary pattern outside clusters. the DM ellipsoidal shape. In fact, Okabe et al. (2018) have
shown that gas distribution follows the elliptical shape of
DM but tends to be more circular due to the dissipative
4.2. Impact of cluster structural properties baryonic processes (see also Velliscig et al. 2015). We find
Let us now explore the azimuthal symmetries traced by hot that the hot gas quadrupolar signature is smaller than the
gas and DM distribution inside clusters, and see if they are DM (β2DM > β2hot gas ), confirming that the hot gas dis-
related to the structural properties of cluster halos. We thus tribution tends to be more circular than DM one. This is
focus here on different angular properties of matter distri- also illustrated in Fig. B.1 in appendix and it confirms re-
bution by considering the multipolar ratio βm at different lations between both hot gas and DM ellipticity, and their
multipolar order m. Following the description in Sect. 2, quadrupoles.
the structural properties we will consider are: the halo el- In the bottom left panel of Fig. 5, we extend our investi-
lipticity, , the center offset, Rof f , and the mass fraction of gation to the 3-D elliptical halo shape. As expected, the cor-
substructures, fsub . relation between ellipticity and quadrupole remains strong,
In Fig. 5, we show the multipolar ratio βm and its mean, even if high 3-D ellipticity (3D > 0.15) is degenerate with
considering different radial apertures R, and as a function the 2-D quadrupolar ratio. Indeed due to projection effects,
the structural properties of cluster halo. The multipolar mo- strongly-elliptical halo shape can produce low quadrupolar
ments and their ratios have been computed for both DM (at signature. This degeneracy is reduced by considering larger
different radial apertures) and hot gas (with radial aperture radial aperture, such that for a radial aperture of 2R200 , the
R < R200 ) distributions, and are respectively in blue and quadrupolar ratio and 3-D ellipticity are strongly correlated
red, respectively. with a Spearman coefficient ρSP ∼ 0.5.
In the top left panel, we show the possible correlation In the bottom right panel of Fig. 5, we finally probe
between the center offset and the dipolar symmetry traced the amount of mass inside sub-halos via the substructure
by β1 . We focus on m = 1, because the dipolar symmetric fraction. To quantify this last structural property, the best
excess must in principle reflect the mis-centering of mass choice is to consider larger harmonic orders meaning small
distribution, whereas the offset center parameter directly angular scale decomposition. We directly sum multipolar
quantifies differences between peak center and center of ratios βm from m = 3 to 9 to obtain the overall level of az-
Article number, page 8 of 15Gouin et al.: Gas distribution from clusters to filaments in IllustrisTNG
0.5 0.5
459 222 195 180 168 DM with R=[0 0.5]R200
DM with R=[0 1]R200 61 178 218 223 310 255 SP= 0.55
DM with R=[0 2]R200 SP= 0.80
0.4 Hot Gas with R=[0 1]R200 0.4 SP= 0.82
SP= 0.59
0.3 0.3
SP= 0.39
2(R)
1(R)
SP= 0.60
0.2 SP= 0.70 0.2
SP= 0.56
0.1 0.1
0.0 0.0
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Roff DM
2D
0.5 0.7
42 354 282 192 126 132 117 SP= 0.19
81 219 315 291 144 114 81 SP= 0.25
SP= 0.40 0.6 SP= 0.38
0.4 SP= 0.50 SP= 0.59
SP= 0.37 0.5 SP= 0.34
0.3
0.4
3, . . . , 10(R)
2(R)
0.2 0.3
0.2
0.1
0.1
0.0 0.0
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.1 0.2 0.3 0.4 0.5
DM fsub
3D
Fig. 5. Top left panel: Distribution of βm dipole contribution (m = 1) as a function of the center of mass offset. Top right panel:
Distribution of βm quadrupole contribution (m = 2) as a function of the 2-D ellipticity of DM. Bottom left panel: Distribution of
βm quadrupole contribution (m = 2) as a function of the 3-D ellipticity of DM. Bottom right panel: High azimuthal symmetries
βm contribution (summing contributions from m = 3, 4, 5, 6, 7, 8, 9) as a function of the mass fraction of substructures.
The mean profiles of β are shown by solid lines, and the errorbars are the errors on the mean computing by bootstrap re-sampling.
