Joint HST, VLT/MUSE and XMM-Newton observations to constrain the mass distribution of the two strong lensing galaxy clusters: MACS J0242.5-2132&MACS J0949.8+1708

We present the strong lensing analysis of two galaxy clusters: MACS J0242.5-2132 (MACS J0242, $z=0.313$) and MACS J0949.8+1708 (MACS J0949, $z=0.383$). Their total matter distributions are constrained thanks to the powerful combination of observations with the Hubble Space Telescope and the MUSE instrument. Using these observations, we precisely measure the redshift of six multiple image systems in MACS J0242, and two in MACS J0949. We also include four multiple image systems in the latter cluster identified in HST imaging without MUSE redshift measurements. For each cluster, our best-fit mass model consists of a single cluster-scale halo, and 57 (170) galaxy-scale halos for MACS J0242 (MACS J0949). Multiple images positions are predicted with a $rms$ 0.39 arcsec and 0.15 arcsec for MACS J0242 and MACS J0949 models respectively. From these mass models, we derive aperture masses of $M(R<$200 kpc$) = 1.67_{-0.05}^{+0.03}\times 10^{14} M_{\odot}$, and $M(R<$200 kpc$) = 2.00_{-0.20}^{+0.05}\times 10^{14} M_{\odot}$. Combining our analysis with X-ray observations from the XMM-Newton Observatory, we show that MACS J0242 appears to be a relatively relaxed cluster, while conversely, MACS J0949 shows a relaxing post-merger state. At 200 kpc, X-ray observations suggest the hot gas fraction to be respectively $f_g = 0.115^{+0.003}_{-0.004}$ and $0.053^{+0.007}_{-0.006}$ for MACS J0242 and MACS J0949. MACS J0242 being relaxed, its density profile is very well fitted by a NFW distribution, in agreement with X-ray observations. Finally, the strong lensing analysis of MACS J0949 suggests a flat dark matter density distribution in the core, between 10 and 100 kpc. This appears consistent with X-ray observations.


INTRODUCTION
One of the most promising avenues towards understanding the nature of dark matter is to study its gravitational influence on the Universe's large-scale structure, particularly within the most massive galaxy clusters. These gravitationally bound clusters act as the largest natural laboratories, allowing not only to observe the large-scale baryonic physics, but also to indirectly probe dark matter thanks to the effect of gravitational lensing. Gravitational lensing is the phenomenon of optical distortion of background images, occurring when a massive foreground object -like a cluster, the "lens" -is on its line-of-sight. Gravitational lenses act as magnifying telescopes of objects in the background, creating in some cases multiple images of a same source, ★ E-mail: joseph.allingham@sydney.edu.au and allowing observers to study objects in the distant Universe (for a review, see Kneib & Natarajan 2011).
For all these reasons, since the first discovery of the gravitational giant arc of Abell 370 (Hammer 1987;Soucail et al. 1988) to the modern surveys of galaxy clusters and gravitational lenses such as the Cluster Lensing And Supernovae survey with Hubble (CLASH, from one source through gravitational lensing allows one to constrain the mass distribution within the lens, and to characterise the dark matter density profile within it. The descriptive potential of gravitational lensing has already been showcased at multiple occasions such as in (Richard et al. 2014a;Jauzac et al. 2014Jauzac et al. , 2016cDiego et al. 2015aDiego et al. ,b, 2016Diego et al. , 2018Diego et al. , 2020Grillo et al. 2015;Caminha et al. 2017;Williams et al. 2018). Using the combination of high resolution images taken with the Hubble Space Telescope (HST) and the Dark Energy Survey (DES) for photometric analysis in the one hand, and the Multi-Unit Spectroscopic Explorer (MUSE, see Bacon et al. 2014) for spectroscopy in the other, we were able to securely identify cluster members and multiple images systems. This combination has proven to be particularly successful over the past few years (e.g. Treu et al. 2016;Lagattuta et al. 2017Lagattuta et al. , 2019Jauzac et al. 2016aJauzac et al. , 2019Jauzac et al. , 2021Grillo et al. 2016;Mahler et al. 2017;Caminha et al. 2019).
In this paper, we repeat a similar exercise, looking at two galaxy clusters, MACS J0242.5−2132 and MACS J0949.8+1708 (i.e. RXC J0949.8+1707), hereafter MACS J0242 and MACS J0949 respectively, initially discovered by the MAssive Cluster Survey (MACS, PI: Ebeling, Ebeling et al. 2001). We combined multi-band HST and ground-based imaging with spectroscopy from VLT/MUSE with the lensing modelling technique presented in detail in Richard et al. (2014b) which makes use of the publicly available L software (Kneib et al. 1996;Jullo et al. 2007). We then confront our lensing results to the intra-cluster gas distribution observed by the XMM-Newton X-ray Observatory.
It is common practice to use the combined baryonic analysis of the X-ray signal and the Sunyaev-Zel'dovich effect (SZ) to understand the thermodynamics of galaxy clusters. One can then reconstruct the total matter density of galaxy clusters by making a number of hypotheses such as hydrostatic equilibrium or polytropic temperature distribution (see Tchernin et al. 2018). Furthermore, as the analysis of multi-wavelengths observations (optical, Sunyaev-Zel'dovich effect, X-rays) characterises the thermodynamics of the intra-cluster medium (ICM; see Sereno et al. 2017), a careful comparison between these and a strong lensing analysis can provide clues on the possible differences between expected and observed baryon and dark matter distributions.
As an example, the study in merging galaxy clusters of the offset between the position of the centre of dark matter, luminous galaxies and X-ray emission can be used to constrain the cross-section of self-interacting dark matter (SIDM, see Tulin & Yu 2018, for an overview). In fact, simulations of colliding clusters suggests the cold dark matter (CDM) distribution to be bounded to the luminous distribution; while in SIDM scenarios dark matter lags behind baryonic matter (Massey et al. 2011;Robertson et al. 2016Robertson et al. , 2017. For instance, Robertson et al. (2017) present SIDM simulations with anisotropic scattering, yielding an offset between the galaxies centre and that of dark matter (DM) smaller than 10 kpc for an interaction / = 1 cm 2 .g −1 . This was pioneered in Clowe et al. (2004) and Bradač et al. (2008), and has now become more and more popular as shown in, e.g. Merten et al. (2011);Harvey et al. (2015); Massey et al. (2015Massey et al. ( , 2018; Jauzac et al. (2016bJauzac et al. ( , 2018. In this article, we focus on the lensing-based mass reconstructions of the two clusters. Utilising the ICM detected in the X-rays to infer the dark matter halo profile, we compare the results of our lensing reconstruction to the XMM-Newton X-ray data from CHEX-MATE Collaboration et al. (2021), processed following the X-COP pipeline (Ghirardini et al. 2019) for these two clusters. We present a broader context for such comparisons, i.e. new models of baryonic matter distribution rooted in lensing analysis to constrain the electronic densities of galaxy clusters, in a companion paper (Allingham et al. in prep.).
Our paper is organised as follows. In Section 2, we present the observations used for our analysis. The methods to extract multiple image candidates, and to build cluster galaxy catalogues are presented in Section 3. The lensing reconstruction method is introduced in Section 4, the mass models are described in Section 5, and conclusions are presented in Section 6. Throughout this paper, we assume the ΛCDM cosmological model, with Ω = 0.3, Ω Λ = 0.7, and 0 = 70 km/s/Mpc. All magnitudes use the AB convention system (Oke 1974).

