Unveiling the Merger Dynamics of the Most Massive MaDCoWS Cluster at z = 1.2 from a Multiwavelength Mapping of Its Intracluster Medium Properties

The thermal SZ effect (tSZ; Sunyaev & Zel'dovich 1972, 1980) corresponds to a variation of the apparent brightness of the cosmic microwave background (CMB) due to the inverse Compton scattering of CMB photons on energetic electrons within any reservoir of hot plasma along the line of sight:

$$\begin{eqnarray}&&\displaystyle \frac{{\rm{\Delta }}{I}_{\mathrm{tSZ}}}{{I}_{0}}={y}_{\mathrm{tSZ}}\,f(\nu ,{T}_{e}),\end{eqnarray} \tag{ 1 }$$

where f(ν, T_e) characterizes the frequency dependence of the tSZ spectrum (Birkinshaw 1999; Carlstrom et al. 2002) and T_e is the electronic temperature of the plasma. The Compton parameter y_tSZ gives the amplitude of the spectral distortion in the direction $\hat{n}$. It is expressed as

$$\begin{eqnarray}&&{y}_{\mathrm{tSZ}}(\hat{n})=\displaystyle \frac{{\sigma }_{{\rm{T}}}}{{m}_{e}{c}^{2}}\int {P}_{e}\,{dl},\end{eqnarray} \tag{ 2 }$$

where m_e is the electron mass, c is the speed of light, ${\sigma }_{{\rm{T}}}$ is the Thomson scattering cross section, and P_e is the electron pressure distribution of the gas. Being almost redshift independent,²² the thermal SZ effect allows us to directly measure the ICM pressure distribution up to high redshifts. It depends only mildly on the ICM temperature through the relativistic corrections to the tSZ spectrum (Itoh et al. 1998; Pointecouteau et al. 1998). More details can be found on the information gain brought by spatially resolved SZ observations to probe ICM astrophysics in the review of Mroczkowski et al. (2019).

We conducted spatially resolved SZ observations of MOO J1142+1527 in 2017 October with the NIKA2 camera (OpenTime: 082-17, PI: F. Ruppin) installed at the Institut de Radioastronomie Millimétrique (IRAM) 30 m telescope. We have observed this cluster for an effective time of 10.4 hr. The pointing center was chosen to be ${\left({\rm{R}}.{\rm{A}}.,\mathrm{decl}.\right)}_{{\rm{J}}2000}$ = (11:42:46.6, +15:27:15.0) according to the estimate of the SZ centroid position found by Gonzalez et al. (2015) using CARMA. We defined the scanning strategy in a similar way as the one presented in Adam et al. (2015) and Ruppin et al. (2017). A succession of on-the-fly raster scans of $8\times 4\,{\mathrm{arcmin}}^{2}$ with 10'' steps between each subscan has been realized in four different directions in equatorial coordinates (J2000) at a scanning speed of 40 arcsec/s. The cluster has been observed at a mean elevation of 554. The weather conditions at the time of the observations were quite good with a mean zenith opacity of 0.19 at 150 GHz, 0.32 at 260 GHz, and a rather stable atmosphere.

We use Uranus as a primary calibrator of the data. Following the baseline calibration procedure described in Perotto et al. (2019), we obtain total calibration uncertainties of 6% and 8% at 150 and 260 GHz, respectively. These estimates take into account the absolute calibration uncertainty of 5% on the Uranus flux density expectations reported in Moreno (2010). The distribution of pointing corrections realized at regular intervals during the observations of MOO J1142+1527 is characterized by a mean of 19 and a standard deviation of 12. More details on the instrumental performance of the NIKA2 camera at the time of the observations can be found in Adam et al. (2018) and Perotto et al. (2019).

The selection of valid detectors and the removal of cryogenic vibrations and cosmic-ray glitches from the raw data have been realized following the pre-processing method detailed in Adam et al. (2015). We removed the spatially correlated noise contaminants induced by both the atmospheric emission and the electronic readout system using an iterative procedure similar to the one described in Ruppin et al. (2018). The data measured by each array are treated separately. For each detector timeline, a contaminant template is defined as a combination of a common mode computed using all of the valid detectors in the considered array, a common mode estimated across the timelines of detectors sharing the same readout electronic board, and the elevation path of the detector in the plane of the sky. This allows us to simultaneously model the atmospheric and electronic contaminants as well as the timeline drift induced by air mass variations during the scan. At the end of each iteration, we locate the map pixels with a signal-to-noise ratio (S/N) higher than 4 and remove the corresponding signal amplitude in each detector timeline before the common mode estimations of the next iteration. This allows us to reduce the bias induced by the SZ signal on the estimate of the contaminant templates. The filtering of the SZ signal is therefore reduced at each iteration. We stop the iterative procedure when the variation of the SZ peak amplitude caused by this decrease of the signal filtering is lower than 0.1%. This corresponds to a total of 13 iterations of the raw data analysis. We project the processed timelines onto two different pixelized grids. The first one is defined by a pixel size of 0984 equal to the one considered in the Chandra analysis described in Section 4. This allows us to directly combine the NIKA2 and Chandra maps in Section 7 in order to estimate the projected distributions of the cluster thermodynamic properties. For the second one, we use a pixel size of 3'' in order to increase the computing efficiency of the SZ deprojection procedure described in Section 6 without significantly degrading the NIKA2 angular resolution at 150 and 260 GHz. All of the individual scans are finally coadded using an inverse variance noise weighting of the data samples in each pixel to obtain the final maps shown in Figure 1.

Zoom In Zoom Out Reset image size

The methodology applied to estimate the contaminant templates based on two different common modes allows us to significantly reduce the amount of residual-correlated noise in the final maps. The residual noise power spectrum has been estimated based on null maps computed from the semi-difference of coadded scans issued from two equivalent subsamples following the procedure described in Adam et al. (2016) and Ruppin et al. (2018). The noise power spectra measured at 150 and 260 GHz are fitted by a model defined as the sum of a white-noise component and a power law to account for the spatial correlations of the residual noise. Although the power-law model obtained at 260 GHz significantly differs from being constant, we find that the noise power spectrum measured at 150 GHz is well modeled by a simple white-noise component. For this reason, the diagonal elements of the noise correlation matrix at 150 GHz dominate over non-diagonal ones. We can therefore assume that the error associated with the signal measured in the map pixels at 150 GHz is given by the root mean square (rms) value in each of them. This results in a significant decrease of the computation time of the deprojection procedure detailed in Section 6.

This significant improvement in the correlated contaminant removal comes at the cost of a high filtering of the extended SZ signal at S/Ns lower than the 4σ threshold used in the iterative analysis of the raw data. We compute the circular transfer function resulting from the NIKA2 observations and data processing at 150 GHz using simulations as described in Adam et al. (2015). We find that the SZ signal filtering is on average 17% larger than the one resulting from the analysis procedure described in Ruppin et al. (2018) in the range of angular scales that can be constrained by NIKA2, i.e., [0.25–6.5] arcmin. However, the SZ map obtained at 150 GHz in Ruppin et al. (2018) was significantly contaminated by spatially correlated residual noise. In this paper, we choose to favor an analysis method that allows us to simultaneously measure a nearly flat noise power spectrum at 150 GHz and an extension of the region where the SZ signal is significant that is already larger than the one where the X-ray signal measured by Chandra is significantly different from the background. This allows us to maximize the S/N in the maps of the ICM temperature and entropy obtained in Section 7.