The β values for the DM distribution with apertures R < 0.5 × R200 ,R < 1 × R200 and R < 2 × R200 , are respectively plotted in
light, medium, and dark blue. The β values for 2-D hot gas distribution with R < R200 is plotted in red.
imuthal symmetries for small angular scales, and compare as shown by its significant correlation with the halo prop-
it to the fraction of substructures. Multipolar ratio and fsub erties. The hot gas plasma distribution remains smoother
tend to correlate well for both hot gas and DM with corre- and more circular than DM with lower values of multipolar
lation coefficients around ρSP ∼ 0.4. In particular, we can ratio βm for almost all orders m.
distinguish between small (fsub < 0.1) and high substruc-
ture fractions (fsub > 0.1) which is an important criterion
to separate dynamically relaxed and non-relaxed clusters
(Cui et al. 2017). Notice that, as the same as for 3-D ellip-
5. Azimuthal distribution related to cluster
ticity, by considering large radial apertures (R < 2R200 ), we physical properties
increase significantly the correlation between the substruc- In this section, we will not attempt to distinguish between
ture fraction and the level of azimuthal symmetries up to the different angular features in 2-D mass distribution, but
ρSP ∼ 0.6. rather on assessing whether the overall departure from cir-
We have shown that different angular features quanti- cular symmetry can be related to cluster physical proper-
fied by multipolar ratios at different orders m are power- ties. We thus focus on a single variable β to estimate the
ful tracers of distinct structural properties of cluster halos. amount of azimuthal symmetries that are in excess com-
Even when considering 2-D azimuthal distribution, the cor- pared to the circular one:
relation with the 3-D structural properties is strong, and
can be further improved by integrating matter distribution N
beyond R200 . Moreover, the azimuthal hot plasma distribu-
X
β= βm . (12)
tion appears to follow well the azimuthal DM distribution, m=1
Article number, page 9 of 15A&A proofs: manuscript no. main
0.5 1.0 39 369 474 264 75 24
339 459 255 108 81 Dark matter
Hot gas
0.4 All gas
0.8
SP= 0.09
(R = [0 1]R200)
SP= -0.16
(R = [1 2]R200)
0.3
0.6
SP= 0.14
0.2
0.4
0.1 SP= 0.21
0.2 SP= 0.29
Dark matter
0.0 WHIM
Dark matter 0.0
WHIM 1 2 3 4 5 6 7
Connectivity
0.8
SP= 0.11 Fig. 7. Distribution of the azimuthal symmetric excess β (as
(R = [1 2]R200)
defined in Eq. 12) computed at cluster peripheries in (1 <
0.6 SP= 0.36
R[R200 ] < 2) as a function of the halo connectivity, for DM
(black) and WHIM (orange). The mean profiles of β and their
errors are shown in solid lines.
0.4
0.2 5.1. Mass and connectivity dependency
We first discuss the relation between departures from circu-
0.0 lar symmetry and the cluster mass, inside (R < R200 ) and
13.8 14.0 14.2 14.4 14.6 14.8 15.0 at the cluster outskirts (1 < R[R200 ] < 2) shown in top and
log(M200[M /h]) bottom panels of Fig. 6, respectively.
Fig. 6. Distribution of the azimuthal symmetric excess β (as Focusing on the dark matter distribution inside halos
defined in Eq. 12) as a function of the halo mass, inside clusters (R < R200 ), we note that the azimuthal symmetric excess
(R < R200 ) in the top panel, and at cluster peripheries in (1 < is slowly increasing with the cluster mass, on average. In
R[R200 ] < 2) in the bottom panel. The mean profiles of β and fact, the non-circularity quantified by β is strongly domi-
their errors are shown in solid lines. The color of points and lines nated by the quadrupole (m = 2) inside clusters, and traces
represent different matter component: dark matter (black), hot
the elliptical halo shape, as discussed previously in Sect. 4
gas (red), WHIM (orange), and all gas (light brown).
and illustrated in Fig. B. Therefore, the increase of the az-
imuthal symmetric excess with the halo mass must reflect
the increase of the DM halo ellipticity, in agreement with
Despali et al. (2014). Nevertheless, we find that the correla-
tion between the DM azimuthal symmetric excess and halo
This azimuthal symmetric excess, β, is the defined as the mass is low, with ρSP ∼ 0.1.
