Exploiting NIKA2/XMM-Newton imaging synergy for intermediate mass, high-$z$ galaxy clusters within the NIKA2 SZ Large Program

High-resolution mapping of the intra-cluster medium (ICM) up to high redshift and down to low masses is crucial to derive accurate mass estimates of the galaxy cluster and to understand the systematic effects affecting cosmological studies based on galaxy clusters. We present a spatially-resolved Sunyaev-Zel'dovich (SZ)/X-ray analysis of ACT-CL J0215.4+0030, a high redshift ($z=0.865$) galaxy cluster of intermediate mass ($M_{500}\simeq3.5\times10^{14}\;\mathrm{M_\odot}$) observed as part of the ongoing NIKA2 SZ Large Program, a follow up of a representative sample of objects at $0.5 \leqslant z \leqslant 0.9$. In addition to the faintness and small angular size induced by its mass and redshift, the cluster is contaminated by point sources that significantly affect the SZ signal. Therefore, this is an interesting case study for the most challenging sources of the NIKA2 cluster sample. We present the NIKA2 observations of this cluster and the resulting data. We reconstruct the ICM pressure profile by performing a joint analysis of the SZ signal and of the point sources in the NIKA2 150 GHz map. We obtain high-quality estimates of the ICM thermodynamical properties with NIKA2. We compare the pressure profile extracted from the NIKA2 map to the pressure profile obtained from X-ray data only by deprojecting XMM-Newton observations of the cluster. We combine the NIKA2 pressure profile with the X-ray deprojected density to extract detailed information on the ICM. The radial distribution of its thermodynamic properties indicate that the cluster has a disturbed core. The hydrostatic mass of the cluster is to be compatible with estimations from SZ and X-rays scaling relations. We conclude that the NIKA2 SZ large program can deliver quality information on the thermodynamics of the ICM even for one of its faintest clusters, after a careful treatment of the contamination by point sources.


