Close-up view of an ongoing merger between the NGC 4839 group and the Coma cluster – a post-merger scenario

ABSTRACT

1 INTRODUCTION

According to the current cosmological concordance model, galaxy clusters form hierarchically through a combination of rare major merger events and more gentle continuous accretion of smaller groups of galaxies throughout cosmic time along filamentary structures (e.g. Kravtsov & Borgani 2012; Vikhlinin et al. 2014). The latter actually represents the dominant channel of galaxy cluster growth in mass and in the number of member galaxies (see e.g. Berrier et al. 2009; Dolag et al. 2009; Genel et al. 2010). The best sites for studying structure formation processes are the galaxy cluster outskirts, which represent the transition region between the virialized intracluster medium (ICM) approximately in hydrostatic equilibrium, and the infalling material from the surroundings. Mergers and accretion events often leave imprints on the distribution of the hot ICM such as shocks, cold fronts, and ram pressure stripped tails which could be observed with X-ray observations (e.g. Sun et al. 2006, 2010; Markevitch & Vikhlinin 2007; Su et al. 2017, among others). In particular, the appearance of extended tails of ram pressure stripped gas provides valuable information for recovering the 3D geometry of a merger event, the orbital stage of a subhalo (early infall, pre-/post-pericenter passage), and even ICM plasma properties such as viscosity, magnetic fields, thermal conduction (Roediger et al. 2015a,b, among others). Structure formation processes in galaxy clusters can be studied with radio observations of radio relics, which are believed to trace large-scale shock waves generated by a merger or accretion, (e.g. Ensslin et al. 1998; van Weeren et al. 2009; Di Gennaro et al. 2018).

The Coma cluster of galaxies (Abell 1656), the third brightest X-ray cluster, is one of the nearest and best-studied galaxy clusters. Optical and X-ray observations have revealed a wealth of substructure in the Coma cluster (Colless & Dunn 1996; Vikhlinin, Forman & Jones 1997; Briel et al. 2001; Neumann et al. 2003; Adami et al. 2005; Andrade-Santos et al. 2013, among others). One of the most prominent is the group of galaxies associated with the elliptical galaxy NGC 4839. It lies in the cluster outskirts (∼1 Mpc in projection) south-west of the cluster centre. The X-ray image (see Fig. 1) exhibits an edge-like structure at the head of the group and an elongated tail of ram pressure stripped gas towards the south-west, i.e. opposite to the direction to the Coma centre. The NGC 4839 group appears to be merging with the Coma cluster core, and the tail direction is approximately aligned with a filament connecting the Coma cluster with Abell 1367, which, in turn, is part of the ‘Great Wall’ (e.g. Geller & Huchra 1989; Neumann et al. 2001; Brown & Rudnick 2011). It has long been debated whether observations are consistent with a simple radial infall or imply a tangential orbit (Biviano et al. 1996), and whether we observe the first passage (Colless & Dunn 1996; Neumann et al. 2001; Akamatsu et al. 2013, among others) or the group has already passed the Coma cluster centre (Burns et al. 1994).

Figure 1.

Upper row: XMM–Newton image of the Coma Cluster (left-hand panel) and the NGC 4839 group (right-hand panel) in the 0.5–2.5 keV energy band. Middle row: Surface brightness image divided by the best-fitting β-model. Bottom row: Projected temperature map. The white dashed circle marks the radius of r₅₀₀  = 47 arcmin (Planck Collaboration X 2013). The white scale bar indicates 10 arcmin.

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Based on galaxy redshifts, Colless & Dunn (1996) constrained the 3D geometry of the Coma-NGC 4839 merger using a simple dynamical two-body model, in which the two clusters were considered as point masses following a linear orbit under their mutual gravity. They estimated that the angle between merging objects and the observer is most likely to be α = 74°|$^{+5}_{-10}$|⁠, i.e. the merger happens almost in the plane of the sky, the true 3D separation is 0.8 ± 0.1 h⁻¹ Mpc and the infall velocity is |$1700^{+350}_{-500}$| km s⁻¹. Colless & Dunn (1996) argued that the NGC 4839 group is just beginning to penetrate the Coma cluster.

Coma, as a typical merging cluster, also hosts a radio halo and a relic. The Coma radio relic is located ∼2.1 Mpc in projection from the cluster centre, beyond the NGC 4839 group, but in the same south-west direction. Based on radio and optical observations, Brown & Rudnick (2011) suggested that the Coma radio relic is due to an infall shock, caused by the infall of a ‘wall’ of galaxies possibly associated with NGC 4839 into the Coma cluster. However, large radio relics (radio gischt), in general, are believed to be associated with outgoing merger shocks (e.g. Bonafede et al. 2009; van Weeren et al. 2010, among others). Analyses of XMM–Newton (Ogrean & Brüggen 2013) and Suzaku observations (Akamatsu et al. 2013) revealed a tentative temperature discontinuity across the Coma relic, which has been interpreted as a shock front with a Mach number of M ∼ 2. Moreover, a tentative detection of a pressure jump at the position of the radio relic has been reported (Erler et al. 2015) based on the thermal Sunyaev–Zel’dovich effect data extracted from the first public all-sky data release of Planck.

