IllustrisTNG Simulations Research Articles

The relationship between galaxy and halo sizes in the Illustris and IllustrisTNG simulations

ABSTRACT Abundance matching studies have shown that the average relationship between galaxy radius and dark matter halo virial radius remains nearly constant over many orders of magnitude in halo mass, and over cosmic time since about z = 3. In this work, we investigate the predicted relationship between galaxy radius re and halo virial radius Rh in the numerical hydrodynamical simulations Illustris and IllustrisTNG from z ∼ 0–3, and compare with the results from the abundance matching studies. We find that Illustris predicts much higher re/Rh values than the constraints obtained by abundance matching, at all redshifts, as well as a stronger dependence on halo mass. In contrast, IllustrisTNG shows very good agreement with the abundance matching constraints. In addition, at high redshift it predicts a strong dependence of re/Rh on halo mass on mass scales below those that are probed by existing observations. We present the predicted re/Rh relations from Illustris and IllustrisTNG for galaxies divided into star forming and quiescent samples, and quantify the scatter in re/Rh for both simulations. Further, we investigate whether this scatter arises from the dispersion in halo spin parameter and find no significant correlation between re/Rh and halo spin. We investigate the paths in re/Rh traced by individual haloes over cosmic time, and find that most haloes oscillate around the median re/Rh relation over their formation history.

Effects of baryonic feedback on the cosmic web

We study the effect of baryons on the cosmic web---halos, filaments, walls, and voids. To do so, we apply a modified version of NEXUS, a cosmic web morphological analysis algorithm, to the IllustrisTNG simulations. We find that halos lose more than 10% of their mass due to baryons, mostly to filaments and a small portion to walls and voids. However, the mass transfer does not significantly shift the boundaries of structures, leaving the volume fractions of the cosmic structures largely unaffected. We quantify the effects of baryonic feedback on the power spectrum and the probability density function of the density field for individual cosmic structures. For the power spectrum, most suppression due to feedback can be accounted for by including $M\ensuremath{\ge}{10}^{12}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}/h$ halos, without considering other cosmic structures. However, when examining the probability density function of the density field, we find nearly 100% suppression of the emptiest regions and 10%-level effects (boost or suppression) in the remaining regions of filaments, walls, and voids. Our results indicate the importance of modeling the effects of baryons in the whole cosmic web, not just halos, for cosmological analysis beyond two-point statistics or field-based inferences.

The contribution of magnetized galactic outflows to extragalactic Faraday rotation

ABSTRACT Galactic outflows driven by star formation and active galactic nuclei blow bubbles into their local environments, causing galactic magnetic fields to be carried into intergalactic space. We explore the redshift-dependent effect of these magnetized bubbles on the Faraday rotation measure (RM) of extragalactic radio sources. Using the IllustrisTNG cosmological simulations, we separate the contribution from magnetic bubbles from that of the volume-filling magnetic component expected to be due to the seed field originating in the early universe. We use this separation to extract the redshift dependence of each component and to compare IllustrisTNG model predictions with observation measurements of the NRAO VLA sky survey (NVSS). We find that magnetized bubbles provide a sizeable contribution to the extragalactic RM, with redshift-independent 〈|RM|〉 ≃ 13 rad/m2 for sources at redshifts z ≥ 2. This is close to the mean residual RM of 16 rad/m2 found from NVSS data in this redshift range. Using the IllustrisTNG simulations, we also evaluate a simple model for the contribution to residual RM from individual host galaxies and show that this contribution is negligible at high-redshift. While the contribution from magnetic bubbles in the IllustrisTNG model is currently compatible with observational measurements of residual RM, the next-generation RM sky surveys, which will be free from the wrapping uncertainty, have larger statistics and better sensitivity should be able to observe predicted flat contribution from magnetic bubbles at large redshifts. This should allow to experimentally probe magnetic bubbles and check models of galaxy feedback in cosmological simulations.