Introduction
As the last stage of hierarchical structure formation, galaxy clusters constitute the most massive gravitationally bound structures in the Universe. They form through gravitational collapse of matter and accretion of local material in the density peaks at the intersection of cosmic web filaments. As such, they are a direct tracer of the matter distribution in the Universe, and their abundance in mass and redshift constitutes an excellent probe of large-scale structure formation physics. The latter being dominated by gravitational processes, these observables are very sensitive to the underlying cosmology, such as the initial conditions in the primordial Universe and its contents and evolution in time (Huterer et al. 2015). Galaxy clusters can therefore be used as cosmological probes (for reviews, see e.g. Carlstrom et al. 2002;Allen et al. 2011).
In the last few years, large catalogs of galaxy clusters (e.g. Planck Collaboration XXVII 2016; Bleem et al. 2020;Adami et al. 2018;Rykoff et al. 2016) were assembled and used for cosmological purposes (e.g. Planck Collaboration XXIV 2016;Boc-quet et al. 2019;Pacaud et al. 2018;Costanzi et al. 2019). When combined with cosmological constraints from other probes, the results of these analyses seem to exhibit a slight discrepancy with cosmological parameters inferred from the analysis of the CMB power spectrum (see e.g. Planck Collaboration VI 2018; Salvati et al. 2018). This difference could either arise from new physics, or simply reflect an incomplete knowledge of the relations and tools used for the cosmological exploitation of cluster surveys (Ruppin et al. 2019b;Salvati et al. 2019Salvati et al. , 2020. A precise knowledge of the systematic effects affecting the estimation of cosmological parameters from galaxy clusters surveys is therefore crucial. Currently, one of the main limiting factors for cluster-based cosmological analyses comes from the relations used to infer fundamental properties of galaxy clusters from large surveys. In particular, every cluster-based cosmological analysis strongly relies on the knowledge of the masses of clusters (see e.g. Pratt et al. 2019, for a review). Since most of the mass budget of a cluster comes from dark matter, the total mass of a cluster is not directly Article number, page 1 of 14 arXiv:2009.02563v2 [astro-ph.CO] 8 Sep 2020 observable, and must be inferred either from its gravitational effect or from empirical scaling relations linking cluster masses to observables. Among these observables are probes based on the thermodynamical properties of the gaseous intra-cluster medium (ICM), such as the Sunyaev-Zel'dovich effect in millimeter wavelengths (e.g. Planck Collaboration XI 2011) or X-rays luminosity (e.g. Pratt et al. 2009).
The Sunyaev-Zel'dovich (SZ) effect (Sunyaev & Zeldovich 1972) has been proven an excellent way to detect a large number of galaxy clusters up to high redshift thanks to its redshift independence. Moreover, the integrated SZ surface brightness is a low-scatter mass proxy (see e.g. Pratt et al. 2019;Planck Collaboration XI 2011;Planck Collaboration X 2011;Planck Collaboration XII 2011), making large catalogs of SZ-detected clusters an efficient way to probe cosmology. The largest cluster catalog to date was obtained from Planck observations in millimeter wavelengths (Planck Collaboration XXVII 2016) and includes ∼1200 clusters up to z 0.9, while ground-based CMB experiments such as the Atacama Cosmology Telescope (ACT, Hilton et al. 2018) and the South Pole Telescope (SPT, Bleem et al. 2020) go deeper in redshift and detect clusters down to lower masses. Most scaling relations used to estimate the mass of SZ-detected clusters were calibrated on small samples of lowredshift clusters with masses inferred from X-ray observations (see Planck Collaboration XI 2011; Arnaud et al. 2010). These clusters being on the low end of the redshift distribution of SZ catalogs, an evolution of the scaling relations with redshift could have a significant impact on the cosmological parameters estimated from these samples. In addition to the scaling relation, SZ-based cosmological analyses also rely on the knowledge of the pressure profile of galaxy clusters. In the self-similar scenario, galaxy clusters are expected to be scaled replicas from one another. Hence, their pressure distribution should be well described by a universal pressure profile (Press & Schechter 1974;Böhringer et al. 2012). Similarly to the scaling relation, some of the most used measurements of universal pressure profiles have been conducted on low-redshift clusters (e.g. Planck Collaboration V 2013; Arnaud et al. 2010, hereafter A10), and a variation of this profile with redshift could also have great implications on SZ cosmology (Ruppin et al. 2019b).
So far, X-ray follow-ups deep enough to measure annular temperature profiles of z > 0.3 SZ-discovered clusters have concentrated on representative samples of the highest-mass systems. They are the "easiest" systems to observe, their high X-ray brightness leading to good precision on the radial temperature distribution -see e.g. Bartalucci et al. (2017) for a discussion of the entropy and pressure profiles of five massive (M > 5 × 10 14 M ) clusters at z ∼ 1. For such objects, the ICM properties are expected to be dominated by simple shock heating and compression due to gravitational collapse. Nonetheless, low-mass galaxy clusters are key to understanding non-gravitational processes, because these effects are more apparent in their shallower potentials. Different processes (such as e.g. supernovae winds, AGN feedback, radiative cooling) affect the ICM entropy in different ways (both in terms of the level and the characteristic timescale), so that the gas history is expected to depend sensitively on their relative contribution. This can significantly change the profile shapes , affecting the selection function at low mass and introducing additional scatter into the observable-mass relations. The evolution and scatter of thermodynamical profiles at low mass is thus a key information needed to disentangle and understand the respective role of each process. This makes the study of distant low-mass objects essential to our understanding of galaxy clusters as a whole.
The reconstruction of the intra-cluster medium properties through SZ observations faces several challenges. Among them is the large diversity in the SZ fluxes of clusters. The link between a cluster mass and its integrated SZ signal implies that low mass clusters are fainter than massive ones. For follow-ups of individual clusters, this means the time needed to reach a given significance level of detection increases when the mass of clusters goes down. Another challenge is the contamination by point sources. Dusty galaxies and radio sources can emit in millimeter wavelengths. Depending on their angular position with respect to the center of the cluster, they may have a large impact on the observed 2D-shape of the ICM. Indeed, the spectral signature of the SZ effect at frequencies lower that 217 GHz being a surface brightness decrement, the contamination by these point sources can compensate the SZ flux. To remedy this, the spectra of millimetric sources can be estimated (provided data are available at other frequencies) and extrapolated to the wavelengths of interest, giving an estimation of the amplitude of the contamination (see e.g. Sayers et al. 2013;Adam et al. 2016;Ruppin et al. 2018). Distant clusters can also be difficult to observe as their apparent angular size diminishes with redshift. Therefore, these surveys were not sensitive to potential substructures in the ICM. High angular resolution observations of high redshift clusters may reveal significant deviations from our knowledge of nearby clusters. The analysis presented in this paper will face these three challenges, and use NIKA2 SZ observations to overcome them. For a review of high angular resolution SZ observations and of the associated challenges, see Mroczkowski et al. (2019).
In this paper, we present the study of the second observed cluster of the NIKA2 SZ Large Program, a high-resolution follow-up of 50 SZ-detected clusters at 0.5 z 0.9 from the Planck and ACT galaxy cluster catalogs (Planck Collaboration XXVII 2016;Hasselfield et al. 2013). ACT-CL J0215.4+0030 is one of the lowest mass and highest redshift of the Large Program sample, with M 500 3.5 × 10 14 M and z = 0.865. It was discovered by the Atacama Cosmology Telescope with a significance level of 5.5σ (Menanteau et al. 2013;Hilton et al. 2018, for the most recent data release), and is below the detection threshold in the Planck catalog (Planck Collaboration XXVII 2016). The NIKA2 maps of the cluster also exhibit a strong contamination by point sources that have a large impact on the observed SZ signal (Kéruzoré et al. 2020). This target therefore combines the challenges associated to low mass, high redshift, and point source contamination. The first analysis of NIKA2 SZ observations was presented in Ruppin et al. (2018) as a science verification study, targetting one of the most massive, closest clusters of the NIKA2 SZ Large Program with a long exposure time, therefore reaching a high peak signal-to-noise ratio (SNR) of ∼ 14σ. By contrast, in this paper, we tackle the challenges associated with the characterization of a cluster observed with standard conditions for the NIKA2 SZ Large Program, and on the low mass, high redshift part of the sample. The study of NIKA2 observations of a comparable distant and low mass cluster was recently presented by Ricci et al. (2020), outside the framework of the NIKA2 SZ Large Program. Here, we tackle similar challenges, and in addition face a strong point source contamination. This analysis is therefore designed as a "worst case scenario" for the NIKA2 SZ Large Program. This paper is organized as follows. In Sect. 2, we describe the key elements of the NIKA2 SZ Large Program. In Sect. 3, we describe the NIKA2 and XMM-Newton data used for this analysis, the observations and the data reduction leading to the SZ and X-ray maps of the ICM. In Sect. 4, we present the identification of point sources that limit the estimation of the SZ signal of the cluster. In Sect. 5, we present the deprojection of the pressure profile of the cluster by performing a joint fit, modeling both the ICM seen through the SZ effect and the point sources of known positions. In Sect. 6, we present the results of this analysis through the recovered pressure profile and total integrated SZ signal, and combine this pressure profile with X-ray data to completely characterize the thermodynamics of the ICM. We finish with our conclusions for this study and its implications for the NIKA2 SZ Large Program in Sect. 7.

