On the formation of cold fronts in massive mergers

Transcription

1 Mon. Not. R. Astron. Soc. 357, (2005) doi: /j x On the formation of cold fronts in massive mergers H. Mathis, 1 G. Lavaux, 1,2 J. M. Diego 1 and J. Silk 1 1 University of Oxford, Astrophysics, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH 2 Ecole Normale Supérieure de Cachan, Avenue du Président Wilson, Cachan, France Accepted 2004 November 1. Received 2004 October 15; in original form 2003 December 2 ABSTRACT Using adiabatic hydrodynamical simulations, we follow the evolution of two symmetric cold fronts forming in the remnant of a violent z = 0.3 massive cluster merger. Because the fronts develop after the first passage of the two gas cores of the merging subclusters, and because they soon move ahead of their associated dark matter cores, both the structure and the location of our simulated cold fronts may correspond to a stage that is later than that of most cold fronts observed so far. The cold fronts are preceded by a roughly spherical shock that originates in the centre of the cluster and disappears in the outer regions after 1.6 Gyr. The cold fronts last longer, until z 0. We follow the spatial evolution of the gas of the subcluster cores, and find that a fraction of this gas is liberated in the intracluster medium after core passage, but mainly at apocentre, and that it does not fall back onto the cluster centre. Conversely, we trace back the low-temperature gas constituting the fronts and find that it is initially associated with the two dense cores of the merging clusters. In addition, we find some evidence for discontinuity of the gas velocity field across the edge of the forming cold fronts, suggesting the presence of a contact discontinuity there. In the light of other recent work, we then speculate on the physical mechanism resulting in the cold fronts. We suggest that sloshing induced by strongly varying ram pressure along the subcluster s orbit and/or spatial segregation between the dark matter and gas components of the cores of the subclusters results in strong tidal forces on the gas, and that these forces could be responsible for the deposition of part of the cold dense gas in the surrounding hot intracluster medium. This deposited gas then expands, cools down further, and constitutes the cold fronts. Keywords: hydrodynamics shock waves galaxies: clusters: general intergalactic medium. 1 INTRODUCTION High-resolution X-ray temperature images obtained by Chandra of the intracluster medium (ICM) show that large cold regions in pressure equilibrium with their surrounding medium are a very common phenomenon in massive clusters (Markevitch et al. 2000; but see also Vikhlinin, Markevitch & Murray 2001; Mazzotta et al. 2001; Sun et al. 2002; Markevitch & Vikhlinin 2001; Markevitch, Vikhlinin & Mazzotta 2001; Dupke, White & Bregman 2002). Their high gas density largely compensates for the factor of 1.3 to 4 drop in temperature, so that their X-ray surface brightness is still typically higher than the rest of the ICM. The whole cold region is commonly referred to as a cold front, even if strictly speaking the term only describes the upstream contact interface of the cold gas with the hot ICM. Employing the term in its loose sense, these cold fronts are extended structures with sizes of one hundred to a few hundred kiloparsecs, observed up to a significant fraction of the virial radius. In these aspects they differ from the very dense clumps of gas or- hxm@astro.ox.ac.uk biting the ICM, which extend to a few tens of kiloparsecs at most. These clumps are much more difficult to observe except in the central regions of clusters (Fujita et al. 2002): they are expected to be the direct remainders of the cores of massive haloes that have merged with the cluster. They do, however, share at least three characteristics with cold fronts. First, both have a high X-ray surface brightness. Secondly, they are in pressure equilibrium with the ICM. Thirdly, cold dense subclumps will be preceded by shocks propagating in the ICM (see, for example, Vikhlinin & Markevitch 2002; Markevitch et al for recent observations) if they orbit at supersonic speeds. This is also the case to many cold fronts, which are thought to originate from recent mergers. In fact, for clusters that have undergone significant recent mergers, there is a known close link between subclumps and cold fronts: we will present further evidence in this paper. Numerical simulations have already addressed the formation of cold fronts: in a pioneering simulation of merging clusters of galaxies using Eulerian hydrodynamics, Roettiger, Loken & Burns (1997) studied cluster subcluster idealized mergers, and showed that substructures, shocks and adiabatic cooling could result in very complex temperature patterns. Ricker & Sarazin (2001) have addressed the C 2005 RAS