Based on a weak gravitational lensing survey performed with the Subaru/Suprime-Cam, Okabe et al. (2014) detected a subhalo associated with the NGC 4839 group and measured its mass to be |${\sim } 10^{13} \, \mathrm{M}_{\odot }$|⁠, assuming a Navarro–Frenk–White (NFW) profile with a truncation radius of ∼100 kpc. Curiously, the X-ray peak derived from the XMM–Newton image is spatially coincident with the NGC 4839 elliptical galaxy, but both are shifted ≃ 1 arcmin ≃ 30 kpc towards the west from the weak-lensing mass centre (see fig. 2b in Sasaki et al. 2016).

Figure 2.

Radial X-ray surface brightness profile of the Coma cluster based on the XMM–Newton data. The solid line shows the best-fitting β-model with core radius r_c = 9.9 arcmin ≃ 277 kpc and β = 0.71. The sector containing NGC 4839 was excluded. The dashed vertical line marks r₅₀₀ and the dotted line shows the outer bound of the radial range used for fitting.

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Here, we analyse available XMM–Newton and Chandra observations. To constrain the 3D geometry and a trajectory of the infalling group, we compare the X-ray maps with smoothed-particle hydrodynamic (SPH) simulations. In Sections 2 and 3 we describe general X-ray properties of the Coma cluster and the NGC 4839 group, respectively. The simulation set-up is outlined in Section 4, followed by a discussion of pre-merger and post-merger scenarios in Section 5. We discuss the mass and gas temperature of the NGC 4839 group in Section 6 and summarize our findings in Section 7.

All our results are scaled to a flat ΛCDM cosmology with Ω_m = 0.3, Ω_Λ = 0.7, and a Hubble constant H₀ = 70 km s⁻¹ Mpc⁻¹, which implies a linear scale of 27.98 kpc arcmin⁻¹ at Coma’s redshift |$z$| = 0.0231 (NED¹ data base). For the Coma cluster, we assume r₅₀₀ ≃ (47 ± 1) arcmin ≃ (1.315 ± 0.028) Mpc and r₂₀₀ ≃ 1.5r₅₀₀ as in Planck Collaboration X (2013), where r₅₀₀ and r₂₀₀ are the radii within which the mean density of the cluster is 500 and 200 times the critical density of the Universe, respectively.

2 COMA

2.1 X-ray surface brightness

For our analysis, we used publicly available XMM–Newton data, namely, the data from the EPIC/MOS (European photon imaging camera/metal oxide semiconductor) detector. The data were prepared by removing background flares using the light curve of the detected events above 10 keV and renormalizing the ‘blank fields’ background to match the observed count rate in the 11–12 keV band (Churazov et al. 2003). The resulting background-subtracted, exposure- and vignetting-corrected XMM–Newton image of the Coma cluster in the 0.5–2.5 keV energy band is presented in Fig. 1 (upper row). The zoom-in view of the NGC 4839 group is shown in the right-hand panel.

2.2 Temperature map

Figure 3.

Pure statistical uncertainties (arising from the photon counts) of the temperature measurements for different plasma temperatures (4, 7, 10, and 15 keV) plotted against source photon counts. In the projected temperature map shown in the bottom row of Fig. 1, each value of the temperature was calculated using regions with ∼3000 photon counts.

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3 The NGC 4839 group

3.1 Observations and analysis

For the analysis of the NGC 4839 group, we use available archival XMM–Newton observations which cover the group and its vicinity. Some of the pointings – namely, 0652310201, 0652310301, 0652310501, 0652310601, and 0652311001 – were strongly affected by flares and, as a consequence, excluded from our analysis. From other observations, flares were removed by discarding all 15-s long time bins which contain more than six counts with energy above 10 keV per bin. The total effective exposure (see Table 1) of all observations (MOS data²) used in the analyses in this Section is 283 ks, and for those centred on the NGC 4839 group, the exposure is 114 ks. Fig. 4 (all panels except the lower right) shows the background-subtracted, exposure- and vignetting-corrected XMM–Newton image in the 0.5–2.5 keV energy band. Point sources were excluded to highlight the diffuse emission SW from the core of the NGC 4839 group (tail) and towards the direction of the Coma cluster centre. Regions labelled as ‘Tail’ and ‘Interface’ (Fig. 4, upper left-hand panel) are analysed in Sections 3.1.1 and 3.1.2, regions ‘inner tail’, ‘main tail’, ‘bkg’, and ‘Coma ICM’ are discussed in Section 6.