DATA
To determine the cluster mass distributions as robustly as possible, we include both imaging and spectroscopic information when constructing lens models. This combination is especially powerful, allowing us to identify and confirm individual components of the model (such as multiple-image constraints and cluster members), while simultaneously rejecting interlopers along the line of sight. We complement the observations we have with HST and VLT/MUSE with XMM-Newton X-ray Observatory observations to cross-check our lensing model results. Figures 1 and 2 present a stack of the imaging, spectroscopic, and X-ray data for clusters MACS J0242 and MACS J0949 respectively.

Hubble Space Telescope
As part of the MACS survey (Ebeling et al. 2001), both targets in our study have publicly available HST data. Snapshot (1200s) imaging of MACS J0242 taken with the Wide Field Planetary Camera 2 (WFPC2, Holtzman et al. 1995) exist for both the F606W and F814W bands (PID:11103, PI: Ebeling), supplemented by an additional 1200s image taken with the Advanced Camera for Surveys (ACS, Ford et al. 1998) in F606W (PID: 12166, PI: Ebeling). Similarly, shallow imaging for MACS J0949 have been taken with the ACS in both F606W (PID:10491, PI: Ebeling) and F814W (PID: 12166, PI: Ebeling). Archival processed versions of these datasets are available from the Hubble Legacy Archive 1 .
Following the initial MACS data, MACS J0949 was subsequently observed as part of the RELICS survey (Coe et al. 2019) -under the name RXC J0949.8+1707 -and thus there are additional data sets for this cluster. Specifically, ACS imaging in F435W, F606W and F814W provide wider, deeper coverage of the cluster field in optical bands, while coverage in F105W, F125W, F140W and F160W bands using the Wide Field Camera 3 (WFC3, Kalirai et al. 2009) provide information in the near-IR regime. These data are also publicly available 2 , and therefore in this work combine all of the imaging (save for the F435W band, which is too low S/N for our purposes) to create our master data set. A summary of all available HST imaging can be found in Table 1.

DESI Legacy Survey
Since the available HST imaging for MACS J0242 are shallow and colour information is limited to a WFPC2-sized footprint, we com-plement these data with additional multi-band ground-based imaging from the Dark Energy Spectroscopic Instrument (DESI) legacy archive. To enhance the HST data as much as possible, we extract cutout images in three optical bands -g, r and z, see Abbott et al. (2018). The images are centred around the MACS J0242 brightest cluster galaxy (BCG) located at ( = 40.6497 deg, = −21.5406 deg), and extend over a full ACS field of view. Combining the space-and ground-based information allow us to improve our galaxy selection function during lens modelling (see Section 3). The DESI data are summarised in Table 2.

Spectroscopy
In addition to imaging, our lensing reconstruction makes use of the Multi Unit Spectroscopic Explorer (MUSE; Bacon et al. 2014) observations at the Very Large Telescope. Such observations are invaluable to obtain redshift information. Both clusters were observed with MUSE as part of the filler large programme "A MUSE Survey of the Most Massive Clusters of Galaxies -the Universe's Kaleidoscopes" (PI: Edge). Data for each cluster consists of a single MUSE pointing, divided in a series of three exposures of 970 seconds. To reduce the effects of bad pixels, cosmic rays, and other systematics, each successive exposure is rotated by 90 degrees, and a small (∼ 0.05 ) dither pattern is applied. We reduce the raw data following the procedure detailed in Richard et al. (2021). Details of the observations for both clusters are summarised in Table 3.

X-ray data
We searched the XMM-Newton archive for publicly available observations of the two systems of interest. MACS J0242 was observed for a total of 70 ks (OBSID:0673830101), and MACS J0949 for a total of 36 ks (OBSID:0827340901). We analysed the two observations using XMMSAS 17.0, and the most up-to-date calibration files. We used the XMMSAS tools mos-filter and pn-filter to extract light curves of the observations and filter out periods of enhanced background, induced by soft proton flares. After flare filtering, the available clean exposure time is 61 ks (MOS) and 53 ks (PN) for MACS J0242, and 35 ks (MOS) and 34 ks (PN) for MACS J0949.

SPECTROSCOPIC & PHOTOMETRIC ANALYSES
In this section, we present the key steps to obtain cluster galaxy catalogues and (candidate) background multiple image systems for both MACS J0242 and MACS J0949: from the source extraction to the selections of galaxies and identification of cluster galaxies specifically, using both the multi-band imaging in hand for the two clusters as well as the spectroscopy from VLT/MUSE.

Spectroscopic analysis
We here present the analysis of the spectroscopic observations described in Sect. 2.2. In spite of the field of view of the MUSE cubes, 1 × 1 , being smaller than that of HST or DES, we can still access the redshift of a large number of foreground, cluster and background galaxies.
In order to detect specifically multiple image systems, we use MUSELET (MUSE Line Emission Tracker), a package of MPDAF (Muse Python Data Analysis Framework) which removes the constant emission from bright galaxies in the field, and is optimised for the detection of the faintest objects. For more details about the technique, we refer the reader to (Bacon et al. 2016) and (Piqueras et al. 2017). We go through each of the 3681 slices of this subtracted MUSE datacube, and identify the bright detections.
We complete this technique with CatalogueBuilder (see Richard et al. 2021) for a thorough and systematic analysis. The latter embeds the MUSELET analysis, but also uses a modified version of MARZ (see Hinton et al. 2016), which is better tuned to the resolution and spectral profiles specific to MUSE data. CatalogueBuilder also uses the position data of the deepest field available (in this case HST/ACS). These make it easier to confirm the likely source of the multiple images which we are looking for. Using the spectroscopic information, we adjust with our own custom redshifting routine the detected spectra to the known absorption lines, and notably [OII], [OIII] and Ly-. We then obtain catalogues containing coordinates and redshifts, such as Tables 6 and A1. We also consider multiple detections within a radius of < 0.5 and a redshift separation of < 0.05 to be a unique object. All redshifts are supposed known with a precision estimated to = 0.0001.
We can associate to these detections Signal-to-Noise (S/N) ratios. As we also know the type of pattern the absorption lines should match, we can use the S/N ratio and spectral patterns to define different confidence levels. We only keep in all catalogues, including for example in Sect. A, detections judged to be "good" or "excellent" (identifiers 3 and 4 in MARZ and CatalogueBuilder). In the case of several detections representing a same object, we merge them keeping the best quality of detection.
The distribution of redshifts in each cluster is shown in Fig. 3 for the full MUSE frame. We measure 36 and 96 good spectroscopic redshifts in MACS J0242 and MACS J0949 respectively. Due to the small statistics, this distribution is not Gaussian but it is sufficient to constrain the redshift of the clusters, which we estimate to be 0.300 ≤ ≤ 0.325 and 0.36 ≤ ≤ 0.41 for MACS J0242 and MACS J0949 respectively. For the current analysis, we define the redshift of each cluster by that of their BCG, i.e. respectively 0.3131 and 0.383 for MACS J0242 and MACS J0949 respectively.