Shock-induced Stripping of the Satellite Interstellar and Circumgalactic Medium in IllustrisTNG Clusters at Z ∼ 0

Using the IllustrisTNG simulation, we study the interaction of large-scale shocks with the circumgalactic medium (CGM) and interstellar medium (ISM) of star-forming (SF) satellite galaxies in galaxy clusters. These shocks are usually produced by mergers and massive accretion. Our visual inspection shows that approximately half of SF satellites have encountered shocks in their host clusters at z ≤ 0.11. After a satellite crosses a shock front and enters the post-shock region, the ram pressure on it is boosted significantly. Both the CGM and ISM can be severely impacted, either by stripping or compression. The stripping of the ISM is particularly important for low-mass galaxies with and can occur even in the outskirts of galaxy clusters. In comparison, satellites that do not interact with shocks lose their ISM only in the inner regions of clusters. About half of the ISM is stripped within about 0.6 Gyr after it crosses the shock front. Our results show that shock-induced stripping plays an important role in quenching satellite galaxies in clusters.

DS+: A method for the identification of cluster substructures

Context. The study of cluster substructures is important for the determination of the cluster dynamical status, assembly history, and the evolution of cluster galaxies, and it allows us to set constraints on the nature of dark matter and cosmological parameters. Aims. We present and test DS+, a new method for the identification and characterization of group-sized substructures in clusters. Methods. Our new method is based on the projected positions and line-of-sight (l.o.s. hereafter) velocities of cluster galaxies, and it is an improvement and extension of the traditional method of Dressler & Shectman (1988, AJ, 95, 985). We tested it on cluster-size cosmological halos extracted from the IllustrisTNG simulations, with virial masses 14 ≲ log(M200/M⊙) ≲ 14.6 that contain ~190 galaxies on average. We also present an application of our method on a real data set, the Bullet cluster. Results. DS+ is able to identify ~80% of real group galaxies as members of substructures, and at least 60% of the galaxies assigned to substructures belong to real groups. The physical properties of the real groups are significantly correlated with those of the corresponding detected substructures, but with significant scatter, and they are overestimated on average. Application of the DS+ method to the Bullet cluster confirms the presence and main properties of the high-speed collision and identifies other substructures along the main cluster axis. Conclusions. DS+ proves to be a reliable method for the identification of substructures in clusters. The method is made freely available to the community as a Python code.

Interacting galaxies in the IllustrisTNG simulations − IV: enhanced supermassive black hole accretion rates in post-merger galaxies

ABSTRACT We present an analysis of the instantaneous supermassive black hole (SMBH) accretion rates in a collection of 1563 post-merger galaxies drawn from the IllustrisTNG simulation. Our sample consists of galaxies that have experienced a merger in the last simulation snapshot (within ∼ 160 Myrs of coalescence) in the redshift range 0 < z < 1, with merger stellar mass ratios >1: 10 and post-merger stellar masses >1010M⊙. We find that, on average, the accretion rates of the post-mergers are ∼1.7 times higher than in a control sample and that post-mergers are three to four times more likely to experience a luminous active galactic nuclei (AGN) phase than isolated galaxies. SMBH accretion rate enhancements persist for ∼2 Gyrs after coalescence, significantly exceeding the ∼500 Myr lifetime of star formation rate enhancements. We find that the presence of simultaneous enhancements in both the star formation and SMBH accretion rates depends on both the mass ratio of the merger and on the gas mass of the post-merger galaxy. Despite these accretion rate enhancements, only ∼35 per cent of post-mergers experience a luminous AGN (Lbol > 1044erg/s) within 500 Myrs after coalescence, and fewer than 10 per cent achieve a luminosity in excess of Lbol > 1045erg/s. Moreover, only ∼10 per cent of the highest luminosity (Lbol > 1045erg/s) AGN in the IllustrisTNG galaxy sample are recent mergers. Our results are therefore consistent with a picture in which mergers can (but do not always) trigger AGN activity, but where the majority of galaxies hosting high luminosity AGN are not recent mergers.

Formation of a barred galaxy in a major merger: The role of AGN feedback

Among the many processes involved in galaxy evolution, those of bar formation, quenching, and feedback from an active galactic nucleus (AGN) seem to be connected, however, the nature of these relations remains unclear. In this work, we aim to elucidate them by studying the formation of a barred galaxy in a major merger of two disks in the IllustrisTNG simulations. This merger involves a coalescence of two supermassive black holes and a sudden switch to the kinetic mode of AGN feedback implemented in the simulations, which leads to the removal of the gas from the inner part of the galaxy, followed by quenching of star formation and the formation of the bar. This causal relation between AGN feedback and bar formation explains a number of correlations observed in the data, such as the higher frequency of bars among red spirals and the presence of central gas holes in barred galaxies. In such a picture, the bars do not feed the black holes, so their presence does not increase the AGN strength, and they do not cause quenching. However, bars do form in regions characterized by a low gas fraction resulting from AGN feedback. This scenario is probably applicable to many barred galaxies, not only those formed in major mergers.