2 802 H. Mathis et al. evolution of the X-ray luminosity and temperature of the ICM in a series of off-axis mergers of idealized subclusters. They showed that the overall luminosity and temperature increase due to merging shocks and regions of gas compression that are observationally unresolved can strongly bias the cluster mass if it is derived assuming a non-merging cluster. More recently, Nagai & Kravtsov (2003) and Bialek, Evrard & Mohr (2002) have shown that cold fronts like those found by Markevitch et al. (2000) can form as a result of massive mergers in a cosmological setting. Both groups found that their simulated cold fronts occurred when the subcluster gas strays from its local potential minimum and expands adiabatically. Both groups pointed out that further observations and simulations need to be carried out to evaluate the expected frequency of cold fronts in massive mergers and to compare this with observations. In fact, massive mergers need not be the only process responsible for cold fronts. For example, even minor mergers may sufficiently disturb the gravitational potential of the cluster to induce a sloshing motion of the central X-ray gas, which could result in cold fronts (Markevitch et al. 2001, for A1795). Another possibility suggested by Dupke et al. (2002) and Dupke & White (2003) in the case of A496 is that the sloshing of the gas could be driven by the motion of the cd galaxy in the gravitational potential of the cluster. Any assessment of the respective contributions of these origins to the cold-front phenomenon requires a clear picture of the physical mechanisms at stake in coldfront formation, together with realistic estimates for their lifetimes in the surrounding ICM. Heinz et al. (2003) have recently suggested ram-pressure stripping as a possible mechanism for the formation of some of the cold fronts. They did not include dark matter in their simulations, but studied the partial unbinding of a dense clump of gas in a fixed gravitational potential undergoing stripping from an external, uniform wind representing the surrounding ICM. In this paper we study only those cold fronts occurring as a possible result of major mergers, focusing on the interplay between the dark matter and the gas of the subcluster cores orbiting in the newly formed ICM. Like Nagai & Kravtsov (2003) and Bialek et al. (2002), we follow the late formation of a massive cluster in the CDM cosmology using hydrodynamical adiabatic simulations with particularly high resolution. We employ an entropy-conserving DM+SPH scheme that is suited to following the Lagrangian evolution of the flow and the history of the gas of the cold front. We set the initial conditions to merge two equal-mass haloes into a very massive, but plausible, M final object to bring out the interesting features. Our merger takes place at z = 0.3. It produces by z = 0.18 two cold fronts which develop in a 500-kpc-thick plane containing the orbits of the two merging cores and expand in the wake of an almost spherically symmetric bow shock. This shock results from the supersonic motion of the merging subcluster cores in the ICM, once they have reached beyond first passage. The dense gas cores of the two accreted haloes survive until close to the present time, when they eventually merge. While a small fraction of the gas particles of the subclumps is tidally stripped at the first closest encounter, both cold fronts develop later, after core passage but mainly right before apocentre passage of the subclumps. By the time the dark matter cores start to fall back to the cluster centre, 10 per cent of the subclump gas has already been liberated from the local gravitational potential of the subclumps, and has been deposited at the location of the cold front. Conversely, we find that the cold gas of the ICM that we call the cold front mainly consists of particles initially within the dense cores of the merging subclusters. Simulated X-ray images show that the highest luminosity peaks are associated with the cold dense subclumps before core passage, with both the subclumps and the cold fronts at apocentre passage, when cold fronts mainly develop, and once again with only the cores after their apocentre passage. However, sharp boundaries in X-ray simulated images first correspond to the bow shocks at the epoch of cold-front formation, and then to the cold fronts themselves, the shocks dissolving in the outskirts of the cluster. This sequence suggests that the cold fronts forming in our simulations correspond to a stage that is later than that captured by most observations. We speculate on the physical mechanisms responsible for the ejection of part of the gas from the local gravitational potential of the subclump. Strong gradients in ram pressure between the core passage of the subclumps and the apocentre of their orbits can induce sloshing of the gas inside the subclumps. Another possible cause for the unbinding of the gas could be the spatial decoupling at first passage between the bulk of the gas and the bulk of the dark matter components of the subclumps, resulting in strong tidal forces acting on the gas component could unbind a fraction of the gas. Once this fraction of cold gas is ejected from the local gravitational potential of the subclump, it cools down even further to pressure equilibrate with the intracluster medium and forms a cold front. This paper is organized as follows: in Section 2 we present the simulations. In Section 3 we discuss qualitatively the evolution of the post-merger ICM. Sections 4 and 5 give quantitative aspects of the development of the two main features apparent on the maps: shocks and cold fronts. Section 6 discusses possible mechanisms for the origin of the cold fronts. We summarize and conclude in Section 7. 2 OBTAINING A MASSIVE CLUSTER MERGER 2.1 Initial conditions We assume a concordance CDM cosmology with parameters 0 = 0.3, b h 2 = 0.024, = 0.7, h = 0.7. To study a major merger, as an alternative to resimulating at higher resolution a cluster selected from a low-resolution simulation, we directly constrain the initial Gaussian density field so that it has the usual CDM power spectrum but encapsulates information on where and how the z = 0 target cluster should form. For this purpose we use the van de Weygaert & Bertschinger (1996) implementation of the Hoffman Ribak algorithm. We want an equal-mass massive merger to take place at z 0.5; this is obtained if we constrain the initial density field so that it has two Gaussian peaks of standard deviation r = 5 Mpc, with the same amplitude A = 5.3 σ r (where σ r is the root mean square value of the unconstrained initial density field when smoothed with a Gaussian kernel of standard deviation r), and separation d = 27 Mpc. Note that adjusting the initial velocities of these peaks adds but little control over the final merger at the expense of additional tuning, so we have only constrained the densities. The above set-up results in a very massive M virial mass cluster at z = 0, which follows a Navarro Frank & White (NFW) density profile, and which formed in an equal-mass merger of two Virgo-sized clusters at z merg = 0.3. [z merg is the epoch at which the friends-of-friends groupfinder with linking length times the mean dark matter (DM) interparticle separation merges the two clusters.] 2.2 Simulation details We employ DM and SPH particles in a 100-Mpc box and start the simulation at z start = 100. The DM and SPH particle masses and softening lengths read M DM = M and M SPH =

3 Cold fronts in massive mergers 803 Figure 1. z = 0 projected 2D dark matter density of the simulation. The region shown is 100 Mpc wide and we have projected a 10-Mpc-thick slice normal to the z-direction and centred on the cluster. The two merging subcusters at the origin of the cold fronts have been accreted at z = 0.3 from the WNW SE direction, where remains of a filament are still visible M, and r soft,dm = r soft,sph = 40 kpc. The softening lengths are kept fixed throughout in comoving coordinates. The equations of motion are integrated with the public version of GAD- GET (Springel, Yoshida & White 2001) 1, which we have modified to include the standard entropy conservation scheme proposed by Springel & Hernquist (2002). The gas is single-phase, monoatomic with adiabatic index γ = 5/3 and obeys a perfect gas equation of state. We do not include cooling, heating, thermal conduction, magnetic fields, nor mechanical or thermal AGN/supernova feedback as our focus is on the capability of a massive merger to induce large, long-lasting cold fronts even in a simple adiabatic evolution. We focus on 11 outputs equally spaced between z merg and z = 0.1, and three outputs at z = 0.06, z = 0.03 and z = 0. The final virial mass and radius of the cluster, where the enclosed dark matter density drops to 200 times the critical density, are m vir = M and r vir = 3.4 Mpc. Fig. 1 gives the projected 2D density of the dark matter of a slice taken through the simulation, with the cluster at the centre. The size of the region shown is 100 Mpc on each side, and the slice is 10 Mpc thick and normal to the z-direction. The two massive subclusters merging at z = 0.3 infall along a diagonal filament spanning from the lower left to the upper right. Once it has formed, the cluster still accretes smaller clumps of DM, mostly from this filament. 2.3 Tracking the cores of the merging subclusters The two merging subclusters have fairly similar, Virgo-size masses. Following Bialek et al. (2002), we select their two cores (both gas and DM) before z merg, using a linking length of 0.05 times the mean interparticle separation. From z merg down to z = 0, the x-, y- and z-coordinates of the centres of mass of the subclusters vary in amplitude by 1 Mpc. However, from shortly before core passage onwards, we find that the trajectories of the core of the subclus- 1 See volker/gadget ters are roughly confined to a constant-z slab with thickness 300 kpc, which simplifies our analysis. At core passage, the centres of mass of the dark matter and gas components of the subclusters are 580 kpc apart. Fig. 2 shows the two cores projected along the z-direction at four different epochs. The cores have their first close encounter shortly before z = 0.2, then reach their apocentre, and finally mix at z = 0. We label as subclusters 1 and 2 the haloes approaching at z merg from the lower left corner (dark) and upper right (red) corners respectively. In the following discussion, we will refer to CG 1 (CDM 1 ) and CG 2 (CDM 2 )asthe gas (DM) of the two subcluster cores. The resulting numbers of particles and masses of the two cores are N DM,1 = , N SPH,1 = , M DM,1 = M, M SPH,1 = M and N DM,2 = , N SPH,2 = 7200, M DM,2 = M, M SPH,2 = M respectively. The upper left, upper right and lower left-hand panels of Fig. 3 respectively give the evolution of the x-, y- and z-positions of the centres of mass of the gas and of the dark matter components of the core of the subcluster that has accreted from the lower left of the simulation (CG 1 and CDM 1 correspond to the black and red curves). The lower right-hand panel of Fig. 3 shows the evolution of the same centres of mass in the zy-plane (in the x-direction, there is no significant information), with z = 0.28 as the leftmost point. While the trajectories of the centres of mass of the dark matter and of the gas component match until core passage (z 0.22, the fourth point from the left), they then separate from one another, with the centre of mass of the gas catching up with that of the dark matter at z 0.18 (the sixth point from the left). Possible reasons for CG 1 and CDM 1 following different paths at first passage include the ram pressure from the approaching CG 2 and from its surrounding gas, which will affect the orbit of the collisional component only. This spatial decoupling suggests that significant sloshing of the gas of CG 1 might be induced shortly after core passage. Later on, the centres of mass of the gas and of the dark matter follow fairly well separated orbits until the final merging: the formation of the cold front at z 0.16 systematically offsets the centre of mass of the gas to high-y values. Fig. 4 gives Figure 2. Positions of the gas particles of the clumps CG 1 (black) and CG 2 (red) at four different redshifts in the xy-plane. The particles were selected shortly after the z = 0.3 merger using a friends-of-friends groupfinder with a small linking length parameter b = Note the stripping of some gas particles at z = 0.2 shortly after the first passage, and the extended tongues typical of the cold fronts at z = 0.1.

