The observational features of the massive galaxy cluster "El Gordo" (ACT-CL J0102-4915), such as the X-ray emission, the Sunyaev-Zel'dovich (SZ) effect, and the surface mass density distribution, indicate that they are caused by an exceptional ongoing high-speed collision of two galaxy clusters, similar to the well-known Bullet Cluster. We perform a series of hydrodynamical simulations to investigate the merging scenario and identify the initial conditions for the collision in ACT-CL J0102-4915. By surveying the parameter space of the various physical quantities that describe the two colliding clusters, including their total mass (M ), mass ratio (ξ), gas fractions (f b ), initial relative velocity (V ), and impact parameter (P ), we find out an off-axis merger with P ∼ 800 h −1 70 kpc, V ∼ 2500 km s −1 , M ∼ 3 × 10 15 M ⊙ , and ξ = 3.6 that can lead to most of the main observational features of ACT-CL J0102-4915. Those features include the morphology of the X-ray emission with a remarkable wake-like substructure trailing after the secondary cluster, the X-ray luminosity and the temperature distributions, and also the SZ temperature decrement. The initial relative velocity required for the merger is extremely high and rare compared to that inferred from currently available Λ cold dark matter (ΛCDM) cosmological simulations, which raises a potential challenge to the ΛCDM model, in addition to the case of the Bullet Cluster.Throughout the paper, we assume a flat ΛCDM cosmology model with Ω m = 0.30, Ω Λ = 0.70, and the Hubble constant H 0 = 70 h 70 km s −1 Mpc −1 .

We study a merger of the NGC 4839 group with the Coma cluster using X-ray observations from the XMM-Newton and Chandra telescopes. X-ray data show two prominent features: (i) a long (∼600 kpc in projection) and bent tail of cool gas trailing (towards south-west) the optical center of NGC 4839, and ii) a 'sheath' region of enhanced X-ray surface brightness enveloping the group, which is due to hotter gas. While at first glance the X-ray images suggest that we are witnessing the first infall of NGC 4839 into the Coma cluster core, we argue that a post-merger scenario provides a better explanation of the observed features and illustrate this with a series of numerical simulations. In this scenario, the tail is formed when the group, initially moving to the south-west, reverses its radial velocity after crossing the apocenter, the ram pressure ceases and the ram-pressure-displaced gas falls back toward the center of the group and overshoots it. Shortly after the apocenter passage, the optical galaxy, dark matter and gaseous core move in a north-east direction, while the displaced gas continues moving to the south-west. The 'sheath' is explained as being due to interaction of the re-infalling group with its own tail of stripped gas mixed with the Coma gas. In this scenario, the shock, driven by the group before reaching the apocenter, has already detached from the group and would be located close to the famous relic to the south-west of the Coma cluster.

Several types/classes of shocks naturally arise during formation and evolution of galaxy clusters. One such class is represented by accretion shocks, associated with deceleration of infalling baryons. Such shocks, characterized by a very high Mach number, are present even in 1D models of cluster evolution. Another class is composed of "runaway merger shocks", which appear when a merger shock, driven by a sufficiently massive infalling subcluster, propagates away from the main-cluster center. We argue that, when the merger shock overtakes the accretion shock, a new long-living shock is formed that propagates to large distances from the main cluster (well beyond its virial radius) affecting the cold gas around the cluster. We refer to these structures as Merger-accelerated Accretion shocks (MA-shocks) in this paper.We show examples of such MA-shocks in 1D and 3D simulations and discuss their characteristic properties. In particular, (1) MA-shocks shape the boundary separating the hot intracluster medium (ICM) from the unshocked gas, giving this boundary a "flower-like" morphology. In 3D, MA-shocks occupy space between the dense accreting filaments.(2) Evolution of MA-shocks highly depends on the Mach number of the runaway merger shock and the mass accretion rate parameter of the cluster. (3) MA-shocks may lead to the misalignment of the ICM boundary and the splashback radius.(racc rsp) if the gas adiabatic index is γ = 5/3 (see e.g. Shi 2016b) 1 .However, the evolution of galaxy clusters is more complicated than those one-dimensional (1D) self-similar solutions. Two major processes tend to break the self-similarity (and also spherical symmetry) of galaxy clusters, i.e. active galactic nucleus (AGN) feedback (see e.g. Werner et al. 2019, for a recent review) and cluster mergers (e.g. Sarazin 2002). The former process perturbs the gas in cluster cores (e.g. 100 kpc); the latter one, 1 Specifically, the alignment of the racc and rsp holds when γ = 5/3 only if the cluster mass accretion rate parameter (Γ) is in the range of 0.5 ≤ Γ ≤ 5 (Shi 2016b; see the definition of Γ in Section 2).