Figure 4.

Upper left: XMM–Newton image (0.5–2.5 keV) of the NGC 4839 group showing the elongated tail and the enhanced X-ray emission towards the direction of the Coma cluster (north-east of the NGC 4839 nucleus). Point sources were excluded. The dashed circle marks r₅₀₀. The annular sectors are used in the analysis discussed in Sections 3.1.1 and 3.1.2. Upper right: The zoom-in view of the rectangular region marked with a white box (20 × 20 arcmin²) in the left-hand panel. The white scale bar indicates 10 arcmin. Bottom left: The same image as in the upper panel, but showing regions discussed in Section 6. Bottom right: Chandra image (0.5–2.5 keV) covering the same region as in the upper right-hand panel.

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The NGC 4839 group was also observed with the ACIS-I detector onboard the Chandra X-ray observatory in very faint (VFAINT) mode (ObsID 12887), with a total exposure time of 43 ks. The initial data processing is done using the recent calibration data and following the procedure described in Vikhlinin et al. (2005). This includes filtering of high background periods, application of the calibration corrections to the detected X-ray photons, and determination of the background intensity in each observation. The right-hand panel of Fig. 4 shows the available Chandra observation of the NGC 4839 group. Since the Chandra observation is relatively short and covers only the core of the group and the inner tail, only XMM–Newton data were used for the spectral analysis.

3.1.1 The tail of NGC 4839

Figure 5.

Radial temperature and electron density profiles along the tail of the NGC 4839 group (see regions in Fig. 4, upper left-hand panel). In blue, we show the results of spectral fitting with the ICM abundance fixed at 0.3 solar, while the case with varying gas metallicity is shown in red.

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3.1.2 Interface between Coma and the NGC 4839 group

Figure 6.

‘Interface’ region between the NGC 4839 group and the Coma cluster. The profiles are centred on NGC 4839 (see Fig. 4, upper left) with small radii (≲1 arcmin) lying in the core of the group and larger radii (≳7–8 arcmin) corresponding to the main Coma cluster. Surface brightness and temperature profiles result from the spectral fitting of an absorbed single-temperature thermal plasma model (phabs × apec). The exact regions are labelled as ‘interface’ in Fig. 4 (upper left-hand panel).

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4 SIMULATION METHODS

We performed SPH simulations to investigate the merging scenario of NGC 4839 group by using the gadget-2 code (Springel, Yoshida & White 2001). To simplify the merger process, we only consider the interaction between a main cluster and an infalling subcluster. Each body is further modelled as a spherical object consisting of a dark matter (DM) halo and gas atmosphere. A detailed description of the simulation method has been given in Zhang, Yu & Lu (2014, 2015). Here, we only provide a brief summary.

• The merging process is modelled in Cartesian coordinates (x, y, |$z$|⁠). The centre of mass of the merging system is initially set at rest at the origin of the coordinates. The merger plane coincides with the x–y plane. The DM haloes and gas haloes follow the NFW profile (Navarro, Frenk & White 1997) and the Burkert profile (Burkert 1995) within the virial radius for the density profiles (see equations 1–4 in Zhang et al. 2014). We fix the masses of haloes as described below and set the concentration parameter of the main cluster c = 4 according to the weak-lensing measurement (Okabe et al. 2014). The concentration parameter of the subcluster, however, is determined from the mass–concentration relation of Duffy et al. (2008).

• The merger configuration between two clusters is described by the following four parameters: the virial mass of the main cluster M₂₀₀, the mass ratio between the main cluster and the subcluster ξ (> 1), the initial relative velocity V₀, and the impact parameter P₀. Motivated by recent weak-lensing studies (Okabe et al. 2014), we fix the Coma cluster mass at |$M_0=1.2\times 10^{15}{\, \mathrm{M}_\odot }$| in all our simulations, but vary the other three parameters to find a ‘best-fitting’ model for NGC 4839 (see Table 2 for the parameter settings used in the simulations). We consider two different values for the mass ratio between Coma and the NGC 4839 group: ξ = 10 and 60. The former corresponds to the mass ratio estimate of Colless & Dunn (1996), and the latter is motivated by the gas mass estimate obtained in Section 3.1.1: if we assume the baryon fraction of |${\sim } 10{{\ \rm per\ cent}}$|⁠, then the total mass of the NGC 4839 group is |${\sim } 10^{13} \, \mathrm{M}_{\odot }$|⁠. We return to the question of the mass ratios below.