The surface brightness maps of MOO J1142+1527 obtained at the end of the analysis of the NIKA2 data at 150 and 260 GHz are shown in Figure 1. They correspond to the grids made of 0984 pixels and centered on the SZ peak coordinates measured by CARMA (Gonzalez et al. 2015). For visual purposes, we have smoothed the maps with an additional 8'' and 5'' FWHM Gaussian filter at 150 and 260 GHz, respectively. We measure the rms noise at the map center to be $98\,\mu \mathrm{Jy}/\mathrm{beam}$ and $423\,\mu \mathrm{Jy}/\mathrm{beam}$ at these effective resolutions of 20'' and 13'' at 150 and 260 GHz, respectively. These estimates have been obtained following the procedure described in Adam et al. (2017a). Simulated noise maps are computed from the NIKA2 residual noise power spectra at 150 and 260 GHz and from astrophysical contaminant models (Béthermin et al. 2012; Planck Collaboration et al. 2014, and Tucci et al. 2011). The latter allows us to take into account the contributions induced by both the cosmic infrared background (CIB) shot noise and clustering and the CMB temperature anisotropies in the residual noise. As the processing methodology adopted to analyze the NIKA2 raw data has enabled the reduction of the amount of residual-correlated noise compared to previous NIKA2 studies, the instrumental and atmospheric noise contributions are comparable to the one induced by CIB shot noise at 150 GHz. We add all of the noise contaminants in quadrature in order to estimate the S/N in each map pixel at 150 and 260 GHz.

We observe a significant negative SZ signal in the NIKA2 map at 150 GHz shown in the left panel of Figure 1. The SZ peak is found at a position of ${\left({\rm{R}}.{\rm{A}}.,\mathrm{decl}.\right)}_{{\rm{J}}2000}$ = (11:42:45.9, +15:27:12.0) with a significance of 17σ at  ∼10'' from the pointing center. We compute the SZ surface brightness profile from the NIKA2 map at 150 GHz and measure an S/N higher than 3 up to 11 away from the SZ peak. This is comparable to the extension of the diffuse X-ray emission recovered by Chandra as described in Section 4. We find some evidence of an elliptical morphology of the SZ signal with an east–west orientation. We fit the 3σ S/N contour with an ellipse and measure a flattening f = 1 − b/a = 0.19 where a and b are the major and minor axis length, respectively. This is consistent with the SZ morphology found by CARMA (Gonzalez et al. 2015). However, the NIKA2 instrumental performance allows us to further resolve the ICM structure. This will enable constraining the radial pressure profile in Section 6.

We do not detect any significant SZ signal in the NIKA2 260 GHz map shown in the right panel of Figure 1 as anticipated given the expected SZ signal and the noise level at this frequency. Based on the value of the peak SZ surface brightness at 150 GHz, the tSZ spectrum analytic expression, and the NIKA2 bandpasses at the time of the observation, the expected value of the peak SZ surface brightness at 260 GHz is found to be $540\,\mu \mathrm{Jy}/\mathrm{beam}$. This corresponds to 1.3 times the rms noise found at the NIKA2 map center at this frequency. However, we detect several point sources in the NIKA2 map at 260 GHz including one within the region where a significant SZ signal is measured at 150 GHz. This source is detected at 25'' to the east of the NIKA2 SZ peak at 150 GHz. This position is consistent with a radio source found in the Faint Images of the Radio Sky at Twenty-Centimeters survey (FIRST; Becker et al. 1995), which covers the northern sky at 1.4 GHz. We highlight this position with a green cross in both NIKA2 maps in Figure 1. The signal emitted by this source is partly compensating for the negative SZ signal induced by MOO J1142+1527 at 150 GHz. This explains the origin of the hole in the SZ signal found at this position in the NIKA2 map. For this reason, it is essential to estimate the expected flux of this source at 150 GHz before constraining the ICM pressure profile from a deprojection of the NIKA2 data to minimize the bias induced by this contaminant.

The X-ray observations of MOO J1142+1527 were obtained in the VFAINT data mode for a total exposure of 46.96 ks using the Advanced CCD Imaging Spectrometer (ACIS)-I chips on board the Chandra X-ray Observatory. We follow the data reduction procedure described in McDonald et al. (2017) and references therein. We have reduced the data using the Chandra Interactive Analysis of Observations (CIAO) software v4.10 based on the calibration database (CALDB) v4.8.0 provided by the Chandra X-ray Center (CXC). We have used the chandra_repro script to reprocess the level 1 event files using the latest charge transfer inefficiency corrections and time-dependent gain adjustments. The ACIS particle background for very faint mode observations is also cleaned based on outer pixel pulse heights during this analysis step. We use the lc_clean routine based on M. Markevitch's program (Markevitch 2001) to remove flares from light curves created with a temporal bin size of 259.28 s. We find a total, cleaned exposure time of 46.19 ks.

The exposure map associated with the observations has been computed in an energy band restricted from 0.5 to 7 keV and a center-band energy of 2.3 keV as recommended by the CXC. Point sources have been identified using the wavdetect script based on a wavelet decomposition technique (e.g., Vikhlinin et al. 1998). We also perform a visual inspection of the regions enclosing the detected sources. A mask has been generated using the resulting list of point sources. It is used in Section 4.2 to produce a cleaned event list from which the X-ray surface brightness profile as well as the X-ray spectrum are extracted. We define the X-ray background as a combination of (1) a particle and instrumental background, and (2) a local astrophysical background. For the particle and instrumental background, we normalize unscaled stowed background files to the count rate observed in the 9–12 keV band. The significant diffuse emission from the cluster has only been detected by the I3 chip. The remaining three ACIS-I chips are therefore used as an estimate of the local astrophysical background once both particle background and point sources have been removed.

We show an exposure-corrected map of the Chandra observations of MOO J1142+1527 after background and point-source subtraction in the left panel of Figure 3. The diffuse X-ray emission is significantly detected within a region of similar angular scale as the one obtained with the NIKA2 SZ observations (see Figure 1). The X-ray peak (blue cross) is detected at the same location as the radio source observed in the FIRST map in the left panel of Figure 2. We note that a careful analysis has been made in order to show that the X-ray peak is not contaminated by an X-ray point source but is really caused by an over-density within the ICM. In particular, the wavdetect routine has been used in different energy intervals within the soft and hard bands to confirm that no X-ray point source is detected at the X-ray peak position. Therefore, together with the results obtained on the radio emission of the central AGN in Section 3, we find that the latter has an X-ray luminosity compatible with 0 and a radio luminosity at 1.4 GHz of ${L}_{1.4\mathrm{GHz}}\,=(1.373\pm 0.007)\times {10}^{25}\,{\rm{W}}\,{\mathrm{Hz}}^{-1}$. This clearly indicates that the BCG hosting the AGN is a member of the corona class and should have an X-ray cool core according to Sun (2009). The cluster emission is clearly elongated westward with respect to the X-ray peak. For this reason, the large-scale morphology of the cluster is similar to the one observed in the NIKA2 map at 150 GHz (see Section 2.3).

Zoom In Zoom Out Reset image size

As the X-ray emission is clearly not azimuthally symmetric, we choose to use both the cluster large-scale centroid and the X-ray peak for all estimates shown in this paper unless otherwise noted. The centroid position is computed iteratively within a circular region of 1' radius centered on the last estimate of the centroid location. We initialize this position to the X-ray peak one. A comparison between the locations of the X-ray peak, the X-ray centroid, and the SZ peak is discussed in Section 5.

