RXCJ1111.6+4050 galaxy cluster: the observational evidence of a transitional fossil group

We present a detailed kinematical and dynamical study of the galaxy cluster RXCJ1111.6 + 4050 (RXCJ1111), at z = 0 . 0756 using 104 new spectroscopic redshifts of galaxies observed at the Telescopio Nazionale Galileo and SDSS DR16 public archive. Our analysis is performed in a multiwavelength context in order to study and compare mainly optical and X-ray properties using XMM-Newton data. We find that RXCJ1111 is a galaxy cluster showing a velocity distribution with clear deviations from Gaussianity, that we are able to explain by the presence of a substructure within the cluster. The two cluster components show velocity dispersions of 644 ± 56 km s − 1 and 410 ± 123 km s − 1 , which yield dynamical masses of M 200 = 1 . 9 ± 0 . 4 × 10 14 M ⊙ and 0 . 6 ± 0 . 4 × 10 14 M ⊙ for the main system and substructure, respectively. The 2D spatial distribution of galaxies and X-ray surface brightness of RXCJ1111 presents an elongation in the North-South direction. These observational facts, together with a gradient of 250-350 km s − 1 Mpc − 1 in the velocity field, following the NNE-SSE direction, suggest that the merger axis between the main system and substructure is slightly tilted with respect to the line-of-sight. The substructure is characterized by a magnitude gap ∆ m 12 ≥ 1 . 8, so it fits the "fossil-like" definition of a galaxy group. From the X-ray observations, we estimate a M 500 , X = 1 . 68 ± 0 . 25 × 10 14 M ⊙ , which is in good agreement with the dynamical masses when two galaxy components are considered separately. This suggests that the mass estimates obtained from X-ray and velocity dispersion are compatible even for non-relaxed clusters, at least when we are able to identify and separate galaxy clumps and derive masses by considering the virialized regions. We propose a 3D merging model and find that the fossil group is in an early phase of collision with the RXCJ1111 main cluster and placed at ∼ 8 ◦ ( ± 3 ◦ ) from line-of-sight. This merging model would explain the slight increase found in the T X with respect to what we would expect for relaxed clusters. Due to the presence of several brightest galaxies, after this collision, the substructure would presumably lose its fossil condition. Therefore, RXCJ1111 represents the observational evidence that the fossil stage of a system can be temporary and transitional.


Introduction
In recent decades, it has been well established that galaxy clusters are very dynamic structures in constant evolution that increase their mass in collision processes, either with low-mass systems or with massive clusters.Large mergers between highmass clusters are among the most energetic events in the Universe.However, numerical simulations show that the accretion of small groups of galaxies is the main mechanism of evolution in clusters (e.g.Berrier et al. 2009;McGee et al. 2009).Today, much observational evidence supports this hypothesis, such as the optical detection of substructures in the galaxy member distribution, inhomogeneities in the gas distribution by the study of X-ray and radio diffuse emission, or even the presence of complex dark matter halos in weak lensing data (Feretti 2002;Martinet et al. 2016).Studying mergers in low-mass systems is much more challenging than in massive clusters.It requires hundreds of spectroscopic redshifts per cluster and X-ray observations with long exposures to obtain data with sufficient signalto-noise ratio from the weak diffuse emission.
The study of collisions involving small galaxy groups, and in particular the dynamical and kinematical properties, is a fundamental step in understanding the cluster evolution.One important question that is still unclear is the nature of fossil groups (FGs) and how these peculiar structures form and evolve.Fossil systems (groups and galaxy clusters) are dominated by a single luminous elliptical galaxy, similar to brightest cluster galaxies (BCGs) or even to cD galaxies, at the centre of the extended X-ray emission.Today, there are several scenarios to explain the evolutionary picture in which FGs became fossils in the early Universe.One proposes that FGs grow through minor mergers alone, only accreting a few galaxies at z ≥ 1, leaving FGs enough time to merge galaxies in one very massive and luminous object (Ponman et al. 1994;D'Onghia et al. 2005).Another scenario proposes that FGs could be a transitional status for some systems.In this sense, fossil systems could become non-fossil ones in the end due to the accretion of nearby galaxy systems, or FGs could even be swallowed by other more massive systems (von Benda-Beckmann et al. 2008).An alternative evolutionary scenario suggests that FGs could have been formed in the very early Universe but with a primordial deficiency of mid-and lowluminous galaxies (Mulchaey & Zabludoff 1999).
RXCJ1111.6+4050(hereafter RXCJ1111) was identified by G. O. Abell in 1958 and catalogued as Abell 1190 (Abell 1958), a galaxy cluster with richness R = 2. RXCJ1111 was also detected in the ROSAT All Sky Survey (NORAS; Böhringer et al. 2000) and designated as J1111.6+4050 as part of the MCXC catalogue (Piffaretti et al. 2011).Very recently, this cluster has also been observed using XMM-Newton X-ray satellite under the CHEX-MATE Heritage programme (Arnaud et al. 2021).In optical, this cluster was also detected in the SDSS-DR6 and SDSS-DR8 photometric samples as a galaxy overdensity using the redMaPPer algorithm (Wen et al. 2009;Rykoff et al. 2016).It has also been covered by the Pan-STARRS1 footprint and the Legacy Surveys DR9 images.In addition RXCJ1111 has been identified through its Sunyaev-Zeldovich (SZ) signal in the first and second Planck cluster catalogues and was named PSZ1 G172.64+65.29 (Planck Collaboration XXIX 2014) and PSZ2 G172.88+65.32 (Planck Collaboration XXVII 2016).The FIRST VLA Survey also covered this target region (Becker et al. 1995) in the 300 square degree initial observations.
In this work, we analyse the RXCJ1111 cluster of galaxies using optical, X-ray and radio data in order to disentangle the dynamical state and the main physical properties of this system that shows clear signs of substructure.The intracluster medium (ICM) and galaxy components react on different timescales to cluster evolution showing many observational effects at numerous spectral frequencies.Thus, multi-wavelength analysis of galaxy clusters is the ideal approach to investigating merging processes.Our main aim is to find a coherent dynamical scenario in agreement with the effects observed at different wavelengths.
Only the combination of spectroscopic information, X-ray and radio observation, will help us to obtain a satisfactory answer for the questions of this is a merging cluster, and if we are looking at pre-or post-merger phase, what kind of structures are involved, and whether the X-ray and dynamic mass estimates are in good agreement.Here, we explore the dynamics of RXCJ1111 with the aim of answering all these questions.This paper is organised as follows.In Sect. 2 we describe the new spectroscopic observations as well as the X-ray data.We analyse the optical and galaxy properties of RXCJ1111 in Sects.3 and 4, and compare them with X-ray properties in Sect. 5.In Sect.6 we present the main dynamical features and propose a plausible 3D merger model for the cluster in Sect.6.2.We conclude this paper by summarising our results in Sect.7.