We stress here that, we do not intend to find an exact match between our simulations and observations in this study, but rather to understand the possible merger scenario(s). That is the reason why we did not survey a large parameter space, but test a few specified merger cases with large/small mass ratios and high/low initial angular momentum. We also only present the simulation results while assuming the LOS is parallel to the |$z$|-axis, since, as mentioned above, available estimates of the viewing angle (Colless & Dunn 1996) favour a plane of the sky merger. Moreover, if the group is on its first radial infall into the Coma cluster, as it is widely assumed, the group is expected to move supersonically with an infall velocity of ∼2000 km s⁻¹. The LOS velocity of the NGC 4839 group relative to the Coma cluster is only V_r ≃ 470 km s⁻¹ (Adami et al. 2005), i.e. much smaller compared to the local speed of sound. Thus, to reconcile the measured LOS velocity with the first radial infall, the viewing angle should be close to 90°.

5 RESULTS

We discuss two possible merger scenarios for the NGC 4839 group in this section, including (1) the group is in the pre-merger stage (i.e. before the primary pericentric passage⁴); (2) the group is near the primary apocenter. We show that our SPH simulations favour the latter scenario, but the former one still cannot be definitely excluded.

5.1 Pre-merger scenario

Fig. 7 (top and middle panels) shows the X-ray surface brightness distribution in the runs R60V500P2000 and R60V1000P3000 at |$t=-0.5{\rm \, Gyr}$|⁠, where the dashed line shows the trajectory of the infalling subcluster throughout the simulation. In this image, we see a straight gaseous tail trailing the subcluster. The subcluster, however, still retains most of the gas in its gravitational potential well, because it has not yet entered the high gas density region in the main cluster. Therefore, in this scenario, the gas mass of the tail |${\sim } 10^{12} \, \mathrm{M}_{\odot }$| (see Section 3.1.1) can be used to estimate the total mass of the group |$M_{200} \sim 10^{13} \, \mathrm{M}_{\odot }$|⁠, assuming a gas mass fraction of |${\sim } 10{{\ \rm per\ cent}}$| (Vikhlinin et al. 2006; Sun et al. 2009). Fig. 7 (lower panel) shows the profiles of the X-ray surface brightness and the X-ray emission weighted temperature along the line connecting the centres of the two clusters. The vertical dashed line in this panel marks the position of the shock front. Notice that the shock front itself is not prominent in the X-ray surface brightness profile. Typically, shock fronts are detected in X-ray images as surface brightness edges. Our simulations suggest that the shock front, associated with the NGC 4839 group, is actually located close to the lowest surface brightness region in the X-ray image (Fig. 7) and not in a region of surface brightness enhancement. Motivated by these results, one can expect to detect a bow shock at a distance of ≃ 5–6 arcmin (the lowest surface brightness region in Fig. 6) from the contact discontinuity (cold front), corresponding to the leading edge of the group. At the same time, the stand-off distance Δ, i.e. the distance between a stagnation point and the closest point on the bow shock, can be estimated from the Mach number (Moekel 1949; Farris & Russell 1994; Verigin et al. 2003; Zhang et al. 2019, among others). According to equation (35) in Verigin et al. (2003) (see also equation A4 in Zhang et al. 2019), for the NGC 4839 group, infalling radially and with a Mach number ≃ 1.5, the stand-off distance Δ ≃ 0.7 × R_cf, where R_cf ≃ 1 arcmin is the curvature radius of the cold front. Thus, we have a clear contradiction between predictions for the bow shock position. Projection effects do not play a significant role here, since, as discussed above, the merger should happen almost in the plane of the sky if the NGC 4839 group is on its first infall into Coma. So we conclude that available X-ray data and our calculations of the stand-off distance disfavour the pre-merger stage.

Figure 7.

Upper and middle panels: X-ray surface brightness distribution of the runs R60V1000P3000 and R60V500P2000 at |$t=-0.5{\rm \, Gyr}$|⁠. The white contours show the distribution of the mass surface density. The black dashed curves reveal the trajectory of the infalling subcluster. Lower panel: profiles of the X-ray surface brightness and X-ray emission weighted temperature (for R60V500P2000) along the line connecting the centres of the two merging subclusters. The horizontal axis represents the distance from the centre of the main cluster. Note that the tail is symmetric and the bow shock is not prominent in the X-ray surface brightness map/profile and is actually located in the region of minimal surface brightness (for details see the text).