Following Maughan et al. (2008) and McDonald et al. (2016), we extract the X-ray spectrum in the 0.7–7.0 keV band using the specextract script in a core-excised circular annulus centered on the large-scale centroid and mapping the radii 0.15R₅₀₀ < r < R₅₀₀. We iteratively estimate the value of R₅₀₀ based on the best-fit value of the spectroscopic temperature T_X (see Section 4.2) and the M₅₀₀−T_X scaling relation from Vikhlinin et al. (2009), and we find a value of 790 ± 87 kpc. This is compatible with the result obtained with the core-excised scaling relation of Bulbul et al. (2019), i.e., R₅₀₀ = 916 ± 127 kpc. The scaled stowed background files are used to compute the spectrum of the particle background to be subtracted from the measured spectrum. We repeat the same procedure in the remaining three ACIS-I chips to measure the spectrum of the local astrophysical background. The final X-ray spectrum measured in the cluster region is shown with blue points in the right panel of Figure 3. We group the energy channels to obtain an S/N higher than 5 in each bin. This spectrum presents enough statistics to enable estimating the mean spectroscopic temperature of the ICM.

With low-S/N X-ray data, it is not possible to extract a temperature profile. Hence, we evaluate a mean spectroscopic temperature from the fitting of the cluster spectrum shown in the right panel of Figure 3. The cluster spectrum is fitted jointly with the astrophysical-background spectrum using CIAO's Sherpa package. We fit the whole spectrum using a combination of XSPEC models (v12.10.0e; Arnaud 1996) including a single-temperature plasma (APEC; Smith et al. 2001) for the cluster emission, a soft X-ray Galactic background (APEC; k_BT_X = 0.18 keV, Z = Z_⊙, z = 0) combined with a hard X-ray cosmic spectrum (BREMSS; k_BT_X = 40 keV) for the astrophysical background, and a Galactic absorption model (PHABS). For the latter, we fix the Galactic column density to the value found by Kalberla et al. (2005) at this latitude: ${n}_{H}=2.92\times {10}^{20}\,{\mathrm{cm}}^{-2}$. We also fix the cluster redshift to the value estimated from the combination of the Gemini/GMOS, Keck/DEIMOS, and Keck/MOSFIRE spectroscopy measurements presented by Gonzalez et al. (2015), i.e., z = 1.19, in the cluster-emission model. We allow the ICM spectroscopic temperature and the different model normalizations to vary in the analysis. Given the cluster redshift, an iron emission line is expected at an energy of ∼3 keV. As it is not significantly detected in the measured spectrum, we choose to fix the ICM metallicity to Z = 0.3Z_⊙.

The best-fit total model is shown by the red line in the right panel of Figure 3. It is given by the sum of the cluster-emission model (orange) and the astrophysical-background model (gray). The lower panel of the figure displays the ratio of the difference between the data and the best-fit model with the measurement uncertainty in each energy bin. We do not measure any deviations larger than 3σ, and no significant systematic effect is identified in these residuals. We measure a reduced χ² of 1.15 ± 0.18 for this analysis based on 59 degrees of freedom. We find that the cluster spectroscopic temperature is given by T_X = 8.63 ± 1.86 keV within a radius range 119 < r < 790 kpc. We find a consistent result if we use the R₅₀₀ estimate obtained with the Bulbul et al. (2019) scaling relation. This single temperature measurement is shown as a blue point in the right panel of Figure 4. It is a key parameter to define the X-ray emission-measure profile of the cluster in Section 6. As has been shown by Bourdin & Mazzotta (2008), the variation of the neutral hydrogen column density across the field of view can have a significant impact on the ICM temperature estimate. Therefore, a second analysis has been done with a free Galactic column density value. The best-fit value of this parameter is found to be ${n}_{H}=14.68\times {10}^{20}\,{\mathrm{cm}}^{-2}$ with an associated ICM temperature of T_X = 7.75 ± 2.13 keV. As the fitted hydrogen column density is much higher than the expected one, the normalization of the cluster model increases to compensate for the absorption that is significant between 0.7 and ∼2 keV. This explains why we find a lower spectroscopic temperature associated with this increased Galactic absorption. We find a reduced χ² of 1.14 ± 0.18 for this second analysis based on 58 degrees of freedom. Setting the Galactic column density as a free parameter does not significantly improve the spectrum fit. Furthermore, the temperature estimates obtained with the two analyses are compatible, and the fitted value of n_H is in tension with the expected one. Therefore, we choose to keep our first temperature estimate obtained with a fixed hydrogen column density in the sections that follow.

Zoom In Zoom Out Reset image size

Following the methodology introduced by McDonald et al. (2017), we extract the cluster surface brightness profile in the 0.7–2.0 keV band in 20 annuli defined by

$$\begin{eqnarray}&&{r}_{\mathrm{out},i}=(a+{bi}+{{ci}}^{2}+{{di}}^{3}){R}_{500}\,i=1...20\end{eqnarray} \tag{ 4 }$$

where (a, b, c, d) = (13.779, 8.8148, 7.2829, 0.15633) × 10⁻³. This definition of the radial binning has been optimized to enable an efficient sampling of the X-ray surface brightness profile of galaxy clusters from Chandra observations up to z ∼ 2. We use the dmextract routine to extract a surface brightness profile from the event list masking the identified point sources. The profile is estimated using both the X-ray peak and the large-scale centroid. We correct the surface brightness profiles for the vignetting effect based on the normalized exposure map estimated in the same energy band. The estimated profile centered on the large-scale centroid is shown in the left panel of Figure 4. The inner slope of the profile is relatively constant, which is expected because the large-scale centroid is offset westward with respect to the X-ray peak location (see Section 5). Significant constraints are established up to an angular distance from the centroid of ∼11, which corresponds to a physical distance of 562 kpc at the cluster redshift. As this detection radius is similar to the one found with the NIKA2 SZ data at 150 GHz, we will highlight it in each figure of the estimated ICM profiles obtained in Section 6. The slight increase in surface brightness observed at an angular distance of ∼015 is due to the X-ray peak brightness averaged in the fourth annuli defined by Equation (4). This Chandra X-ray surface brightness profile along with the spectroscopic temperature estimate are the key inputs that are considered in Section 6 to deproject the ICM density profile.

We first describe the methodology followed to estimate the ICM density profile and present our results.

6.1.1. Method

We measure the ICM electron-density profile n_e(r) from the cluster-emission integral given by

$$\begin{eqnarray}&&\mathrm{EI}\equiv \int {n}_{e}{n}_{p}\,{dV}\end{eqnarray} \tag{ 5 }$$

where n_p is the proton density within the ICM, and V is the volume. The emission integral is related to the cluster surface brightness profile through the cooling function computed in the same energy band, Λ (T, Z), depending on the ICM temperature T and metallicity Z. We take into account the effects of the Galactic absorption and the variations of the effective area as a function of energy and position in the field of view to measure the cooling function. This is done by computing the normalization factor of the APEC model associated with the cluster spectrum in each annulus considered for the extraction of the surface brightness profile. This normalization factor is associated with a count rate R measured in the annulus of area A, and it depends on both the ICM temperature and the effective area at this position. It is given by

$$\begin{eqnarray}&&\mathrm{norm}(R,A)=\displaystyle \frac{{10}^{-14}}{4\pi {[{d}_{A}(1+z)]}^{2}}\int {n}_{e}{n}_{p}\,d{\rm{\Omega }}{dl}\end{eqnarray} \tag{ 6 }$$

where d_A is the angular diameter distance, and $d{\rm{\Omega }}$ and dl are the solid angle and line-of-sight differential elements, respectively. We therefore compute the conversion coefficient between emission integral and surface brightness at each projected distance from the cluster center. We further correct this estimate for the spatial variations of the ICM temperature assuming a universal temperature profile from Vikhlinin et al. (2006) normalized to the mean spectroscopic temperature T_X (see Section 4.2). This profile is represented as a black line in the right panel of Figure 4. We apply the conversion coefficient to the X-ray surface brightness profiles extracted on both the X-ray peak and the large-scale centroid in order to obtain the associated emission-measure profiles:

$$\begin{eqnarray}&&\mathrm{EM}(r)=\int {n}_{e}{n}_{p}\,{dl}.\end{eqnarray} \tag{ 7 }$$

