CHEX-MATE: towards a consistent universal pressure profile and cluster mass reconstruction

TL;DR

This work tackles the problem of deriving a universal pressure profile (UPP) for the intracluster medium by jointly inferring the UPP and individual cluster masses $M_{500}$ from combined X-ray and tSZ data. The authors implement a gNFW-based model for the scaled pressure distribution $P(r)=P_{500}(M_{500},z)\mathbb{P}(x)$ with $x=r/R_{500}$, allowing the mass-scaling exponent $\delta$, intrinsic scatter $\sigma_{int}(x)$, and a cross-calibration factor $\eta_T$ between X-ray and tSZ pressures to vary within a Bayesian framework. They perform end-to-end joint fits to a CHEX-MATE DR1 subsample of 24 clusters, obtaining a self-consistent UPP with $\eta_T\approx1.05$ and a mass scale that remains close to dynamical priors while correlating with MMF3 masses; allowing $M_{500,i}$ to vary reduces biases in the inferred UPP and propagates mass uncertainties into the UPP. The results demonstrate the critical need to couple the UPP shape, its mass scaling, and individual masses for robust tSZ cosmology analyses, and lay groundwork for applying the method to the full CHEX-MATE sample and for incorporating relativistic tSZ corrections in future work.

Abstract

In a self-similar paradigm of structure formation, the thermal pressure of the hot intra-cluster gas follows a universal distribution once the profile of each cluster is normalised based on the proper mass and redshift dependencies. The reconstruction of such a universal pressure profile requires an individual estimate of the mass of each cluster. In this context, we present a method to jointly fit, for the first time, the universal pressure profile and individual cluster $M_{500}$ masses over a sample of galaxy clusters, properly accounting for correlations between the profile shape and amplitude, and masses scaling the individual profiles. We demonstrate the power of the method and show that a consistent exploitation of the universal pressure profile and cluster mass estimates when modelling the thermal pressure in clusters is necessary to avoid biases. In particular, the method, informed by a cluster mass scale, outputs individual cluster masses with same accuracy and better precision than input masses. Using data from the «Cluster HEritage project with XMM-Newton: Mass Assembly and Thermodynamics at the Endpoint of structure formation», we investigate a sample of $\sim 25$ galaxy clusters spanning mass and redshift ranges of $2 \lesssim M_{500}/10^{14} \; \mathrm{M}_{\odot} \lesssim 14$ and $0.07 < z < 0.6$.

Figures (13)

• Figure 1: Pressure profiles for the 28 galaxy clusters investigated in this work reconstructed from XMM-Newton (orange) and Planck (blue) data. XMM-Newton data profiles below $r/R_{500}=0.03$ are shaded and these pressure bins are not considered in our analysis (see text).
• Figure 2: Normalised data pressure profiles and best-fit gNFW models, and their relative difference. Top: coloured profiles show the individual data pressure profiles (from Fig. \ref{['fig:pressureprofs']}) for the 24 clusters normalised by the best $P_{500, i}$ and $R_{500, i}$ when fitting the individual masses with dynamical mass estimates as priors. Green, red, and blue correspond to the fits assuming respectively $\delta=2/3$, $\delta=2/3+0.12$, and $\delta$ as a free parameter. Bottom: in grey data pressure profiles normalised by $P_{500, i}$ and $R_{500, i}$ considering the masses fixed in the fit and setting them to the dynamical mass estimates. The solid black profile in each panel indicates the best-fit gNFW profile for that case, with the dotted profiles showing the fitted intrinsic scatter $\mathbb{P}(x) \exp[\pm \sigma_{\mathrm{int}}(x)]$. The dashed profiles in the top (bottom) panels correspond to the best-fit gNFW for the mass fixed (fitted) cases.
• Figure 3: Masses obtained from the joint fit to data by taking Gaussian priors centred on dynamical estimates. We compare the results to dynamical (top) and MMF3 (bottom) mass estimates. The colour scheme is identical as in Fig. \ref{['fig:dynamicalfit']} for the different values of $\delta$. Uncertainties of fitted masses are calculated as the standard deviation of the marginalised posterior distribution for each cluster mass parameter.
• Figure 4: Scatter of pressure profiles for the 24 clusters in our sample. Shaded area indicates 16th to 84th percentiles for the intrinsic scatter profile fitted to data pressure profiles ($\delta$ free case). The intrinsic scatter may not be reliably constrained beyond $x \sim 0.4$. The dashed line shows the scatter of the individual normalised profiles with respect to the best-fit gNFW model. Statistical uncertainties of the individual pressure profiles are indicated with crosses and circles for the pressure bins corresponding to XMM-Newton and Planck data, respectively. All scatters are given in $P_{500} \mathbb{P}(x)$ units.
• Figure 5: Distribution of the 24 best-fit $M_{500}$ obtained from the thermal pressure profile fits when $\eta_T$ is let free in the fit. We present the average mass along the sample for fixed UPPs from the literature with circles and diamonds for the cases where $\eta_T$ is let free in the fit and fixed to $\eta_T = 1.05$, respectively. We also give the $M_{500}^{\mathrm{fit}}$ distributions and average masses of the sample obtained from the joint fits of the UPP and individual cluster masses, with $\eta_T$ and $\sigma_{\mathrm{int}}$ free in the fits. Different colours correspond to results obtained with the parameters specified in Table \ref{['tab:uppliterature']} and our three results assuming different $\delta$ values. The horizontal dashed line indicates $8.5 \times 10^{14}$ M$_{\odot}$ as a reference, with the shaded area corresponding to a $10\%$ dispersion around this value.