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Moreover, since the stripped gas is distributed mostly along the trajectory of the infalling subcluster before the core passage, runs R60V500P2000 and R60V1000P3000 show different tail directions relative to the centre of the main cluster if the LOS is perpendicular to the merger plane (see Fig. 7). These two runs have different initial angular momenta. In practice, however, there is a degeneracy while determining the angular momentum of the subcluster and the viewing angle from the Chandra/XMM–Newton X-ray images (the wake of NGC 4839 is nearly parallel to the radial direction of Coma in the sky plane). In spite of this, tails of the subclusters remain almost straight and symmetric in both runs, because there is no sharp turn in their motion (it only occurs near the apocenter when the merging system has a relatively small initial angular momentum, see Section 5.2 for more discussion). This is obviously different from what we observe in NGC 4839. In this regard, our simulations disfavour the pre-merger scenario. However, we stress that it is still possible to explain the observed ‘wiggling’ tail as a result of von Kármán vortex shedding, which generally occurs behind a moving blunt body with a Reynolds number ≳ 100 (e.g. Williamson 1996). The onset of vortex shedding, however, is usually delayed in numerical simulations since numerical viscosity suppresses growth of the instabilities (Braza, Chassaing & Ha 1986). We simply estimate the vortex shedding period T_vortex of the wake if assuming the Strouhal number St = D/T_vortexU ≃ 0.2, where |$U\ (\sim 2000{\rm \, km\, s^{-1}})$| and |$D\ (\sim 200{\rm \, kpc})$| are the velocity and size of the infalling cluster in the simulation. The period |$T_{\rm vortex}\sim 0.5{\rm \, Gyr}$| is thus shorter than (or comparable to) the crossing time (size of the subcluster divided by the velocity of an oncoming stream of the surrounding gas) of the subcluster.

5.2 Post-merger scenario

Fig. 8 shows the time evolution of the X-ray surface brightness and X-ray weighted temperature distributions in the run R10V500P2000. The panels illustrate four different merger stages, i.e. (1) pre-merger, (2) post-pericentric passage, (3) apocentric passage, and (4) secondary core accretion (from left to right). The simulated image shown in Fig. 8 panel (3a) (apocentric passage) resembles the observed X-ray morphology (see Figs 1 and 4). Our simulation provides a good match with the real X-ray observations (compare panel 3a in Fig. 8 with the upper panel of Fig. 1), when the subcluster is close to, but shortly after, the primary apocentric passage. The subcluster trails a large and asymmetric tail, whose formation could be understood in the following way:

• During the pericentric passage, the gas in the NGC 4839 group is driven by the ram pressure and forms a tail trailing the galaxy.

• When the subcluster approaches apocenter, it slows and reverses its radial velocity.

• At the same time, the ram pressure decreases and the subcluster gas falls into the local gravitational potential well of the group.

• Shortly after the apocenter passage, the DM, stars, and the gaseous core are moving towards the Coma cluster centre, while the displaced gas moves in the opposite direction, forming the structure as in the panel (3a) of Fig. 8.

Figure 8.

Time evolution of the X-ray surface brightness (top row) and X-ray weighted temperature (bottom row) distributions of the run R10V500P2000. These panels illustrate four stages of the merger process (from left to right): pre-merger, post-pericentric passage, apocentric passage, and secondary core accretion. The white contours show the mass surface density (top panels) and the X-ray surface brightness (bottom panels) distributions. The black dashed curve in the top panels shows the trajectory of the infalling subcluster with the initial infall located at the top left of the box. The gas mass belonging to the subcluster within the red box marked in panel (3b) is |$M_{\rm gas}\simeq 5\times 10^{12}{\, \mathrm{M}_\odot }$|⁠, broadly consistent with the gas mass estimate from the X-ray analysis. Panel (3a) provides a good match with the X-ray morphology of the NGC 4839 group, when the subcluster crosses the apocenter (compare with Fig. 1), which favours the post-merger scenario.

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The last two stages are illustrated in Fig. 9 showing the flow patterns in and around the infalling group. As argued above, this structure is formed when the subcluster is turning sharply. This is the reason why the run R10V500P2000 gives a better match with the observations than R10V1000P4000 (the infalling subcluster holds larger angular momentum in this run). For the large impact parameter (R10V1000P4000), there is no strong interaction between the infalling group and the main cluster. After pericentric passage, the core of the subcluster remains roughly round, while X-ray data clearly show an edge-like structure at the head of the group.

Figure 9.

The slice in gas velocities (taken in the merger plane) for the post-merger scenario, overlapped with the X-ray surface brightness (white contours). The colourmap colour codes absolute values of velocities in the rest frame of the mass centre of the merging clusters (Coma  + NGC 4839). Arrows show the velocity vectors. The left-hand and right-hand panels show the moments before and after the apocentric passage, respectively. As the NGC 4839 group approaches the apocenter (left-hand panel), it slows. The ram pressure decreases and the tail gas falls back towards the core of the group, driven by the gravitational drag from the subcluster. Just after the apocentric passage (right-hand panel), the NGC 4839 group starts its second infall into the Coma cluster core, while the gaseous tail is moving in the opposite direction (towards the south-west). The right-hand panel shows the same time as panels (3a) and (3b) in Fig. 8.