sum all the azimuthal symmetry contributions up to the or- Focusing on the hot gas inside clusters, we found that
der N . As discussed in Appendix A, we have chosen N = 4 the anisotropy of hot gas distribution tends to decrease
because adding larger orders (from 5 to 9) do not alter the with the halo mass. Hot gas in galaxy groups (M200 <
conclusions of this section. Indeed, each multipole orders 1014 M /h) appears more asymmetric than in massive clus-
from m = 5 to 9 contributes to less than 10% to the matter ters, on average. This might be explained be the fact that,
multipolar expansion, and thus, they constitute minor har- as detailed in Sect. 3, hot gas is not the dominant com-
monic orders to represent matter distribution (as shown in ponent in groups (representing only 68% of all gas) and is
Fig. A.2). concentrated in the core of galaxy groups (hot gas is only
dominant up to R ∼ 0.6). In contrast, the ICM of mas-
Based on the analysis of the radial gas distribution dis- sive clusters is almost exclusively in the form of hot plasma
cussed in Sect. 3, we focus on two radial apertures and and spatially extends up to R ∼ 1.2. One can thus inter-
two gas phases. First, we consider the interior of clusters pret that behaviour by the fact that hot gas material inside
(R < R200 ) and we investigate the azimuthal symmetric ex- massive clusters is mostly gravitationally heated whereas in
cess β of both hot plasma and DM distributions. Secondly, galaxy groups the hot gas distribution might be governed by
we consider the cluster peripheries (1 < R[R200 ] < 2) and anisotropic accretion processes, and thus, it appears highly
investigate the filamentary patterns in WHIM and DM az- asymmetric. In accord with this interpretation, we found
imuthal distribution via the β variable. Notice that we have that considering all gas cells inside group and cluster ha-
also studied the azimuthal matter distribution for larger ra- los, the anti-correlation between azimuthal symmetry of gas
dial apertures from 2 to 5 R200 . We found a weak correlation component and halo mass is removed. It means that only
between the cluster physical properties and the azimuthal the hot plasma medium is strongly anisotropic inside galaxy
gas distribution for apertures 2 < R[R200 ] < 3, and the two groups.
quantities become uncorrelated beyond radial distances of Focusing on cluster peripheries from 1 to 2 R200 in bot-
3R200 . tom panel of Fig. 6, we show that the anisotropic signa-
Article number, page 10 of 15Gouin et al.: Gas distribution from clusters to filaments in IllustrisTNG
tures of DM and WHIM are increasing with the cluster sult is in agreement with previous investigations on ICM
mass. The small increase of DM azimuthal symmetric ex- asymmetry to probe cluster dynamical state (Vazza et al.
cess with halo mass, must be induced by the amount of 2011; Eckert et al. 2012; Capalbo et al. 2021). Moreover, at
filamentary structures which are expected to be more mas- cluster peripheries the azimuthal distribution of WHIM and
sive and more numerous around massive objects compared DM also trace well the cluster relaxation level. This can be
to low-mass one (Aragón-Calvo et al. 2010b; Codis et al. explained by the fact that the cluster dynamical state must
2018; Sarron et al. 2019; Kraljic et al. 2020; Gouin et al. be affected by the number of cosmic filaments connected to
2021). Regarding the azimuthal level of WHIM gas, there is clusters, as shown in Gouin et al. (2021).
a strong mass dependency: WHIM distribution around mas- Secondly, the influence of the cluster mass-assembly his-
sive clusters is significantly more asymmetric than around tory on the azimuthal matter distribution is investigated by
low-mass groups. In fact, we see in Fig. 3 that WHIM gas considering two variables, the mass accretion rate and the
from 1 to 2 R200 is rapidly infalling into massive clusters, formation redshift of clusters in the middle and right pan-
whereas WHIM in galaxy group environments is slowly in- els, respectively. Both cluster accretion history proxies are
falling and back-splashing. In agreement with this dynam- correlated with gas and DM azimuthal symmetric excess,
ical picture, one can expect that WHIM gas is strongly in particular inside cluster halo, with ρSP ∼ 0.6. The faster
asymmetric around massive objects because it is infalling the cluster accretes material and the more recently formed,
along filamentary structures. This is consistent with Rost the more asymmetric its hot medium. This is coherent with
et al. (2021) who found that gas preferentially enters into the result of Chen et al. (2020) who show that the ellipticity
massive clusters funneled by filaments. In contrast, WHIM of ICM seems to be an imprint of the mass assembly his-
around groups are more isotropically distributed because it tory of clusters. Besides the ICM, we found that WHIM and
is rather accumulating (and ejected) at group peripheries, DM inside the filamentary structure at the cluster periph-
and thus it must trace filaments more faintly. ery shows a similar tendency. Indeed, Gouin et al. (2021)
To confirm if WHIM anisotropic distribution outside have shown that the cosmic filaments connected to clusters
clusters is in general the result of filamentary pattern sur- affect cluster assembly history. Nevertheless, the correla-
rounding them, we show in Fig. 7 the azimuthal symmetric tion between the azimuthal symmetry and mass-assembly
excess β as a function of the connectivity of halos. As we can history decreases up to ρSP ∼ 0.3 at cluster peripheries,
see, the number of cosmic filaments that are connected to suggesting that the mass distribution in the inner regions
clusters and the departure from spherical symmetry are sig- is more sensitive to the cluster past accretion history.