The NIKA2 SZ Large Program
This work presents the first standard analysis of an individual cluster within the NIKA2 SZ Large Program (hereafter LPSZ). In this section, we give a brief description of this program; more detailed information can be found in Mayet et al. (2020).
The NIKA2 camera (Adam et al. 2018a;Bourrion et al. 2016;Calvo et al. 2016) is a dual-band millimeter camera operated at the IRAM 30-meter telescope located at Pico Veleta, Spain. It uses kinetic inductance detectors (KIDs, Day et al. 2003;Shu et al. 2018) to simultaneously map the sky at 150 and 260 GHz with a large field of view (6.5 ), a high angular resolution (17.6" and 11.1" at 150 and 260 GHz, respectively) and sensitivity (9 and 30 mJy · s 1/2 at 150 and 260 GHz, respectively). The performance and detailed specifications of NIKA2 are presented in Perotto et al. (2020, hereafter P20). NIKA2 and its pathfinder, NIKA (Catalano et al. 2014), have proven to be especially well designed for SZ analyses of intermediate to high redshift clusters, taking full advantage of the instruments performance to extract information about the thermodynamics of the ICM (see e.g. Adam et al. 2014Adam et al. , 2015Adam et al. , 2016Adam et al. , 2017aAdam et al. ,b, 2018bRicci et al. 2020;Romero et al. 2018;Ruppin et al. 2017Ruppin et al. , 2018Ruppin et al. , 2020. As part of the NIKA2 guaranteed time, the NIKA2 SZ Large Program seeks to get a high resolution follow-up of ∼ 50 SZdetected galaxy clusters from the Planck and ACT catalogs (Planck Collaboration XXVII 2016;Hasselfield et al. 2013). This sample covers a wide range of masses (3 M 500 /10 14 M 10) at intermediate to high redshifts (0.5 z 0.9). The high resolution observations of the ICM with NIKA2, combined with prior knowledge of the clusters integrated SZ fluxes from the Planck and ACT catalogs, will allow us to achieve a precise knowledge of the dynamical state of the ICM for high redshift clusters, with the ability to detect substructures in clusters (e.g. overpressure regions or merger events). This will enable an evaluation of the mean pressure profile of galaxy clusters at higher redshift than current measurements and with a great precision. In addition, the combination of NIKA2 SZ observations with X-ray followups of clusters in the LPSZ sample will enable the computation of hydrostatic masses of the clusters, which will be used for a calibration of the SZ-mass scaling relation at high-redshift. The high-redshift, high-precision measurement of these two ingredients will be used to reanalyze the large SZ cluster surveys with an evaluation of the possible redshift evolution of the relations, and with an improved control of the systematics coming from the knowledge of the dynamical state of the ICM (Ruppin et al. 2019b,a). The NIKA2 observations of the LPSZ sample are ongoing. Millimeter observations of galaxy clusters enable the mapping of their ICM via the thermal Sunyaev-Zel'dovich effect. It consists in the inverse Compton scattering of CMB photons on the hot electrons of the ICM, resulting in a spectral distortion of the CMB. The relative variation of CMB intensity due to the tSZ effect is given by

Observations of the intra-cluster medium in ACT
where I 0 is the CMB specific intensity, T e is the electron temperature of the ICM, f (ν, T e ) is the spectral dependance of the SZ effect, and y is the amplitude of the distortion, referred to as the Compton parameter, which is proportional to the line-of-sight integrated pressure of the ICM: Observations of galaxy clusters through the SZ effect can therefore be used to reconstruct the pressure distribution in the ICM. We notice that Eqs. 1 and 2 do not include any redshift dependance, meaning the SZ effect does not suffer any cosmological dimming when observing high redshift clusters. It is therefore an ideal probe to detect and study galaxy clusters on wide ranges of redshifts, as long as observations are conducted with a high enough angular resolution (for a review of SZ effect observations and of the physics involved, see e.g. Mroczkowski et al. 2019)

Observations and data reduction
The NIKA2 observations used in this paper were conducted during the fourteenth run of NIKA2 (N2R14). This run is one of those used for the performance assessment of NIKA2, and is therefore thoroughly described in P20; we give here the key elements relevant to our observations. The observations of ACT-CL J0215.4+0030 were performed in five sessions from the 17th to the 22th of January, 2018. All sessions occured between 16:00 and 22:15 UT. The focus of the telescope was checked at the beginning of each session. The pointing coordinates and beam stability were checked on average every hour, and were deemed stable enough that no focus corrections were needed during the observing sessions. The cluster was observed for a total of 8.6 hours in stable conditions, and with an average opacity of τ 225 = 0.175 ± 0.05. Since standard LPSZ conditions required 9 hours of observations with an average zenith opacity at 225 GHz τ 225 = 0.1, we expect the SNR in our recovered profiles to fall slightly short of our goal.
The observations were performed as series of four raster scans of 8 × 4 arcminutes with 10 arcseconds steps between subscans, with angles of (0, 45, 90, 135) degrees with respect to the right ascension axis. The center of these scans was chosen at the coordinates reported for this cluster by the first ACT SZ catalog, i.e. (RA, Dec) J2000 = (02h15m28.8s +00 • 30'33.0") (Hasselfield et al. 2013).
The NIKA2 data were calibrated following the baseline procedure described in P20. They were then reduced using the most correlated pixels method from P20: common modes are adjusted on the time-ordered information (TOIs) by groups of most-correlated detectors outside of a 2 arcminutes diameter disk, and subtracted from the data as a correlated noise estimate. The filtering of large angular scales induced by this data processing is evaluated by computing a transfer function on a simulation including synthetic signal and correlated noise. This allows us to identify that the signal is well-preserved (with a transfer function greater than 0.8) down to wavenumbers of 0.5 arcmin −1 . The power spectrum of the residual correlated noise is computed on a noise map obtained from the half-differences of the individual scan maps. More details on the noise power spectrum and the transfer function are given in Appendix A. More details on data reduction and calibration can be found in P20, as well as in previous NIKA2 (and NIKA) SZ papers, e.g. Ruppin et al. (2018); Adam et al. (2015Adam et al. ( , 2016).