Source extraction
We first align all images from a given instrument (HST/ACS, HST/WFC3, HST/WFPC2 and DESI) to the same coordinates, and pixelate them accordingly to allow for direct colour comparison of detected objects. In order to extract all detected objects from the multi-band imaging in hand for each cluster, we run the SExtractor software (Bertin & Arnouts 1996) in dual-image mode, for each passband of each instrument. For each instrument, we adopt a reference pass-band and a position of reference. The former sets the Kron-like magnitude of each detection, while the latter sets its location. The number of bands per instrument as well as the reference pass-band used are listed in Tables 4 and 5 for MACS J0242 and MACS J0949 respectively.
For each instrument, we then apply several cuts and selection criteria to the output catalogues from SE . That allows us to build a complete multi-band catalogue composed only of galaxies. We summarise the different steps of this process: (i) All detections without reliable magnitude measurements (i.e. MAG_AUTO=-99) and incomplete (or corrupted) data are removed from all catalogues. This includes isophotal data and memory overflow that occurs during deblending or extraction.
(ii) All objects with a stellarity greater than 0.2 are removed as et al.  Table 3. Summary of MUSE observations for MACS J0242 and MACS J0949. Columns 1 to 3 indicate respectively the name of the cluster, its average redshift, and the ID of the ESO programme. For each pointing, we then give the observation date in column 4, the right ascension, R.A., and declination, Dec., of the centre of the field of view in columns 5 and 6, the total exposure time in column 7, and the full width at half maximum (FWHM) of the seeing during the observations in column 8. they are likely to be stars rather than galaxies. We additionally mask all detections very close to bright stars.
(iii) For a given cluster, only objects detected in all pass-bands are kept.
(iv) All objects with a Signal-to-Noise ratio (S/N) smaller than 10 are removed.
Tables 4 and 5 are listing the number of detections remaining once each of these criteria are applied for each instrument, for MACS J0242 and MACS J0949 respectively.

Spectroscopic redshift identification
Now that we have a galaxy catalogue for each instrument, we can match our detection with spectroscopic redshift measurements from VLT/MUSE. In order to ensure a MUSE detection corresponds to a photometric one, we compare the positions measured by Sextractor in the different filters for all objects, using a Haversine function 3 . If the separation angle between objects from the spec-3 The Haversine angle reads as H = 2 arcsin √︄ sin 2 2 − 1 2 + cos 1 cos 2 sin 2 2 − 1 2 . troscopic and the photometric catalogues is smaller than 0.5 , we consider the detection to be of the same objects, and hence associate the spectroscopic redshift to the photometric detection. This error is equal to 2.5 MUSE pixels, and captures the positional uncertainty on spectroscopic detections.  Table 6. Critical lines for a source at = 3.0627 (redshift of system 1) are shown in red. The MUSE field of view is shown in pink.
Out of this step, we attribute a spectroscopic redshift to 20, 25, and 25 sources in the DES, HST/WFPC2 and HST/ACS catalogues for MACS J0242. In the case of MACS J0949, we attribute a spectroscopic redshift to 54, and 49 sources in the HST/ACS and HST/WFC3 catalogues.

Cluster galaxy selection
The next step is the identification of cluster galaxies specifically. For that we are using colour-magnitude selections for each clusters.
The first step consists in applying the red sequence technique (e.g. Gladders & Yee 2000). Using the catalogues after source extraction selections and spectroscopic redshift identification, we compute for both clusters a series of colour-magnitude (CM) diagrams. We compute these for each instrument. As each pass-band represents a magnitude, we can respectively compute 3 and 1 CM diagrammes for DES and HST/WFPC2 for MACS J0242 (none for HST/ACS as only one band is available), and 1 and 6 for HST/ACS and HST/WFC3 for MACS J0949.
As shown in Fig. 4, cluster members are expected to follow a main sequence (magenta line). To calibrate our selections, we use spectroscopically confirmed cluster members. We then remove all detections with a magnitude exceeding max , which varies depending on instruments and filters. For MACS J0242, we have max = 22 for HST/WFPC2, 23.5 for DES/z, and 24.5 for DES/r. For MACS J0949, we have max = 21.5 for HST/WFC3 and 22.5 for HST/ACS. We then perform a linear regression and obtain the main sequence. We give in Appendix B the fits for all colour-magnitudes used for both clusters.
Galaxies selected as cluster members are galaxies which have a colour within 2 of the main red sequence for HST/ACS and HST/WFC3, and within 3 for HST/WFPC2 and DES. is the et al.  Table 8. In pink, we display the MUSE field of view.
weighed colour standard deviation of the spectroscopically confirmed cluster galaxy sample. These limits are highlighted as black rectangles in Fig. 4. For an instrument with more than 2 pass-bands, we can compute more than one CM diagram, and thus only retain cluster member identifications compatible with all colour-magnitude diagram selections. We summarise in Tables 4 and 5 for MACS J0242 and MACS J0949 respectively, the number of galaxies identified as cluster members per instrument once these colour-magnitude selections are applied. In some cases, spectroscopically confirmed cluster galaxies fall outside the colour-magnitude selection. These objects are ultimately conserved in our cluster galaxy catalogue. However, we do not include them in the CM cut counts, to show the effect of the photometric selection.

Instrument catalogue combination
We now assemble the galaxy catalogues for each instrument before merging these into a final cluster galaxy catalogue for each cluster. We match the coordinates of sources with the already defined 0.5 separation angle. MACS J0242 and MACS J0949 were imaged with different instruments, and thus have different coverage. We define the camera of reference as the camera with the highest resolution. In the case of the both clusters, it is HST/ACS, but the reference band is chosen as F606W for MACS J0242, and F814W for MACS J0949. MACS J0242 was observed with HST/ACS in only one band. Moreover, MACS J0242 was observed with HST/WFPC2 in 2 pass-bands, but the shape of the camera field of view does not cover the entire ACS field of view. MACS J0242 has DES observations in 3 passbands, covering a wide field of view. However the quality of these observations is lower than the ones we have from space. We therefore   require for a given cluster member selected galaxy in HST/ACS to be at least present in DES or WFPC2 in order to be included into the final cluster member catalogue. MACS J0949 was imaged with HST/ACS and WFC3 cameras. HST/WFC3 has a smaller field of view than ACS. We detected multiply imaged systems out of the WFC3 field of view. In order to account for the gravitational effect of individual galaxies on these systems, we include all galaxies detections from at least one camera to our galaxies catalogue. Finally, cluster galaxies located at a distance larger than 40 from the cluster centre and with a magnitude difference to the BCG of Δ > 4 are ignored. Due to their small mass, these galaxies would only have a very small impact on the strong lensing configurations observed.