Optical spectroscopy
Even though RXCJ1111 has been observed in radio frequencies, X-ray and several broad-band photometric data, the spectroscopic information in the literature and databases is relatively poor.We selected 43 spectroscopic redshifts from the SDSS-DR16 database within a region of 15 radius with respect to the centre of the cluster, which is too sparse a sample to investigate this low-redshift cluster.Therefore, in June 2020 we carried out spectroscopic observations at the 3.5m Telescopio Nazionale Galileo (TNG) telescope at Roque de los Muchachos Observatory.
One of the most used techniques to obtain a large number of galaxy redshifts in a limited field is multi-object spectroscopic (MOS) observations.In June 2020, we carried out MOS observations of RXCJ1111 covering a region of about 17 × 17 .We mapped this region with five MOS masks including 198 slitlets.The masks were designed in order to avoid overlaps with the SDSS redshift sample and maximise the number of new redshifts.We used the 3.5 m TNG telescope and its spectrograph DOLORES.The instrumental set-up was used with the LR-B grism 1 and slits of 1.6 width; this offers a dispersion of 2.75 Å per pixel between 370 and 800 nm of wavelength coverage.We acquired a single 1800 s exposure per mask.
The spectra were extracted using standard IRAF packages and calibrated in wavelength using helium, neon and mercury lamps.The spectroscopic redshifts of galaxies were obtained by correlating the scientific spectra with those assumed to be templates (from the Kennicutt Spectrophotometric Atlas of Galaxies; Kennicutt 1992) using the technique by Tonry & Davis (1979) and implemented as the task RVSAO.XCSAO in IRAF environment.This method detects and correlates the main features present in the acquired spectra (i.e. the Ca H and K doublet, Hδ, G band, and MgI in absorption, and the OII, OIII doublet, and Hα and Hβ in emission) with those present in the template spectra.We used five templates corresponding to different galaxy morphologies (elliptical, Sa, Sb, Sc, and Irr types).At the end of the process we obtained a radial velocity estimate and the corresponding correlation error for 109 galaxies in the field of RXCJ1111.We added to this sample 43 redshifts retrieved from the SDSS-DR16 spectroscopic database, and thus our spectroscopic sample (see Table A.1) includes 152 redshifts in a region of 17 × 17 (see Fig. 1).The full redshift sample presents a median S/N of 7 and a median error in cz of 91 km s −1 , respectively.We detected 37 star-forming galaxies, characterised by the presence of [OII], [OIII] and/or Hα emission lines with equivalent widths >10 Å.
Twelve target galaxies were observed in two different masks.These double-redshift measurements allowed us to estimate realistic errors (including systematic ones) by comparing the two redshifts obtained with the XCSAO correlation procedure.We find that both redshift estimates are in agreement and their corresponding errors are similar.So, we confirm that XCSAO provides, in this case, not only statistical errors, but also realistic uncertainties.
Table A.1 lists the complete spectroscopic sample considered in this work (see also Fig. 1).Column 1 lists the ID number (cluster members are marked), Cols. 2 and 3 show the J2000 equatorial coordinates of galaxies, Col. 4 the heliocentric radial velocity (v = cz) with their corresponding errors (∆v), and Cols. 5 and 6, the complementary r and i dered magnitudes, respectively.The last column includes some comments regarding particular features of some galaxies.Figure 2 shows the velocity distribution of galaxies around the cluster main redshift.

Optical photometry
We also work with the SDSS DR16 photometric data in order to complement our spectroscopic MOS TNG observations.We consider the extinction-corrected dered magnitudes g and r that assume the Schlegel et al. (1998) reddening maps, within a circular region of 12 radius.The mean depth (at ∼90%  Sect. 3.3).The white contours correspond to X-ray surface brightness after removing point sources using a pixel mask.In the upper right corner, the inset shows a magnified image of the cluster core.The labels BCG, 2 and 3 indicate the brightest cluster galaxy, and the second and third brightest galaxies, respectively.The green contours represent the diffuse radio emission observed with the VLA.North is up and east to the left.completeness) of this photometric sample is r = 21.5, which is in agreement with SDSS DR12 estimates 2 .Comparing the photometric and spectroscopic samples in the regions covered by the MOS masks, we find that the completeness of the spectroscopic sample is ∼50% for galaxies down to magnitude r = 18.5.However, this completeness increases up to ∼60% for galaxies with magnitude r ≤ 19.5 in an inner region of 5 arcmin radius from the centre of the cluster.The quality of the spectra allows us to obtain redshifts even for some faint galaxies with r > 21.

X-ray data
The XMM-Newton observations, with ID 0827031101, of the RXCJ1111 galaxy cluster, were obtained from the XMM-Newton data archive.This target was observed as part of the CHEX-MATE Cluster Heritage project (PIs: M. Arnaud and S. Ettori; Arnaud et al. 2021).We used SAS v20.0 to perform the X-ray imaging and spectroscopic data reduction, closely following the scheme described in Chon & Böhringer (2015).After cleaning the data from times of X-ray flares, the usable exposure amounts to 34 ks for both MOS instruments and to 26 ks for pn.
A147, page 3 of 16 Fig.2. Galaxy redshift distribution in the range 0.02 < z < 0.11.The dashed vertical lines delimit the redshift range including 104 galaxy members assigned to RXCJ1111 according to 2.7σv clipping.The inner plot shows the velocity distribution in the cluster rest frame.The black Gaussian curve represents the velocity reconstruction according to the biweight method and assuming that all the galaxies are part of a single system.The velocity corresponding to the BCG, and the second and the third brightest galaxies are labelled as BCG, 2 and 3, respectively.We removed the point sources and the backgroundsubtracted and exposure-corrected images from all three detectors were combined in the 0.5 to 2 keV band, which is shown in Fig. 3. RXCJ1111 has a round appearance on intermediate scales, but it shows a bright extension to the south and seems to be embedded in a larger north-south filament with a length of about 1.8 Mpc, as traced in X-rays.The centre is disturbed with a bar-like feature oriented in northwest-southeast direction with two small X-ray peaks inside.
For the spectral analysis, the contribution from the particle background was removed by rescaling the filter wheel closed (FWC) spectrum to the spectrum of the corner events of the observation.We considered three X-ray background components representing the unresolved point sources, the Local Hot Bubble and a cool absorbed thermal model when fitting an APEC cluster model to the spectroscopic data in XSPEC.