NIKA2 maps of the cluster
The resulting NIKA2 maps are presented in Fig. 1. In the left panel, corresponding to the 150 GHz map, we identify the cluster as the signal decrement in the center of the map, characteristic of the thermal SZ effect at frequencies lower than 217 GHz. The peak of this surface brightness decrement is detected with a 8.5σ significance. Solid black contours indicate significance levels greater than 3σ spaced by 1σ. The noise standard deviation maps used to evaluate these confidence levels are obtained by Monte Carlo realizations of noise generated from the power spectrum of residual correlated noise weighted by the associated weight map. We notice a high level of residual correlated noise, with large noise bands surrounding the SZ decrement of the cluster. Given this noise level, we assume the contribution of the kinetic SZ effect (kSZ, Sunyaev & Zeldovich 1980) to the signal to be negligible; hence, all further mention of the SZ effect will only refer to the thermal SZ effect.
We also note hints of strong contamination by point sources. Indeed, sub-millimeter or radio sources emit a flux that can compensate the SZ decrement and create "holes" in the apparent shape of the ICM. This seems to be the case in the NIKA2 150 GHz map, where we see positive point sources very close to the cluster, as well as possible holes1. This is particularly concerning in the case of this cluster because of its small spatial extension: the area with a signal-to-noise ratio greater than 3σ is ∼1 arcmin 2 , corresponding to ∼10 times the solid angle of the NIKA2 instrumental beam at 150 GHz. A single point source near the cluster can therefore have a great impact on the observed shape of the ICM.
In the right panel, corresponding to the 260 GHz map, we do not see any indication of SZ detection. The SZ signal, which is expected to be slightly positive in this frequency channel, is not detected given the noise level. For this cluster, the peak amplitude of the SZ signal of the cluster is expected to be ∼ 0.2 mJy/beam, which is ∼ 4 times smaller than the instrumental noise at the center of the map. However, this map allows us to clearly identify point sources very near the center of our cluster, indicating that a careful evaluation of the contamination by these sources must be performed before we can retrieve accurate information on the ICM.

X-ray observations of ACT-CL J0215.4+00309
ACT-CL J0215.4+0030 was observed by XMM-Newton for a total observation time of 37 ks. Data (OBSID: 0762290501) were retrieved from the archive and the standard procedures (see e.g. Bartalucci et al. 2017) were followed to produce cleaned and calibrated event files; apply the vignetting correction; produce background files; detect and exclude point sources; and subtract the background. The observation time after cleaning was 35/29 ks (MOS/pn).
The wavelet-smoothed image of the cluster shown in Fig. 2 indicates that the object may be somewhat disturbed. Deprojected, PSF-corrected gas density and temperature profiles were produced from the X-ray data as described in e.g. Pratt et al. (2010). In view of the likely perturbed nature of the object, we produced the density and temperature profiles both for the X-ray and the SZ peak, although the resulting profiles are not markedly  different. The density and temperature profiles, centred on the SZ peak, are shown in Fig. 2. The projected temperature profile, extracted directly from 2D spectra, is also shown for reference, but only the deprojected profile will be used in this paper. The hydrostatic total mass profile, obtained under the assumption of spherical symmetry, was derived using the Monte Carlo procedure described in detail in Démoclès et al. (2010) and Bartalucci et al. (2018). This profile is shown in Fig. 8.

Contamination by point sources
As discussed in §3.1, a precise estimation of the contamination by point sources is crucial in order to be able to retrieve accurate properties of the cluster via the SZ effect. This is because the flux of point sources can partially or fully compensate the SZ decrement and disturb the apparent shape of the cluster. In the case of ACT-CL J0215.4+0030, this effect is even more important due to the fact that the cluster is faint (with a peak surface brightness lower than 1 mJy/beam at 150 GHz) and has a small spatial extension compared to the NIKA2 camera resolution. In this section, we investigate the origin of the contamination and detail the procedure used to estimate the amplitude of this contamination in the NIKA2 150 GHz map.

Identification of point sources
The SZ decrement can be affected by positive point sources that are either foreground sources, background ones, or sources that belong to the cluster. In any case, they can be dusty sub-millimeter galaxies (SMGs), with stronger emission at frequencies higher than the those covered by the NIKA2 bandpasses2, or radio sources, emitting mostly at lower frequencies. The former are easier to identify in NIKA2 SZ observations, as their fluxes are stronger in the 260 GHz map where we expect a low contribution of the SZ signal (see §3.1.3), while the latter often require data from external datasets to be identified, especially if they cannot be seen directly in the SZ decrement.
In the case of ACT-CL J0215.4+0030, at least four sources are detected with a SNR greater than 3 in the NIKA2 260 GHz map (top right panel of Fig. 1). Their fluxes in this band appear to be higher than in the 150 GHz map, promoting SMGs rather than radio sources. Cross-matching of their positions with sources from the Herschel Stripe-82 Survey catalog (HerS, Viero et al. 2014) allows us to confirm this hypothesis, as well as to identify a fifth SMG in the north-eastern part of the cluster. Fig. 3 shows a composite multi-wavelength map of the cluster region. The green circles are centered on the positions of the five SMG identified in the HerS catalog, and the radius of each circle correspond to the full width at half-maximum (FWHM) of the SPIRE (Spectral and Photometric Imaging Receiver) instrumental beam in the 250 µm band, which has the best resolution of all three bands. The orange-shaded areas represent the SNR of the NIKA2 260 GHz map where it is greater than 3σ. We see the agreement between NIKA2 and SPIRE for the positions of the three sources in the most central part of the cluster -from left to right, SMG1, SMG2 and SMG4. In the north-eastern sector, we see SMG3, the source identified in the HerS catalog with no counterpart with SNR > 3σ at 260 GHz in NIKA2. In the southern region, two sources seem to be resolved in NIKA2 at 260 GHz, while only one source (hereafter S5) is identified in the HerS catalog. Comparing the positions of the identified sources for the two instruments shows that the source identified in HerS is the weakest of the two seen by NIKA2. This complicates the estimation of the contamination of the SZ signal by these sources, as there is no clear way to determine if the flux of S5 in the SPIRE bands comes from a single source or from a combination of the two. The estimation of this contamination will therefore not be computed by following the same procedure as with SMG1-4, and will be detailed in §4.3.