4 804 H. Mathis et al. Figure 3. The black and red lines show the spatial evolution after z merg = 0.3 of the centre of mass of the gas and dark matter (respectively) of the core of the subcluster that has accreted from the lower left of the simulation (referred to as CG 1, CDM 1 in the text). Upper left- and right-hand panels correspond to the x- and y-positions as a function of time, while the lower left-hand panel is the z-position. The lower right-hand panel is the evolution in the zy-plane: note the different paths followed by the centres of mass of dark matter and gas at z 0.22 (z 0.22 is the epoch of the first core passage of the dark matter subclumps), before CG 1 catches up with CDM 1 at z 0.18 when the cold front is being generated. In y-coordinates, the centre of mass of the gas is then offset to the outer parts of the cluster with respect to the centre of mass of the DM. This offset reaches 200 kpc by z = 0.12: the dark matter has already fallen back towards the centre while the centre of mass of the gas is still stationary. It is a likely consequence of the upper right cold front, which has already fully developed at this point. simulation and centred on the most bound DM particle of the cluster at z = 0. Here and in all the following, the spatial analysis of the plots and the discussion are in comoving length. We employ a 500-kpcthick slice also centred on the cluster in the z-direction. (Quantities are evaluated locally and then projected along the line of sight, here the z-direction; owing to the small thickness of the slice, we expect only minor blurring because of projection effects, but we will specify when they could affect our conclusions.) We focus on the gas and dark matter densities using the Mpc 2 maps, and on two direct observables using the 6 6 Mpc 2 maps: the X-ray emissionweighted temperature (we assume the only contribution is thermal Bremsstrahlung), and the Compton y-parameter (or equivalently, the integrated pressure). Figs 5, 6, 7 and 8 show consecutive maps of, respectively, the lineof-sight integrated gas and dark matter 3D densities (in arbitrary units), the line-of-sight emission-weighted temperature of the ICM (in K), and the Compton y-parameter (in arbitrary units). We divide the post-merger evolution of the ICM into three consecutive phases, which are most easily identified in the maps of the gas and of the DM density (Figs 5 and 6), where the positions of CG 1, CG 2 and CDM 1, CDM 2 correspond to the dark peaks. First, we define a phase of initial compression of the intervening gas, between z merge and z = 0.22, when the two subcluster cores are approaching. Secondly, we associate the period z = 0.2 to z = 0.12 with the epoch of generation of the cold fronts, and thirdly, we single out a final relaxation from z = 0.1 to z = 0. In the remainder of this section, we only give a qualitative description of this sequence, and conclude with maps of the X-ray surface brightness and with a brief comparison with observations: we defer the quantitative analysis to the subsequent two sections. Figure 4. The black and red lines show the evolution after z merg = 0.3 of the velocity (in km s 1 )ofthe centre of mass of the gas and of the dark matter, respectively, of the core of the subcluster accreted from the lower left of the simulation (CG 1, CDM 1 ). The top left-hand panel shows the amplitude of the 3D velocity, while the upper right-, lower left- and lower right-hand panels give v x, v y and v z, respectively. the position and velocity of the centres of mass of the gas and dark matter components (black and red respectively) of the core of the same subcluster. It is a useful tracer of the acceleration and it can approximately locate the maxima of the force acting on the two clumps. 3 POST-MERGER EVOLUTION OF THE ICM In this section, we track the post-merger evolution of the ICM using maps of and 6 6 Mpc 2 slices cut in the xy-plane of the 3.1 Compression of the intervening gas The first four panels of Figs 5 to 8 show how the intracluster gas between the two subcluster cores is compressed as they approach the centre from the lower left- and upper right-hand corners respectively. The compression at the centre of the forming cluster is obvious in the temperature maps (Fig. 7), where a slab of hot gas with a dumbbell pattern extending in the NE SW direction and which is normal to the axis of merging of the subclusters gradually builds up between z = 0.24 and z = 0.22 and then starts expanding at z = The top panel in fig. 5 of Markevitch et al. (2000) presents a schematic picture of the first stage of a massive merger that they use to model their Chandra observation of A2142. (This picture was first derived from simulations by Roettiger et al and later confirmed by Ricker & Sarazin 2001.) In the first stage, so-called merger shocks in the nomenclature of Markevitch et al. (2000) would theoretically take place in the ICM as the subcluster gas surrounding one core and carried out in its motion hits the gas of the other subcluster with an opposite direction of motion. (At z = 0.22, CG 1 and CG 2 have velocities of the order of 1700 km s 1 with respect to the rest frame of the simulations, and twice this for their relative velocity, while the speed of sound in the unshocked ICM is of the same order: 2200 km s 1 for K.) Unfortunately, our simulation lacks the resolution to bring out these merger shocks, but it clearly shows the compression of the gas. 3.2 Generating the cold fronts At z = 0.2, the fourth panel of Fig. 7 shows the first stage of expansion of the compressed gas in the wake of/over the diverging cores, which have reached beyond the first passage. According to

5 Cold fronts in massive mergers 805 Figure 5. Series of snapshots, from z = 0.26 (top left-hand panel) to z = 0 (bottom right-hand panel), of the decimal logarithm of the 3D gas density integrated along a 500-kpc-thick slice. Each image shows the same Mpc 2 region in the xy-plane. The values shown range from 0.17 to 10 5 (units are arbitrary here), and the colour scale shows the temperature and is the same for all snapshots. the lower left-hand panel of fig. 5 of Markevitch et al. (2000), as the subcluster cores head towards their apocentre, it is expected that they will induce a new series of shocks ( bow shocks ) if they move supersonically in the central cluster regions where the gas has previously been heated by the merger shocks. However, because our simulation is not able to differentiate between the bow and merger shocks predicted by Markevitch et al. (2000), nor to study their interactions, we will denote the two shocks clearly identified