Cluster galaxy catalogues
Sect. 3.2 describes all the steps for the identification of cluster members, including colour-magnitude selections as well as spectroscopic identifications. All galaxies identified as cluster members and used for our lensing modelling are listed in Appendix, in Tables A3 and  A4 for MACS J0242 and MACS J0949. Our final catalogues include 58 and 170 galaxies for MACS J0242 and MACS J0949 respectively.
In order to probe the robustness of our catalogues, we conducted the following verification analysis. We isolated only the spectroscopic detections, and then reinjected them into our photometric selection. We found respectively 15 out of 16 and 34 out of 34 galaxies retained within the photometric selection for MACS J0242 and MACS J0949. As these spectroscopic detections were used to define these selections, they are expected to be selected. Thus, in order to estimate the contamination by galaxies out of the cluster redshift boundaries, we examined the number of selected spectroscopic detections out of the cluster. We find a maximum 2 (2) out of 54 (97) galaxies of our sample contaminants, i.e. 4% (2%) contamination of our sample in cluster MACS J0242 (MACS J0949). Thus we are confident in our galaxy selection. Nevertheless, for accuracy, we removed these known out-of-cluster galaxies from the final catalogue.

Multiple image systems
In Sect. 3.1, we described the preliminary steps leading to the multiple image system catalogue. At this point, this is simply a catalogue of reliable detections with redshift > 0.6. The second step in the identification of multiple image systems is to look for similarities between these detections, starting with their spectra. We then look at their positions and see if they are compatible with a lensing geometry.  The MUSE field of view being narrower than the HST one, one can also look at the colour and morphology of possible multiple images. If a given set of multiple images presents at the same time compatible positions, colours, morphologies and, if available, redshift, we consider them as a multiple image system.
In Fig. 5, we show a colour composite HST image of four MUSE detections, 4 multiple images of the same galaxy located at redshift = 4.89. In the case of MACS J0949, we force extract emission from the MUSE cube corresponding to the location of multiple images previously identified by the RELICS collaboration (obtained through private communication); we only reveal marginal identification as explained in Sec. 5.1.2. The final list of system used in this analysis is presented in Table 8.

STRONG LENSING MASS MODELLING
The mass distribution of each cluster is reconstructed using the Lenstool software 4 (Kneib et al. 1996;Jullo et al. 2007), in its parametric mode. The optimisation is performed in the image plane with a Markhov Chain Monte-Carlo algorithm (MCMC) assuring the sampling of parameter space. It optimises the predicted positions of multiple images while fitting an underlying mass distribution composed of large-scale halo(s) to describe the overall cluster potential, and small-scale halos to account for local perturbers such as cluster galaxies.
For both clusters, we describe any potential using a dual Pseudo-Isothermal Elliptical matter distribution (dPIE, see Kassiola & Kovner 1993) which, as described in Elíasdóttir et al. (2007), has 4 https://projets.lam.fr/projects/lenstool/wiki two different pivot scales: a core radius, which describes the potential evolution due to the baryonic matter content, and a cut radius that describes the dark matter potential. A dPIE potential is described by seven parameters (excluding the redshift): the central coordinates, the ellipticity , the position angle , the core and cut radii, core and cut respectively, and a fiducial central velocity dispersion . The fiducial central velocity dispersion in Lenstool relates to the true three dimensional central velocity dispersion with 0 = √︁ 3/2 , as detailed in Bergamini et al. (2019), Appendix C.
For each cluster, we assume one single large-scale dark matter halo to describe the overall cluster potential. It is described by a large velocity dispersion (∼ 10 3 km.s −1 ), a large core radius (∼ 10 2 kpc) and large cut radius. We optimise all the parameters of the potential, excluding the cut radius which we fixed to values ≥1 Mpc as it is located far from the strong lensing region and thus cannot be constrained by multiple images only. The position of each cluster halo is allowed to vary within 10 of the cluster centre, i.e. the et al.
position of the BCG. The ellipticity of the halo is limited to values < 0.8. The cut radius is fixed to 1.5 Mpc for both MACS J0242 and MACS J0949, as our investigation to model the ICM through lensing shows that this value provides a better fit to the X-ray observations (see our companion paper Allingham et al. in prep.). This value is in agreement with Chang et al. (2018), taking in consideration the higher mass range of the clusters we are exploring here.
The BCG of each cluster is also modelled independently, using a dPIE potential. The BCG has a strong gravitational influence in the cluster core, and will thus impact the geometry of multiple images quite strongly (Newman et al. 2013a). We fix their core to a small value of 0.30 kpc for cluster MACS J0242 and 0.25 kpc for MACS J0949. For their positions, position angle, and ellipticity, we fix their values to the shape parameters in outputs of SExtractor. Finally, we only optimise its their velocity dispersion and cut radius.
Each individual cluster member is modelled by its own dPIE potential. Their positions, ellipticities and position angles are obtained with the photometric extraction.
We again assume a small but non-null value for core . Their cut radii and velocity dispersions are optimised using their magnitude and assuming the Faber-Jackson scaling relation (Faber & Jackson 1976). All cluster members cut radii and velocity dispersions are rescaled with regard to a unique set of parameters ( cut,0 , 0 ). This allows us to optimise each cluster galaxy potential using a remarkably small number of parameters. cut and are allowed to vary between 1 and 50 kpc, and 100 and 300 km.s −1 respectively. As mentioned earlier, the Faber-Jackson relation being scaled to a reference magnitude 0 , we use the reference pass-band of the main camera for each cluster, ACS/F606W ( 0 = 20.0205) and ACS/F814W ( 0 = 19.5085) for MACS J0242 and MACS J0949 respectively.
As the centre of the cluster-scale halo and the BCG are aligned, the core , cut and parameters of both potentials are degenerate. Due to the limited number of lensing constraints, we proceed incrementally to model the potential, to narrow the parameters space. First, we include the BCG in the scaling relation of the cluster galaxies and optimise the cluster-scale halo and the scaling relation parameters as described above. Second, we run a model with the BCG optimised independently, only optimising cut and as explained above. However in this case, the cluster-scale halo parameters are allowed to vary within a restricted range, defined gaussianly around the best fit values obtained from the first model. This way, we can limit the degeneracy between the cluster-scale and BCG halos, and obtain physical values to describe the BCG potential.
Finally, we added a completely free dPIE potential south to the main cluster halo of MACS J0949. This structure has already been included in the public RELICS models and correspond to the location of three candidate multiply-imaged systems 4, 5 and 6 as shown in Fig. 6. We optimised their redshifts as well as the potential and to prevent nonphysically high value we imposed gaussian priors on core , cut and velocity dispersion.