Modelling the galaxy–halo connection with semi-recurrent neural networks

ABSTRACT We present an artificial neural network design in which past and present-day properties of dark matter haloes and their local environment are used to predict time-resolved star formation histories and stellar metallicity histories of central and satellite galaxies. Using data from the IllustrisTNG simulations, we train a tensorflow-based neural network with two inputs: a standard layer with static properties of the dark matter halo, such as halo mass and starting time; and a recurrent layer with variables such as overdensity and halo mass accretion rate, evaluated at multiple time steps from 0 ≤ z ≲ 20. The model successfully reproduces key features of the galaxy halo connection, such as the stellar-to-halo mass relation, downsizing, and colour bimodality, for both central and satellite galaxies. We identify mass accretion history as crucial in determining the geometry of the star formation history and trends with halo mass such as downsizing, while environmental variables are important indicators of chemical enrichment. We use these outputs to compute optical spectral energy distributions, and find that they are well matched to the equivalent results in IllustrisTNG, recovering observational statistics such as colour bimodality and mass–magnitude diagrams.

Finding the Missing Baryons in the Intergalactic Medium with Localized Fast Radio Bursts

The missing baryon problem is one of the major unsolved problems in astronomy. Fast radio bursts (FRBs) are bright millisecond pulses with unknown origins. The dispersion measure of FRBs is defined as the electron column density along the line of sight, and accounts for every ionized baryon. Here we measure the baryon content of the universe using 22 localized FRBs. Unlike previous works that fixed the value of dispersion measure of FRB host galaxies and ignored the inhomogeneities of the intergalactic medium (IGM), we use the probability distributions of dispersion measures contributed by host galaxies and IGM from the state-of-the-art IllustrisTNG simulations. We derive the cosmic baryon density of (1σ), with a precision of 7.0%. This value is dramatically consistent with other measurements, such as the cosmic microwave background and Big Bang nucleosynthesis. Our work supports that the baryons are not missing, but residing in the IGM.

Mock galaxy surveys for HST and JWST from the IllustrisTNG simulations

ABSTRACT We present and analyse a series of synthetic galaxy survey fields based on the IllustrisTNG simulation suite. With the IllustrisTNG public data release and JupyterLab service, we generated a set of 12 light-cone catalogues covering areas from 5 to 365 square arcmin, similar to several JWST Cycle 1 programs, including JADES, CEERS, PRIMER, and NGDEEP. From these catalogues, we queried the public application programming interface to generate simple mock images in a series of broad-band filters used by JWST-NIRCam and the Hubble Space Telescope cameras. This procedure generates wide-area simulated mosaic images that can support investigating the predicted evolution of galaxies alongside real data. Using these mocks, we demonstrate a few simple science cases, including morphological evolution and close pair selection. We publicly release the catalogues and mock images through MAST, along with the code used to generate these projects, so that the astrophysics community can use these products in their scientific analyses of JWST deep field observations.

The main sequence of star-forming galaxies across cosmic times

ABSTRACT By compiling a comprehensive census of literature studies, we investigate the evolution of the main sequence (MS) of star-forming galaxies (SFGs) in the widest range of redshift (0 < z < 6) and stellar mass (108.5–1011.5 M⊙) ever probed. We convert all observations to a common calibration and find a remarkable consensus on the variation of the MS shape and normalization across cosmic time. The relation exhibits a curvature towards the high stellar masses at all redshifts. The best functional form is governed by two parameters: the evolution of the normalization and the turnover mass (M0(t)), which both evolve as a power law of the Universe age. The turn-over mass determines the MS shape. It marginally evolves with time, making the MS slightly steeper towards z ∼ 4–6. At stellar masses below M0(t), SFGs have a constant specific SFR (sSFR), while above M0(t) the sSFR is suppressed. We find that the MS is dominated by central galaxies. This allows to turn M0(t) into the corresponding host halo mass. This evolves as the halo mass threshold between cold and hot accretion regimes, as predicted by the theory of accretion, where the central galaxy is fed or starved of cold gas supply, respectively. We, thus, argue that the progressive MS bending as a function of the Universe age is caused by the lower availability of cold gas in haloes entering the hot accretion phase, in addition to black hole feedback. We also find qualitatively the same trend in the largest sample of star-forming galaxies provided by the IllustrisTNG simulation. Nevertheless, we still note large quantitative discrepancies with respect to observations, in particular at the high-mass end. These can not be easily ascribed to biases or systematics in the observed SFRs and the derived MS.