6 806 H. Mathis et al. Figure 6. As Fig. 5, but for the decimal logarithm of the 3D dark matter density integrated through the slice. The values of the density shown range from 0.5 to (in arbitrary units); the colour scale is the same for all snapshots. after first passage in front of the moving subcluster cores as bow shocks or simply shocks. These shocks are clearly seen as the two central red parallel slabs in the z = 0.18 frame of Fig. 7 and at subsequent epochs, and are fairly centrally symmetric with respect to one another. They expand up to the virial radius until z = 0.12, and dissolve later in the far outskirts of the cluster (IGM, filaments) not seen on the maps. The birth of the shocks is also very clear in the z = 0.18 panel of the Compton y-parameter (Fig. 8): for instance,

7 Cold fronts in massive mergers 807 Figure 7. Decimal logarithm of the line-of-sight X-ray emission-weighted temperature, in a 6 6 Mpc 2 xy-region corresponding to the centre of Fig. 5 (the z-coordinates of the slice are the same as in Fig. 5). The temperature ranges from to K; the colour scale is the same for all snapshots. the steep pressure rise due to the lower bow shock is at the lower left edge of the central red zone. Fig. 7 shows little temperature variation between the upstream and downstream flows (excluding the broad shock region) at z = 0.18 and at z = This is due to the adiabatic expansion and cooling of the gas in the wake of the shocks. Two symmetric cold fronts gradually develop in this zone: they are already visible at z = 0.16, as blue half-circles at coordinates (42.5, 48.5) and

8 808 H. Mathis et al. Figure 8. As Fig. 7, but for the decimal logarithm of the Compton y-parameter of the gas (or pressure integrated over the 500-kpc-thick slice). (For technical reasons, the zone shown has been downshifted vertically by 1 Mpc.) The normalization is arbitrary but the colour scale is the same for all snapshots. (44, 49.8) Mpc. Both reach their final position by z = 0.12, where their shape is reminiscent of the bow-shaped features observed in the high-resolution X-ray images. Relevant observations here include first, the top left-hand panel of fig. 4 in Markevitch, Vikhlinin & Forman (2003) for the merging cluster 1E ; secondly, the left-hand panel in fig. 4 of Markevitch et al. (2003) for A754, although we caution that in this last case the cold front probably corresponds to the very early stage of the ones we have simulated;

9 Cold fronts in massive mergers 809 and thirdly, the Chandra picture of the merging cluster A168 recently analysed by Hallman & Markevitch (2004) which precisely corresponds to the fully developed z 0.12 stage of our simulation. The variation of the Compton y-parameter is smooth all over the cold fronts in the z = 0.1 panel of Fig. 8. In addition, from z = 0.16 down to z = 0.1, a filament of gas joining CG 1 and CG 2 is visible on the temperature maps. It has a lower temperature and a higher density than its immediate surrounding ICM and it is even clearer on the gas density maps (Fig. 5). We have checked that this gas has an entropy comparable to the gas in CG 1 and CG 2. This filament traces continuous accretion on the central regions; it may correspond to the gas particles of CG 1, CG 2 that have been unbound at the first close encounter of the cores as well as to the particles that have been gradually stripped off in the wake of the cores by ram pressure as these clumps orbit in the ICM but that do not end up in cold fronts because of their position. Alternatively, this gas may be continuously leaking from the already formed cold fronts and may be feeding directly into the centre of the cluster. 3.3 Final relaxation The shocks keep on extending out of the frame shown on the temperature maps. Their integrity is already broken at z = 0.12 but some features persist in the far outskirts down to the present day. On the other hand, the cold fronts remain fairly stationary and stable on the temperature maps until z = 0.03 and only weaken by z = 0. In the meantime, the subclump cores merge as they reach their second close encounter: this is well traced in the gas and DM density maps in Figs 5 and 6. The cold fronts survive the shock preceding them; they stall in their outward propagation, but they do not wash out in temperature maps as much as the shock does in the z = 0.12 and z = 0.10 maps. As a result, if major mergers are the main formation channel of cold fronts, their smaller duty cycle could make the bow shocks that they are associated with intrinsically more difficult to detect in X-ray temperature maps. We stress here that the temperature and Compton y-parameter maps of Figs 7 and 8 have been obtained on a 500-kpc-thick slice containing the orbits of the two subcluster cores. This has allowed us to achieve high spatial resolution and to visualize precisely any interesting features. In reality, limited resolution and projection effects will degrade the maps. Recent observations have improved by large factors in resolution (Chandra reaches 1 arcsec, corresponding to a proper size of 3.5 h 1 kpc at z = 0.3, or 1 to 2 pixels in the maps of Figs 5 to 8), but projection effects may still significantly smooth and distort the smallest details shown on our maps. Features that are prominent and asymmetric with respect to the cluster centre such as cold fronts will be the least affected, but patterns that are more symmetric with respect to the centre and that extend over a larger area such as shocks may suffer significantly from projection. With these caveats in mind, we first give in the next paragraph snapshots of simulated X-ray images. Then, we compare the respective positions that we find for our subcluster cores and for our cold fronts with available observations. 3.4 An X-ray picture of the ICM X-ray emission is strongly concentrated at the cluster centre, and observations of temperature variations that are weak and far from the centre present a major challenge. However, because of their strong luminosity contrasts, cold fronts and even bow shocks are now routinely seen in X-ray observations of the ICM: we check here whether we find the same contrast in our simulations. Fig. 9 gives Mpc 2 snapshots of the decimal logarithm of the X-ray surface brightness (units are arbitrary) integrated over the same 500-kpc-thick slice normal to the z-direction and cutting through the cluster centre that was used for Figs 5 to 8. We find avariety of morphologies. The z = 0.26 to z = 0.22 maps show the two roughly spherical, clearly separated bright (in white) subcluster cores caught before their first close encounter. (At z = 0.26 and z = 0.24 the upper right peak of X-ray emission is slightly out of the z-slab.) At z = 0.16 (right-hand panel in the second row), as they orbit towards their apocentres, the two cores begin to lose a fraction of their gas in their wake, seen as diffuse white emission, and at the same time, the transition from red to diffuse red in the lower left- and upper righthand parts of the image becomes sharper, the direct signature of the merging shock propagating outwards. At z = 0.12 (central panel in third row) the cores contract, acquire an elongated shape, and fall back in the central potential well, preceded by a thin stream of gas accreting to the cluster centre. At the same time, the cold fronts are most clearly visible, for example at the sharp colour contrast between orange and diffuse red at (42, 48) Mpc. The bow shocks are also visible on the maps farther from the centre, for example at (42, 46.8 Mpc) for the lower left one. The central peak of the z = 0 map shows what seems to be a fairly relaxed core, but a number of gradients remain in the intermediate regions, some 1 Mpc away from the centre. Even though these gradients are not as sharp as at z = 0.12 for example, those associated with cold fronts [for example at (42, 48) Mpc] could still be observed. Before comparing with observations, we caution that X-ray luminosity is generally expected to be much more compact and peaked than, for instance, the Sunyaev Zeldovich effect measuring the Compton y- parameter. We note that this is not the case when comparing Figs 9 and 8. For example, the z = 0.14 panel is strikingly more peaked in the Compton y-parameter. We stress that this is artificial, though, and is the result of having both a different dynamic range and a different colour scale in the two maps. Even though some of the Chandra X-ray luminosity pictures look similar to the ones shown here, a direct comparison is not straightforward, because our cold fronts, which develop after the first passage of the cores, are likely to correspond to a stage of merger that is more evolved than that generally observed. In fact, as they reconstructed the dark matter distribution using weak lensing, Clowe, Gonzalez & Markevitch (2004) found the cold front of 1E to trail the dark matter component of the associated subcluster; in A3667, using the gas density distribution inside the front, Vikhlinin & Markevitch (2002) also found that the centre of curvature of the cold front lags behind the centre of the dark matter subclump. Let us focus on the simulated subcluster that has accreted from the lower left of the simulation. In the xy-plane we show, the dark matter subcluster core CDM 1 is ahead of its associated cold gas clump only between z = 0.2 and z = 0.18 (right after core passage): see Fig. 3. Thereafter, the cold gas core together with the forming cold front are ahead of the dark matter core in the xy-plane, the opposite to what is observed. Again, we stress that projection effects need careful assessment before a definitive conclusion can be reached: consider for example the complex relative paths of the centres of mass of CG 1 and CDM 1 in the zy-plane shown in the lower right-hand panel of Fig. 3. Markevitch et al. (2003) note that the cold front they observe in the merging cluster A754 at the north of the eastern galaxy concentration does not seem to be associated with any galaxy concentration. They suggest that this cold front is either dragged along by a dark matter subclump with no clear optical counterpart or that