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Fig. 8 shows that the subcluster penetrates the central gas core of the main cluster and a large fraction of gas is stripped away from its potential well through this process. We measure the gas mass belonging to the subcluster within the red box marked in panel (3b) (integrated over the LOS), i.e. |$M_{\rm gas}\simeq 5\times 10^{12}{\, \mathrm{M}_\odot }$|⁠. This result is of the same order of magnitude as the gas mass estimate obtained in Section 3.1.1. We note that the post-merger scenario requires a smaller mass ratio (i.e. higher mass of the NGC 4839 group) than that of the pre-merger scenario. Otherwise, after the primary core passage, the subcluster loses almost all its gas. In panels (1b) and (2b), prominent shock waves are driven by the infalling subcluster. However, shocks usually move faster than the subcluster after pericentric passage (Zhang et al. 2019). Thus, we do not expect to see shocks near NGC 4839. The absence of a shock is also illustrated in Fig. 10 which shows the X-ray surface brightness and X-ray emission weighted temperature for the post-merger scenario, i.e. shortly after the apocenter passage, along the line connecting the group and the main cluster. No very sharp features are seen in the profiles and the amplitude of temperature variations is markedly smaller compared to the pre-merger case shown in Fig. 7, bottom panel.

Figure 10.

Same as in the bottom panel of Fig. 7, but for the post-merger scenario (R10V500P2000, t  = 1.6 Gyr). The surface brightness and temperature profiles bear some morphological similarities with the pre-merger profiles, but the shock between the group and the main cluster is now absent. As a result, no very sharp features are seen in the profiles and the amplitude of temperature variations is markedly smaller.

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At the moment when the subcluster is near the apocenter, the bow shock associated with the first infall of NGC 4839 has propagated south-west much farther away from the core of the group and its current position is roughly consistent with the Coma radio relic (Giovannini, Feretti & Stanghellini 1991). We will discuss the origin of the Coma relic in more detail in Lyskova et al. (in preparation). The observed hot ‘sheath’ region, as seen in the X-ray data (see Figs 1 and 4), that surrounds the brighter NGC 4839 subcluster core, can be also explained under the post-merger scenario. If the impact parameter of the merger is not too high, then the subcluster, just after the apocenter passage, starts moving through its own tail of stripped gas (see flow patterns in Fig. 9, right-hand panel). An increased temperature and gas density in the ‘sheath’ region could be due to interaction of the re-infalling subcluster with the stripped gas mixed with the Coma ICM. One possible mechanism here is the ‘stolen atmosphere’ effect (described in Sheardown et al. 2018), when intracluster gas, surrounding the subcluster, is drawn into the NGC 4839 group potential and compressed/heated. We defer the discussion of the nature of observed ‘sheath’ for future work.

To check results obtained with the SPH simulations, we also ran a flash simulation using the same merging parameters as those used in run R10V500P2000. The simulated surface brightness and temperature maps are consistent with results of the SPH simulations. Moreover, Sheardown (2019) inspected a large set of flash simulations of idealized binary cluster mergers and independently reached the same conclusion that the NGC 4839 group is most likely to have passed by the Coma core from the north-east with a small impact parameter and is now on its next infall.

6 DISCUSSION

6.1 Mass of the NGC 4839 group

As discussed above, the mass of the NGC 4839 group is poorly constrained. We briefly summarize here the mass and the mass ratio estimates |$\xi = M_{\mathrm{ vir}}(\rm Coma)/M_{vir}(\rm NGC~4839)$| available in the literature. From the analysis of the velocity distributions of the cluster/group members, Colless & Dunn (1996) obtained the virial masses of |${\simeq } 1.3 \times 10^{15} \,$| and |${\simeq } 8.6 \times 10^{13} \, \mathrm{M}_{\odot }$| for the Coma cluster and the NGC 4839 group, respectively. So their mass ratio is ≃ 15.

Based on the weak-lensing signal, Okabe et al. (2014) measured the Coma virial mass of |$M_{\mathrm{ vir}}(\rm Coma) = 1.2 \times 10^{15 } \, \mathrm{M}_{\odot }$| and the total mass of the NGC 4839 group within the tidal (truncation) radius M(r < 98 kpc|$) \simeq 1.6 \times 10^{13} \, \mathrm{M}_{\odot }$|⁠. This estimate was obtained assuming that the group mass density outside the truncation radius, r_t = 98 kpc, is close to zero. This measurement can constrain the virial (M₂₀₀) mass of the NGC 4839 group, assuming that the mass profile within r_t has not been modified by the merger. We described the mass density with the NFW profile and explored a range of M₂₀₀ and c₂₀₀. The weak-lensing estimate agrees reasonably well with the group virial mass of |$\gt 1\times 10^{14} \, \mathrm{M}_{\odot }$|⁠. The NFW mass profiles with |$M_{200} \sim 10^{13} \, \mathrm{M}_{\odot }$| are in more than 3σ tension with the weak-lensing estimate. In Table 3, we provide a summary of the NGC 4839 group mass (and the mass ratio) estimates. Note that this table is not intended to cover all Coma mass measurements available in the literature.