Estimation of the sub-millimetric contamination
To estimate the contamination of each source in the SZ signal, we need to know their fluxes in the NIKA2 150 GHz band. In this section, we describe the process used to do so, based on the fit of the Spectral Energy Distribution (SED) of each source.

SED adjustment
Each source is fitted in the NIKA2 260 GHz map as a 2D Gaussian with fixed FWHM = 12.5", which is the reference beam pattern with which the maps are calibrated (as described in P20). The amplitude of the Gaussian gives us the flux of the source at the reference frequency of 260 GHz. We then take the value of the flux of the sources in each band of Herschel's SPIRE instrument, i.e. 250, 350 and 500 µm (1200, 860 and 600 GHz respectively), in the HerS catalog. The SED of each source is adjusted using these three fluxes, combined with the measurement of their flux in the NIKA2 260 GHz band. We use a modified blackbody spectrum model, where the SED can be written as: where B ν (T) is the black-body spectrum at temperature T, and A 0 , the amplitude of the SED at the frequency ν 0 = 500 GHz, β, is the spectral index of the dust, and T its effective temperature, The SED of each source is fitted using a Monte Carlo Markov Chains (MCMC) analysis (and the emcee python package, Foreman-Mackey et al. 2013) in order to get a complete sampling of the posterior distribution. We emphasize the absence of sub-millimetric information on these sources at higher frequencies, e.g. from observations of the cluster region with the PACS instrument (Photodetector Array Camera & Spectrometer, Poglitsch et al. 2010), which were used in previous NIKA and NIKA2 studies of other clusters (Adam et al. 2016;Ruppin et al. 2018). We are therefore strongly affected by the degeneracy between the three parameters of the SED (see e.g. Désert et al. 2008;Magnelli et al. 2012;Smith et al. 2013;Berta et al. 2016), and all three of them cannot be left completely free. We choose to lift this degeneracy by linearly adjusting A 0 on the data. Since the spectral index and temperature of the dust are also degenerated, the prior knowledge of the spectral index β is given by a normal distribution, β ∼ N (2, 0.5), as suggested by SED measurements of large samples of galaxies (see e.g. Magnelli et al. 2012). Flat priors are given for the temperature, i.e. 0 < T < 50 K.
At each step of the MCMC, we apply a color correction to the SPIRE fluxes by interpolating pre-existing measurements3, and to the NIKA2 260 GHz flux (see §8.1.2 of P20). As an example, we show the SED of SMG1 in the left panel of Fig. 4. The data points used to constrain the SED (SPIRE + NIKA2 260 GHz) are shown, as well as the best-fitting SED and the 1σ and 2σ confidence intervals on this result.

Inference of the 150 GHz flux
The SED adjustment outputs a sampling of the posterior probability distribution in the (β, T) parameter space for each source. Each sample of this distribution is then used to compute a SED through Eq. 3. Each SED is extrapolated to compute a flux value at 150 GHz, and a color correction is applied to estimate the value of the contamination in the NIKA2 150 GHz map, as described in P20. Kernel density estimation is then used on the sample of fluxes to compute a probability density function (PDF) for the amplitude of the contamination of each source. Combining this and the results of the 260 GHz fit, we have a precise knowledge of the position of each source in the NIKA2 maps, and have a PDF for its flux in the NIKA2 SZ map. The results of this computation for SMG1 are shown in the right-hand panel of Fig. 4. The SED results illustrated in the left-hand panel are extrapolated at 150 GHz and color-corrected to get a distribution of fluxes, which is used to compute the probability distribution function for the flux of the source.

Results
We report in Table 1 the positions and fluxes of the six sources contaminating our SZ signal. The last column reports the 150 GHz flux inferred from the extrapolation of the SED of each source in the NIKA2 150 GHz bandpass (Adam et al. 2018a, P20), except for the last two sources. We see that these fluxes can be as high as 0.74 mJy, while the peak SZ flux of the cluster in the NIKA2 map is below 0.8 mJy. This calls for an extreme carefulness when accounting for this contamination in our analysis of the SZ signal.

Additional considerations
Radio contamination. One of the sources (SMG2) also exhibits emission in the radio wavelengths. It is detected in the latest FIRST catalog (Helfand et al. 2015) with a 2.22 ± 0.10 mJy flux density at 1.4 GHz. The lack of coverage of the cluster region in other radio frequencies prevents us from fitting the radio part of this source's SED. We resort to modeling it as a power law F(ν) = F(ν 0 ) × (ν/ν 0 ) α , with a spectral index α = −0.7 ± 0.2, as found to be a good description of most radio galaxies (Condon 1984). The extrapolation of this power law in the NIKA2 bandpass gives an estimation of the flux of the galaxy due to radio emission, F radio (150 GHz) = 83 +127 −50 µJy. This contribution is added to that    computed from the sub-millimeter prediction to infer the total flux of the source at 150 GHz, although it only accounts for a small fraction of the total.
Double southern source. As discussed in 4.1, the complex structure in the southern part of the map appears in NIKA2 to be two sources, with only one identified in the HerS catalog. We label these sources S5 and S6 in Table 1. Although the positions matching seem to indicate that the source present in the HerS catalog is the faintest of the two seen by NIKA2, we cannot be sure that it is the case. We choose to measure the fluxes of these two sources in the NIKA2 150 GHz map directly, as they are far enough from the cluster that no SZ signal is expected. The recovered fluxes of the two sources in the NIKA2 150 GHz map, as well as their position in this map, are reported in Table 1. They will be subtracted from the 150 GHz map in order to avoid a bias in the fit of the SZ signal (see §5).

ICM reconstruction by MCMC analysis
In this section, we present the procedure used to derive thermodynamical properties of the ICM from the NIKA2 map. This is done using the NIKA2 SZ pipeline, most of which is described in Ruppin et al. (2018). In this study, this pipeline is adapted in order to better account for the contamination by point sources described in §4.