The ICM electron-density profile n_e(r) is estimated from the cluster-emission-measure profile using a forward-fitting Bayesian framework. The cluster electron-density distribution is modeled by a Vikhlinin parametric model (SVM; Vikhlinin et al. 2006) simplified by Mroczkowski et al. (2009) and given by

$$\begin{eqnarray}&&{n}_{e}(r)={n}_{e0}{\left[1+{\left(\displaystyle \frac{r}{{r}_{c}}\right)}^{2}\right]}^{-3\beta /2}{\left[1+{\left(\displaystyle \frac{r}{{r}_{s}}\right)}^{\gamma }\right]}^{-\epsilon /2\gamma },\end{eqnarray} \tag{ 8 }$$

where n_e0 is the central density of the ICM, r_c is the core radius, and the inner and outer slopes of the profile are given by β and , respectively. The γ parameter gives the width of the transition located at a radius r_s at which an additional steepening in the profile occurs. The value of γ is fixed at three since it provides a good fit of all of the cluster profiles considered in the analysis of Vikhlinin (2006). We assume the ionization fraction of a fully ionized plasma with an abundance of 0.3Z_⊙, i.e., ${n}_{e}/{n}_{p}=1.199$ (Anders & Grevesse 1989) in order to estimate the proton-density profile in Equation (7). We perform a Markov Chain Monte Carlo (MCMC) analysis to estimate the best-fit value of the five free parameters of the SVM model given the cluster-emission-measure profiles measured on both the X-ray peak and the large-scale centroid. This allows us to estimate the best-fit parameters that maximize the following Gaussian likelihood function:

$$\begin{eqnarray}\begin{array}{rcl}-2\mathrm{ln}\,{{\mathscr{L}}}_{{\rm{X}} \mbox{-} \mathrm{ray}} & = & {\chi }_{\mathrm{CXO}}^{2}\\ & = & {\sum }_{i=1}^{{N}_{\mathrm{bin}}}[({\mathrm{EM}}_{\mathrm{CXO}}-\widetilde{\mathrm{EM}})/{\rm{\Delta }}{\mathrm{EM}}_{\mathrm{CXO}}{]}_{i}^{2}\end{array}\end{eqnarray} \tag{ 9 }$$

where N_bin is the number of bins in the emission-measure profile EM_CXO estimated from the Chandra data with uncertainties given by ΔEM_CXO, and $\widetilde{\mathrm{EM}}$ is the model of the emission-measure profile obtained from the integration of the SVM profile along the line of sight. The best-fit electron-density profile along with its error bars are estimated from the Markov Chains after ensuring their convergence and applying a burn-in cutoff discarding half of the samples at the beginning of each chain.

6.1.2. Results

The fitted emission-measure profiles are compared with the data in Appendix A. We do not find any significant emission-measure residuals if the X-ray peak is used as the deprojection center. A 3σ residual is found in the annulus containing the X-ray peak if we use the X-ray large-scale centroid as the deprojection center. We note however that the ICM density model defined in Equation (8) is adapted to fit the extracted profiles from the cluster core up to the detection radius.

The density profiles estimated from the analysis of the emission-measure profiles obtained on the X-ray peak and the X-ray large-scale centroid are shown in the left panel of Figure 6 in purple and green, respectively. The density distributions are very well constrained from the cluster core up to 0.7R₅₀₀. The density values at radii larger than ∼ 600 kpc are obtained without significant constraints. We highlight this in the figure using a vertical dashed line showing the 3σ detection radius in the Chandra data. As the density estimates obtained beyond this radius are only extrapolations from the SVM model, we choose to focus our study in the radius range r < 0.7R₅₀₀. We observe a significant impact of the choice of deprojection center on the estimate of the ICM density distribution in the cluster core. There is an order-of-magnitude difference between the density estimates measured at 10 kpc from the X-ray peak and the X-ray large-scale centroid of MOO J1142+1527. This is due to the peculiar morphology of the cluster hosting its highest-density core at ∼100 kpc from the large-scale centroid (see Section 5). Both density profiles are however fully compatible at r ≳ 300 kpc from the chosen deprojection center.

Zoom In Zoom Out Reset image size

These results show the limit of a 1D analysis to describe the core dynamics of disturbed galaxy clusters. Indeed, if we assume the cuspiness $\alpha \equiv | d\,\mathrm{log}({n}_{e})/d\,\mathrm{log}(r)|$ to be a good proxy to estimate the core dynamics of MOO J1142+1527 (Vikhlinin et al. 2007), this cluster can either host a cool core (α_peak = 0.95) or a disturbed core (α_centroid = 0.04) depending on the deprojection center that we choose. In the following, we will consider the profiles measured with respect to the X-ray peak to describe the core dynamics, and the ones centered on the large-scale centroid to estimate the integrated quantities such as Y₅₀₀.

The Chandra data do not allow us to estimate the ICM pressure profile of MOO J1142+1527 because the photon statistics are too low to measure a well-defined temperature profile using X-ray spectroscopy (see Section 4.2). However, the NIKA2 SZ map at 150 GHz enables us to directly measure the pressure distribution of the cluster (see Section 2.1). In this section, we describe the analysis procedure that we used to constrain the pressure profile and present our results.

6.2.1. Method

We use the pipeline developed for the NIKA2 SZ large program (Perotto et al. 2018) and detailed in Ruppin et al. (2018) in order to estimate the pressure profile of MOO J1142+1527. The cluster pressure distribution is modeled by a generalized Navarro–Frenk–White model (gNFW; Nagai et al. 2007), given by

$$\begin{eqnarray}&&{P}_{e}(r)=\displaystyle \frac{{P}_{0}}{{\left(\tfrac{r}{{r}_{p}}\right)}^{c}{\left(1+{\left(\tfrac{r}{{r}_{p}}\right)}^{a}\right)}^{\tfrac{b-c}{a}}},\end{eqnarray} \tag{ 10 }$$

where a defines the width of the transition between the inner and the outer slopes c and b, P₀ is a normalization constant, and r_p is a characteristic radius. All of these parameters are freely varying in an MCMC analysis performed to estimate the best-fit pressure profile of MOO J1142+1527 given the NIKA2 SZ map at 150 GHz and the integrated Compton parameter measured by CARMA, i.e., ${Y}_{500}=(9.7\pm 1.3)\times {10}^{-5}\,{\mathrm{Mpc}}^{2}$ (Gonzalez et al. 2015).