MACS J0242 model
In MACS J0242, we detected six systems of multiple images with MUSE. Their positions and redshifts are given in Table 6. We provide the best fit parameters of our model in Table 7. The fixed values are highlighted by an asterisk. Our best-fit model yields predicted multiple images with a of 0.39 of the observed positions. The  Table 8. The external/tangential critical lines for a source at redshift = 3.65 are represented in red -this redshift being compatible with sources 4, 5 and 6, according to the best fit optimisation. inclusion of an external shear component does not provide a significant improvement to the mass model, i.e. a of 0.38 compared to our best-fit mass model of 0.39 . This error is smaller than the positional error associated to spectroscopic detections. However, the error on the position of the multiply-lensed images is associated to their photometric detections, with much smaller positional error.
The geometry of the cluster is typical of a relaxed cool-core cluster. The density profiles peak in the centre, and the transition between the BCG and the DM halo appears to be very smooth as illustrated in Fig. 7. No other significant structure are identified. Figure 7 shows Table 7. Best fit parameters of the strong lensing mass models for MACS J0242 and MACS J0949. We here list the central coordinates, Δ and Δ in arcsec, relative to the centre, the ellipticity, , the position angle in degrees, , the core radius in kpc, core , the cut radius in kpc, cut , and the velocity dispersion in km.  the surface density profile, Σ, and includes a 68% confidence interval around the best contours, as a function of the distance to the cluster centre. The inner part of the profile, 50 kpc, is dominated by the BCG potential, while at larger radii, the dark matter halo takes over. This pivot scale of about 50 kpc corresponds to the core radius of the DM halo, and the separation between the two different regimes of the dPIE potential. However, disentangling the potential influence of the BCG and the DM of the halo would require a much finer study of the stellar mass distribution of the BCG with a spectral energy distribution (SED) fit, which is beyond the scope of this article.
We find the total density profile (baryonic and dark matter) of MACS J0242 to be well fitted by a Navarro-Frenk-White profile (NFW, see Navarro et al. 1996) in the region between 20 and 1000 kpc. We limit the reconstruction to radii ≥ 20 kpc as the Kron-like magnitude radius of the BCG is about 10 kpc, and we attempt to limit the influence of stellar physics within the fit. In order to compare it to the NFW fit of cluster MACS J0949, we arbitrarily take 20 kpc to be a good compromise of strong lensing potential reconstruction without stellar physics contamination. For regions > 200 kpc, the cluster-scale DM halo should dominate the whole matter distribution. As the DM halo dPIE parameters 0 and core are well constrained through strong lensing, this region beyond multiple images constraints and below the cut-off radius cut is expected to be well represented by a NFW profile. With NFW parameters = 3.42 × 10 −22 kg.m −3 and = 209.9 kpc, we find a reduced 2 = 1.11. In order to compare our results to the X-ray data, we extrapolate the masses Δ, comprised within an overdensity Δ using where is the critical density at the cluster redshift, and (< ) the total mass enclosed within a given radius, . At large radii ( > 200 kpc), the strong lensing mass reconstruction only provides an estimate of the true mass distribution as there is no strong lensing constraints to precisely and accurately estimate the mass distribution in the outskirts. It therefore only provides a pure extrapolation of the inner core mass distribution, and only a weak-lensing analysis would provide a precise mass estimate in this region of the cluster, however this is beyond the scope of this analysis. We also compute 2 ( < 200 kpc), the integrated mass within a radius of 200 kpc. This mass is a direct output of the lensing mass reconstruction. These values are all listed in Table 9.

MACS J0949 model
In MACS J0949, we identified several objects located behind the cluster with the MUSE observations. However most of them appear to be singly lensed. Through the techniques exposed in Sect. 3, we detected a multiple image system in the MUSE field at redshift = et al.  The green and red curves -with error bars -represent respectively the BCG and DM halo reconstructions, and the full cluster is shown in blue. The magenta dashed line represents the NFW fit of the total density from Lenstool reconstruction -all galaxies and DM halo. The cyan line shows the fit to the X-ray data. Bottom row: Cluster MACS J0949. Blue: Our model, with 68% confidence interval. Cyan: Lenstool model from RELICS. We note that error bars were obtained on a different sample (2,000 realisations for our model, 100 for RELICS). Green: Glafic RELICS model, realised under the same conditions. Red: region of the multiple images constraints. -Right panel: Volume mass density. The reconstruction of the XMM-Newton data is shown in black, given with 1 error bars in yellow. The green and red curves represent respectively the BCG and DM halo reconstruction, and the full cluster is shown in blue. The magenta dashed line represents the NFW fit to the Lenstool reconstruction. The cyan line shows the fit to the X-ray data.
4.8902. This system 1 is composed of five multiple images, including four in the field, and one counterpart 1.3 located outside the MUSE field of view, and detected in the HST imaging. We also detect a fifth image, image 1.5, located close the BCG of the cluster. Images 1.4 and 1.5 (see Fig. 2), straddling the central critical curve of the cluster, allow to set stringent constraints on the inner slope of the mass density profile (as exhibited in Schneider et al. 1992;Newman et al. 2013b;Caminha et al. 2017).
Careful consideration of the HST images allowed us to detect secondary, fainter emission knots for four multiple images in system 1 -all except the central one which is hidden by the emission of the BCG. This is shown in Fig. 5. The MUSE spectroscopic analysis of these three images which compose system 2 shows a faint Lypeak for all of them, allowing us to measure a redshift of 4.8844, very close to that of system 1. We interpret system 2 either as part of the same galaxy, or a companion galaxy of system 1's source. The Ly-halo of system 1 extends, and the potential secondary peak emission coincides with system 2 emission knots. We include 4 multiple images of system 2 as additional constraints to our mass model, the fifth image being demagnified we restrain ourselves from including it in our mass model. The coordinates and redshifts of the multiply imaged systems are given in Table 8. We give a list of the singly imaged objects in Appendix A.
The inspection of HST images also led to the discovery of system 3, composed of two multiple images. These faint detections in the South of the cluster were equally present in the MUSE field. A faint and a priori inconclusive detection of Ly--see Fig. 8 -is consistent with the redshift optimisation of this system using only system 1, or 1 and 2 as constraints. We therefore conclude that this system's redshift is 5.8658. However the stack of the spectra presents a S/N ratio < 2, and the MUSE data are sensible to sky perturbations in the speculated Ly-bandwidth. We therefore decide not to use this as a redshift constraint, but to let the redshift free during the model optimisation.
At last, we detect three candidate multiply lensed images in the South of the HST field of view, in a region not covered by the MUSE observations. We included these three candidate systems 4, 5 and 6 in our mass model, letting their redshifts as free parameters. Their detection supposes the presence of a Southern halo as described in Sect. 4. For systems 3, 4, 5 and 6, our best fit mass model gives the respective redshifts: 4.85 +1.52 −0.70 , 3.76 +1.57 −0.80 , 3.63 +1.67 −0.74 and 3.57 +0.35 −1.08 . Similarly to MACS J0242, we model the mass distribution of the cluster scale halo and the BCG galaxy separately. The best-fit mass model parameters are listed in Table 7, and gives a of 0.15 . The addition of an external shear component does not improve the mass model, and gives a of 0.16 . In a similar fashion to MACS J0242, although the degeneracy between the cluster scale halo and the BCG is still present, the BCG optimisation converges. The is particularly small which may be explained by the lack of constraints in our model. Indeed, as shown in e.g. Johnson & Sharon (2016), a larger number of constraints may increase the value of the but could also improve the accuracy of the model. Similarly to MACS J0242, we compute integrated and 3D masses for MACS J0949. These are listed in Table 9 and discussed further in Sect. 6. We compare our model of MACS J0949 to the two publicly available models from the RELICS collaboration 5 . Comparing the surface density profiles, we find a 1 agreement between the model presented in this article and the Lenstool RELICS model as can be seen in Fig. 7. As for the RELICS model obtained using the Glafic lensing algorithm (presented in Oguri 2010), its density profile is in agreement with our model, although the most stringent constraints (in the ∈ [40, 100] kpc region) yield a slightly smaller surface density. The overall profile from the Lenstool RELICS public release model presents a flatter density profile and an excess in mass after 80 kpc (coincidental with the Einstein radius of system 1). This could be partially explained by the more massive structure in the South of the cluster, which is slightly offset from the South bright galaxy surrounded by systems 4, 5, and 6 as mentioned before ( 2 (< 100 kpc) = 13.02 × 10 12 compared to 2 (< 100 kpc) = 7.65 × 10 12 for our model). We report a very good agreement between the measured spectroscopic redshift obtained from MUSE observations with the photo-used by the RELICS team (obtained through private communication with K. Sharon). Our model presents a significantly lower of 0.15 , in comparison to 0.58 . The reconstructed mass distribution appears to be more elliptical than the X-ray surface brightness obtained with XMM-Newton as shown in Fig. 2. The 3D density profile is presented in Fig. 7. It confirms the inflexion point in the density profile at 100 kpc, and therefore suggests that the cluster is still undergoing a relaxing phase. The NFW profile fit in the ∈ [20, 1000] kpc region yields NFW parameters = 1.23 × 10 −22 kg.m −3 , = 405.5 kpc, for a reduced 2 = 1.90. The quality of this fit is thus not comparable to that of cluster MACS J0242, mostly due to the flatter density profile in the ∈ [40, 100] kpc region.
Looking at the galaxy distribution within the cluster, we observe four bright and massive galaxies, of comparable magnitude to the BCG 6 . We could extrapolate all of these bright galaxies to have been the BCG of former galaxy clusters, which would have merged with MACS J0949 in the past. However, the X-ray observations show a diffuse emission centred on the BCG and thus do not provide any evidence of recent merger events. Therefore, our analysis strongly suggests a unique dominant cluster scale dark matter component. Nonetheless, we stress that the magnitude gap between the BCG and the second-brightest cluster galaxy in MACS J0242 is much larger than in MACS J0949. According to Trevisan & Mamon (2017), this is an additional argument to claim that the former cluster is more relaxed, and that MACS J0949 went through a recent merging event.
Our interpretation of the dynamical state of MACS J0949 and its lensing power could be further constrained with additional spectroscopic or imaging observations. The clear identification of the spectroscopic redshift of system 3, and of additional systems would et al.  Figure 9. MACS J0949 reconstruction of the full image plane of system 1 from the unique extended emission images 1.1 and 2.1. Their region, highlighted with the yellow box is cut out and deprojected into the source plane, and casted back in the image plan to produce the full system. We clearly observe a continuous emission between the North-East image 1.4 and the central one 1.5. We display in green the contours of the Ly-extended emission from the VLT/MUSE narrow-band image centred at 715.869 nm and 1.625 nm wide, showing the four detected multiple images of system 1, and three of system 2 (see Fig. 2 for more details). The last images 1.3 and 2.3 of these systems are located outside of the VLT/MUSE field of view. The critical lines are displayed in red, for redshift = 4.8902 of system 1. The pink overlay represents the MUSE narrow-band contours.
particularly assist constraining the dark matter halo ellipticity, core radius and velocity dispersion.