Pressure profile
As discussed earlier, the amplitude of the SZ effect -and therefore the surface brightness of a cluster observed in the millimeter domain -is proportional to the electron pressure integrated along the line-of-sight (Eq. 2). Millimeter maps of a cluster can therefore be used to constrain the distribution of pressure in the ICM. Assuming a spherical symmetry, this distribution can be described by a radial pressure profile of the ICM. This pressure profile is integrated along the line of sight to compute a map of the Article number, page 7 of 14 Compton parameter of the cluster. We choose to model the pressure distribution with a generalized Navarro-Frenk-White profile (gNFW, Nagai et al. 2007) : where b and c are respectively the external and internal slope of the profile, r p is a characteristic radius of transition between the two regimes, a is the steepness of the transition, and P 0 is a normalization constant.

MCMC analysis
We use MCMC sampling to fit the pressure profile of ACT-CL J0215.4+0030. At each step of the MCMC, a pressure profile is computed using Eq. 4 and integrated along the line of sight (Eq. 2) to get a Compton parameter y profile. This profile is projected on the same pixelated grids as the NIKA2 map to compute a Compton parameter map to be compared with the data. The resulting y-map is convolved with the NIKA2 beam, i.e. a 2D gaussian function with FWHM = 18.5". The y-map is centered on the coordinates of the peak in SZ surface brightness in the NIKA2 150 GHz map. The y-map is then converted to surface brightness units using a conversion coefficient C conv . This coefficient depends on the NIKA2 150 GHz bandpass, but also on the atmospheric opacity, and the shape of the SZ spectrum. Therefore, the coefficient is adjusted in our fit with a Gaussian prior, with a standard deviation of 10% in order to take into account the uncertainty on the absolute calibration of the NIKA2 data.
In order to deal with the point source contamination, rather than using the fluxes obtained by SED extrapolation and subtracting the sources in our NIKA2 150 GHz map, we fit each source simultaneously with the pressure of the ICM. To do so, 2D Gaussian functions corresponding to the NIKA2 150 GHz beam pattern B 150 are added to the NIKA2 model. Their amplitudes are left as free parameters. A prior on the flux of each source is given by the probability density obtained from the SED extrapolation (see §4.2). This has the advantage of naturally taking into account the uncertainty on the extrapolated source fluxes. Sources S5&6, for which we could not fit and extrapolate a SED, are directly subtracted from the data using their fluxes and positions measured in the NIKA2 150 GHz map (see §4.3). Since they are far from the cluster (outside R 500 ), this reduces the number of parameters of our MCMC analysis without altering the quality of the recovered profiles. The resulting surface brightness map is then convolved with the transfer function to account for filtering effects due to data processing. We also ran the joint fit with flat priors on the point sources fluxes in order to ensure that our results were prior-independent and that the fluxes recovered by the joint fit without prior were compatible with those extrapolated from the SED adjustment of each source (see §5.3).
Our ability to constrain the pressure profile in the outskirts of the cluster, represented in our model by the external slope of the pressure profile b, is limited by the angular coverage of NIKA2. Constraints on the large-scale emission can be obtained by using the integrated SZ signal within an aperture of radius R 500 : where D A is the angular diameter distance at the cluster redshift. The integrated Compton parameter was measured in the ACT survey, D 2 A Y ACT 500 = (4.07 ± 1.13) × 10 −5 Mpc 2 (Hasselfield et al. 2013, hereafter H13). We take this into account in our likelihood. For each set of parameters sampled in our MCMC, the value of Y 500 is computed and compared to that of the ACT survey.
To summarize, at each iteration of the MCMC, the model map is computed from the following set of parameters ϑ: The probability that these parameters describe our data is obtained by combining our prior knowledge of the data with the likelihood that compares the model M with the data D: where C the noise covariance matrix, which is evaluated by computing the covariance of Monte-Carlo noise realizations generated from the correlated noise power spectra (see Appendix A, as well as previous NIKA (2) papers, e.g. Adam et al. 2016;Ruppin et al. 2018). The MCMC analysis is performed using the emcee python package (Foreman-Mackey et al. 2013). The convergence of the chains is monitored using theR test of Gelman & Rubin (1992). The sampling is performed using 30 walkers. A burn-in time of 400 iterations is removed from the chains, leaving 4 × 10 5 points in the final posterior distribution.

Consistency of point sources flux estimations
Among the parameters evaluated by our MCMC reconstruction of the ICM are the fluxes of the four point sources near our cluster. We compare these measurements with the ones obtained by SED extrapolation described in §4. The results are found to be compatible, but since we used the SED extrapolation results as priors for the ICM reconstruction, the two measurements are not strictly independent. In order to be able to run the comparison, we repeat our MCMC reconstruction of the ICM with uninformative priors on the flux of each source. The posterior distribution becomes independent of the SED extrapolation measurement, and the two estimation of point source fluxes can be compared. The results are shown in Fig. 5. We see that the results of both estimations of the point sources fluxes are compatible within 1σ. This gives confidence in our estimation of the fluxes, and therefore of the SZ signal in the contaminated regions of the map. Moreover, although this shows that no information is gained from using the SED extrapolation as priors for the joint ICM+point sources fit, the priors greatly reduce the time needed for the MCMC to converge, reducing the available sampling volume in the parameter space.

Results
The MCMC procedure described in the previous section is used to find the parameters that best fit the NIKA2 150 GHz map as the sum of the SZ signal for an ICM described by a gNFW pressure profile and of contamination by 4 point sources, convolved by the NIKA2 instrumental response and by the data processing transfer function. The 2D model and residuals are shown in Fig. 6. Since no high-SNR structures are seen in the residuals map -save for the western structure at the edge of the map, well outside the cluster -, we can say that there is no evidence for substructures or departure from sphericity in the NIKA2 data. In addition, Fig. 7 shows the surface brightness profiles of the NIKA2 map and of the model. We see no significant offset between the two profiles, further indicating that the gNFW + point sources model is a good description of our data. We insist on the fact that this figure is only an illustration of the compatibility between the data and model in 1D, and that the fit was performed in the NIKA2 map, not on the radial profile.