At each step of the analysis, the pressure profile is integrated along the line of sight to obtain a Compton parameter map model. The latter is convolved with a 177 FWHM Gaussian kernel and with the analysis transfer function (see Section 2.2) to account for the small- and large-scale signal filtering in the NIKA2 data. The filtered Compton parameter map is converted into an SZ surface brightness map model using a conversion coefficient obtained by integrating the SZ spectrum within the NIKA2 bandpass at 150 GHz. Relativistic corrections are applied to the SZ spectrum based on the results of Itoh et al. (1998) using a temperature profile obtained by combining the Chandra density profile (see Section 6.1) and the pressure profile. We model the radio-source signal with a 2D Gaussian model centered at the position found in the FIRST survey. We fix the Gaussian FWHM to the NIKA2 angular resolution at 150 GHz and let the amplitude $\tilde{F}$ vary within a Gaussian prior based on the estimate obtained from the SED fit in Section 3. The SZ map model $\tilde{M}$, obtained from the sum of the cluster and radio-source signals, and the corresponding integrated Compton parameter $\tilde{Y}$ are finally compared with the NIKA2 and CARMA data using the following Gaussian likelihood:

$$\begin{eqnarray}\begin{array}{rcl}-2\mathrm{ln}\,{{\mathscr{L}}}_{\mathrm{SZ}} & = & {\chi }_{\mathrm{NIKA}2}^{2}+{\chi }_{\mathrm{CARMA}}^{2}+{\chi }_{\mathrm{radio}}^{2}\\ & = & {\sum }_{i=1}^{{N}_{\mathrm{pixels}}^{\mathrm{NIKA}2}}{\left[{\left({M}_{\mathrm{NIKA}2}-\tilde{M}\right)}^{T}{C}_{\mathrm{NIKA}2}^{-1}({M}_{\mathrm{NIKA}2}-\tilde{M})\right]}_{i}\\ & & +{\left[\displaystyle \frac{{Y}_{500}-\tilde{Y}}{{\rm{\Delta }}{Y}_{500}}\right]}^{2}+{\left[\tfrac{{F}_{150\mathrm{GHz}}-\tilde{F}}{{\rm{\Delta }}{F}_{150\mathrm{GHz}}}\right]}^{2}\end{array}\end{eqnarray} \tag{ 11 }$$

where M_NIKA2 and C_NIKA2 are the NIKA2 SZ surface brightness map and noise covariance matrix, respectively, at 150 GHz, and Y₅₀₀ is the CARMA integrated Compton parameter measured with the uncertainty ΔY₅₀₀. As the raw data analysis method detailed in Section 2.2 has allowed us to measure an almost flat noise power spectrum in the NIKA2 map at 150 GHz, the pixel-to-pixel correlation induced by residual-correlated noise in the NIKA2 map is negligible compared to the rms noise within each pixel at this frequency. We therefore assume that the NIKA2 χ² is given by

$$\begin{eqnarray}&&{\chi }_{\mathrm{NIKA}2}^{2}=\sum _{i=1}^{{N}_{\mathrm{pixels}}^{\mathrm{NIKA}2}}[({M}_{\mathrm{NIKA}2}-\tilde{M})/{M}_{\mathrm{RMS}}{]}_{i}^{2}\end{eqnarray} \tag{ 12 }$$

where M_RMS is the map of the rms noise in each pixel of the NIKA2 map at 150 GHz. It is computed from simulated noise maps including the instrumental, atmospheric, and astrophysical contaminants (see Section 2.3). The fact that we do not need to use a noise covariance matrix at 150 GHz to account for the residual noise properties at this frequency allows us to decrease the computation time of the likelihood value at each step of the MCMC from 0.2 s to 0.5 ms. We compute the best-fit pressure profile and its associated error bars from the samples remaining in the Markov Chains after their convergence and a burn-in cutoff discarding the first 50% of each chain.

6.2.2. Results

The combination of the Chandra density profile and NIKA2 pressure profile allows us to estimate the other ICM thermodynamic properties of MOO J1142+1527 without relying on X-ray spectroscopy.

Under the ideal-gas assumption, the ICM temperature profile and the Voit entropy parameter²³ profile are estimated from the following equations:

$$\begin{eqnarray}&&{k}_{{\rm{B}}}{T}_{e}(r)=\displaystyle \frac{{P}_{e}(r)}{{n}_{e}(r)}\,\,\mathrm{and}\,\,{K}_{e}(r)=\displaystyle \frac{{P}_{e}(r)}{{n}_{e}{\left(r\right)}^{5/3}},\end{eqnarray} \tag{ 13 }$$

where k_B is the Boltzmann constant. We show the temperature and entropy profiles obtained from the combination of the Chandra density profile (see Section 6.1) and NIKA2 pressure profile (see Section 6.2) in Figure 7. We use the same color scheme as the one considered in Figure 6 in order to differentiate the profiles measured using the X-ray peak (purple) and the X-ray large-scale centroid (green) as deprojection centers.

Zoom In Zoom Out Reset image size

The temperature profiles (left panel) estimated with these two deprojection centers are significantly different at radii r ≲ 100 kpc. We measure a monotonically decreasing temperature from the X-ray centroid up to 0.7R₅₀₀. The central temperature around the SZ peak reaches high values around 14 keV within the enclosed region defined in Figure 5 (orange line). However, the profile estimated by considering the X-ray peak has the typical shape expected for a cool-core cluster. The temperature increases from a low central value of ∼4 keV up to a maximum of 9 keV at 170 kpc from the X-ray peak. It then decreases at larger radii. These profiles estimated from the combination of X-ray and SZ results are also compatible with the mean ICM temperature estimated from the Chandra spectroscopic data (blue point). We emphasize the large leap forward that such a joint analysis of SZ and X-ray data allows us to make on the characterization of the ICM temperature profile at z > 1. Indeed, having a precise measurement of the central temperature, the inner slope of the profile, and the location of the maximum temperature value with X-ray spectroscopy would require an increase of the Chandra exposure of at least an order of magnitude.

The entropy profiles estimated from the combination of the NIKA2 and Chandra results are shown in the right panel of Figure 7. The outer slopes of both profiles are compatible with the self-similar expectation obtained from non-radiative simulations and are shown with a pink dashed line (Voit et al. 2005). However, the radial distribution of the gas entropy estimated by using the X-ray peak is significantly different from the one obtained with the large-scale centroid at r ≲ 100 kpc. We measure a flat entropy distribution at a high value of $\sim 230\,\mathrm{keV}\,{\mathrm{cm}}^{2}$ around the X-ray centroid. This is consistent with the disturbed ICM activity at the location of the SZ peak (see Section 5). On the other hand, the entropy profile estimated using the X-ray peak is monotonically increasing from a low central value of $\sim 25\,\mathrm{keV}\,{\mathrm{cm}}^{2}$ at 20 kpc from the deprojection center up to $\sim 600\,\mathrm{keV}\,{\mathrm{cm}}^{2}$ at 0.7R₅₀₀. This profile is consistent with the one expected for a cool-core cluster in which the central radiative cooling is balanced by the activity of the radio-loud AGN detected within the BCG. The central entropy value estimated from this profile depends on the flux of the radio source considered in the NIKA2 MCMC analysis. A flattening of the radio-source SED at high frequency (e.g., Hogan et al. 2015) would indeed result in a higher expected flux at 150 GHz and, therefore, to a higher central value of the deprojected pressure distribution from the NIKA2 data. However, we have checked that the central entropy value is always lower than $\sim 70\,\mathrm{keV}\,{\mathrm{cm}}^{2}$ if we consider a point-source flux lower than 4 mJy at 150 GHz. This shows that the existence of a cool core at the position of the X-ray peak holds even if the radio-source flux at frequencies ν > 100 GHz remains at the same value measured by CARMA at 31 GHz.

Finally, we compare our constraints on the entropy profile of MOO J1142+1527 with the results obtained by Sanders et al. (2017) from the analysis of Chandra data measured on the cluster $\mathrm{SPT}\,\mathrm{CLJ}0156$-5541 at z = 1.22 (gray profile). A refined analysis based on the assumption of an underlying dark-matter potential enabled theses authors to estimate an entropy profile with a total of 2300 X-ray counts. However, the comparison of this profile with baseline entropy distributions extracted from simulations is difficult because of the large error bars associated with this estimate. Here, we show that a joint analysis combining a slightly lower number of X-ray counts (see Section 4) with high angular resolution SZ observations results in a highly constrained entropy profile even at z > 1.