Relensing in MACS J0949
On Fig. 9, we display the extracted emission of images 1.1 and 2.1 detected in MACS J0949 from the MUSE narrow-band centred on = 715.869 nm within a yellow box. In order to verify the robustness of the lensing model of MACS J0949, we then infer the emission in the source plane ( = 4.8902), before projecting it back to the image plane with our lens model, to obtain a re-lensed prediction.
The other multiple images on the MUSE field, 1.2, 1.4, 1.5, 2.2 and 2.4 are correctly predicted. Their Lyman-detections are also listed in Table 8. Images 1.4 and 1.5 emission appear to be connected. This is simply due to the extended source emission of system 1 and 2, as a number of faint multiple images of system 2 are predicted between 1.4 and 1.5, in agreement to the MUSE observations on the narrow-band.

Stellar mass estimate
The strong lensing analyses are giving us an estimate of the total mass enclosed in each clusters.
We further compare our strong lensing mass with an estimate stellar mass. We use the reference cluster members catalogue magnitudes described in Sect. 3, converted into K-band luminosity 7 , and use 7 We take the K-band reference here to be the KPNO Flamingos Ks filter.
it as a proxy for stellar mass. For the scaling relations we refer the reader to Hogg et al. (2002); Lin et al. (2006). These catalogues were established over the entire observable clusters, although the faintest galaxies were cut out beyond distances of 40 from the centre. Once the catalogue established, we adapt the Salpeter initial mass function, and use the mass-to-light relationship for red quiescent galaxies derived by Arnouts et al. (2007) on the SWIRE-VVDS-CFHTLS surveys, based on the Bruzual & Charlot (2003) stellar population models: given the parameters { , } = {−0.18 ± 0.04, +0.07 ± 0.04}. While we acknowledge our studied clusters are within a redshift range presenting large uncertainties in the relationship presented in Arnouts et al. (2007, see Fig. 9), we refer the reader to the detailed comparison made in Appendix D, Fig. 28 of Ilbert et al. (2010). Although the former appears to overestimate the stellar mass by an average 0.2 dex for red sequence galaxies, it also appears to be reasonably well calibrated for ∈ [0.3, 0.4]. We present the inferred stellar masses for both clusters in Table 9.
In order to have a theoretical reference, we compare our estimates with the stellar mass predicted using the formula derived by Giodini et al. (2009). This relationship, established for poor clusters, with redshifts 0.1 ≤ ≤ 1, relates the total mass of the cluster to its stellar fraction ( ★ / 500 here) using the relation: . ( Let us notice the high (∼ 50%) logarithmic scatter in the data fitting this relationship. As this relationship was established using X-ray measurements of 500 , and that strong lensing is not a direct probe of this value, we use the NFW reconstruction obtained through X-ray for the 500 values (see Fig. 7). For MACS J0242, the field of view considered is quite large (DES: 182 ), as we consider all galaxy in HST/WFPC2 or DES, and thus our cluster member catalogue is assumed to be relatively complete. We measure a stellar mass ★ = (6.484 ± 0.615) × 10 12 for MACS J0242. Let us notice these error bars are only associated to the error on the measured magnitude and the parameters and eq. (2). We obtain a difference between our measured value and the predicted value of ★,Giodini = (8.332 ± 1.128) × 10 12 . We may explain this discrepancy by the variable conditions for selecting a galaxy within the galaxy catalogue. Indeed, the field of view being different between WFPC2, ACS and DES, as well as the poorer imaging quality of the latter instrument, we expect our error bars to be far larger than those computed given the error on the measured magnitude.
For MACS J0949, we require that a galaxy is detected in either HST/ACS or HST/WFC3 to include it in the final catalogue. Because the field of view of WFC3 is smaller than that of ACS, a large number of selected cluster member galaxies are weakly constrained, as ACS only contains two bands here. This method is adapted to our lensing analysis, the main goal of this paper, as galaxies far from the cluster centre are particularly important to constrain the southern halo. However, when considering the stellar content of the cluster, we might be selecting too many galaxies. Our analysis yields ★ = (1.392 ± 0.137) × 10 13 . Similarly to MACS J0242, we compare our measurement with the predicted value following the Giodini et al. (2009) formula. We obtain a stellar mass ★,Giodini = (1.369 ± 0.302) × 10 13 . This difference, however small, can give us an estimate of the overestimation of our cluster member catalogue. Table 9. Mass and radius measurements for MACS J0242 and MACS J0949. All error bars show a 68% confidence interval. We here list ★ , the stellar mass, 2D ( < 200 kpc), the mass distribution obtained in projection on the plane of the cluster, within a radius of 200 kpc, and Δ and Δ , defined in eq. (1). Masses are given in 10 14 and distances in kpc. The X-ray masses are following the NFW fit.