Moderately strong shocks arise naturally when two subclusters merge. For instance, when a smaller subcluster falls into the gravitational potential of a more massive cluster, a bow shock is formed and moves together with the subcluster. After pericenter passage, however, the subcluster is decelerated by the gravity of the main cluster, while the shock continues moving away from the cluster center. These shocks are considered as promising candidates for powering radio relics found in many clusters. The aim of this paper is to explore the fate of such shocks when they travel to the cluster outskirts, far from the place where the shocks were initiated. In a uniform medium, such a "runaway" shock should weaken with distance. However, as shocks move to large radii in galaxy clusters, the shock is moving down a steep density gradient that helps the shock to maintain its strength over a large distance. Observations and numerical simulations show that, beyond R 500 , gas density profiles are as steep as, or steeper than, ∼ r −3 , suggesting that there exists a "Habitable zone" for moderately strong shocks in cluster outskirts where the shock strength can be maintained or even amplified. A characteristic feature of runaway shocks is that the strong compression, relative to the initial state, is confined to a narrow region just behind the shock. Therefore, if such a shock runs over a region with a pre-existing population of relativistic particles, then the boost in radio emissivity, due to pure adiabatic compression, will also be confined to a narrow radial shell.1 The boundary separating the gaseous atmosphere of the main cluster from that of the subcluster is a contact discontinuity, a.k.a. cold front.

Observations reveal that the peaks of the X-ray map and the Sunyaev-Zel'dovich (SZ) effect map of some galaxy clusters are offset from each other. In this paper, we perform a set of hydrodynamical simulations of mergers of two galaxy clusters to investigate the spatial offset between the maxima of the X-ray and the SZ surface brightness of the merging clusters. We find that significantly large SZ-X-ray offsets (> 100 kpc) can be produced during the major mergers of galaxy clusters (with mass > 1 × 10 14 M ⊙ ). The significantly large offsets are mainly caused by a 'jump effect' occurred between the primary and secondary pericentric passages of the two merging clusters, during which the X-ray peak may jump to the densest gas region located near the center of the small cluster, but the SZ peak remains near the center of the large one. Our simulations show that merging systems with higher masses and larger initial relative velocities may result in larger offset sizes and longer offset time durations; and only nearly head-on mergers are likely to produce significantly large offsets. We further investigate the statistical distribution of the SZ-X-ray offset sizes and find that (1) the number distribution of the offset sizes is bimodal with one peak located at low offsets ∼ 0 and the other at large offsets ∼350-450h −1 kpc, but the objects with intermediate offsets are scarce; and (2) the probabilities of the clusters in the mass range higher than 2 × 10 14 h −1 M ⊙ that have offsets larger than 20, 50, 200, 300, and 500h −1 kpc are 34.0%, 11.1%, 8.0%, 6.5%, and 2.0% respectively at z = 0.7. The probability is sensitive to the underlying pairwise velocity distribution and the merger rate of clusters. We suggest that the SZ-X-ray offsets provide a probe to the cosmic velocity fields on the cluster scale and the cluster merger rate, and future observations on the SZ-X-ray offsets for a large number of clusters may put strong constraints on them.Our simulation results suggest that the SZ-X-ray offset in the Bullet Cluster, together with the mass ratio of the two merging clusters, requires a relative velocity larger than 3000 km s −1 at an initial separation 5 Mpc. The cosmic velocity distribution at the high-velocity end is expected to be crucial in determining whether there exists an incompatibility between the existence of the Bullet Cluster and the prediction of a ΛCDM model.