nificantly correlated for both the DM and the WHIM gas-
phase. In agreement with Galárraga-Espinosa et al. (2021a)
who found that WHIM gas phase is strongly dominant in 6. Conclusions
cosmic filaments, we conclude that azimuthal distribution In this study, we have explored how gas and DM compo-
of WHIM tends to follow DM by tracing cosmic filamentary nents is distributed in galaxy cluster environments from
structures connected to clusters at their peripheries. their cores to their connection to cosmic filaments. We fo-
cused on the matter distribution in 415 galaxy clusters envi-
5.2. Accretion history dependency ronments, defined as the region extending up to 5R200 , ex-
tracted from the IllustrisTNG simulation. Their gas phases,
We have seen that the hot plasma traces well the halo prop- defined thanks to the temperature-density diagram, and
erties of clusters, whereas the WHIM azimuthal distribution their motions were first investigated as a function of cluster-
correlates with filamentary patterns connected to clusters. centric distances and cluster masses. This allowed us to
Given these findings, one can ask oneself whether the gas identify the most relevant gas phases and radial apertures
azimuthal distribution can also trace the overall cluster dy- to further study the azimuthal distribution of the gas in
namics and its recent mass-assembly history, as well as DM. clusters. By decomposing the matter distribution in har-
We refer here to Sect. 2, for details on the mass accretion monic space, we statistically explored the angular features,
rate Γ (see Eq. 1) and the formation redshift zf orm (see also called azimuthal symmetries, in gas and DM distri-
Eq. 2) which are two proxies of cluster mass-assembly his- butions around clusters. Previous multipolar expansion of
tory, and the relaxedness parameter χDS used to estimate dark matter (Gouin et al. 2017) and galaxy (Gouin et al.
cluster dynamical stat (see Eq. 6). 2020) distributions in cluster environments have revealed
In Fig. 8, we show the dependency of azimuthal symmet- the usefulness of this approach to statistically probe the
ric excess β with the different cluster properties: relaxed- cosmic filamentary pattern outside clusters. In the present
ness (left panels), mass accretion rate (middle panels), and extension to these Gouin et al. (2017) and Gouin et al.
formation redshift (right panels). The azimuthal symmet- (2020) studies, we focused on gas distribution to explore
ric excess of hot gas and DM inside clusters (R < R200 ) is how azimuthal symmetries of gas in different phases trace
presented in the top panels, whereas the bottom ones show cluster physical and dynamical properties as well as the
the WHIM and DM anisotropic level at cluster peripheries "reference" dark matter distribution. The radial and az-
(1 < R[R200 ] < 2). imuthal gas distribution from clusters inner regions to their
The departure from circular symmetry is fist analysed connection to filaments shows that:
as a function of the relaxation level of clusters (left panels).
We found that, the more circular the matter distribution (1) Galaxy cluster environments are key places regions
(β −→ 0) the more dynamically relaxed the cluster halo where the warm diffuse gas is infalling into clusters, and
(χDS > 1). Inside clusters, halo relaxedness and asymme- heated to become the hot plasma inside cluster cores (as
try are strongly correlated for both DM and hot gas, with also discussed by Martizzi et al. 2019, in the large cosmic
ρSP ∼ 0.5, showing that the azimuthal distribution of hot web picture). In detail, the hot gas phase is dominant
plasma is a powerful probe of cluster dynamics. This re- inside clusters, up to around 1 R200 , and is well virialised
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