Member selection and global properties
In order to analyse the internal dynamics of RXCJ1111, it is essential to carry out a good selection of member galaxies.For this purpose, one of the most suitable methods uses velocity "caustics", which are related to the escape velocity from the cluster (Diaferio et al. 2005;Lemze et al. 2009) and allow us to separate cluster members from foreground and background galaxies.However, this method works well with large spectroscopic samples, typically with more than 300 redshifts, and we do not find reliable results when applying this procedure to our sample.Thus, we used a similar but simpler technique based on the galaxy position in the projected (r, cz) space, where r is the projected cluster-centric distance and cz is the galaxy line-ofsight (LOS) velocity (see Fig. 4, top panel).We apply an iterative 2.7σv clipping in the cz coordinate, considering a radial profile of the expected velocity dispersion (Mamon et al. 2010).We first find the mean velocity and estimate initial velocity dispersion using the rms estimator.In successive steps we obtain stable and converging values of v and σv.This method yielded a selection of 104 cluster members, 3 foreground galaxies, and 45 background galaxies.Figure 2 shows the redshift distribution of the galaxies in the range 0.06 < z < 0.11 listed in Table A.1.
The selection of 104 galaxy members shows a mean velocity v = 22653 ± 95 km s −1 (z = 0.0756) and a rms of 890 ± 98 km s −1 (errors at 95% c.l.) in the cluster rest frame.In order to estimate a robust velocity dispersion, σv, we use the bi-weight scale estimator (Beers et al. 1990), which is a procedure that offers satisfactory results for samples showing possible inhomogeneities.Applying this method to the 104 redshifts, we obtain 845 +106 −90 km s −1 .This result is in contrast with that obtained by Lopes et al. (2018), who report a σv = 562 +31 −26 km s −1 using the bi-weight estimator.In our case, both rms and bi-weight σv estimations are in agreement within the errors.However, in order to check the stability of σv and discard possible deviations from the mean σv along the cluster, we study the variation of this magnitude with the distance to the cluster centre (assumed as the BCG position).
Figure 4, bottom panel, shows that the integral σv profile is almost completely flat for the whole cluster.This suggests that estimations of the σv are stable and robust even for radii as small as r < 0.2 Mpc, which reveals that there are no obvious inhomogeneities in the velocity field (Girardi et al. 1996).This fact is also supported by the agreement between values obtained using the rms and bi-weight estimators, as we see in the previous paragraph.However, in the following analyses we assume the more reliable value of σv = 845 +106 −90 km s −1 , obtained using the biweight estimator given the robustness of this method in cases where the statistics clearly departs from the Gaussian distribution.The constancy of σv variations in the velocity distribution, in particular it rules out a dependence of the mean velocity with the cluster-centric distance (see Fig. 4, middle panel).We only find a mild increase of about 650 km s −1 for radius r < 0.25 Mpc region.This may suggest that the dynamics of the cluster could be disturbed in its central region.We analyse this in detail in following sections.
The BCG of RXCJ1111 (the ID 83) presents a velocity of 23 428 ± 5 km s −1 (according to the SDSS spectroscopic database), which is almost 800 km s −1 higher with respect to the A147, page 4 of 16 Fig.4. Study of the velocity field of RXCJ1111.Top panel: measured LOS velocity, in the cluster rest frame, of the 104 galaxy members vs projected distance to the centre.The cluster centre is assumed to be the position of the BCG.Middle and bottom panels: integral mean velocity and LOS velocity dispersion, also in the cluster rest frame, shown as radial profiles with respect to the cluster centre.These values are computed by considering all galaxies enclosed in that radius.The first value computed is estimated from the first five galaxies closest to the centre.The error bars are at the 68% c.l. mean velocity of the cluster.Lopes et al. (2018) obtained a similar offset, 704 km s −1 .In addition to BCG, which shows a magnitude r = 14.17, we identified two further bright galaxies (IDs 60 and 67, with magnitudes r = 14.55 and 15.21), which we label BCG2 and BCG3, respectively.These two galaxies are located at 1 .30and 2 .25 towards the north and south of BCG, respectively, almost configuring an alignment in the north-south direction.The X-ray surface brightness shows a double peak inside a SE-NW elongated inner region, and the BCG2 position coincides completely with the NW maximum of this double-peaked emission (see Fig. 1).On the other hand, the main BCG is shifted by about 20 arcsec with respect to the SE X-ray peak, while BCG3 is placed to the south, where the X-ray profile shows an elongation in the external part.Therefore, the BCGs configuration is somehow linked to the X-ray diffuse emission of the cluster.This means that galaxies and the hot gas of the ICM are interacting in some way.We analyse this interaction in Sects.4.2 and 6.
We also detect 37 galaxies showing [OII] emission lines, labeled in Table A.1 as emission line galaxies (ELGs).The spectral resolution and S/N of our data allow us to detect [OII] emission lines with equivalent width >8 Å.Ten out of 37 ELGs are cluster members, 2 are located in the cluster foreground (with v < 20 206 km s −1 ), while the rest (25 galaxies) are in the background (showing v > 25 122 km s −1 ).So, the ELG members represent the 9.6% of the cluster members in our sample.This is a typical fraction of ELGs in a cluster environment, which indicates that star-forming processes have been quenched in RXCJ1111, as expected in high galaxy density environments and ICM showing high T X (Laganá et al. 2008).  2 but now the global fit (black curve) corresponds to two Gaussian components (in blue and red)."BCG" (in red), "2" and "3" (in blue) coloured labels agree with the most likely component.

Velocity field
In general, any departure of the global velocity distribution along the LOS from a Gaussian is a reliable indicator that reveals the systems are dynamically disturbed or that there is substructure (Ribeiro et al. 2011;de Carvalho et al. 2017).We measure skewness and kurtosis in order to investigate the shape of the velocity distribution of RXCJ1111.The skewness is related with the asymmetry of the velocity distribution, while the kurtosis indicates distributions presenting thinner or fatter tails.In our case, RXCJ1111 presents a velocity distribution that shows a skewness and kurtosis of 0.27 ± 0.18 and −0.34 ± 0.28, respectively.Accordingly with our sample, we performed a Markov chain Monte Carlo (MCMC) method with 10 000 simulations assuming a Gaussian profile with an average centre equal to zero and a standard deviation equal to one, sampled with 104 points.Errors were computed from the standard deviation of the values obtained.The positive skewness suggests that the velocity distribution is skewed to the right, while the kurtosis is almost compatible with zero.So, the global velocity distribution of RXCJ1111 is slightly asymmetric, with a skewness difference of 1.5σ from zero.That is, the velocity distribution shows a small asymmetry relative to the normal Gaussian shape.This suggests that RXCJ1111 presents a dynamically disturbed state, probably dominated by two or more interacting substructures (see following sections).
The skewness obtained for the velocity distribution of RXCJ1111 supports the hypothesis that the cluster may be composed of two galaxy clumps, each of them showing its Gaussian velocity distribution and both introducing distortions in the global velocity distribution.With this idea in mind, we fitted two Gaussian profiles to the global velocity distribution.The result is shown in Fig. 5. Table 1 lists the main parameters obtained for this two-component fit.The best fit corresponds to two substructures with a difference in mean velocity of ∼1500 km s −1 , one of them at ∼−270 km s −1 with respect to the main velocity of RXCJ1111 with a σv = 644 ± 56 km s −1 , which would constitute the main system.We found a secondary substructure at ∼1270 km s −1 with respect to the cluster main velocity, with a σv = 410 ± 123 km s −1 , that we label FG (we justify the name of this label in Sect.4.1).As shown in Fig. 5, BCG presents a velocity offset of about +1050 km s −1 with respect to the main system, while only −550 km s −1 with respect to the secondary A147, page 5 of 16 Table 1.Global properties for the whole cluster and clump components detected in RXCJ1230.

Structure
Notes.N gal of the main system and FG subcluster have to be taken as guide values.Galaxies with v < 600 and v > 600 km s −1 are assumed to belong to the main clump and FG substructure, respectively.The masses are dynamical ones.substructure.On the other hand, BCG2 and BCG3 are almost centred on the main system velocity distribution, showing only a velocity offset of about −75 km s −1 .Briefly, the velocity field of RXCJ1111 is consistent with a double cluster, where the secondary substructure contains a very bright galaxy, BCG.On the other hand, BCG2 and BCG3 are part of the most populated component, the main body of the cluster.The membership relations between BCGs and the different substructures are discussed in detail in Sect. 4.

Two-dimensional galaxy distribution
Spectroscopic samples, in practice, are affected by magnitude incompleteness.So, in order to get information of the galaxy distribution of the whole cluster, we adopt the photometric SDSS DR16 catalogues.Using the g and r dered magnitudes, we constructed the (g − r vs. r ) colour-magnitude diagram (CMD) and we selected likely members from the red sequence (RS) (see Fig. 6) and blue cloud (Gavazzi et al. 2010) following the technique detailed in Barrena et al. (2012).The RS fitted follows the expression g − r = −0.185(±0.004)× r + 1.20(±0.08)and we selected both likely early-type and late-type galaxy members, residing in the RS and blue-cloud (below the RS), respectively.This locus is defined by r < 21.5 as magnitude completeness, the RS ± 3 × rms as upper limit, and −0.1509 × r + 3.0125 as lower limit in g − r colour, respectively.This selection yields 926 likely members.
We used the likely members in order to explore the galaxy distribution.With this aim in mind, we constructed the contour levels of the isodensity galaxy distribution of the RXCJ111 likely member shown in Fig. 1 (blue contours).This map was obtained by computing the cumulative contribution of 926 small Gaussian profiles (with σ = 1 arcsec width) positioned on each individual member over a grid of 258 × 200 points.The contour map obtained reveals a double-peaked distribution clearly elongated in the NNE-SSW direction, which is oriented ∼25 • (see Sect. 3.4) with respect to the north-south direction.The most significant peak is very close to BCG2.It is important to note that the BCG2 and BCG3 galaxies are both surrounded by many members and likely members, while BCG is placed in a region where the galaxy distribution is not so high.We note that RXCJ1111 presents a galaxy distribution and X-ray surface brightness profile that are almost coincident, and that follow similar elongations and orientations.We discuss this in detail in Sect.6.1.