We further describe the properties of the cluster cool core by computing the isochoric cooling time and freefall time profiles given by

$$\begin{eqnarray}&&{t}_{\mathrm{cool}}(r)=\displaystyle \frac{3}{2}\displaystyle \frac{({n}_{e}+{n}_{p})\,{k}_{{\rm{B}}}{T}_{e}}{{n}_{e}{n}_{p}\,{\rm{\Lambda }}({T}_{e},Z)}\,\,\mathrm{and}\,\,{t}_{\mathrm{ff}}(r)=\sqrt{\displaystyle \frac{2r}{g(r)}},\end{eqnarray} \tag{ 14 }$$

where $g(r)=G\cdot B\cdot {M}_{\mathrm{HSE}}(r)/{r}^{2}$ is the gravitational acceleration caused by the total mass $B\cdot {M}_{\mathrm{HSE}}(r)$ within a sphere of radius r, and G is the gravitational constant. The hydrostatic bias B = 1/(1−b) is a correction applied to the hydrostatic mass profile M_HSE(r) to account for the departure of the gas dynamical state from hydrostatic equilibrium. We use the same ionization fraction considered in Section 6.1 in order to estimate the proton-density profile n_p(r) from the electron-density distribution n_e(r) obtained by considering the X-ray peak as a deprojection center. Furthermore, we use the cooling function estimated by Sutherland & Dopita (1993) for an optically thin plasma with a 0.3Z_⊙ metallicity to compute ${\rm{\Lambda }}({T}_{e},Z)$ from the temperature profile centered on the X-ray peak, shown in Figure 7. The freefall time is estimated by using the hydrostatic mass profile computed from the combination of the Chandra density and NIKA2 pressure profiles (see Section 6.4 below). We use an hydrostatic bias parameter fixed to b = 0.2, following the results of numerical simulations and the comparisons between weak lensing and SZ/X-ray cluster-mass estimates (see, e.g., Figure 10 in Salvati et al. 2018). The cooling-time profile as well as the ratio t_cool/t_ff are represented in the left panel of Figure 8 in magenta and gray, respectively. We measure a cooling time at 20 kpc from the X-ray peak location of t_cool = (0.51 ± 0.13) Gyr. This is compatible with the distribution of central cooling times estimated by McDonald et al. (2013) on a sample of SPT-selected cool-core clusters. We note that this central cooling time is fairly low given the cluster redshift. This supports the results shown in Figure 6 of McDonald et al. (2013) on the absence of significant redshift evolution of the gas cooling properties in cluster cores. We measure a ratio t_cool/t_ff ≃ 9 at the core of MOO J1142+1527. The relationship between the minimum value of t_cool/t_ff and the central entropy is therefore consistent with the distribution measured on the sample of X-ray selected clusters at a mean redshift $\langle z\rangle =0.17$ dubbed the Archive of Chandra Cluster Entropy Profile Tables (ACCEPT; Voit & Donahue 2015). In summary, although MOO J1142+1527 displays many features of a morphologically disturbed galaxy cluster (see Section 5) at a redshift z = 1.2, its core properties are very similar to those observed in typical cool-core clusters at low redshift.

Zoom In Zoom Out Reset image size

The estimates of both the density and pressure profiles of MOO J1142+1527 allow us to infer the total mass of this cluster independently of any scaling relation calibrated at lower redshifts. We estimate the total mass enclosed within a radius r under the hydrostatic equilibrium assumption:

$$\begin{eqnarray}&&{M}_{\mathrm{HSE}}(r)=-\displaystyle \frac{{r}^{2}}{{\mu }_{\mathrm{gas}}{m}_{p}{n}_{e}(r)G}\displaystyle \frac{{{dP}}_{e}(r)}{{dr}},\end{eqnarray} \tag{ 15 }$$

where m_p is the proton mass and ${\mu }_{\mathrm{gas}}=0.61$ is the mean molecular weight of the gas. The hydrostatic mass profiles computed from the density and pressure profiles estimated by using the X-ray peak and the X-ray large-scale centroid as deprojection centers are both represented in the right panel of Figure 8 in purple and green, respectively. The profiles are compatible with each other from the cluster core up to 0.7R₅₀₀; although, the inner slope of the profile measured from the X-ray centroid is shallower than the one obtained at the X-ray peak. The hydrostatic mass profile of MOO J1142+1527 is used to compute its density-contrast profile $\langle \rho (r)\rangle /{\rho }_{c}$, where $\rho (r)={M}_{\mathrm{HSE}}(r)/V(r)$, V(r) is the cluster volume at a radius r, and ρ_c is the critical density of the universe at z = 1.2. This allows us to directly measure the value of R₅₀₀. The estimates of R₅₀₀ measured from the two mass profiles enable us to compute the total mass of the cluster M₅₀₀ as well as its integrated Compton parameter Y₅₀₀. The results are summarized in Table 2.

Table 2.  Estimates of the R₅₀₀ Radius, Hydrostatic Mass (M₅₀₀), and Integrated Compton Parameter (Y₅₀₀) Computed from the Combination of the Chandra Density and NIKA2 Pressure Profiles

	X-Ray Centroid	X-Ray Peak
R500 [kpc]	841 ± 31	812 ± 41
${M}_{500}\,[\times {10}^{14}\,{{\rm{M}}}_{\odot }]$	6.06 ± 0.68	5.49 ± 0.85
${Y}_{500}\,[\times {10}^{-4}\,{\mathrm{arcmin}}^{2}]$	2.95 ± 0.21	2.96 ± 0.23

Note. The values estimated by considering both the X-ray centroid and peak emission as deprojection centers are compared.

Download table as:  ASCIITypeset image

The results obtained with the two mass profiles are all compatible within their 1σ confidence intervals. The error bars associated with the estimates derived from the mass profile measured using the X-ray peak are, however, larger than the ones obtained with the X-ray centroid. A spherical model is indeed ill-suited to subtract the extended emission to the west of the X-ray peak without creating strong residuals to its east in both Chandra and NIKA2 data. While using the X-ray centroid as the deprojection center induces residuals around the X-ray peak because the X-ray signal is not azimuthally symmetric in this area, the extended emission is subtracted with more accuracy in this case. More quantitatively, the minimum χ² value obtained at the end of the NIKA2 MCMC analysis (see Section 6.2) is decreased by 11% if we use the X-ray centroid instead of the X-ray peak as the deprojection center. Although considering the X-ray peak as the deprojection center is mandatory to have an accurate description of the cluster core properties (see Section 6.3), using the X-ray centroid leads to both more accurate and more precise estimates of the integrated quantities of MOO J1142+1527 such as M₅₀₀ and Y₅₀₀. We therefore discuss the results obtained with the X-ray centroid as follows.

