Mon. Not. R. Astron. Soc. 389, 967–688 (2008) doi:10.1111/j.1365-2966.2008.13626.x Simulating the Bullet Cluster Chiara Mastropietro and Andreas Burkert Universitats¨ Sternwarte Munchen,¨ Scheinerstr.1, D-81679 Munchen,Germany¨ Accepted 2008 June 20. Received 2008 June 10; in original form 2007 November 6 ABSTRACT Downloaded from https://academic.oup.com/mnras/article/389/2/967/974617 by guest on 24 September 2021 We present high resolution N-body/smoothed particle hydrodynamics (SPH) simulations of the interacting cluster 1E0657-56. The main and the subcluster are modelled using extended cuspy cold dark matter (CDM) dark matter haloes and isothermal β-profiles for the collisional component. The hot gas is initially in hydrostatic equilibrium inside the global potential of the clusters. We investigate the X-ray morphology and derive the most likely impact parameters, mass ratios and initial relative velocities. We find that the observed displacement between the X-ray peaks and the associated mass distribution, the morphology of the bow shock, the surface brightness and projected temperature profiles across the shock discontinuity can be well reproduced by offset 6:1 encounters where the subcluster has initial velocity (in the rest frame of the main cluster) 2.3 times the virial velocity of the main cluster dark matter halo. A model with the same mass ratio and lower velocity (1.5 times the main cluster virial velocity) matches quite well most of the observations. However, it does not reproduce the relative surface brightness between the bullet and the main cluster. Dynamical friction strongly affects the kinematics of the subcluster so that the low-velocity bullet is actually bound to the main system at the end of the simulation. We find that a relatively high concentration (c = 6) of the main cluster dark matter halo is necessary in order to prevent the disruption of the associated X-ray peak. For a selected subsample of runs we perform a detailed three-dimensional analysis following the past, present and future evolution of the interacting systems. In particular, we investigate the kinematics of the gas and dark matter components as well as the changes in the density profiles and the motion of the system in the LX–T diagram. Key words: methods: N-body simulations – galaxies: clusters: individual: 1E0657-56 – dark matter – X-rays: galaxies: clusters. in the plane of the sky (Barrena et al. 2002). As the core passage 1 INTRODUCTION must have occurred ∼0.15 Gyr ago we have the unique opportu- The ‘Bullet Cluster’ 1E0657-56 represents one of the most com- nity to study this interaction in a very special short-lived stage, far plex and unusual large-scale structures ever observed. Located at away from thermal and dynamical equilibrium. As a result of the a redshift z = 0.296 it has the highest X-ray luminosity and tem- encounter, the collision-dominated hot plasma and the collision- perature of all known clusters as a result of overheating due to a less stellar and dark matter components have been separated. The recent supersonic Mach M ∼ 3 (Markevitch et al. 2002; Marke- galaxy components of both clusters are clearly offset from the asso- vitch 2006) central encounter of a subcluster (the bullet) with its ciated X-ray emitting cluster gas (Liang et al. 2000; Barrena et al. main cluster. The 500-ks Chandra ACIS-I image of 1E0657-56 (fig. 2002). In addition, weak and strong lensing maps (Clowe, Gon- 1 in Markevitch 2006) shows two plasma concentrations with the zalez & Markevitch 2004; Bradacˇ et al. 2006; Clowe et al. 2006) bullet subcluster on the right-hand side of the image being deformed show that the gravitational potential does not trace the distribution in a classical bow shock on the western side as a result of its motion of the hot cluster gas that dominates the baryonic mass but follows through the hot gas of the main cluster. The analysis of the shock approximately the galaxy distribution as expected for a collision- structure leads to the conclusion that the bullet is now moving away less dark matter component. The likelihood to find such a high- from the main cluster with a velocity of ∼4700 km s−1 (Markevitch velocity cluster encounter in a cold dark matter (CDM) cosmol- 2006). The line-of-sight velocity difference between the two sys- ogy has recently been investigated by Hayashi & White (2006) using tems is only 600 km s−1 suggesting that the encounter is seen nearly the Millenium Run simulation. According to the newest estimates from X-ray and gravitational lensing results the Hayashi & White (2006) likelihood becomes ∼0.8 × 10−7 (Farrar & Rosen 2007) E-mail: [email protected] (CM) which means that 1E0657-56 represents an extremely rare system C 2008 The Authors. Journal compilation C 2008 RAS 968 C. Mastropietro and A. Burkert in a CDM universe. Recent numerical works (Milosavljevicetal.