Space-velocity correlations
In the past, many techniques were developed to study the existence of substructures in clusters.One of the most successful procedures is the combined study of positions and velocities of galaxy members.The presence of different subclusters modifies the velocity field of galaxies; thus, by analysing the spacevelocity correlations, we can explore the internal kinematics of galaxy clusters.
In a first step, and given the evidence of bimodality exposed in Sect.3.3, we divided the galaxy members in two subsamples.The interaction between the two substructures could induce inhomogeneities in the velocity distribution.Therefore, we looked for significant gaps in the velocity histogram of RXCJ1111, which separates the galactic population of the two clumps.The most significant gap is detected at around 600 km s −1 (see Fig. 5).The existence of two substructures with v < 600 km s −1 and v > 600 km s −1 is supported by the fact that BCG2 and BCG3 would be associated with the low-velocity clump, while the BCG would be the brightest galaxy of the highvelocity clump.We analysed the spatial distribution of these two galaxy samples and found no evidence of spatial bimodality.This study suggests that the two galactic populations are intermingled at least in projection.However, the results found in Sect.3.2 and the two Gaussian fit shown in Fig. 5 strongly support the existence of two interacting substructures.
We performed a second test to check the existence of possible space-velocity segregation.We combine galaxy positions and velocities by applying the classical δ-statistics Dressler & Schectman (DS) test (Dressler & Shectman 1988), which identifies substructure searching for subsystems whose mean velocities and/or dispersion deviate from the global cluster values.
A147, page 6 of 16 Fig.7. Spatial distribution of the 78 cluster members inside a region of 7.5 × 7.5 , 0.65 Mpc (∼0.6 r 200 ) at the cluster redshift, from the cluster centre.Cluster member positions are marked with a square with size proportional to exp(δ i ) computed using the δ i deviations obtained in the DS test.Red and blue correspond respectively to galaxies with higher and lower δ i deviations from the mean, δ i .The large and small black lines represent the directions of the velocity gradients of the whole sample in the inner region, respectively.Similarly, the magenta and green lines represent the orientations of the galaxy density distributions and X-ray surface brightness map, respectively.The BCG, BCG2 and BCG3 positions are marked with filled dots.
After running this procedure using 1000 Monte Carlo simulations, we did not find any converging result.Figure 7 shows the δ-statistics test over a central region of 7.5 × 7.5 , which includes 78 cluster members.The outer regions are not considered in this test because they are not well enough sampled, and a lack of spatial sampling may introduce a biased result.We find a mean deviation of 0.22 ± 0.18, with a p-value statistics of 0.15, which is very low and means that there are not significant deviations.Thus, substructures are not significantly spatially segregated, and both galaxy populations are spatially mixed in the plane of the sky.However, we note that galaxies in the south part of the cluster present higher δ i with respect to the mean, while the northern area shows systematically lower δ i deviations.Thus this test reveals an evidence of a clear velocity gradient in the north-south direction.
In order to analyse the velocity gradient we fitted a plane in the space-velocity frame.In a first step, we consider the full cluster member sample, obtaining the expression ∆v = 9.77x − 26.91y + 43.6, where x and y are positions (following the RA and Dec coordinates, in arcmin with respect to BCG; positive values correspond to the north and west directions), which shows a gradient of 325(±350) km s −1 Mpc −1 in a 110 • (±8 • ) angle (anticlockwise, from west to north; ∆v takes positive values towards the south).In a second step, similarly, we only take into account the 78 cluster members inside the well-sampled region of 7.5 ×7.5 , and we find ∆v = 8.11x−20.54y+61.3, which presents a gradient of 254(±465) km s −1 Mpc −1 in a 112 • (±14 • ) angle.Therefore, velocity gradients are consistent in both cluster member samples, and this analysis confirms a slight increase in radial velocities towards the south part of the cluster and following the NNE-SSW direction.
Figure 7 also shows the orientations of the 2D spatial galaxy distribution of likely members and the X-ray surface brightness.We fitted ellipses to the blue and white contours shown in Fig. 1, between 3.5 and 7 from BCG to avoid the inner regions where we detect double-peaked profiles.This study reveals that galaxy distribution isocontours present a mean orientation3 of 115 • ± 4 • (see magenta line in Fig. 7), while X-ray contours are oriented 91 • ± 6 • (green line in Fig. 7).Therefore, the velocity gradient, the likely member distribution and the X-ray surface brightness are all oriented within 90 • −115 • , so the cluster shows a clear elongation in the NNE-SSW direction, produced by the overlapping galaxy populations showing slightly different velocity distributions.This finding supports the fact that the cluster contains two galaxy clumps, one main body towards the north and a second substructure almost aligned in the LOS, but slightly shifted towards the south.
We tried to associate individual galaxies to each substructure using a 3D version of the Kaye's Mixture Model (KMM) algorithm (Ashman et al. 1994).This procedure separates the different components in velocity space, providing a probability that a given galaxy belongs to an individual component.The KMM algorithm needs a starting input configuration, so we provide two input lists.First, we used a list of galaxies associated with the southern cluster region (i.e. the galaxies marked with red squares in Fig. 7, which correspond to galaxies showing slightly higher δ i in the DS-test).Second, we used a list of galaxies with v > 600 km s −1 with respect to the mean velocity of the cluster.Our findings after running the KMM procedure on these two galaxy lists are not conclusive, and after running this algorithm iteratively we did not find a reliable result.The p-value to obtain this KMM result by chance is always higher than 0.23 (23% probability).The KMM procedure and the DS test are in agreement: no significant spatial segregation is detected for the main and secondary substructures.So, both galaxy populations are mixed in the plane of the sky.Thus, the two populations seem to be almost completely aligned in the LOS.