The masses also can be estimated via X-ray scaling relations. To convert M₅₀₀ to M₂₀₀, we use the following relation (obtained for the concentration parameter c = 4): R₅₀₀/R₂₀₀ = 0.65 and M₅₀₀/M₂₀₀ = 5/2 × (0.65)³ = 0.69. If the NGC 4839 group is characterized by 4 keV gas, then according to the M–T relation (Vikhlinin et al. 2006; Sun et al. 2009), its |$M_{500} \simeq 2.9 \times 10^{14} \, \mathrm{M}_{\odot }$| and |$M_{200} \simeq 4.2 \times 10^{14} \, \mathrm{M}_{\odot }$|⁠. For the Coma cluster with its 8 keV gas, the M–T relation gives |$M_{200} \simeq 1.26 \times 10^{15} \, \mathrm{M}_{\odot }$|⁠. These arguments suggest that the mass ratio between the subcluster and the main cluster is ≃ 3. However, such a mass ratio implies a major merger scenario and is disfavoured by our simulations – in this case, the Coma cluster would be dramatically disturbed, and strong shocks, propagating to the north-east and south-west, would be generated. The best-fitting post-merger simulation with the mass ratio of ξ ∼ 10 provides a good match to the observed morphology of the tail of the group, but the measured ratio of gas temperatures in the tail and in the main cluster do not agree well with simulations. In the simulations, the temperatures of the main cluster and the tail of the subcluster are ≃5 keV and ≃0.5–1 keV, correspondingly, i.e. the temperature ratio is ∼5–10. However, the observed ratio of the X-ray temperatures ≃8 keV/4 keV = 2 is noticeably different. As a consequence, the mass ratio derived from the M–T relation is several times smaller than in simulations.

6.2 Temperature of the NGC 4839 group

The projected spectra analysed in Section 3 have not been corrected for the additional contribution that might come from the Coma gas along the LOS but outside the volume occupied by the tail. This was motivated by the much higher surface brightness of the tail region compared to the typical Coma brightness at the same distance (see the upper panel of Fig. 1). Even if we redo our spectral analysis using the ‘Coma ICM’ region (see Fig. 4, lower left-hand panel) as a background, the main conclusions remain unchanged. However, according to Fig. 4, the NGC 4839 group seems to coincide with some surface brightness enhancement. For the post-merger scenario, the observed tail is formed when the core of the group turns sharply at the apocenter. So the overall surface brightness enhancement, which was previously thought to be shocked gas (e.g. Neumann et al. 2001), in our simulations is actually group gas, stripped before the apocenter passage, and partly mixed with Coma gas. To account for its contribution to the observed spectra, we treat the region adjacent to the core of the group (marked as ‘bkg’ in Fig. 4, lower left-hand panel) as the actual background. We extract and fit the ‘bkg’ spectrum with an absorbed single-temperature thermal plasma model. Results are provided in Table 4. We model the ‘main tail’ (see Fig. 4, lower left-hand panel) spectrum with two APEC components. One component is for the ‘background’ gas, the other is for the tail gas. We fix the temperature and the abundance of the ‘background’ gas at best-fitting values from the previous step (see Table 4) and vary its normalization along with parameters of the APEC model representing the tail gas. Since the 3D geometry of the merger is poorly known, we allow the background normalization to vary by a factor of ∼2 relative to the best-fitting values for the single-temperature fit. As a result, for the two-temperature model, the ‘main tail’ temperature decreases to ≃ 2.4 keV. Note that both the single- (two free parameters) and the two-temperature (three free parameters) models provide an adequate fit to the data (Fig. 11). While the modest residuals seen in the bottom panel of Fig. 11 suggest that the spectrum is more complicated than our model, the main point we want to emphasize is that the two-temperature model fit with the temperature of one component fixed at 6.4 keV, produces very reasonable normalizations of two components, consistent with an assumption of a cool 2.4 keV group gas embedded into a hotter ICM of the main cluster mixed with the outer layers of the tail. We analysed also the ‘inner tail’ region (see Fig. 4, lower left-hand panel) in a similar way. The temperature of the inner tail is found to be ≃ 2.2 keV, if we assume that the abundance of heavy elements is 0.5 Z_⊙. A higher metallicity gives higher temperature and larger uncertainties (see Table 4). If the tail temperature is indeed 2.4 keV, then the NGC 4839 group mass is |$M_{200} \simeq 1.9 \times 10^{14} \, \mathrm{M}_{\odot }$| from the M–T relation, and the mass ratio between Coma and the group is ≃6.6. While this does not resolve the discrepancy between observations and simulations completely, it certainly reduces the tension.

Figure 11.

