X-ray galaxy clusters abundance and mass temperature scaling

Abstract

The abundance of clusters of galaxies is known to be a potential source of cosmological constraints through their mass function. In the present work, we examine the information that can be obtained from the temperature distribution function of X-ray clusters. For this purpose, the mass-temperature (M − T ) relation and its statistical properties are critical ingredients. Using a combination of cosmic microwave background (CMB) data from Planck and our estimations of X-ray cluster abundances, we use Markov chain Monte Carlo (MCMC) techniques to estimate the ΛCDM cosmological parameters and the mass to X-ray temperature scaling relation simultaneously. We determine the integrated X-ray temperature function of local clusters using flux-limited surveys. A local comprehensive sample was build from the BAX X-ray cluster database, allowing us to estimate the local temperature distribution function above ∼1 keV. We model the expected temperature function from the mass function and the M − T scaling relation. We then estimate the cosmological parameters and the parameters of the M − T relation (calibration and slope) simultaneously. The measured temperature function of local clusters in the range ∼1-10 keV is well reproduced once the calibration of the M − T relation is treated as a free parameter, and therefore is self-consistent with respect to the ΛCDM cosmology. The best-fit values of the standard cosmological parameters as well as their uncertainties are unchanged by the addition of clusters data. The calibration of the mass temperature relation, as well as its slope, are determined with ∼10% statistical uncertainties. This calibration leads to masses that are ∼75% larger than X-ray masses used in Planck.

Cluster counts: Calibration issue or new physics?

“…where A T −M is the normalization parameter, ∆ is the density contrast chosen for the definition of a cluster, expressed with respect to the total background matter density 1 of the Universe at redshift z, and M ∆ is the mass of the cluster according to the same definition. We note that the 2/3 exponent is consistent with the existing data (Ilić et al 2015). The dispersion is taken into account in the calibration according to the earlier remark; more details on this procedure can be found in Ilić et al (2015).…”

“…We note that the 2/3 exponent is consistent with the existing data (Ilić et al 2015). The dispersion is taken into account in the calibration according to the earlier remark; more details on this procedure can be found in Ilić et al (2015). Relation (7) can then be used to determine the integrated temperature function and becomes:…”

“…Given the above tension, obtaining a reliable mass proxy with a well-determined calibration has become a critical issue in clusters studies and has been the focus of many works in the recent literature (Wang et al 2016;Planck Collaboration VI 2018). Ilić et al (2015) used a different approach in the context of the ΛCDM model, treating A T −M as an additional free parameter to be determined, and constrained it using MCMC techniques with a robust local X-ray clusters sample and Planck CMB measurements as data. In the present work, we follow the same approach and add A T −M as a free parameter in the analysis, in a more general cosmological context.…”

“…We use in our analysis the sample of X-ray selected clusters of Ilić et al (2015), where a complete description of the catalogue can be found. We summarize its main characteristics here.…”

Calibrating the Planck Cluster Mass Scale with Cluster Velocity Dispersions

“…The comparison of Planck and CARMA-8 measurements by Rodriguez-Gonzalvez et al (2017) shows that this tension is not due to any bias in the Planck flux measurements. Moreover, a recent analysis of the local X-ray cluster temperature function finds that the same mass bias value is needed to reconcile the X-ray cluster abundance with the CMB cosmology (Ilic et al 2015).…”