The BCG membership and substructure
The three brightest galaxies of RXCJ1111 are also aligned in the north-south direction.However, the analysis of their radial velocities reveals that these three galaxies are not part of a single mass halo.They follow very different kinematics.BCG2 and BCG3 are well centred on the velocity distribution of the main body of the cluster, while BCG presents a velocity offset of about 990 km s −1 .In contrast, BCG shows a velocity offset of about 550 km s −1 with respect to the secondary substructure.Thus, from the dynamical point of view, BCG seems to be linked to the secondary substructure.This evidence is supported by the KMM analysis performed in the previous section.In every KMM run, using different input configurations, we find that KMM always estimates a probability >96% that BCG belongs to a secondary substructure, while for BCG2 and BCG3 we obtain a likelihood >99% that these two galaxies are part of main body of RXCJ1111.
By studying a sample of 72 galaxy clusters showing SZ and X-ray emissions, L18 (see Fig. 6 therein) found that only a negligible fraction (<1%) of clusters may contain a BCG showing velocity offset as high as 1000 km s −1 with respect to the main cluster velocity.Even for disturbed galaxy systems, this fraction is lower than 2%.In agreement with this result, Lauer et al. (2014), using a sample of 178 clusters, also find that systems containing BCGs with peculiar velocities >1000 km s −1 represent only a 2% fraction (4 out of 178), while the mean velocity offset of BCGs is about 150 km s −1 for clusters showing a veloc-ity dispersion σv ∼ 600 km s −1 .However, the velocity offset observed in the BCG with respect to the secondary substructure of RXCJ1111, is quite high, 550 km s −1 , which suggests that this galaxy is greatly affected by other gravitational effects.One possibility is that BCG could be undergoing interaction with another mass halo, such as the BCG2 halo.In this way, BCG and BCG2 could be orbiting each other, which is supported by the presence of a bar-like structure observed in the X-ray inner region.
To summarise, given the velocity offset observed in BCG of RXCJ111, the most likely scenario is that BCG belongs to the secondary substructure.However, the substructure seems to be starting to interact with the main body of the cluster.On the other hand an interaction between BCG and BCG2 halos may explain the velocity offset observed in BCG with respect to its galaxy clump, the secondary substructure.2010), a galaxy system is considered a fossil when it shows a magnitude gap between the brightest and the second brightest galaxy members that is greater than two, ∆m 12 ≥ 2, within 0.5 r 200 .This magnitude gap arises naturally in undisturbed systems that have avoided infall into clusters, but where galaxy mergers of the most luminous galaxies produces an extremely bright galaxy that dominates the core of the system.However, the precise value (=2) of the threshold in ∆m 12 is quite arbitrary.The chance to find a value of ∆m 12 > 2 in a typical Schechter function is very small.For instance, Zarattini et al. (2014) checked this definition using spectroscopic information and only confirm five fossil groups showing ∆m 12 > 2 in a sample of 34 systems previously identified as fossil systems by Santos et al. (2007) using photometric samples.Despite the arbitrary definition of a fossil group, the observable ∆m 12 is highly correlated with the evolutionary state of the system.This is confirmed by Zarattini et al. (2021).They find that radial orbits of galaxies are the cause of increasing ∆m 12 in groups.While relaxed systems show a large population of early-type galaxies with radial orbits (see Biviano & Katgert 2003;Biviano & Mamon 2023), except in the central regions where dissipative friction may affect the dynamics of the brightest galaxies, clusters with smaller magnitude gaps that show more disturbed dynamical states and substructures present more isotropic orbits.In other words, fossil systems are very relaxed structures, and this relaxation state is reflected in a large ∆m 12 .
In the case of RXCJ1111 and according to the membership distribution discussed in Sect.4, BCG is part of the secondary substructure, while BCG2 is the brightest galaxy of the main body of the cluster.Consequently, the ∆m 12 of the main body is estimated as |r BCG2 − r BCG3 | = 0.66.On the other hand, in agreement with the velocity distribution, the fourth brightest galaxy, ID 76, which shows a radial velocity of 21 968 ± 5 km s −1 , would be part of the main body, because it shows a velocity difference of ∼−1930 km s −1 with respect to the main velocity of the secondary substructure.This means that the ∆m 12 of the secondary substructure could be only estimated with respect to the fifth brightest galaxy, ID 103, which shows a similar velocity to BCG.In this way, ∆m 12 can only be estimated as a minimum value, because there is a not negligible possibility that the ID 103 galaxy is part of the main body of RXCJ111.Therefore, ∆m 12 = |r BCG − r 103 | = 1.8 in the secondary substructure.
From this analysis we can conclude that the secondary substructure is a fossil group, or at least an almost fossil system (∆m 12 = 1.8−2), which is now interacting with a more massive structure, the main body of the cluster.In Sect.6 we discuss the dynamics of this system.We estimate the intervening dynamical masses and discuss a possible merger scenario.

The interplay between BCGs and ICM
Cluster mergers are characterised by the presence of disturbed ICMs, but galaxies and the ICM interact on different timescales, each revealing different dynamical properties.The hot gas component of the interacting systems often shows the presence of discontinuities in surface brightness and temperature that may not correlate with the most massive galaxies.Figure 8, left panel, shows the SDSS r-band image of the cluster core of RXCJ1111.Superimposed on this image are the innermost X-ray contours around BCG and BCG2.The inner contours show an elongated profile in the SE-NW direction, with a double-peaked X-ray emission (indicated with crosses in that figure), that connects BCG2 and BCG.However, it is important to note that while the NW peak of the X-ray is the main one and perfectly coincide with the BCG2 centre, the SE X-ray peak is substantially shifted with respect to the BCG position.This kind of mismatching between BCG positions and X-ray peaks is typically observed in cluster mergers (see e.g.Lopes et al. 2018).A clear and extreme case is seen most vividly in the case of the Bullet Cluster (Barrena et al. 2002;Clowe et al. 2004), where the gas was separated from the galaxies during the core passage.A similar scenario can be taking place in RXCJ1111.The hot gas associated with the secondary structure, which is more concentrated around BCG, has been shifted away, probably by ram pressure-stripping.In this way, the innermost hot gas of the secondary structure is starting to interact with the main body of RXCJ1111, producing a small displacement of the gas towards the outer regions of BCG.We do not detect any evidence of the presence of shocks and cold fronts in the X-ray images, which could be an indication that the merger is taking place close to the LOS (see Sect. 6.1).

The BCGs radio emission
An interesting phenomenon observed in the cluster merging processes is the presence of strong diffuse radio emission, forming extended halos and radio relics.With the aim of studying the A147, page 8 of 16 radio emission in RXCJ1111, we inspected the public radio data archive.One of the few images available for this cluster is that obtained as part of the VLA Faint Images in the Radio Sky at Twenty-cm (FIRST) survey (Becker et al. 1995) in the frequency 1.4 GHz, with a exposure time of 180 s and using a beam size of 5.4 arcsec.
The contour levels of the Very Large Array (VLA) radio image are shown in Fig. 1, upper right corner, which only reveals radio emission from the three brightest galaxies.The same three radio sources were reported in Owen et al. (1993) and Owen & Ledlow (1997), where no trace of diffuse emission was detected from a cluster halo.The emission observed corresponds to classical radio galaxies with lobes created by jets filled with relativistic plasma (Begelman et al. 1984).BCG presents a very weak central emission, while that from BCG2 and BCG3 is more extended.The emission corresponding to the BCG2 resembles a classical head and tail source.That is, we see central emission and lobes dragged to the south-west.On the other hand, the BCG3 presents lobes that are still on both sides of the galaxy, but are not strictly aligned with the galaxy centre.This suggests that BCG3 is moving with respect to its surrounding medium.
The fact that no diffuse and extended emission has been detected implies that the energy contribution of potential relativistic electrons in the ICM is not large enough to be detected.In consequence, we can infer that the merging process is still in a very early phase.However, more deep radio observations would be necessary in order to completely confirm this hypothesis.

BCG photometric structure
We performed a two-dimensional photometric decomposition of BCG using the GAlaxy Surface Photometry 2 Dimensional algorithm (GASP2D; Méndez-Abreu et al. 2008, 2014).To this end, we used the SDSS r-band image.We modelled the surface brightness distribution of the galaxy assuming both a single Sérsic distribution (Sersic 1968) and a Sérsic+Exponential distribution.GASP2D returns the best-fitting values of the structural parameters of each morphological component by minimising the χ 2 after weighting the surface brightness of the image pixels according to the variance of the total observed photon counts due to the contribution of both galaxy and sky (see also Méndez-Abreu et al. 2017).We obtained a best fit in terms of the χ 2 when using the Sérsic+Exponential model.In principle, this would allow us to fit the low surface-brightness and extended component that BCGs could present (e.g.Nelson et al. 2002;Méndez-Abreu et al. 2012).However, according to the Bayesian information criterion (BIC; Schwarz 1978) we found that adding an extra component to the Sérsic fit did not statistically improve our results.
The right panel of Fig. 8 shows the residuals after subtracting our best Sérsic model to the original SDSS r-band image.We can clearly see the presence of two non-axisimmetric structures.The first one is surrounding the galaxy core and the second one, more extended, resemble the presence of a tidal tail towards the southern region of the galaxy.It is worth noting that both non-axisimmetric structures likely share the same north-south direction and they were also present when modelling the surface brightness with a Sérsic+Exponential model.
We argue that the residuals observed in BCG of RXCJ1111 are likely due to the merger with one or two galaxies.The presence of double nuclei due to the merger of galaxies is common fact that can be studied using photometric (Komossa et al. 2003;Benítez et al. 2013) and spectroscopic (Patton et al. 2016) methods.Our model generated by GASP2D does not reveal signs of Single beta model M 500 (×10 14 M ) 1.68 ± 0.25 M gas (×10 13 M ) 1.97 f gas 11.3% r 500 (arcmin) 9.07 L X (×10 44 erg s −1 ) 0.5 M 500 (L X ) (×10 14 M ) 2.5 T X (keV) ∼3.6 n e0 (cm −3 ) 3.6 × 10 −3 r c 1.77 β 0.673 a double nucleus in the BCG core.However, the excess of light (over the Sérsic model) right to the south of the galaxy centre resembles what would be the final stages of a merger with a relatively massive and concentrated companion (Hendel & Johnston 2015).The outer non-axisimmetric structure has a different apparent shape in its northern and southern parts with respect to the galaxy centre.The northern part resembles the typical shells formed during a minor merger with a relatively gas-poor companion (Mancillas et al. 2019).The southern part shows a tidal tail shape, which could also have been created by a minor merger, but on a less radial orbit with respect to the shells.In summary, even if the details of the past mergers undergone by BCG are difficult to reveal using only the available images, it is clear that BCG shows several signs of recent and past interactions with other galaxies.The structures described in this section cannot be produced due to interactions with the ICM or fast encounters with other cluster galaxies (harassment), nor are they the result of a merger with another bright galaxy.Therefore, within the context described in this paper of the BCG being the central galaxy of a transitional FG, we suggest that it is the result of several galaxy mergers that might be leading to observing the system as a FG.