The observed spectrum (black crosses) of the ‘main tail’ region and the best-fitting models. The single-temperature thermal plasma model is shown in red. The best-fitting gas temperature is 4.2 ± 0.1 keV (see Table 4). A similar quality fit can be obtained with a two-temperature model (blue solid line). In this model, the first component (blue dotted line) is due to the group gas, while the second component (blue dashed line) represents the LOS contribution of the Coma cluster ICM mixed with the stripped group gas. The temperature and abundance of the second component are fixed at the values obtained for the ‘bkg’ region (see Fig. 4, lower left-hand panel), viz., kT = 6.4 keV and Z = 0.25 Z_⊙ (see Table 4). The best-fitting temperature of the tail gas decreases to 2.4 ± 0.3 keV. The green line shows the background from blank fields to which an additional component (representing a variable particle background in these particular observations) is added. Both the single- and two-temperature models fit the spectrum reasonably well (see Table 4). It is therefore plausible that the characteristic temperature of the NGC 4389 gas is ∼2 keV, implying a lower initial mass of the group.

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To some extent the tension between the mass/temperature ratios in simulations and observations also could be weakened if one finds the best-fitting configuration of the merger that exactly matches all available observations, but this task is beyond the scope of our paper.

7 CONCLUSIONS

Coma, as one of the nearest massive galaxy clusters, provides a unique close-up view of ongoing mergers. One of the most striking merger events involves the NGC 4839 group which lies in the Coma cluster outskirts (∼1 Mpc in projection) in the south-west direction from the cluster centre. The X-ray images of the subcluster exhibit a cold front at the head of the group, a ‘sheath’ region of hotter gas enveloping the core of the group, and an elongated tail of ram pressure stripped gas toward the south-west, i.e. the opposite direction of the Coma cluster centre. We discuss two possible scenarios of the merger: (1) the group is on its first infall before the primary pericentric passage, and (2) the group is near the primary apocenter. The data and simulations favour the latter scenario in agreement with the earlier suggestion by Burns et al. (1994).

• Pre-merger scenario

  In the first scenario, the NGC 4839 group comes from the south-west along the filament connecting Coma with Abell 1367 and it has just started to penetrate the Coma ICM, then the group is expected to move supersonically with Mach number ≳1.5. The position of the bow shock, predicted by our simulations, corresponds to a surface brightness minimum along the line connecting the two merging subclusters, while customarily shock fronts are identified with a sharp increase of the surface brightness. However, the expected position of a bow shock cannot be reconciled with the stand-off distance estimate. Thus, we conclude that we do not see a strong shock. We also showed that if the group is on its first radial infall, then the merger is most likely to be almost in the plane of the sky, i.e. non-detection of the shock cannot be attributed to projection effects. Moreover, the pre-merger simulations do not reproduce the observed X-ray appearance of the tail of the NGC 4839 group. In simulations, tails remain almost straight and symmetric, while the observed morphology is more complex. So we conclude, our analysis disfavours the radial infall scenario.

• Post-merger scenario

  In the post-merger scenario, a good match between the modelling and the real X-ray observations is achieved when the infalling group has just passed apocenter. Under this scenario, the observed morphology of the tail is formed in the following way. When the subcluster approaches the apocenter, it slows and then reverses its direction of motion. At the same time, the ram pressure ceases and the group gas falls back into the local potential well of the group, overshooting an equilibrium position and appearing on the other side of the group core. Shortly after apocenter passage, the core of the subcluster starts moving towards the Coma cluster centre, while the displaced gas moves in the opposite direction. The observed ‘sheath’ – a region of slightly denser and hotter gas than the ambient gas in front of the group – could arise due to interaction of the subcluster, now moving back towards the Coma centre, with its own tail gas now mixed with the gas of the main cluster. In the post-merger scenario, we do not expect shocks near NGC 4839 since the bow shock associated with the first infall of the group has already propagated towards the south-west, much farther away from the group. The current position of the shock is roughly consistent with the Coma radio relic.

ACKNOWLEDGEMENTS

The authors thank the anonymous referee for a thorough review and constructive suggestions which helped to improve the paper. This work was partially supported by the Russian Science Foundation (grant 14-22-00271). ER acknowledges the support of STFC, through the University of Hull’s Consolidated Grant ST/R000840/1. ER and AS acknowledge access to viper, the University of Hull High Performance Computing Facility. WF and CJ acknowledge support from contracts NAS8-38248, NAS8- 01130, NAS8-03060, the Chandra Science Center, and the Smithsonian Institution. The flash software used in this work was developed in part by the DOE NNSA ASC- and DOE Office of Science ASCR-supported Flash Center for Computational Science at the University of Chicago. The scientific results reported in this article are based on observations obtained with XMM–Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and the USA (NASA). This work has also made use of Chandra data provided by the Chandra X-ray Center. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

Footnotes

REFERENCES