10 810 H. Mathis et al. Figure 9. Decimal logarithm of the X-ray surface brightness S X (arbitrary normalization). The z-slab and 6 6 Mpc 2 region in the xy-plane are the same as those used in Fig. 7. The colour scale is the same for all snapshots, but we note that the dynamic range is larger than that of Figs 5 to 8. The z = 0.12 snapshot clearly shows the sharp transition associated with the cold fronts, at (42, 48) Mpc for the lower left front, together with the milder gradient associated with the bow shock at, for example, (42, 46.2) Mpc. In reality, projection effects may degrade the sharpness of the weak features, but the strongest contrasts between white and orange colours are likely to remain unaffected.

11 Cold fronts in massive mergers 811 it is an elongated gas concentration completely decoupled from its dark matter core and sloshing independently. Such an evolved stage could be closer to our cold fronts forming out of the dense gas cores after first passage, if significant sloshing/tidal forces are induced at core passage by the spatial decoupling between the dark matter and gas cores (again, consider the trajectory in the zy-plane shown in the lower right-hand panel of Fig. 3 at z = 0.2). 4 RESOLVING SHOCKS IN THE ICM Because the cores of our merging subclusters are massive and because their infalling velocity is high, we expect shocks to develop in the forming ICM. SPH simulations usually delineate the shock fronts rather poorly, but the high resolution of our simulation enables us to circumvent this to some extent. We first compute in a Eulerian approach temperature and pressure profiles over test lines cutting through the lower left shock. Secondly, we adopt a Lagrangian approach and consider entropy variations of test gas particles as a probe of the shocks. Then, we look for a possible discontinuity of the velocity field of the gas at the edge of the cold front, which would be the signature of a contact interface. Finally, we briefly discuss secondary shocks expected in the final stage of the merger. 4.1 Temperature and pressure profiles On each side of the centre of the newly formed cluster, two main shocks develop from z = 0.18 onwards. The overall geometry remains fairly simple and confirms the picture sketched by Markevitch et al. (2000): after first passage, bow shocks develop because of the supersonic (transonic) motion of the dense gas subcluster cores CG 1 and CG 2 inside the newly formed ICM. The top left- and right-hand panels of Fig. 10 show two temperature profiles across the lower left shock at z = 0.20 and z = 0.18 respectively, while the left- and right-hand bottom panels give the Compton y-parameter profiles at the same redshifts. The quantities have been interpolated along two test lines (solid and dashed) reaching from the unaffected ICM (at the exterior of the outermost Figure 10. Temperature and Compton y-parameter projected over a 500-kpc-thick slice in z, computed along a test line cutting through the lower left bow shock and cold front in the xy-plane, at z = 0.2 and z = 0.18 (see text for details on the choice of the test line). The abscissa shows the y-coordinate. The upstream region of the shock corresponds to the left of the temperature and pressure rise. While the cold merging clump is not visible on the z = 0.2 temperature cut, it is evident at y = 48.5 on the z = 0.18 temperature cut. shock front) in the bottom left region of Fig. 7 to the core region of the cluster. These lines probe the highest-temperature zones of the lower left shocks at z = 0.2 and z = 0.18, as well as the cold fronts; they are parallel to the y-axis and each (solid, dashed) line pair is separated by 0.1 Mpc in the x-direction to give an idea of the variations in x. Because these temperature extrema are drifting in the xy-plane, we have slightly changed the endpoints of the lines between z = 0.20 and z = 0.18 in order to better capture interesting features. At z = 0.20, the solid (dashed) test line is at x = 43.1 (43.2) Mpc; at z = 0.18, the solid (dashed) test line is at x = 43.1 (43) Mpc. For clarity, these lines are repeated in Figs 12 and 13, later, which also show the temperature field around the lower left shock at z = 0.20 and z = 0.18 respectively. The abscissa of Fig. 10 is labelled in the global y-coordinate of the simulation in Mpc. Note that, because the test line is not exactly parallel to the direction of propagation of the shock, the scale is slightly dilated, but this has no consequence for our purposes. In fact, the interpretation of either the solid or dashed profile is quite similar for the two redshifts, and reads as follows. At z = 0.20, the subclumps have gone slightly past their first closest encounter (see the top right-hand panel of Fig. 2). The bulk of the CG 2 particles reaches y = 48.8 at x = 43.2 (this is the drop visible on the dashed line), the temperature and pressure rise characterizing the shock are clearly seen at y = The temperature on the solid line rises by a factor of T 2 /T to 3.5, but the pressure rises by a factor of P 2 /P 1 30 to 33 across the shock, where indices 1 and 2 respectively label the upstream and downstream regions. If the shock were normal to the local direction of the flow, the Rankine Hugoniot relations would give an upstream Mach number M 1 = 4.9 from the pressure ratio, and a significantly different M 1 = 2.9 from the temperature ratio. The differences in M 1 are likely due to the standard entropy formulation of Springel & Hernquist (2002) that we have used instead of their conservative form. The standard entropy formulation does not explicitly take into account variations in the smoothing lengths in the equations of motion, and, in this implementation, energy conservation is only guaranteed in the continuous limit. In particular, it is possible that approximate energy conservation biases the conversion of kinetic energy into internal energy, in particular in shock regions where density gradients are steep, and artificial viscosity introduced into the numerics is employed to ensure non-adiabatic heating. Whether it is pressure or temperature that is the most biased is a question that needs to be addressed with a conservative version of entropy formulation. In the downstream region corresponding to the central zone of the newly formed cluster, the temperature of the gas heated at the shock decreases as a result of the adiabatic expansion of the gas in the wake of the shocks; this phenomenon is further catalyzed by the divergent motion of the flow as it is dragged by both CG 1 and CG 2. At z = 0.20, the temperature T 2 of the flow is fairly constant in the solid line over the range y = 49 to 49.5, while it is constant over the range y = 49.2 to 49.5 in the dashed line. On the other hand, the pressure P 2 declines monotonically by a factor of 5 from the peak at y = 49 to y = At z = 0.18, the temperature and pressure profiles probed by the two test lines are similar, except for the respectively higher and lower temperatures probed by the dashed line at y = and y = 48.5 Mpc, corresponding respectively to the red peak at (43, 47.75) Mpc and to the cold subcluster core at (43, 48.5) Mpc in Fig. 12, later (note that the cold front has only started forming at that redshift). At z = 0.18, the subclump cores are already 1.5 Mpc apart in the xy-plane and on their way to their apocentre, and the situation is