MACS J0242 MACS J0949
Mass (  We summarise the estimated stellar fractions for both clusters, ★ 500 = ★ / 500 , as well as the predicted values with the Giodini et al. (2009) formula in Table 10.

Analysis procedure
We used the X-COP analysis pipeline (Ghirardini et al. 2019) to analyse the data and compute the hydrostatic mass profiles of the two systems. We extracted X-ray photon images in the [0.7-1.2] keV band, which maximises the signal-to-background ratio. To estimate the non X-ray background, we used the unexposed corners of the MOS detectors to estimate the cosmic-ray-induced flux at the time of the observations. The difference between the scaled high-energy count rates inside and outside the field of view were then used to estimate the residual soft proton contribution, which was next modelled following the method described in Ghirardini et al. (2018). To determine the spectroscopic temperature profile of the two systems, we extracted spectra in logarithmically spaced concentric annuli centred on the surface brightness peak. The sky background emission was measured in regions located well outside of the cluster's virial radius and described by a three-component model including the cos-mic X-ray background, the local hot bubble, and the galactic halo. The sky background spectrum was then rescaled appropriately to the source regions and added as an additional model component. Finally, the source spectrum was modelled by a single-temperature APEC model (Smith et al. 2001) absorbed by the Galactic , which was fixed to the HI4PI value (HI4PI Collaboration et al. 2016).

Hydrostatic mass reconstruction
We used the publicly available Python package hydromass 8 (Eckert et al. 2022) to deproject the X-ray data and recover the mass under the hypothesis of hydrostatic equilibrium. The X-ray surface brightness and spectroscopic temperature profiles are fitted jointly using a NFW profile to recover the X-ray mass profile. The technique employed here is similar to the method described in Ettori et al. (2019), in which the gas density profile and the parametric mass profile are used to integrate the hydrostatic equilibrium equation and predict the 3D pressure and temperature profiles. The 3D temperature profile is then projected along the line of sight using spectroscopic-like weights (Mazzotta et al. 2004) and adjusted onto the observed spectroscopic temperature profile. The model temperature and gas density profiles are convolved with the XMM-Newton PSF to correct for the smearing introduced by the telescope's spatial resolution, in particular in the cluster's central regions.

MACS J0242
MACS J0242 exhibits all the features of a relaxed, cool-core cluster. Its X-ray morphology is regular and it shows a pronounced surface brightness peak, a central temperature drop, and a metal et al.
abundance peak in its core. The dynamical state of the cluster is best gauged from the X-ray emission, but the optical emission lines of the BCG is an additional, relatively faithful tracer of the presence of a cool core. The NFW mass reconstruction returns a mass 500 = (3.4 ± 0.2) × 10 14 . In order to compare it directly to the lensing mass where multiply imaged systems yield important constraints, we project the NFW density in 2D, and compute 2D (< 200 kpc) = 1.163 +0.036 −0.039 × 10 14 . For an average temperature of 4.5 keV, this is in agreement with the expectations of mass-temperature relations (e.g. Lovisari et al. 2020). The cluster appears to be highly concentrated, with a fitted NFW concentration 200 = 8.2 ± 0.5. At 200 kpc, X-ray observations suggest the gas fraction to be ,200 kpc = 0.115 +0.003 −0.004 . The ellipticity of the cluster obtained with our lensing mass model is not recovered by the X-ray analysis, as it presents a spherical surface brightness. The ICM has its own dynamics and thus is not expected to present a similar ellipticity to the total density of matter. The discrepancy between the ICM and DM halo ellipticity is documented in e.g. (Lee & Suto 2003;Debattista et al. 2008;Lau et al. 2012;Umetsu et al. 2018;Stapelberg et al. 2022). It stems from the collisional character of baryons, allowing the ICM to geometrically relax faster than the cold dark matter halo counterpart, non-collisional.

MACS J0949
MACS J0949 exhibits a regular X-ray morphology with no obvious large substructure. However, its brightness distribution is relatively flat, it shows a high central entropy and central cooling time, and no temperature drop in its core. Therefore, MACS J0949 is not a relaxed cool-core cluster, but its regular morphology indicates that it is not strongly disturbed either. Such properties are typical of postmerger clusters in the process of relaxation after a merging event. The hydrostatic mass profile is well described by an NFW model with 200 = 5.3 +1.3 −1.0 and 500 = 7.4 +1.4 −1.2 × 10 14 . The NFW projected mass yields 2D (< 200kpc) = 1.635 +0.065 −0.072 × 10 14 . Its hydrostatic gas fraction ,500 = 0.155 +0.016 −0.014 is consistent with the Universal baryon fraction (Ade et al. 2016). At 200 kpc, the same gas fraction is measured at ,200 kpc = 0.053 +0.007 −0.006 . Similarly to MACS J0242, the X-ray signal does not present any ellipticity.