Thermodynamic profiles
The pressure profile obtained from our MCMC adjustment is presented on the top left panel of Fig. 8. The blue line marks the best-fitting gNFW profile. The error envelopes are obtained by computing a pressure profile for each set of sampled parameters after a burn-in cutoff and computing the dispersion of these profiles.
We compare this pressure profile with that inferred from the combination of X-rays density and temperature profile (Fig. 2). The comparison between these two profiles is interesting because they represent two independent measurements of the pressure distribution in the ICM in the specific case of a distant cluster. The X-ray only data is superimposed in white on the top left panel of Fig. 8. The two measurements are in agreement within the error bars. The pressure recovered by NIKA2 appears to be higher than the X-ray only pressure in the central region of the ICM, but this effect is not significant given the error bars on both profiles.
Other thermodynamic quantities can be derived by combining this pressure profile with the density profile obtained from X-ray data without spectroscopic information. Namely, we can compute the temperature T e (r), entropy K e (r) and hydrostatic mass M HSE (< r) profiles through k T e (r) = P e (r) n e (r) , K e (r) = P e (r) n −5/3 e (r), and through the equation of hydrostatic equilibrium: where m p is the proton mass, µ the mean molecular weight of the gas, and G the gravitational constant. We use the pressure profile recovered from the NIKA2 data in combination with the density profile from XMM-Newton observations. The density profile is interpolated by a power law in order to compute the value of the density at any given radius. Fig. 8 shows the constraints put on the temperature, entropy and hydrostatic mass profiles (in blue) that can be compared with the same profiles inferred using X-ray only data with spectroscopy (in white). As for the pressure, the profiles exhibit a strong agreement, illustrating the complementarity of high-resolution X-ray and SZ data.
The agreement between the thermodynamic profiles recovered with NIKA2+XMM and XMM-only observations is a great assessment of the possibility to retrieve quality information on the ICM with NIKA2. Indeed, while the cluster was observed for comparable times with the two instruments, this compatibility shows that measurement of great quality can be performed by combining high-resolution SZ and X-ray data, minimizing our reliance on time-expensive X-ray spectroscopy measurements.
Combining high angular resolution SZ and X-ray data also enables a better resolution on the temperature profile than the one obtained through X-ray spectroscopy only. As we can see in Fig. 8, extrapolating the inner slope of the XMM-only temperature profile points toward a core temperature value that is significantly lower than that obtained with the combination of NIKA2+XMM. The error bars on the temperature profile are also smaller on average for the NIKA2+XMM profile. Consequently, the entropy and mass profiles obtained from the SZ+X-ray combination display smaller error bars, leading to a more precise measurement of the thermodynamical properties of the ICM.
The thermodynamic profiles give us access to information on the dynamical state of the ICM. The flatness of the pressure profile in the inner part of the cluster indicates a disturbed core. The central value of the entropy profile (K e,core 200 keV · cm 2 ) also points toward a non-cool core cluster (see e.g. Hudson et al. 2010). We compare the deprojected pressure profile with those of A10 in Figure 9. We see that the pressure profile is not well described by the universal pressure profile of A10, especially in the inner parts of the cluster. However, the ICM of ACT-CL J0215.4+0030 seems to be well described by the mean pressure profile of disturbed clusters in the REXCESS sample (A10). This further points towards disturbed core dynamics of the ICM. Similar conclusions have been drawn by Ricci et al. (2020), who used NIKA2 to image another distant and low-mass cluster.  Fig. 7. Projected radial profiles evaluated in concentric annuli centered on the SZ peak, with widths equal to the NIKA2 instrumental FWHM at 150 GHz. The white points show the radial profile of the NIKA2 SZ signal with 1σ errors. The red curve correspond to the radial profile of our full SZ + point sources model, while the blue curve is the profile of the SZ signal alone. In each case, the envelopes are 1σ and show the dispersion in the posterior distribution sampled by our MCMC. The dotted vertical line shows the limit of the region in which the SNR on the surface brightness profile is 3σ. The dashed black line shows the angle subtended by R 500 as reported in Table 2. We emphasize that this is only a comparison between the angular radial profile and the best fit on the 2D map, and that the fit is indeed performed in 2D -see §5.2.

Integrated quantities
For low angular resolution surveys, the thermodynamic profiles of the ICM of high-redshift clusters cannot be resolved. There-fore, the scaling relation used to compute the mass of a cluster links its integrated SZ signal Y to the mass enclosed within a given radius. We choose the radius R 500 , corresponding to the radius enclosing an average density 500 times greater than ρ c (z), the critical density of the Universe at the redshift of the cluster. Its value can be computed as the radius for which the overdensity contrast δ c is equal to 500, i.e. by solving The recovered value is R 500 = 810.1 ± 41.9 kpc, in agreement with the ACT measurement of H13. The integrated SZ signal inside this radius, Y 500 via Eq. 5: The hydrostatic mass of the ICM enclosed within a radius of R 500 is obtained through Eq. 8: These results are shown in Table 2. For comparison purposes, we also show two measurements of radius and mass for this cluster: from the ACT galaxy clusters catalog H13, where R 500 and M 500 are computed from the match-filtering detection of clusters in the ACT maps assuming a A10 pressure profile. and from the standalone analysis of XMM-Newton data. We see that uncertainty on our measurement of Y 500 is reduced by a factor of 3 compared to the ACT measurement, indicating a significant gain in precision obtained from the high resolution observations. The last line of Table 2 reports the measurement of the hydrostatic mass of the cluster obtained by combining the SZ pressure profile and the X-ray density (Eq. 8  For the other profiles, it shows the profile obtained by combining the maximum likelihood pressure profile from NIKA2+ACT with the density fron XMM-Newton. The blue envelopes show the 1σ and 2σ confidence intervals on these profiles. The white data points show the profiles obtained by combination of XMM-Newton data with and without spectroscopy with 1σ errors. The dotted black line shows the limit of the region in which the SNR on the NIKA2 surface brightness profile is greater than 3. The grey-shaded area shows the region in which the profiles are unconstrained by SZ data, i.e. beyond the measurement of R ACT 500 . masses obtained via the Y 500 − M 500 scaling relation used to build the ACT catalog of H13. The error bar on the NIKA2+XMM mass measurement is smaller than that of the ACT catalog, even though the latter is underestimated as it does not include the uncertainty on the scaling relation regression (see Table 8 of H13). Our mass measurement is also compatible with the mass obtained from the standalone X-ray analysis, although the latter is slightly lower.