12 812 H. Mathis et al. similar to that of two pistons compressing the gas in front of them. Their motion is supersonic in a K hot ICM, so they cause shocks. The upper right-hand panel of Fig. 10 indicates that the shock is some 750 kpc ahead of CG 2 (this is similar on the two test lines because we probe regions where the curvature dy/dx of the shock front is small). Again, the cool dense gas clearly visible at y = 48.5 Mpc and beyond on the temperature profile is associated with the subcluster core and probably also with the nascent cold front. Even though the amplitudes of the jumps in both pressure and density are similar at z = 0.20 and z = 0.18, the shapes of the profiles differ in the downstream region: this is a possible consequence of the readjustment of the gas and dark matter density profiles in the central region of the cluster. 4.2 Entropy variation As an alternative to Eulerian profiles of fluid quantities, we can follow the gas particles themselves to check the adiabaticity of the flow in a Lagrangian approach (see Keshet et al for the original application to tracing shocks in an SPH simulation of the intergalactic medium). We follow the specific entropy of the gas particles to confirm that the large temperature and pressure gradients discussed in Section 4.1 are associated with shocks. At z = 0.28, shortly after the merger, we select all gas particles in the lower left zone of the ICM, with (x, y, z) ([42; 42.5], [47; 48], [48.5; 49.5]) Mpc. We find about 1100 such particles; they are then tracked as they move in the ICM. This Lagrangian region trails the subcluster core CG 1 (see the lower left-hand panel of Fig. 2) in its pre-passage motion to the NW. We expect these particles to catch at least part of the effects of the shock induced by the opposite motion of CG 2, simply because they are in the x-y direction of propagation where the shock going to the lower left seems the strongest on the z = 0.18 map of Fig. 7. The assumption is that the shock has already fully formed and developed as on the z = 0.18 map when our test particles pass through it. Fig. 11 gives the entropy evolution s of these test particles, with s = log (T ρ γ 1 ) proportional to the specific entropy s = C V ln (T ρ γ 1 ). The black, red and green curves respectively give the 10, 50 and 90 per cent quartiles of the distribution. We distinguish two features. First, there is a synchronous increase in s for all particles in the range 0.2 < z < 0.16 (recall that core passage is at z 0.22 to 0.2), although the degree of variation in s differs: it is less than 0.1 (corresponding to Mach number M 1 = v shock /c s,upstr = 2.1) for the 10 first per cent of the particles and more than 0.3 (M 1 = 3.3) for the last 10 per cent. Once the test particles have passed through the shock (z 0.15), the entropy per particle changes very little down to z = 0. The lower limit of 3.3 to the Mach number we find for a tenth of the particles ( s = 0.3) agrees with the estimates ranging from 2.9 to 4.9 we obtained in the previous paragraph from the temperature and density profiles, but it is only relevant for onetenth of the particles. Possible reasons why most of the particles in our test set have lower Mach numbers than 3.3 include the delay in the build-up of the bow shock caused by the oppositely moving subcluster core, and the non-coplanar geometry of the flow. 4.3 Velocity across shocks and cold clumps Figs 12 and 13 show the projected gas velocity field at z = 0.2 and z = 0.18, respectively, of a square slice of width 2 Mpc and thickness 500 kpc spanning over the lower left shock region, overlaid on the colour-coded emission-weighted temperature map selected from the same slice. The colour scale is the same as that shown in Fig. 7. The Figure 11. Evolution s of the entropy of gas particles selected shortly after the merger in a 0.5 Mpc 3 rectangular parallelepiped close to the lower left of the ICM (trailing CG 1 before first core passage), which is only affected by the bow shock at z We define s = log (T ρ 1 γ ), which is proportional to the specific entropy s = C V ln (T ρ γ 1 ), and show the 10, 50 and 90 per cent quartiles of the distribution (black, red and green curves respectively). s = 0.05, 0.1, 0.2 and 0.3 correspond to upstream Mach numbers M 1 = 1.8, 2.1, 2.7 and 3.3, respectively. Note the characteristic synchronous entropy increase between z = 0.2 and z = 0.18 due to the shock, together with the spread in s by more than a factor of 5. Possible reasons for the scatter include the complex trajectories of the test particles (some can encounter a weaker shock), and the delay in the build-up of the shock itself, which may be incomplete at the passage of some of the test particles. velocities have been computed in the rest frame of the simulation, and the longest arrows correspond to 1300 km s 1 at z = 0.2 and to 1435 km s 1 at z = We discuss the two figures in turn. At z = 0.2, while the ICM outside the bow shock (to the lower left) is accreting towards the cluster centre, the amplitude of the velocity of the gas strongly decreases as it hits the shock, for example over the thin yellow line passing over (43.25, 48.6) Mpc. This corresponds to the strongest temperature gradient. In the post-shock downstream region, on the upper right side of the temperature gradient, the velocity of the shocked gas has either significantly decreased (43.5, 49.1) or it is directed outwards from the cluster centre in regions corresponding to the subcluster core or to its wake. (In the rest frame of the shock, both upstream and downstream gas would have inward velocities.) At the 30-kpc resolution shown, there is no evidence for a discontinuity in the direction of the velocity field over the edge of the cold core, for example at (43.2, 48.9) Mpc. In Fig. 13, while the x-range has been kept the same as in Fig. 12, the y-range has been shifted downwards by 1 Mpc to follow the propagation. The same features are apparent, except for the velocityreversing region at the shock, which, together with the zone of highest temperatures, has dilated in size along the direction of the propagation of the shock. The upstream accretion velocity field is weaker than at z = 0.20, possibly because the region is farther from the cluster centre, and the largest of the velocities shown here are found in the immediate wake of the shock at (43.1, 48) Mpc. The emerging cold front can be seen as the lower temperature zone at (43, 48.5) Mpc. It consists of particles that have already started climbing up the local potential well of the subclump, but still move coherently with the flow behind them. Because of its smaller size and smaller temperature drop, it is not yet the fully developed cold front found at later stages of the simulation. The velocity field is