The origin and properties of red spirals: Insights from cosmological simulations

A significant fraction of spiral galaxies are red, gas-poor, and have low star formation rates (SFRs). We study these unusual objects using the IllustrisTNG100 simulation. Among 1912 well-resolved disk galaxies selected from the last simulation output, we identify 377 red objects and describe their properties and origins using a few representative examples. The simulated red spirals turn out to be typically very gas-poor, have very low SFRs, are more metal-rich, and have larger stellar masses than the remaining disks. Only about 13% of red spirals suffered strong mass loss and thus could have resulted from environmental quenching by ram pressure and tidal stripping of the gas, or similar processes. The majority of red disks were probably quenched by feedback from the active galactic nucleus (AGN). This conclusion is supported by the higher black hole masses and lower accretion rates of red disks, as well as the larger total AGN feedback energies injected into the surrounding gas in the kinetic feedback mode implemented in the IllustrisTNG simulations. The timescales of the gas loss correlate with the black hole growth for the AGN-quenched galaxies and with the dark-matter loss for the environmentally quenched ones. The red spirals are more likely to possess bars, and their bars are stronger than in the remaining disks, which is probably the effect of gas loss rather than the reason for quenching.

The merger fraction of post-starburst galaxies in UNIONS

ABSTRACT Post-starburst galaxies (PSBs) are defined as having experienced a recent burst of star formation, followed by a prompt truncation in further activity. Identifying the mechanism(s) causing a galaxy to experience a post-starburst phase therefore provides integral insight into the causes of rapid quenching. Galaxy mergers have long been proposed as a possible post-starburst trigger. Effectively testing this hypothesis requires a large spectroscopic galaxy survey to identify the rare PSBs as well as high-quality imaging and robust morphology metrics to identify mergers. We bring together these critical elements by selecting PSBs from the overlap of the Sloan Digital Sky Survey and the Canada–France Imaging Survey and applying a suite of classification methods: non-parametric morphology metrics such as asymmetry and Gini-M20, a convolutional neural network trained to identify post-merger galaxies, and visual classification. This work is therefore the largest and most comprehensive assessment of the merger fraction of PSBs to date. We find that the merger fraction of PSBs ranges from 19 per cent to 42 per cent depending on the merger identification method and details of the PSB sample selection. These merger fractions represent an excess of 3–46× relative to non-PSB control samples. Our results demonstrate that mergers play a significant role in generating PSBs, but that other mechanisms are also required. However, applying our merger identification metrics to known post-mergers in the IllustrisTNG simulation shows that 70 per cent of recent post-mergers (≲200 Myr) would not be detected. Thus, we cannot exclude the possibility that nearly all PSBs have undergone a merger in their recent past.

The Origin of the Relation Between Stellar Angular Momentum and Stellar Mass in Nearby Disk-dominated Galaxies

The IllustrisTNG simulations reproduce the observed scaling relation between the stellar specific angular momentum (sAM) j s and mass M s of central galaxies. We show that the local j s–M s relation develops at z ≲ 1 in disk-dominated galaxies. We provide a simple model that describes well such a connection between halos and galaxies. The index of 0.55 of the j s–M s relation comes from the product of the indices of the , , and j s ∝ j tot relations, where j tot and M tot are the overall sAM and mass of the halo, respectively. A non-negligible deviation from tidal torque theory, which predicts , should be included. This model further suggests that the stellar-to-halo mass ratio of disk galaxies increases monotonically following a nearly power-law function that is consistent with the latest dynamical measurements. Biased collapse, in which galaxies form from the inner and lower sAM portion of their parent halos, has a minor effect at low redshifts. The retention factor of angular momentum reaches ∼1 in disk galaxies with strong rotations, and it correlates inversely with the mass fraction of the spheroidal component, which partially explains the morphological dependence of the j s–M s relation.