A self-similar spherical collapse model predicts a dark matter (DM) splashback and accretion shock in the outskirts of galaxy clusters while misses a key ingredient of structure formation – processes associated with mergers. To fill this gap, we perform simulations of merging self-similar clusters and investigate their DM and gas evolution in an idealized cosmological context. Our simulations show that the cluster rapidly contracts during the major merger and the splashback radius rsp decreases, approaching the virial radius rvir. While in the self-similar model rsp depends on a smooth mass accretion rate parameter Γs, our simulations show that in the presence of mergers, rsp responds to the changes in the total mass accretion rate Γvir, which accounts for both mergers and smooth accretion. The scatter of the Γvir − rsp/rvir relation indicates a generally low Γs ∼ 1 in clusters in cosmological simulations. In contrast to the DM, the hot gaseous atmospheres significantly expand by the merger-accelerated (MA-) shocks formed when the runaway merger shocks overtake the outer accretion shock. After a major merger, the MA-shock radius is larger than rsp by a factor of up to ∼1.7 for Γs ≲ 1 and is ∼rsp for Γs ≳ 3. This implies that (1) mergers could easily generate the MA-shock-splashback offset measured in cosmological simulations, and (2) the smooth mass accretion rate is small in regions away from filaments where MA-shocks reside. We further discuss the shapes of the DM haloes, various shocks and contact discontinuities formed at different epochs of the merger, and the ram-pressure stripping in cluster outskirts.

Accurate estimation of the merger timescales of galaxy clusters is important for understanding the cluster merger process and further understanding the formation and evolution of the large-scale structure of the universe. In this paper, we explore a baryonic effect on the merger timescale of galaxy clusters by using hydrodynamical simulations. We find that the baryons play an important role in accelerating the merger process. The merger timescale decreases upon increasing the gas fraction of galaxy clusters. For example, the merger timescale is shortened by a factor of up to 3 for merging clusters with gas fractions of 0.15, compared with the timescale obtained with 0 gas fractions. The baryonic effect is significant for a wide range of merger parameters and is particularly more significant for nearly head-on mergers and high merging velocities. The baryonic effect on the merger timescale of galaxy clusters is expected to have an impact on the structure formation in the universe, such as the cluster mass function and massive substructures in galaxy clusters, and a bias of "no-gas" may exist in the results obtained from the dark matter-only cosmological simulations.

X-ray observations of merging clusters provide many examples of bow shocks leading merging subclusters. While the Mach number of a shock can be estimated from the observed density jump using Rankine-Hugoniot condition, it reflects only the velocity of the shock itself and is generally not equal to the velocity of the infalling subcluster dark matter halo or to the velocity of the contact discontinuity separating gaseous atmospheres of the two subclusters. Here we systematically analyze additional information that can be obtained by measuring the standoff distance, i.e. the distance between the leading edge of the shock and the contact discontinuity that drives this shock. The standoff distance is influenced by a number of additional effects, e.g. (1) the gravitational pull of the main cluster (causing acceleration/deceleration of the infalling subcluster), (2) the density and pressure gradients of the atmosphere in the main cluster, (3) the non-spherical shape of the subcluster, and (4) projection effects. The first two effects tend to bias the standoff distance in the same direction, pushing the bow shock closer to (farther away from) the subcluster during the pre-(post-)merger stages. Particularly, in the post-merger stage, the shock could be much farther away from the subcluster than predicted by a model of a body moving at a constant speed in a uniform medium. This implies that a combination of the standoff distance with measurements of the Mach number from density/temperature jumps can provide important information on the merger, e.g. differentiating between the pre-and post-merger stages.