´ of the form: 2007; Springel & Farrar 2007, hereafter SF07) have demonstrated ρ(r) = ρ [1 + (r/r )2]−3/2β . (2) that the relative velocity of the dark matter components associated 0 c with the main and the subcluster is not necessarily coincident with We take the asymptotic slope parameter β = 2/3 (Jones & Forman the speed of the bullet as inferred from the shock analysis. In de- 1984) and rc = 1/2rs (Ricker & Sarazin 2001). The adopted gas tails, Milosavljevic´ et al. (2007) using a two-dimensional Eulerian fraction ranges from a minimum value of 12 per cent, comparable code well reproduced the observed increase in temperature across to the gas mass fraction provided by X-ray observations of galaxy the shock front with a dark halo velocity ∼16 per cent lower than clusters (Vikhlinin et al. 2006; McCarthy, Bower & Balogh 2007), that of the shock, while SF07 found even a larger difference be- to 17 per cent, consistent with the recent WMAP results (Spergel − tween the shock velocity (∼4500 km s 1 in their best model) and et al. 2007). − the speed of the halo (only ∼2600 km s 1). Moreover, according to Assuming a spherically symmetric model, the temperature profile Milosavljevic´ et al. (2007), due to a drop in ram-pressure after the is determined by the condition of hydrostatic equilibrium by the cores’ interaction the gas component of the subcluster can eventu- cumulative total mass distribution and the density profile of the gas Downloaded from https://academic.oup.com/mnras/article/389/2/967/974617 by guest on 24 September 2021 ally be larger than that of its dark matter counterpart. (Mastropietro et al. 2005): The simulations of SF07 represent the most complete three- ∞ μm 1 GM(t) dimensional numerical modelling of the 1E0657-56 system so far. T (r) = p ρ(t) dt, (3) 2 Nevertheless they focus preferentially on the speed of the bullet but kB ρ(r) r t fail in reproducing the observed displacement of the X-ray peaks where M(r) is the total mass within the radius r, mp is the proton which represent an important indicator of the nature of the inter- mass and μ the mean molecular weight. We assume μ = 0.6 for action. In particular, they do not obtain any displacement in the a gas of primordial composition, which appears to be a reasonable X-ray distribution associated with the main cluster suggesting that approximation since the mean temperature of 1E0657-56 is T ∼ the baryonic component is suffering too little ram-pressure. More- 14 keV according to Markevitch (2006) and cooling is dominated over, the concentrations used for the main cluster (and obtained by by bremsstrahlung and almost independent of the metallicity. G and modelling the lensing data) are much smaller than those suggested kB are the gravitational and Boltzmann constants. by CDM (Maccio` et al. 2007) for haloes of similar masses. Masses are assigned to the models according to the weak and The aim of this paper is to investigate the evolution of the Bullet strong lensing mass reconstruction of Bradacˇ et al. (2006). In par- Cluster in details using high resolution smoothed particle hydrody- ticular, we assume that the inferred mass enclosed within the field namics (SPH) simulations. We quantify the initial conditions that of the Hubble Space Telescope (HST) Advanced Camera for Sur- are required in order to better reproduce its observed state and pre- veys (ACS) (Bradacˇ et al. 2006) is comparable to the total projected dict its subsequent evolution. mass of our simulated system (calculated when the two centres of Our model allows us to determine in details the spatial, thermal the mass distribution are at a distance similar to the observed one) and dynamical state of the dark matter and hot gas distribution in within the same area. Since the ACS field represents only the central the Bullet Cluster. fraction of the area covered by the entire system, this mass constraint The paper is organized as follows. Section 2 describes the adopted is strongly influenced by the concentration of the dark matter haloes cluster models and orbital parameters. In Section 3, we perform a (Nusser 2007). With a cosmologically motivated choice of c = 6 projected analysis of our simulations comparing it with the latest (Maccio` et al. 2007) for the main cluster initial halo model, we can X-ray and gravitational lensing results. In Section 4, we select some reproduce the lensing mass reasonably well adopting a main cluster significant models and study in details the three-dimensional kine- total mass (within the virial radius) of ∼8.34 × 1014 M (Table 1), matics and morphology of the interacting systems and their past and almost a factor 1.8 smaller than the mass obtained by fitting lensing future evolution with time, as well as the motion of the main cluster data with extremely low concentrated (c < 2) NFW haloes where along the LX–T diagram.