X-ray properties
We extracted X-ray surface brightness profiles after the subtraction of the X-ray sky and instrumental background.For RXCJ1111 we determined one surface brightness profile for the entire cluster assuming approximate spherical symmetry.We fitted the profiles with βand double β-models.We found that single β-models provide a good fit to the outer parts of the profiles, from which we determined the gas density and gas mass profiles.Only for the southern part of RXCJ1111 does the double β-model provide an interesting alternative.The fit parameters for the profiles are given in Table 2.The parameter M 500 is the mass inside r 500 ; M gas is the gas mass inside the same radius.We do not detect any evidence of the presence of shocks and cold fronts in the X-ray images, which could be taken as an indication of an advanced merger stage.We show below that the merger probably occurs close to the LOS and in this case it is extremely difficult to see the signatures of shocks and to draw conclusions from the present data.The parameter f gas is the gas mass fraction of the total mass, r 500 is the radius projected in the sky, L X is total X-ray luminosity, M 500 (L X ) is the mass estimated from the L X −M relation, T X is the measured X-ray temperature for the cluster region inside r 500 , r c is the core radius, and β is the slope parameter of the electron density profile.
Reg.The temperature of the ICM was also determined from the analysis of the background-subtracted X-ray spectrum.We determined the temperature in nine concentric radial bins for the cluster RXCJ1111.The bins were constructed with a minimum number of 2000 photons per bin.The resulting temperature profile is shown in Fig. 9.The sudden temperature drop of the fitted profile at the centre is an artefact caused by the peculiar location of the innermost data points and is certainly not real, and is ignored in the following analysis.The outer temperature profile of RXCJ1111 can be approximated by a polytropic model with a γ parameter of ∼1.2.We also use the fitting formula of Vikhlinin et al. (2006) to approximate the temperature profile.In this formula we drop the part that describes the central temperature decrease which is an effect of a cool core and so not relevant for RXCJ1111.The equation applied thus has the form In addition, we determined temperatures from the spectra extracted over the entire region inside r 500 and 0.75 r 500 ; the results are provided in Table 3.In Col. 1, the A and B regions correspond to circles of r < r 500 and r < 0.75 r 500 , respectively, while A X and B X are annuli where the central region (core), inside r = 0.15 r 500 , was cut out.The parameter "Z" is the Fe abundance (in solar units with abundances from Asplund et al. 2009), "Norm" is the Astrophysical Plasma Emission Code; (APEC; Smith et al. 2001) normalisation, and f X and L X are the flux and luminosity in the [0.5−2.0]keV band, respectively.
Based on the density and temperature profiles, we determined the gas mass and total mass profile, assuming hydrostatic equilibrium for the derivation of the latter.We find a cluster mass inside r 500 for RXCJ1111 of M 500 = 1.68 ± 0.25 × 10 14 M .The results based on the temperature profile given by Eq. ( 1) and by the polytropic model agree within the error bars.The mass and gas mass profiles determined from the best fit for RXCJ1111 are shown in Fig. 10.For the X-ray luminosity of the cluster in the 0.5 to 2 keV energy band, we obtain a value of L X,500 = 5 × 10 43 erg s −1 .Based on the mass-luminosity relation proposed by Pratt et al. (2009), we expect for this value a cluster mass of about M 500 = 2.5 × 10 14 M .For the mean temperature derived for the entire cluster inside r 500 of 3.6 keV we would expect a cluster mass of about M 500 = 2.4 × 10 14 M (see e.g. the M-T relation in Arnaud et al. 2005).The mass implied by the temperature and X-ray luminosity of the ICM for the case of a more relaxed cluster is therefore higher than the mass determined from the detailed X-ray analysis.This discrepancy can be explained, for example, by the merger state of the cluster.

Dynamics of RXCJ1111
As has been argued in previous sections, we can conclude that RXCJ1111 is formed by one main body and one likely fossil substructure, almost completely aligned in the LOS.Their galactic populations are superimposed on the plane of the sky, but from the velocity analysis we can affirm that the BCG can only be part of the secondary substructure, while BCG2 and BCG3 belong the main body.The X-ray surface brightness map suggests that they are starting to interact.In this section we estimate the dynamical masses and virial radii in order to characterise this complex.
RXCJ1111 shows a velocity distribution (see Fig. 5) that allows us to distinguish between the two galaxy clumps.On the other hand, we detect a ∼30% discrepancy in the mass estimates derived from the temperature profile and the M-T relation (see previous section), which could be due to an X-ray temperature increase.Taking into account these two facts, it is reasonable to assume that the fossil substructure has not yet completely merged into the cluster and that both galaxy halos still keep a roughly dynamical equilibrium.In other words, the velocity distribution of the galaxies is not very disturbed, but the gas temperature has started to increase.In this scenario, it is possible to estimate virial dynamical masses and radii, and compute the mass of the whole cluster as the sum of the individual masses.Galaxies are embedded in the gravitational potential of the cluster, and thus their velocities can be used to estimate the dynamical mass of galaxy clumps.In this way, we use the velocity dispersion, σv, and its relation with the virial mass, M 200 , to estimate the dynamical mass of the components of RXCJ1111.One of the most common ways to determine dynamical masses of clusters from their velocity dispersion is using scaling relations.In the literature there are many examples offering σv−M 200 relations4 (see e.g.Evrard et al. 2008;Saro et al. 2013;Munari et al. 2013;Ferragamo et al. 2020).All of them provide similar values; however, we follow the Ferragamo et al. (2020) relation.This procedure is calibrated using the Munari et al. (2013) simulations, which consider dark matter particles and subhalos, galaxies, and AGN feedback as well.Ferragamo et al. (2020) go one step further and consider the statistical and physical effects in samples containing small numbers of cluster members.Following this prescription, we find dynamical masses of M 200 = 1.9 ± 0.4 × 10 14 M and 0.6 ± 0.4 × 10 14 M for the main cluster and the secondary substructure, respectively.In order to compare these values with that obtained using X-ray emission, we convert M 200 into M 500 following the relation given by Duffy et al. (2008): rescaling M 500 from M 200 assuming a concentration parameter c 200 = 4 (a suitable value for clusters at z < 0.1 and M 200 ∼ 10 14 M ), integrating a Navarro-Frenk-White (NFW) profile (Navarro et al. 1997) and interpolating to obtain M 500 .We thus obtain M 500 = 1.2 ± 0.6 × 10 14 M and 0.3 ± 0.2 × 10 14 M for the main body of the cluster and the substructure, respectively.Therefore, taking into account these values, we can conclude that RXCJ1111 presents a total dynamical mass of M 200 = 2.5 ± 0.6 × 10 14 M and M 500 = 1.5 ± 0.6 × 10 14 M , estimated as the sum of the individual masses of the two clump components.
Quasi-virialised regions can be determined by evaluating the virial radius of each galaxy clump.This radius is usually estimated as the radius of a sphere of mass M 200 inside which the matter density is 200 times the critical density of the Universe at the redshift of the system, 200ρ c (z).Therefore, M 200 = 100 r 3 200 H(z) 2 /G, and so, following this expression, we obtain r 200 ∼ 1.2 and 0.8 h −1 70 Mpc, for the main body and the substructure, respectively.We compile the virial masses and radii in Table 1.
As an exercise, we could compare the total dynamical mass of RXCJ1111 obtained above with that determined assuming the cluster as a single galaxy clump, neglecting its substructured composition.In this way, in Sect.3.1 we show that RXCJ1111 presents a global velocity dispersion σv = 845 +106 −90 .Applying the σv−M 200 relation proposed by Ferragamo et al. (2020), we obtain a global dynamical mass M 200 = 3.3 ± 1.0 × 10 14 M and M 500 = 2.1 ± 0.7 × 10 14 M .Comparing these values with that obtained above assuming substructure, we see that the two numbers agree within 1σ error.However, the results derived from a global velocity dispersion seems to be slightly higher.This fact may be an indication that dynamical masses derived from a global velocity dispersion is overestimated for clusters with evident substructure.