The R₅₀₀ radius measured with this multiwavelength analysis is compatible with the estimate based on the measurement of the mean ICM spectroscopic temperature and the ${M}_{500}\mbox{--}{T}_{X}$ relation from Vikhlinin et al. (2009; see Section 4.1). Moreover, our estimate of M₅₀₀ is fully compatible with the value determined by Gonzalez et al. (2015) using the CARMA integrated Compton parameter along with the Andersson et al. (2011) Y₅₀₀−M₅₀₀ scaling relation, i.e., ${M}_{500}^{\mathrm{CARMA}}\,=(6.0\pm 0.9)\times {10}^{14}\,{M}_{\odot }$. Based on our measurement of the integrated Compton parameter of MOO J1142+1527 computed from the spherical integral of the NIKA2 pressure profile up to R₅₀₀, we estimate the expected mass of this cluster using the Planck scaling relation (Planck Collaboration et al. 2014): ${M}_{500}^{\mathrm{Planck}}=(5.25\pm 0.21)\times {10}^{14}\,{M}_{\odot }$. The cluster mass reported in Table 2 is therefore compatible with the scaling-relation-based value given the error bars of our estimate and the intrinsic scatter associated with the Planck scaling relation calibrated at redshifts z < 0.45. In addition, we compute the pseudo-integrated Compton parameter ${Y}_{X}={M}_{g,500}\times {T}_{X}$ using the gas-mass measurement M_g,500 obtained by integrating the Chandra density profile centered on the X-ray centroid and the mean spectroscopic temperature found in Section 4.2. We estimate the total mass of the cluster using the M₅₀₀−Y_X scaling relation of Arnaud et al. (2010) and find ${M}_{500}^{{Y}_{X}}=(5.19\,\pm 0.25)\times {10}^{14}\,{M}_{\odot }$. Based on all of these different mass estimates, we therefore confirm that MOO J1142+1527 is the most massive galaxy cluster known to date at z > 1.15 from an analysis based on spherical models of the ICM density and pressure distributions and the assumption of hydrostatic equilibrium. We compare all mass estimates of this cluster given in this paper in the left panel of Figure 9. We highlight that our hydrostatic mass estimate obtained by combining the deprojected ICM pressure and density profiles is compatible with the ones computed based on the mass-observable scaling relation calibrated using low-redshift cluster samples.

Zoom In Zoom Out Reset image size

As shown in Section 5, MOO J1142+1527 is not a relaxed cluster, nor can it be considered spherical given the precision of the Chandra and NIKA2 measurements (see Appendix A). Thus, we perform a dedicated analysis in order to estimate a systematic uncertainty caused by both the expected departure of the cluster dynamical state from hydrostatic equilibrium and the modeling error induced by the use of a spherical model to deproject the ICM pressure and density distributions.

We analyze both the Chandra and NIKA2 observations in four angular sectors of 90^◦ opening angles centered on the large-scale X-ray centroid (see inset in the right panel of Figure 9). The density and pressure profiles are estimated in each of these sectors following the methodology described in Sections 6.1 and 6.2. We use Equation (15) to compute the mass profiles based on these results assuming that the ICM is in hydrostatic equilibrium in each sector and that its thermodynamic properties can be described by spherically symmetric distributions. If the cluster was perfectly spherical and morphologically relaxed, these four mass profiles would be compatible at all scales. We represent the hydrostatic mass profiles estimated in each sector in Figure 9. Although these profiles are compatible in the cluster center, we measure significant discrepancies at radii larger than  ∼ 400 kpc. We consider these differences as an indicator of the systematic error associated with the estimate of the total mass of the cluster. As the outer slopes and amplitudes of the four profiles are different, the values of R₅₀₀ estimated from the radial distribution of the density contrast in each sector are also significantly different. Therefore, we choose to define the systematic uncertainty associated with our estimate of the hydrostatic mass of this cluster as the standard deviation between the mass values measured with each profile at a radius of 841 kpc, i.e., the R₅₀₀ estimate given in Table 2. We also measure the mean of these four mass values to define a new estimate of the cluster total mass. The hydrostatic mass of MOO J1142+1527 obtained by this analysis is given by ${M}_{841\mathrm{kpc}}=(7.4\pm 3.4)\times {10}^{14}\,{M}_{\odot }$. Although this result is fully compatible with the hydrostatic mass estimate given in Table 2, we emphasize that the dispersion of the mass estimates between the four angular sectors is three times higher than the error bar associated with the mass measurement at 841 kpc in each sector. Our final estimate of the hydrostatic mass of MOO J1142+1527 is given by the measurement referenced in Table 2 along with this additional systematic uncertainty: ${M}_{500}=(6.06\pm {0.68}^{\mathrm{stat}}\pm {3.40}^{\mathrm{syst}})\times {10}^{14}\,{M}_{\odot }$. Although the disturbed dynamical state of MOO J1142+1527 is not striking from the visual inspection of the NIKA2 map at 150 GHz, this multiwavelength analysis has shown that the precision of the mass measurement of this particular cluster is not limited by the noise properties in the Chandra and NIKA2 data but by our modeling of the ICM thermodynamic properties.

The knowledge of the systematic uncertainty on M₅₀₀ induced by an incorrect modeling of the ICM properties is essential to perform an accurate calibration of the mass-observable scaling relation. This analysis highlights the importance of the combination of SZ and X-ray observations to accurately measure the dynamical properties of high-redshift galaxy clusters. Furthermore, it shows that a 1D modeling of the ICM is intrinsically unsuited to describe the true distributions of the thermodynamic properties of morphologically disturbed clusters. In this context, mapping the average value of the gas properties along the line of sight can provide new insights into the dynamical state of such unrelaxed systems.

Mapping the ICM temperature in disturbed clusters using X-ray spectroscopic data has led to a better understanding of the complex processes occurring in sloshing (e.g., Calzadilla et al. 2019) or merging (e.g., Million & Allen 2009) systems. However, the realization of such maps usually requires thousands of X-ray counts per resolution element in order to have a precise measurement of the relative difference between the temperature estimates in each region of the map. Mapping the ICM temperature of MOO J1142+1527 from its core up to a large fraction of R₅₀₀ based only on X-ray spectroscopic measurements would therefore require more than 1 Ms of exposure with Chandra or XMM-Newton even with a very coarse binning of the map.

The different dependencies of the X-ray and SZ surface brightness with respect to the distribution of density and temperature along the line of sight allow us to combine the Chandra and NIKA2 data at the pixel level in order to map all of the ICM thermodynamic properties of MOO J1142+1527 without relying on X-ray spectroscopy. We follow the methodology described in detail in Adam et al. (2017b) in order to estimate the maps of the ICM pressure (${\bar{P}}_{e}$) and density (${\bar{n}}_{e}$) distributions averaged along the line of sight based on the NIKA2 and Chandra data:

$$\begin{eqnarray}&&{\bar{P}}_{e}(\alpha ,\delta )=\displaystyle \frac{1}{{{\ell }}_{\mathrm{eff}}}\int {P}_{e}\,{dl}=\displaystyle \frac{{m}_{e}{c}^{2}}{{\sigma }_{T}}\displaystyle \frac{{y}_{\mathrm{tSZ}}}{{{\ell }}_{\mathrm{eff}}}\end{eqnarray} \tag{ 16 }$$

$$\begin{eqnarray}&&{\bar{n}}_{e}(\alpha ,\delta )=\displaystyle \frac{1}{{{\ell }}_{\mathrm{eff}}}\int {n}_{e}\,{dl}=\displaystyle \frac{1}{\sqrt{{{\ell }}_{\mathrm{eff}}}}\sqrt{\displaystyle \frac{4\pi \,{\left(1+z\right)}^{4}\,{S}_{X}}{{\rm{\Lambda }}({T}_{e},Z)}}\end{eqnarray} \tag{ 17 }$$

where y_tSZ and S_X are the NIKA2 Compton parameter map and Chandra X-ray surface brightness map, respectively, and ℓ_eff is the map of the effective electron depth given by

$$\begin{eqnarray}&&{{\ell }}_{\mathrm{eff}}=\displaystyle \frac{{\left(\int {n}_{e}{dl}\right)}^{2}}{\int {n}_{e}^{2}\,{dl}}.\end{eqnarray} \tag{ 18 }$$