DISCUSSION & CONCLUSION
In order to reconstruct the mass distribution of strong lensing galaxy clusters MACS J0242 and MACS J0949, we have used the combination of imaging (HST, DES) and spectroscopic (VLT/MUSE) surveys to detect respectively 6 and 2 spectroscopically confirmed multiple image systems. Adding to that, in MACS J0949, we identified four multiply imaged systems, without a confirmed spectroscopic redshift -the spectroscopic emission line not fitting spectral templates convincingly enough, or the images being out of the VLT/MUSE field of view. The imaging data, calibrated with the spectroscopic detections of cluster members, allowed to establish conservative cluster galaxy catalogues, of respectively 58 and 170 galaxies for MACS J0242 and MACS J0949. We then established the strong lensing mass models of both galaxy clusters. We modelled each individual galaxy with a dPIE profile, and included for each cluster a dPIE cluster-scale halo. We present our main results as follows: (i) The on the multiple image positions for the best-fit models are respectively of 0.39 and 0.15 , which is considered as a good quality indicator of the reconstruction. We found that adding a shearfield does not improve the quality of the reconstruction. We note that degeneracies between the BCG and the dark matter halo could hinder the lens model optimisations, and could thus affect our conclusion regarding the morphology of the dark matter distribution in these clusters (see e.g. Limousin et al. 2016).
(ii) Using XMM-Newton X-ray observations from CHEX-MATE Collaboration et al. (2021), processed with the X-COP pipeline Ghirardini et al. (2019), we compare the ICM to the reconstructed dark matter density. The combination of the lensing mass reconstructions with the X-ray analyses of the ICM and the VLT/MUSE spectroscopy shows that MACS J0242 is in a cool-core, relaxed dynamical state, compatible with a NFW profile, while MACS J0949 has a flat distribution between radii of 50 to 100 kpc because it is still undergoing the relaxing process, being in a post-merger dynamical state. In particular, the hot gas fractions at 200 kpc of MACS J0242 and MACS J0949 are ,200 kpc = 0.115 +0.003 −0.004 and 0.053 +0.007 −0.006 respectively. We can for instance compare these results to those of Bonamigo et al. (2018). In Fig. 6, the authors present the cumulative hot gas fraction of each of the three clusters analysed. MACS J0416 is presented as a merging cluster, while MACS J1206 and Abell S1063 (RXC J2248) show a cool-core. These clusters have ,200 kpc 0.09, 0.11 and 0.13 respectively, thus exhibiting the trend of more relaxed clusters displaying higher hot gas fraction values at 200 kpc. This is an additional indication of the relaxed dynamical state of MACS J0242, and the post-merger state of MACS J0949.
(iii) Converting the cluster member catalogue magnitudes into Kband luminosities, we used the Arnouts et al. (2007) mass-to-light ratio relationship to extrapolate the stellar mass detected in both clusters. SED fitting should be performed to obtain a more precise measurement, but this is beyond the scope of this paper. We compare the obtained stellar masses of ★ = (6.48 ± 0.62) × 10 12 and (1.39 ± 0.14) × 10 13 for MACS J0242 and MACS J0949 respectively to the predictions of Giodini et al. (2009), yielding respectively (8.33 ± 1.13) × 10 12 and (1.37 ± 0.30) × 10 13 . Although not identical in the case of MACS J0242, this means our stellar mass estimates appear to be reasonable.
(iv) We fit the XMM-Newton observations to a NFW profile. Projecting this reconstruction, we can measure 2D (< 200 kpc), allowing for a direct comparison with the strong lensing model mass estimates. For MACS J0242, we measure 2D (< 200 kpc) = (1.16 ± 0.04) × 10 14 from the X-rays, to be compared to 1.67 +0.03 −0.05 × 10 14 obtained from our strong lensing analysis. We obtain a sizeable 12.75 difference between these two values. Discrepancies between the X-ray hydrostatic and lensing masses are common, and may be explained by the hydrostatic hypothesis bias, or by the presence of asymmetric structures along the line-of-sight. In the former case, the gas is not perfectly relaxed, and the thermal pressure only accounts for a fraction of the gravitational pressure. Thus, the hydrostatic mass would underestimate the true mass. Moreover, if there is a distribution of substructures or an elongation of the dark matter component along the line-of-sight, the projected lensing mass may overestimate the 3D mass. For instance, Umetsu et al. (2015) display a combination of both these scenarios.
In order to compare cylindrical masses, we define 10% = 0.1 200, . For MACS J0242, with 10% = 170.2 +0.39 −0.45 kpc, we obtain 2D (< 10% ) = (1.41 ± 0.03) × 10 14 with our strong lensing analysis (for which 200 is extrapolated). With 10% = 143.0 +2.7 −2.6 kpc, we get 2D (< 10% ) = (8.06 ± 0.21) × 10 13 with the X-rays NFW inferred profile, yielding ratios of 2D (< 10% )/ 200, = 0.181 ± 0.014 and 0.186 ± 0.012 respectively. This allows us to characterise the ratios of masses measured in the centre and in the outskirts as quite close for X-ray and lensing, in spite of the remarkable difference between the mass measurements. As the strong lensing inferred 200 mass obtained here is an extrapolation at larger radii of a profile based on gravitational lensing occurring at < 200 kpc, we cannot claim the strong lensing ratios to be firmly established. Nonetheless, the extrapolated lensing distribution appears to follow a profile similar to that of the X-rays, at different masses. We can compare this result to the ratios found by Bonamigo et al. (2018) for three clusters exhibiting varied dynamical states (Abell S1063, MACS J0416 and MACS J1206), all around 0.13. Let us notice this study uses three to four potentials across all clusters, and thus our models should be expected to yield larger ratios of core-to-outskirts densities. Moreover, as this comparison uses 200 values from weak-lensing shear-and-magnification analyses (see Umetsu et al. 2014), we can only cautiously compare it to our X-rays and extrapolated strong lensing measurements. As the ratio is much higher for MACS J0242, this comparison is one more indication that the concentration of mass in the centre of MACS J0242 is particularly high relative to its total mass. This is in good agreement with our conclusion of the cluster being in a cool-core, relaxed dynamical state.
In the case of MACS J0949, the cylindrical mass at 10% = 205.6 +0.00 −25.4 is 2D (< 10% ) = (2.07 ± 0.14) × 10 14 using our strong lensing measurements, and with 10% = 184.9 +12.6 −11.6 , 2D (< 10% ) = (1.48 ± 0.05) × 10 14 with the X-rays NFW inferred profile. The respective ratios are 0.140 ± 0.025 and 0.146 ± 0.029. For this cluster again, we notice these ratios to be quite close to one another, supporting the quality of the strong lensing Δ extrapolation in spite of the large difference between the X-rays and strong lensing measured masses. Interestingly, the comparison with the 0.13 ratio from Bonamigo et al. (2018) hints towards a relative concentration of mass slightly more important in MACS J0949.
As we have established through strong lensing models the total matter density distribution in two galaxy clusters, we laid the foundations of our companion paper (Allingham et al. in prep.). In this forthcoming paper, we describe a new method using analytical models of galaxy cluster potentials to predict the ICM distribution, and in the foreseeable future to put constraints on interacting dark matter.

APPENDIX B: ADDITIONAL INFORMATION ON COLOUR-MAGNITUDE DIAGRAMMES SELECTIONS
We here provide the equation of each main red colour sequence for both galaxy cluster MACS J0242 and MACS J0949, according to process described in Section 3.2.3. We also provide all the additional colour-magnitude diagrammes we can plot. Tables B1 and B2 provide respectively the equations of the main colour sequences of clusters MACS J0242 and MACS J0949, and the weighed colour standard deviation of the spectroscopically confirmed cluster galaxy sample . The height of the selection box is 2 away from the main red sequence for HST/ACS and HST/WFC3, and 3 for HST/WFPC2 and DES. This paper has been typeset from a T E X/L A T E X file prepared by the author. Table B1. Equations of the main colour sequences and standard deviations on colours for all colour-magnitude diagrammes of MACS J0242. 1 represents the magnitude in abscissa. Associated graphs are Fig. 4   . Right: F125W vs ( F105W − F125W ). Grey filled circles (with their error bars) have successfully passed all selections described in Section 3.2.1. The magenta line represents the main sequence regression. Blue, gold and red dots represent spectroscopic detections of foreground, cluster and background objects respectively.