Reorientation Rates of Structural and Kinematic Axes in Simulated Massive Galaxies and the Origins of Prolate Rotation

In this work, we analyze a sample of ∼4000 massive (M * ≥ 1011 M ⊙ at z = 0) galaxies in TNG300, the (300Mpc)3 box of the IllustrisTNG simulation suite. We characterize the shape and kinematics of these galaxies with a focus on the kinematic misalignment (Ψint) between the angular momentum (AM) and morphological major axis. We find that the traditional purely shape- or kinematics-based classifications are insufficient to characterize the diversity of our sample and define a new set of classes based on the rates of change of the galaxies’ morphological and kinematic axes. We show that these classes are mostly stable over time and correspond to six distinct populations of galaxies: the rapid AM reorienters (58% of our sample), unsettled galaxies (10%), spinning disks (10%), twirling cigars (16%), misaligned slow reorienters (3%), and regular prolate rotators (galaxies that display major axis rotation; 2%). We demonstrate that the most-recent significant (mass-ratio μ > 1/10) mergers of these galaxies are the primary cause for their present-day properties and find that these mergers are best characterized at the point of the satellite’s final infall—that is, much closer to the final coalescence than has been previously thought. We show that regular prolate rotators evolve from spinning disk progenitors that experience a radial merger along their internal AM direction. Finally, we argue that these regular prolate rotators are distinct from the similarly sized population of rapid AM reorienters with large Ψint, implying that a large Ψint is not a sufficient condition for major axis rotation.

Galaxy formation in the Santa Cruz semi-analytic model compared with IllustrisTNG – I. Galaxy scaling relations, dispersions, and residuals at z = 0

ABSTRACT We present the first results from applying the Santa Cruz semi-analytic model (SAM) for galaxy formation on merger trees extracted from a dark matter only version of the IllustrisTNG (TNG) simulations. We carry out a statistical comparison between the predictions of the Santa Cruz SAM and TNG for a subset of central galaxy properties at z = 0 with a focus on stellar mass, cold and hot gas mass, star formation rate (SFR), and black hole (BH) mass. We find fairly good agreement between the mean predictions of the two methods for stellar mass functions and the stellar mass versus halo mass (SMHM) relation, and qualitatively good agreement between the SFR or cold gas mass versus stellar mass relation and quenched fraction as a function of stellar mass There are greater differences between the predictions for hot (circumgalactic) gas mass and BH mass as a function of halo mass. Going beyond the mean relations, we also compare the dispersion in the predicted scaling relations, and the correlation in residuals on a halo-by-halo basis between halo mass and galaxy property scaling relations. Intriguingly, we find similar correlations between residuals in SMHM in the SAM and in TNG, suggesting that these relations may be shaped by similar physical processes. Other scaling relations do not show significant correlations in the residuals, indicating that the physics implementations in the SAM and TNG are significantly different.

Three-point intrinsic alignments of dark matter haloes in the IllustrisTNG simulation

ABSTRACT We use the IllustrisTNG suite of cosmological simulations to measure intrinsic alignment (IA) bispectra of dark matter subhaloes between redshifts 0 and 1. We decompose the intrinsic shear field into E- and B- modes and find that the bispectra BδδE and BδEE, between the matter overdensity field, δ, and the E-mode field, are detected with high significance. We also model the IA bispectra analytically using a method consistent with the two-point non-linear alignment model. We use this model and the simulation measurements to infer the IA amplitude AIA and find that values of AIA obtained from IA power spectra and bispectra agree well at scales up to $k_\mathrm{max}= 2 \, h \mathrm{Mpc}^{-1}$. For example at z = 1, AIA = 2.13 ± 0.02 from the cross power spectrum between the matter overdensity and E-mode fields and AIA = 2.11 ± 0.03 from BδδE. This demonstrates that a single physically motivated model can jointly model two-point and three-point statistics of IAs, thus enabling a cleaner separation between IAs and cosmological weak lensing signals.

Probing the z ≳ 6 quasars in a universe with IllustrisTNG physics: impact of gas-based black hole seeding models