Summary and conclusions
This paper presented the first analysis of an individual cluster in the NIKA2 SZ large program sample with standard data quality. This analysis faced several challenges. The target, ACT-CL J0215.4+0030, is a cluster of low mass and high redshift, making it a faint target (less than 1 mJy/beam at its peak) and one of the most compact objects of the NIKA2 LPSZ sample. The cluster was observed with NIKA2 for a time estimated sufficient to reach a significance of 3σ at θ 500 on the surface brightness profile, which we fall slightly short of with 3σ at 0.7 × θ 500 . Moreover, the NIKA2 data are strongly contaminated by point sources. This contamination greatly affects the SZ signal because of the small angular size of the cluster, but also because of the strong Article number, page 11 of 14 10 −2 10 −1 10 0 R/R 500 10 −2 10 −1 10 0 10 1 10 2 Normalized pressure profile P/P 500 A10 universal profile A10 cool core A10 disturbed ACTJ0215 (1σ) Fig. 9. Comparison of the deprojected pressure profile obtained from the NIKA2 data with the universal pressure profiles from A10. ACT-CL J0215.4+0030 exhibits a pressure profile similar to those identified as disturbed in A10 (dashed black line).
fluxes of point sources. The possibility to mask the point source contamination, in case no external data is available for spectrum fitting, will be the subject of a future study. Interferometric followups using the Northern Extended Millimeter Array (NOEMA) are also ongoing, allowing to measure the point source contamination directly in the uv plane (as in e.g. Gobat et al. 2019).
In spite of these challenges, we were able to extract the thermodynamical properties of the ICM. The point source contamination was accounted for in a multi-wavelength analysis, used in a joint fit of the pressure distribution of the ICM and of the point source contamination. This way of dealing with the contamination allowed us to fully take into account the uncertainty on the fluxes of point sources in our MCMC analysis. The result of the joint fit gave us access to the pressure profile of the cluster. This pressure profile was compared with the one obtained from the standalone analysis of XMM-Newton data. The results were found to be compatible. The combination of our NIKA2 pressure profile and of the density profile obtained from XMM-Newton also allowed us to explore additional thermodynamical properties of the cluster.
Our conclusions are as follows.
-The pressure profile of ACT-CL J0215.4+0030 is found to be compatible with the profile of disturbed clusters found in A10, but not with the universal profile from the same reference, indicating a disturbed core. Other thermodynamical properties of the ICM (e.g. its core entropy) also point towards the cluster having a disturbed core. -The thermodynamical properties obtained from the combination of NIKA2 and XMM-Newton are very competitive with those obtained using X-ray spectroscopy. As the exposure time needed to be able to extract spectroscopic information -and therefore a temperature profile -from X-ray observations is much higher than the time needed to be able to extract a density profile, and since this time increases steeply with redshift, this means the combination of X-rays and SZ is very well adapted for the measurement of thermodynamical properties of the ICM at high-z. -The NIKA2 observations of this cluster allowed us to improve the precision of the mass of the cluster, both from previous knowledge from the ACT survey and the Y 500 − M 500 scaling relation from A10, and from X-ray only measurements.
Since this analysis deals with the "worst-case scenario" for the NIKA2 SZ large program clusters, we can expect comparable or better precision for most of the clusters of the LPSZ. This is therefore a promising indication of our ability to use NIKA2 capabilities to achieve a precise calibration of the tools needed for cluster cosmology using SZ-detected catalogs of galaxy clusters. function The noise levels in our NIKA2 maps and the filtering due to our data reduction process need to be known for our estimation of thermodynamical properties of the ICM. The power spectrum of the residual noise is estimated on a null map, often referred to as "jackknife" maps. It is presented for the 150 GHz map in the top pannel of Fig. A.1. We see that the power spectrum is not flat, hence there is large-scale correlated noise in our maps. The pixelby-pixel covariance matrix of the noise is therefore computed as the covariance of 10 5 Monte-Carlo noise realizations from this power spectrum.
The filtering due to data processing is computed by applying the complete noise-removal procedure to simulated signal. The transfer function for our data analysis procedure is computed as the ratio between the power spectra of the input simulated map and of the pipeline output. The input simulation is computed as a cluster model with a A10 pressure profile with the mass and redshift of ACT-CL J0215.4+0030, plus a white noise realization. By doing so, we ensure that all angular scales are represented in our input signal and that the transfer function is representative of the full signal filtering. It is presented in the bottom panel of Fig. A.1. For angular scales higher that 0.5 arcmin −1 , it is flat and shows a filtering of less than 20%. It is used as a filter in our forward-modelling approach, described in §5 so that our model undergoes the same filtering as the data it is compared to. More details can be found in previous NIKA2 (and NIKA) SZ papers, e.g. Ruppin et al. (2018); Adam et al. (2015Adam et al. ( , 2016.  (bottom) of our NIKA2 150 GHz data. The steepness of the power spectrum indicates large-scale correlated noise in our maps, which is accounted for in our analysis by the computation of a noise covariance matrix. The transfer function, evaluated on simulations, quantifies the filtering our data went through. We see that angular scales are correctly recovered (with a transfer function above 80%) for k > 0.5 arcmin −1 . For each panel, the grey-shaded regions represent the NIKA2 field of view (left) and instrumental FWHM (right).