Galaxy Cluster Sparsity Data Analysis

Cosmological constraints on the cosmic matter density Ωm, the amplitude of matter density fluctuations on the 8 Mpc/h scale σ8, and the reduced Hubble constant h have been derived in Corasaniti, Sereno & Ettori (2021) from measurements of the average galaxy cluster sparsity, gas mass fraction and BAO (see Fig. 1).

The data used in this analysis are publicly available and presented in several dedicated publications. Here, we simply provide a unique formatted compilation for users who might be interested in inferring cosmological constraints from the same datasets used in our study.

Galaxy Cluster Sparsity

Average sparsity estimates were obtained using weak-lensing mass estimates at M200 and M500 from the Literature Catalogs of Lensing Clusters (LC2) version 3.8 (Sereno 2015). In addition, we have used the mass estimates from the clusters from the HSC-XXL sample (Umetsu et al. 2020).

Given the mass estimates M200 and M500 we have computed the sparsity of each cluster and the uncertainty as:

    \[ \begin{split} s_{200,500} & =\frac{M_{200c}}{M_{500c}}\\ \sigma_{s_{200,500}} & =s_{200,500}\sqrt{\left(\frac{\sigma_{M_{200c}}}{ M_{200c}}\right)^2+\left(\frac{\sigma_{M_{500c}}}{M_{500c}}\right)^2-2r\frac{\sigma_{M_{200c}}}{M_{200c}}\frac{\sigma_{M_{500c}}}{M_{500c}}}   \end{split} \]

with r the correlation coefficient conservatively set to r=0.9.

Here the data file: Selected_LC2_single_HSC_XXL_clusters.dat

If you use the sparsity estimates in a publication or proposal please cite:

  • Corasaniti, Sereno & Ettori (2021)

If you use only the mass estimates please cite the appropriate publication: Umetsu et al. (2020) for the XXLSCC clusters and Sereno (2015) for the others.

Galaxy Cluster Gas Mass Fraction

Gas mass fraction measurements were obtained from several analyses of the temperature and density profile of X-ray clusters from:

  • Eckert et al., A&A, 621, A40 (2019)

File: Cluster_fgas_Eckertetal2019.dat

  • Ettori et al., A&A, 524, A68 (2010)

File: Cluster_fgas_Ettorietal2010.dat

  • Ghirardini et al., A&A, 604, A100 (2017)

File: Cluster_fgas_Ghirardinietal2017.dat

Fig.1: 68% and 95% credible regions in the Ωm8 plane from the joint analysis of average sparsity, gas mass fraction and BAO data (solid lines) compared to the results of the Planck-SZ cluster counts (blue-light blue filled contours), the Planck primary CMB analysis (red and yellow filled contours) and the KV-450 lensing clustering data (beige-light beige filled contours).