Explaining the optical and X-ray properties
By analysing X-ray data (see Sect. 2.3), we find an elongated configuration.The main X-ray emission comes from the north part of the cluster, while a bright extension to the south is also observed.Therefore, on the one hand, X-ray analyses confirm that RXCJ1111 presents an unrelaxed state, and on the other, the mean X-ray emission matches with the north part of the cluster, which includes an emission maximum centred on BCG2.However, we do not see a strong X-ray peak in the centre, but rather a smeared peak, which could also be due to the orbiting central galaxies with their DM halos.In the optical, this scenario would explain the large offset (∼−550 km s −1 ) of BCG with respect to the main velocity distribution of its corresponding clump, the secondary substructure.Two mechanisms can help to retard the BCG.The first is dynamical friction (Merrit 1983(Merrit , 1984(Merrit , 1985)), which is generally strong for a massive BCG, but has the most impact when the galaxy is near the centre of the primary cluster.The second mechanism is simply the deflection of the BCG in its orbit as the result of a non-zero impact parameter.In this case there is no loss of orbital energy, but the component of the BCG's velocity projected onto the LOS is reduced.Neither effect (dynamical friction or deflection) can be significant early in the merger.However, the velocity offset of BCG provides a strong argument that this merger has advanced at least close to core passage.
Once the point-like sources are removed, the rest of the X-ray diffuse emission on small scales is consistent with statistical fluctuations, which is difficult to observe if the merger happens in a direction close to the LOS However, the agreement between X-ray shape emission from hot gas and galaxy spatial distributions is more interesting.Both galaxy distribution and X-ray morphology suggest that the merger is happening almost along the LOS, maybe with a small impact parameter to the south (see Sect. 6.2).
We find that M 500 derived from mass-X-ray luminosity relation and from T X , M 500 (L X ) and M 500 (T X ) are about ∼2.5 and ∼2.4 × 10 14 M , respectively.These values are slightly higher with respect to M 500,X and M 500,dyn .The probable reason behind this discrepancy is that RXCJ1111 is in an early phase of merging (see Sect. 6.2).Thus, an ongoing merger may be producing a small increase in the temperature of the hot gas of the ICM.Similarly, the L X is also enhanced due to the effect produced by the collision of substructures and gas compression.
One of the most interesting questions arises from the comparison between masses derived from X-ray and galaxy dynamics.Assuming two separate galaxy clumps, we obtain M 500,dyn = 1.5 ± 0.6 × 10 14 M and M 500,X = 1.68 ± 0.25 × 10 14 M from X-ray and galaxy dynamics, respectively, which are in quite good agreement within 1σ errors.However, assuming RXCJ1111 to be composed by only one galaxy population, we obtain M 500,dyn = 2.1 ± 0.7 × 10 14 M , which seems to be slightly higher, but within 1σ, with respect to M 500,X .This fact confirms that the most appropriate way to estimate realistic dynamical masses, even in not so relaxed clusters, is to identify the cluster components and consider each galaxy clump separately, thus estimating masses within regions showing a more relaxed state.This method validates similar techniques to determine dynamical masses in a more accurate way, which have been successfully applied for merging clusters in the past (e.g.Girardi et al. 2008;Boschin et al. 2012a).
Summarising, the mass estimates derived from the global dynamics of galaxies, the mass from global T X and L X are somehow overestimated, probably due to the unrelaxed state of RXCJ1111, and hence the importance of estimating dynamical masses in non-virialised clusters taking into account galaxy clumps separately.In addition, a good knowledge of the dynamical state is crucial in order to derive realistic X-ray properties in this type of cluster.

A three-dimensional merger model
As we point out above, both the main cluster and the fossil substructure can be separated in the velocity field, but not in the spatial distribution.The ongoing collision will involve two mass halos with a mass ratio of 3:1.On the other hand, typical X-ray temperatures of relaxed clusters with M 500 ∼ 1.5 × 10 14 M are about 2.1 keV (see e.g.Fig. 9 in Kettula et al. 2013, and references therein); however, we measure a global T X ∼ 3.6 keV.Thus, we measure a ∼∆T X ∼ 1.5 keV enhancement in the Xray temperature of the ICM that may also be explained by the fact that the main cluster and the fossil substructure are starting to collide.Galaxy clusters showing mergers in advanced states present an ICM that is much more disturbed with very high X-ray temperature (see e.g.Boschin et al. 2012b;Barrena et al. 2002).In the following we propose a merger model in order to explain the 3D dynamics of this two-body collision.
The relative dynamics of RXCJ1111 is quite simple and basically described by a interacting main body and substructure with mass ratio of about 3:1.We analyse this interaction from different approaches, based in an energy integral formalism and considering a flat space-time and Newtonian gravity (see e.g.Beers et al. 1982).The three most important observables in a two-body interaction are: the total mass of the two systems computed as the sum of the individual components, M 200,sys ∼ 2.5 ± 0.6 × 10 14 M (see Sect. 6); the relative LOS velocity in the cluster rest frame, V r = 1540 ± 135 km s −1 ; and the projected physical distance.This last term is undefined because both galaxy clumps seem to be superimposed in the plane of the sky.However, we can assume a projected distance of 82 arcsec = 0.12 h −1 70 Mpc, which is the separation between the two intervening brightest galaxies, BCG2 and BCG, assumed to be the gravitational centres of the main cluster and the substructure, respectively.
The Newtonian criterion for the gravitational binding follows the expression V 2 r D ≤ 2GM sys sin 2 α cos α, where α is the projection angle between the line connecting the centres of the two clumps and the plane of the sky.Beers et al. (1982) and Thompson et al. (1982, see also Lubin et al. 1998) developed the formalism, but it is affected by several constraints.First, the components interact radially, so only head-on collisions with zero angular momentum (no rotation) are possible.Second, the evolution starts at t 0 = 0 with a separation of d 0 = 0, and the clumps are moving apart or coming together for the first time in the history in the model considered.Third, the inequality exposed above implicitly excludes unbound solutions.In addition to these limitations, we note that the two clusters are treated as point masses, which is an assumption that clearly fails when the two cluster mass distributions overlap.
The solutions for this model are shown in Fig. 11, which shows a mass-angle representation of the model.Considering the value of M sys , we only find bound and incoming solutions; no bound outgoing solutions are found.So the main cluster and the substructure would be completely tied by the mutual pull of gravity.That is, we find that we are seeing the cluster in a first interaction (at t = 12.462 Gyr at the redshift of RXCJ1111).Two possible bound solutions are found but they are degenerated due to the ambiguity in the projection angle α.These are BI a and BI b , which correspond to 22 +6 −3 and 81 +2 −5 degrees, respectively.Assuming for simplicity that BI a ∼ 22 • and BI b ∼ 81 • , we estimate the actual de-projected (3D) relative distances and velocities between the two clumps.In the first case, BI a ∼ 22 • , the two galaxy clumps would be separated by a distance of ∆d a = 0.13 Mpc, but the fossil substructure would be colliding Fig. 11.Angle-mass representation for the two-body interaction model found for the main cluster body and substructure.The solid and dashed curves represent the bound incoming (BI) solution and uncertainties estimated as possible models with relative velocities 1400 and 1685 km s −1 .The total mass of the system is represented by the horizontal line, with its uncertainty (dashed lines).Two possible bound incoming solutions were found: BI a and BI b at 22 • and 81 • with respect to the plane of the sky.with a relative 3D velocity of ∆v a = 4100 km s −1 .In the second case, BI b ∼ 81 • , the main cluster and substructure would be separated by ∆d b = 0.70 Mpc and would show a ∆v b = 1560 km s −1 .Thus, in the first case, we find that the substructure would be very close to the main cluster, almost completely merged, as close as 0.1 r 200 , showing a very high speed, >4000 km s −1 .In the second scenario, the substructure would be separated ∼0.6 r 200 from the main cluster, and colliding with a 3D velocity of ∼1560 km s −1 .
The first scenario corresponds to a collision at a quite advanced stage, where the halos and ICM of the two components are almost completely fused.With such a high relative velocity and the two ICMs so mixed, we would expect to measure a high gas temperature, which is not observed in the X-ray maps.Nevertheless, the second scenario corresponds to a merger with a substructure at ∼0.70 Mpc from the main cluster centre with a still moderate velocity.This scenario is in agreement with an early stage merger, where ICMs are starting to interact, with a not very high X-ray temperature and no shock fronts observed.Taking into account this geometry, we are viewing these systems from almost along the merger axis, in which case, if a shock front is present, we see it from within the Mach cone.In other words, we cannot see a sharp shock front because our LOS is not tangential to the front.
It is not easy to find a unique and satisfactory explanation for all the observables (e.g.BCG velocity, velocity distributions, velocity gradients, X-ray properties, spatial distributions, cluster morphology, . . .), and given the limitations of the Beers formalism, presented above, it would be a mistake to completely rule out a more advanced merger on the basis of the Beers model.However, we find that the second scenario proposed here for the merger, represented by a bound incoming solution with a projection angle of ∼81 • would be the preferred model to explain the merging state of RXCJ1111.In addition, we have to consider that the substructure and BCG show higher velocities with respect to the main cluster, and thus the substructure is falling in from the front.At t ∼ 0.15 Gyr, the model predicts that the fossil substructure would be completely merged with the main cluster.