ABSTRACT We explore implications of a range of black hole (BH) seeding prescriptions on the formation of the brightest $z$ ≳ 6 quasars in cosmological hydrodynamic simulations. The underlying galaxy formation model is the same as in the IllustrisTNG simulations. Using constrained initial conditions, we study the growth of BHs in rare overdense regions (forming $\gtrsim 10^{12}\, {\rm M}_{\odot }\,h^{-1}$ haloes by $z$ = 7) using a (9 Mpc h−1)3 simulated volume. BH growth is maximal within haloes that are compact and have a low tidal field. For these haloes, we consider an array of gas-based seeding prescriptions wherein $M_{\mathrm{seed}}=10^4\!-\!10^6\, {\rm M}_{\odot }\,h^{-1}$ seeds are inserted in haloes above critical thresholds for halo mass and dense, metal-poor gas mass (defined as $\tilde{M}_{\mathrm{h}}$ and $\tilde{M}_{\mathrm{sf,mp}}$, respectively, in units of Mseed). We find that a seed model with $\tilde{M}_{\mathrm{sf,mp}}=5$ and $\tilde{M}_{\mathrm{h}}=3000$ successfully produces a $z$ ∼ 6 quasar with $\sim 10^9\, {\rm M}_{\odot }$ mass and ∼1047 erg s−1 luminosity. BH mergers play a crucial role at $z$ ≳ 9, causing an early boost in BH mass at a time when accretion-driven BH growth is negligible. With more stringent seeding conditions (e.g. $\tilde{M}_{\mathrm{sf,mp}}=1000$), the relative paucity of BH seeds results in a much lower merger rate. In this case, $z$ ≳ 6 quasars can only be formed if we enhance the maximum allowed BH accretion rates (by factors ≳10) compared to the accretion model used in IllustrisTNG. This can be achieved either by allowing for super-Eddington accretion, or by reducing the radiative efficiency. Our results demonstrate that progenitors of $z$ ∼ 6 quasars have distinct BH merger histories for different seeding models, which will be distinguishable with Laser Interferometer Space Antenna observations.

The GOGREEN survey: constraining the satellite quenching time-scale in massive clusters at z ≳ 1

ABSTRACT We model satellite quenching at z ∼ 1 by combining 14 massive (1013.8 < Mhalo/M⊙ < 1015) clusters at 0.8 < z < 1.3 from the GOGREEN and GCLASS surveys with accretion histories of 56 redshift-matched analogues from the IllustrisTNG simulation. Our fiducial model, which is parametrized by the satellite quenching time-scale (τquench), accounts for quenching in our simulated satellite population both at the time of infall by using the observed coeval field quenched fraction and after infall by tuning τquench to reproduce the observed satellite quenched fraction versus stellar mass trend. This model successfully reproduces the observed satellite quenched fraction as a function of stellar mass (by construction), projected cluster-centric radius, and redshift and is consistent with the observed field and cluster stellar mass functions at z ∼ 1. We find that the satellite quenching time-scale is mass dependent, in conflict with some previous studies at low and intermediate redshift. Over the stellar mass range probed (M⋆ > 1010 M⊙), we find that the satellite quenching time-scale decreases with increasing satellite stellar mass from ∼1.6 Gyr at 1010 M⊙ to ∼0.6−1 Gyr at 1011 M⊙ and is roughly consistent with the total cold gas (HI + H2) depletion time-scales at intermediate z, suggesting that starvation may be the dominant driver of environmental quenching at z < 2. Finally, while environmental mechanisms are relatively efficient at quenching massive satellites, we find that the majority ($\sim 65{\!-\!}80{{\ \rm per\ cent}}$) of ultra-massive satellites (M⋆ > 1011 M⊙) are quenched prior to infall.

Gas distribution from clusters to filaments in IllustrisTNG

Matter distribution in the environment of galaxy clusters, from their cores to their connected cosmic filaments, must in principle be related to the underlying cluster physics and its 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. We first analysed the radial physical properties of gas (velocity, temperature, and density) around 415 galaxy cluster environments from IllustrisTNG simulations at z = 0 (TNG300-1). Whereas hot plasma is virialised inside clusters (< R200), the dynamics of a warm, hot, intergalactic medium (WHIM) can be separated in two regimes: accumulating and slowly infalling gas at cluster peripheries (∼R200) and fast infalling motions outside clusters (> 1.5 R200). The azimuthal distribution of dark matter (DM), hot, and warm gas phases is secondly statistically probed by decomposing their 2D distribution in harmonic space. Inside clusters, the azimuthal symmetries of DM and hot gas trace cluster structural properties well. These include their centre offsets, substructure fractions, and elliptical shapes. Beyond cluster-virialised regions, we find that WHIM gas follows the azimuthal distribution of DM, thus tracing cosmic filament patterns. Azimuthal symmetries of hot and warm gas distribution are finally shown to be imprints of cluster mass assembly history, strongly correlated with the formation time, mass accretion rate, and dynamical state of clusters. The azimuthal mode decomposition of 2D gas distribution is a promising probe to assess the 3D physical and dynamical cluster properties up to their connected cosmic filaments.