13 Cold fronts in massive mergers 813 Figure 12. The z = 0.2 projected gas velocity field in a 500-kpc-thick, 2-Mpc-wide slice cut in the xy-plane around the lower left cold front. The background shows the emission-weighted temperature map using the same colour scale as in Fig. 7. The largest arrows correspond to a velocity of 1300 km s 1, and the resolution of the velocity field is about 30 kpc. Note the discontinuity of the direction of the velocity field over the shock, for example at (43.25, 48.6)Mpc, and its smoothness over the blue, cold dense gas, for example at (43.2, 48.9) Mpc. The vertical solid and dashed lines correspond to the cuts employed to assemble the temperature and pressure profiles in the left-hand panels of Fig. 10. coherent over the bulk of this feature and in its wake down to the 30-kpc-resolution mesh with which we show the velocity field. However, there is evidence for discontinuity in the direction of the velocity field over the front region of the cold feature: at x = 43 Mpc, the velocity vectors rotate between y = 48.4 and y = 48.5 Mpc. This is the likely signature of a contact discontinuity between the flow of cold gas at Kinblue and the flow of hotter, shock-heated gas at K. While the discontinuity in the direction of the velocity field is exactly over the green blue temperature transition at (42.8, 48.4) Mpc, we note that more to the right it reaches inside the blue temperature zone. At (43, 48.45) Mpc for example, the direction discontinuity no longer corresponds to a sharp temperature contrast. However, projection effects over the 500-kpc-thick slice that we have used might blur/shift the x-y velocity field, preventing a definite conclusion. At z = 0.2, the difference between the 2D velocity in the xy-plane of the upstream flow of unshocked cold gas and that of CG 2 projected on a direction normal to the shock is of the order of 2200 km s 1 This would correspond to a Mach number M 1 1ina K upstream gas. (At z = 0.18, the Mach number would only be transonic.) The significant difference between the Mach numbers measured from the x-y 2D velocity field shown in Figs 12 and 13 and the numbers estimated from the ratios of thermodynamic quantities in the previous paragraphs suggest that either the z-component of the velocity is significant or that projection effects are at play over the 500-kpc-thick slice that we employ.

14 814 H. Mathis et al. Figure 13. As Fig. 12, but at z = The colour scale is the same as in Fig. 7. The region shown has been translated downwards from Fig. 12 by 1 Mpc, to better follow the flow. Here, there is evidence for discontinuity in the velocity field at the boundary between the cold dense core/forming cold front and the heated gas downstream of the shock, for example at (42.8, 48.4) Mpc. The vertical solid and dashed lines correspond to the cuts employed to assemble the temperature and pressure profiles in the right-hand panels of Fig Secondary shocks Smaller, secondary shocks will develop at the centre of the cluster during the final inspiralling and merging after z = 0.1. This process is a scaled-down repeat of the initial compression of the ICM gas situated between the cold dense subcluster cores that took place before their first passage. It can be seen in the centre of the last four panels of Fig. 7. At z 0.08, secondary shocks would be confined to the very central region by the convergent gas flows surrounding CG 1 and CG 2,asthese move towards their second close encounter. As a result, shock propagation would be impeded in the direction of the cold front. They could, however, extend in the NE SW direction of the map. After z = 0.08, as the dense cores go past their second close encounter, this coherent flow stops and the secondary shocks would combine with bow shocks and be released. The yellow/red annulus around the dumbbell-shaped light blue zone in the centre of the z = 0.06 panel in Fig. 7 might be associated with these shocks, but increased resolution is needed here. Note that the central red temperature spot at (43, 49) Mpc in the penultimate panel corresponds to the final gas compression before the final merger of the cores. An additional feature in the centre of the z = 0.1 panel of Fig. 7 is the thin tail of cold gas that seems to leak from both cold fronts. It is particularly visible above the lower left front, and is located in the wake of the densest part of CG 2 as this clump falls back towards the cluster centre. The position of these thin tails suggests

15 Cold fronts in massive mergers 815 that they could be associated with the cold gas of CG 2 and CG 1 which has been stripped by ram pressure and cools down further as it is expelled from its local gravitational potential until it achieves pressure equilibrium with the surrounding ICM. (Such a cooling mechanism would be similar to that resulting in cold fronts, even though the origin and resulting shapes are notably different; this is supported by the similarity between the temperatures observed in these tails and in the cold fronts.) Another possibility is that they correspond to gas leaking from the cold fronts and directly feeding the cluster centre, without any interaction with the subclumps. Although Nagai & Kravtsov (2003) state that their secondary bow shocks heat and disrupt their cold fronts, it is not clear that this takes place in our simulation. The secondary shocks seem to affect only the low-temperature tail of the cold fronts, which points to the cluster centre: for example, the upper right cold front is mostly unaffected by the shocks. Mixing or diffusion of the cool phase into the hot ICM may explain the final disruption of the cold fronts. 5 CHARACTERIZING THE COLD FRONTS In this section, we first demonstrate that the features seen in the temperature maps are cold fronts. Then, we select the particles of the lower left cold front and trace them back to elucidate their origin. 5.1 Physical attributes Figs 14 and 15 respectively give the profiles of the Compton y- parameter (in arbitrary units) and of the temperature (in K) taken through the cluster. They have been computed at z = 0.1 on a test line cutting through the longest extension of the cold fronts and through the cluster centre. The profiles have been computed from the value projected over a 500-kpc-thick slab normal to the line of sight (z-direction). The abscissa has an arbitrary origin, with the cluster centre at 2.5 Mpc in the units shown. The pressure profile rises to the centre of the cluster, is smooth on both sides, and there is no discontinuity over the location of the cold fronts. The complex features at the centre could be due to shock- Figure 15. Same cut as in Fig. 14, but for the temperature profile of the gas. The globally symmetric shape is striking: the gas temperature rises to the left, centre and right regions (x loc < 1 Mpc, 2 < x loc < 3 Mpc, and x loc > 5Mpc). Between these zones, the regions of lower temperature correspond to the cold fronts and to the cold tails trailing the gas clumps when they fall back to the centre. Cold zones extend over more than 1 Mpc along the direction plotted. (For orientation, the upper right cold front of the ICM is mapped to the right of the figure.) ing/compression of the intervening gas. The temperature profile, on the other hand, is symmetric but discontinuous. The temperature rises in the centre and on the edges of the test line, but drops by afactor of 4 to 6 in the regions 1 < x loc < 2 and 3.5 < x loc < 5 Mpc with respect to the outer temperature value. The exterior discontinuity corresponds to the envelope of the cold fronts. At z = 0.1, CG 1 and CG 2 are 1 Mpc apart. While the interior temperature discontinuity at x loc = 2 Mpc is sharp and goes over CG 2, CG 1 is slightly out of the slice, resulting in a smoother interior temperature discontinuity at x loc = 3.5 Mpc. Assuming that pressure equilibrium has been achieved between the interior of the cold front and the surrounding ICM, the factor of 3 to 4 drop in temperature yields afactor of 3 to 4 increase in the density of the gas of the cold front compared with that of the ICM. Both cold fronts form behind the merger shocks induced by the motion of the cores. Even though the gas downstream of the shocks cools down as it expands adiabatically (see Figs 12 and 13), we will show in the next subsection that this process cannot be responsible for the formation of cold fronts: the particles constituting the fronts have a clear-cut origin. Figure 14. Profile of the Compton y-parameter (in arbitrary units) of the cluster over a test line passing through the cold fronts and through the cluster centre. The profile has been computed from the value projected over a 500- kpc-thick slab normal to the z-direction at z = The origin of the abscissa has been chosen so that the cluster centre is at 2.5 Mpc. Note that the pressure rise to the centre of the cluster is smooth on both sides, and that the signature of the merging bow shocks has reached beyond the ranges shown here. The complex features seen at 2.5 Mpc may be due to the combination of the remains of the cold, high-pressure merging subclumps and the secondary shocks. 5.2 Tracing the origin of the cold fronts We now assess the origin of the matter constituting the cold fronts. We set up a method to select SPH particles in the simulation directly from both spatial criteria and from various temperature or pressure thresholds taken in the maps of Figs 7 and 8. We can then combine selection masks along different directions in the case the target is conveniently expressed as an intersection of lines of sight. To select the cold fronts, we combine two cuts in two projected, emission-weighted temperature maps along two orthogonal lines of sight through the cluster. Particles of the cold fronts are selected at z = 0.1 once the cold fronts are well developed. We then trace them back to shortly after z merg and find that almost all of them originate in the two subcluster cores: gas particles from the lower left cold front come from CG 2, while those from the upper right cold front come from CG 1. Fig. 16 shows the origin of particles so selected around