Summary and conclusions
We present a detailed study of the kinematical and dynamical state of the galaxy cluster RXCJ1111+4050.Our analysis is based on new spectroscopic observations acquired at the 3.5m TNG telescope and complementary SDSS-DR16 spectroscopic redshifts in a region of ∼1 r 200 .We selected 104 cluster members around z = 0.0756.The study of the velocity field confirms the presence of significant deviations from Gaussianity, which were explained by the presence of a substructure in the cluster.The galaxy membership reveals that the secondary substructure is a a fossil-like group, with a magnitude gap ∆m 12 ∼ 1.8 that is merging with the main cluster.
The X-ray surface brightness map shows a clear elongated shape in the north-south direction, which is in agreement with the 2D spatial distribution of galaxies and a velocity gradient of about 250−350 km s −1 Mpc −1 , also close to that direction.These facts, together with an indistinguishable galaxy population projected onto the plane of the sky, indicate that the main cluster and substructure of RXCJ1111 lie almost aligned along the LOS, showing a small misalignment towards the south.
We use the velocity dispersion to estimate dynamical masses, and obtain M 200 = 1.9 ± 0.4 × 10 14 M and 0.6 ± 0.4 × 10 14 M for the main cluster and the secondary substructure, respectively.The total mass of RXCJ1111 derived from X-rays is in very good agreement with the dynamical estimates when individual galaxy clumps are considered, but not when the cluster is assumed to be composed by a single component.This clearly suggests that the most appropriate way to estimate dynamical masses in non-relaxed galaxy clusters is by identifying galaxy clumps and computing the total mass as the sum of the different components, which should be more virialised than the whole cluster.In the end, the methodology followed here represents an example to obtain realistic dynamical masses, which is crucial, for instance, to establish scaling relations from different approaches (e.g.X-ray, optical, weak lensing).
The observed excess in the X-ray temperature agrees with the fact that the substructure is starting to collide.This merger is characterised by a mass ratio of 3:1.We propose a possible merger model consistent with a two-body configuration where cluster and substructure are aligned with ∼9 • (±3 • ) from the LOS, with an impact velocity of ∆v rf ∼ 1600 km s −1 .This model also predicts that the main cluster and fossil substructure will be completely joined in about 0.15 Gyr.
To summarise, RXCJ1111 represents observational evidence that the fossil feature of galaxy systems is a transitional stage, which supports the results obtained by von Benda-Beckmann et al. (2008) via simulations.The dynamical analysis presented here demonstrates that a fossil-like group is falling into the RXCJ1111 main cluster.The ongoing collision might accelerate the interaction between the three BCGs observed, causing the cluster to show a smaller ∆m 12 in the near future (in <0.15 Gyr), by fully incorporating the BCG and its corresponding galaxy population into the dynamics of the whole cluster, and thus losing its fossil condition.

Fig. 1 .
Fig. 1.RGB colour composite image obtained by combining g -, r -, and i -band images of 23 × 23 field of view from the Pan-Starrs1 public archive.Yellow squares and circles indicate the galaxies observed in our spectroscopic MOS observations and SDSS-DR16 spectroscopic redshifts, respectively.The blue contours show the isodensity galaxy distribution of likely cluster members (see Sect. 3.3).The white contours correspond to X-ray surface brightness after removing point sources using a pixel mask.In the upper right corner, the inset shows a magnified image of the cluster core.The labels BCG, 2 and 3 indicate the brightest cluster galaxy, and the second and third brightest galaxies, respectively.The green contours represent the diffuse radio emission observed with the VLA.North is up and east to the left.

Fig. 3 .
Fig. 3. XMM-Newton image of the cluster RXCJ1111.6+4050 in the 0.5 to 2 keV energy band.The size of the image is 21.5 (width) by 20 (height) arcmin.North is up and east is to the left.

Fig. 5 .
Fig.5.The same distribution shown in the inner plot of Fig.2but now the global fit (black curve) corresponds to two Gaussian components (in blue and red)."BCG" (in red), "2" and "3" (in blue) coloured labels agree with the most likely component.

Fig. 6 .
Fig.6.Colour magnitude diagram (g − r , r ) of galaxies in a region of 12 radius.The red symbols correspond to spectroscopically confirmed members.The large dots are the three brightest galaxies, BCG, BCG2 and BCG3.The solid line represents the red sequence fitted g − r = −0.185(±0.004)× r + 1.20(±0.08).The dashed lines delimit the locus where likely members are selected.

Fig. 8 .
Fig. 8. Cluster core region of RXCJ1111 including the two brightest galaxies.Left: SDSS r-band image (3 × 3 field) around BCG and BCG2.The white contours correspond to X-ray surface brightness.The black circles indicate the galactic centres, while crosses indicate the Xray peak positions.Right: residuals obtained after subtracting the bestfit model acquired with GASP2D to BCG SDSS r-band image within a region of 1 × 1.4 .The arrows point the northern and southern shells surrounding the core of BCG.Both images are oriented with north up and east to the left.
Table 1 lists the main properties of RXCJ1111 and summarises the main velocities and dispersions detailed in Sect.3.2.