This map provides an estimate of the line-of-sight extension of the ICM in each pixel. We follow the procedure introduced by Adam et al. (2017b) and compute two estimates of this map based on the ICM density profiles obtained using the X-ray peak and X-ray centroid as deprojection centers. Thus, these maps give an estimate of the effective path length in a more resolved way than the global result issued from the method pioneered in Mroczkowski et al. (2012). The uncertainty associated with the estimate of ℓ_eff is dominated by the departure of the ICM geometry from the spherical model used in this analysis. We favor the X-ray peak instead of the X-ray centroid to compute the final maps ${\bar{P}}_{e}(\alpha ,\delta )$ and ${\bar{n}}_{e}(\alpha ,\delta )$ because our goal is to accurately map the ICM thermodynamic properties of MOO J1142+1527 in the core area. However, we compute the uncertainties associated with these maps using both estimates of ℓ_eff. The two ℓ_eff maps considered in this analysis are shown in Figure 10. We measure a minimum effective electron depth of ∼500 kpc at the X-ray peak in the ℓ_eff map obtained using the density profile centered on the X-ray peak. The cluster extent increases toward the outskirts and reaches a value of ∼1400 kpc at 1' from the X-ray peak.

Zoom In Zoom Out Reset image size

The Compton parameter map measured by NIKA2 is deconvolved from the transfer function in order to minimize the bias induced by the large-scale filtering of the SZ signal. We estimate the standard deviation in each pixel of the pressure map by computing two samples of 1000 realizations of ${\bar{P}}_{e}$ using NIKA2 noise maps also deconvolved from the transfer function instead of y_tSZ in Equation (16) and the two realizations of ℓ_eff. We also take into account the effect of the point-source subtraction in the Compton parameter map by simulating different realizations of y_tSZ marginalizing over the radio-source flux given the constraints obtained in Section 3.

The Chandra map is corrected for vignetting and then processed through an adaptative filter using the CIAO csmooth routine. This allows us to produce a map where the minimum angular scales match the effective angular resolution of 20'' adopted for the ${\bar{P}}_{e}$ map and where the minimum S/N is equal to 3. Several realizations of this filtered map are made by taking into account the Poisson fluctuations of the X-ray signal and shuffling the pixel values of the X-ray background map before subtracting it from the Chandra surface brightness map. We use these S_X realizations along with the two ℓ_eff ones in order to compute two samples of 1000 realizations of ${\bar{n}}_{e}$ maps from Equation (17).

The temperature and entropy maps of MOO J1142+1527 are estimated from the combination of the pressure- and density-map realizations:

$$\begin{eqnarray}&&{k}_{{\rm{B}}}{\bar{T}}_{e}={\bar{P}}_{e}/{\bar{n}}_{e}\,\,\mathrm{and}\,\,{\bar{K}}_{e}={\bar{P}}_{e}/{\bar{n}}_{e}^{5/3}.\end{eqnarray} \tag{ 19 }$$

The results obtained by using the ℓ_eff map computed with the ICM density profile centered on the X-ray peak are shown in both panels of Figure 11. We indicate the location of the BCG with a green cross. The signal-to-noise contours estimated from the knowledge of the temperature and entropy fluctuations in each pixel from the 2000 realizations of the ${\bar{P}}_{e}$ and ${\bar{n}}_{e}$ maps are shown with black lines, with the lower contour at 3σ. The error maps obtained from the ${\bar{P}}_{e}$ and ${\bar{n}}_{e}$ map realizations and used to compute these S/N contours are shown in Appendix B. We measure the spatial distribution of the ICM temperature and entropy up to a distance of 0.5R₅₀₀ from the cluster centroid. We emphasize that the S/Ns on these temperature and entropy estimates take into account the effect of the differences between the two density profiles estimated in Section 6.1 on the ℓ_eff map. We show the distributions of the temperature values obtained in the core and in the southwest regions of the cluster from the Monte Carlo realizations of temperature maps computed by using the two estimates of ℓ_eff in Figure 12. As the density estimates given at the location of the X-ray peak by the two profiles shown in Figure 6 are significantly different, the two distributions of the core temperature shown in the left panel are consequently different. This explains why the S/N on the core temperature and entropy values shown in Figure 11 is much weaker than the one reached in the intermediate regions of the cluster where the temperature and entropy values obtained with the two estimates of ℓ_eff are fully compatible (see right panel of Figure 12). This highlights the high degeneracy between the error maps and the considered ℓ_eff map. Using both estimates of the ℓ_eff map (see Figure 10) to compute the realizations of ${\bar{P}}_{e}$ and ${\bar{n}}_{e}$ enables taking part of this degeneracy into account to estimate the S/N contours shown in Figure 11.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

A prominent feature, particularly in the entropy map shown in Figure 11, is the significant detection of a cool core at the location of the BCG. The temperature measured at this location is at least two times lower than the one observed in the surrounding regions, and the entropy is three times lower than the mean entropy value measured in the whole map. Furthermore, the core appears to be well-delimited. The core entropy averaged along the line of sight is enclosed between 100 and $200\,\mathrm{keV}\,{\mathrm{cm}}^{2}$ within a circular region extending over a ∼120 kpc radius from the BCG. We measure a significant increase of the ICM temperature to the west of the BCG. This feature is consistent with the merging scenario described in Section 5 as we expect the gas within this region to be shock-heated by the infalling subcluster (B) from the northwest to the southeast of the main halo (A). The entropy measured at the location of the infalling galaxy group is slightly lower than the one observed at similar radii from the cluster BCG but in different directions. This could be a hint of the presence of a second core associated with this merging substructure. However, this difference is not significant given the entropy fluctuations at this location.

An interesting feature identified in both maps is the presence of a high-temperature and -entropy region southward of the BCG location. While the relative difference between the temperature measured in this region and the one observed at the cluster centroid varies between all of the realizations of ${\bar{T}}_{e}$, its absolute value is always twice as high as the one measured in the cool core. The interpretation of this feature is quite challenging given its location with respect to the different structures in the galaxy distribution (see Section 5). There is however a hint of an additional peak in the galaxy distribution observed by Spitzer to the east of the BCG (labeled 'C' in Figure 5). If this galaxy group is actually in a post-merger state and has undergone a head-on collision from the southwest regions to its current location, the ICM would have been shock-heated at the collision point during the merging process, and the gas within the substructure would have been stripped away from its potential well. This would explain both the high temperature measured to the south of the X-ray peak and the low gas density observed to the east of the cluster at the location of the galaxy group (C). We note however that deeper observations would be needed to confirm this possible scenario. In particular, higher-exposure X-ray observations would enable measuring the X-ray spectroscopic temperature in the region to the south of the X-ray peak. With our current X-ray data set, the spectrum extracted in this region is well fitted by an absorbed APEC model with k_BT = 10 keV (χ²/ndf = 0.55) as well as with k_BT = 5 keV (χ²/ndf = 0.52). An XMM-Newton proposal led by I. Bartalucci, also an author on this paper, has been accepted to map the X-ray emission of MOO J1142+1527 for a total of 105 ks. The larger effective area of XMM-Newton combined with this higher exposure should enable measuring a precise value of the spectroscopic temperature in this region of the cluster.

We emphasize the complementarity between the results of the 1D analysis described in Section 6 and the maps of the ICM thermodynamic properties described in this section to explore the merger dynamics of MOO J1142+1527. To the best of our knowledge, this is the very first time that such a detailed analysis of the ICM has been achieved at z > 1. This study paves the way for an in-depth characterization of the ICM properties of very high-redshift galaxy clusters from a combination of spatially resolved X-ray and SZ observations.