16 816 H. Mathis et al. Figure 16. Tracing of the gas particles of the lower left cold front. Lefthand panel: position in the xy-plane of the particles of the cold front. The particles have been chosen below an appropriate threshold in temperature at z = Right-hand panel: same particles once they have been traced back to z = The particles of the two cores CG 1 and CG 2 are shown in red and green respectively. There is a clear overlap between CG 2 and the initial position of most of the particles of the cold front. the lower left cold front. The particles inside the mask are shown in the left-hand panel: their position at z = 0.28 is given in black in the right-hand panel, and CG 1 and CG 2 have been overplotted in red and green, respectively. There is a clear overlap between the particles traced back from the mask and those of CG 2, showing that the bulk of the mass of the lower left cold front originates in CG 2. There is a small additional contribution to the mass of the cold front from gas particles that were originally in the upper left surroundings of CG 1, and also from a few fuzzy particles of the z = 0.28 ICM (for example the group of particles at (44, 45) Mpc). Conversely, if we follow the forward evolution of CG 1 and CG 2 from z merg,wefind that the envelope of the position of the outer particles of both clumps at z = 0.1 corresponds well with the location of the cold fronts, while their inner densest part has already fallen back into the central region of the cluster. This is seen by comparing the location of the red clump of the lower left-hand panel of Fig. 2 with the left-hand panel of Fig. 16. Apart from the cold-front zone and from the cold tails observed at z = 0.1, neither CG 1 nor CG 2 loses particles to the surrounding ICM. Because the evolution is qualitatively very similar for the upper and lower cold fronts, we will deal exclusively with the upper cold front (associated with CG 1 ) in the rest of this study. We can probe the origin of these gas particles that are located in the bottom of the gravitational potential well of CDM 1 if, at z = 0.1, we select the particles with the highest pressure in the upper coldfront region. The left-hand panel of Fig. 17 compares the spatial distribution at the epoch of formation of the cold front (z 0.16) of particles selected according to their pressure only, in red, with the positions of particles of CG 1 (in black). The right-hand panel traces back both ensembles to shortly after z merg. While the particles with the highest pressure at z = 0.1 trace as expected the minimum of the potential well, they do not map back exactly onto CG 1 :anumber of particles stem from its close surroundings and from the lower right outskirts of CG 2. To summarize, the particles of the cold fronts are essentially composed of the particles of the cores of the two subclumps. Cold-front particles evolve coherently until the end of the simulation. Interestingly, the gas particles located at the bottom of the local gravitational potentials associated with the CDM 1 /CDM 2 substructures once they are heading to their second passage do not originate exclusively from the cores of the merging clusters but also from their initial outskirts; Figure 17. Tracing of the high-pressure gas particles of the upper right cold-front region. Left-hand panel: projection in the xy-plane of the z = 0.16 positions of the particles selected at z = 0.1 by their high pressure (in red) in a3 4 Mpc 2 region encompassing CG 1 : these particles map the bottom of the local gravitational potential well. The z = 0.16 positions of the particles of CG 1 are repeated in black: note on one side of the potential well the extended plume up to y 51 and x 44.5 Mpc which constitutes the cold front, on the other side a set of particles falling back to the cluster centre (or trailing CG 1 ). Right-hand panel: the corresponding positions of the two sets of particles at z = While a fair fraction of the red particle overlaps with CG 1 at z = 0.28, some initially surrounding particles, and some particles from the lower right of CG 2 also end up with high pressure in the bottom of the CDM 1 potential well at z = 0.1. in fact, they take the position of some initially very dense core gas particles. 6 FORMATION OF THE COLD FRONTS This section proposes clues to the physical mechanism responsible for the formation of our simulated cold fronts, focusing on the cold front associated with CG 1 (upper right of Fig. 7). We first analyse and interpret the spatial distribution of the gas particles in the dark matter gravitational potential. Then we make links with other recent work simulating the formation of cold fronts. The gravitational potential W of the gas particles is obtained only from the contribution of the cluster dark matter particles: we neglect the contribution of the gas particles, of the large-scale structure, and of the cosmological constant. In Fig. 18, we plot in black the position of each particle of CG 1 in the gravitational potential W, while the red set corresponds to particles selected at z = 0.1 by their high pressure in a region centred on the upper right cold front (see Section 5.2 above). Because the red set has been overplotted, it can hide black particles; note in addition that, when a particle belongs to both sets, it appears in red. The positions are projected along a single axis in abscissa, here the y-axis of the simulation. The left- and right-hand Figure 18. Positions of the CG 1 particles (in black) in the gravitational potential W created by the DM particles of the whole cluster. The red points give the positions of the particles that have the highest pressure at z = 0.1. (These particles do not necessarily belong to CG 1.) The left- and right-hand panels correspond to z = 0.16 and z = 0.12 respectively.