The extended ROSAT-ESO Flux Limited X-ray Galaxy Cluster Survey (REFLEX II) IV. X-ray Luminosity Function and First Constraints on Cosmological Parameters

TL;DR

REFLEX II constructs the local X-ray luminosity function from a large, well-defined cluster sample and compares it to cosmological models to constrain Ω_m and σ_8. The analysis combines a mass-function framework with an L_X–M scaling relation, incorporating intrinsic scatter, measurement errors, and a detailed survey selection function. While no strong evolution of the XLF is found up to z ≈ 0.4, the resulting Ω_m ≈ 0.29 and σ_8 ≈ 0.77–0.80 depend sensitively on the scaling relation calibration, particularly its slope. The work finds good agreement with PLANCK cluster results but tension with PLANCK CMB constraints, highlighting the critical role of scaling-relations calibration for cluster-based cosmology and the value of REFLEX II in tightening parameter estimates over previous surveys.

Abstract

The X-ray luminosity function is an important statistic of the census of galaxy clusters and an important means to probe the cosmological model of our Universe. Based on our recently completed REFLEX II cluster sample we construct the X-ray luminosity function of galaxy clusters for several redshift slices from $z = 0$ to $z = 0.4$ and discuss its implications. We find no significant signature of redshift evolution of the luminosity function in the redshift interval. We provide the results of fits of a parameterized Schechter function and extensions of it which provide a reasonable characterization of the data. Using a model for structure formation and galaxy cluster evolution we compare the observed X-ray luminosity function with predictions for different cosmological models. For the most interesting constraints for the cosmological parameters $Ω_m$ and $σ_8$ we obatain $Ω_m \sim 0.27 \pm 0.03$ and $σ_8 \sim 0.80 \pm 0.03$ based on the statistical uncertainty alone. Marginalizing over the most important uncertainties, the normalisation and slope of the $L_X - M$ scaling relation, we find $Ω_m \sim 0.29 \pm 0.04$ and $σ_8 \sim 0.77 \pm 0.07$ ($1σ$ confidence limits). We compare our results with those of the SZ-cluster survey provided by the PLANCK mission and we find very good agreement with the results using PLANCK clusters as cosmological probes, but we have some tension with PLANCK cosmological results from the microwave background anisotropies. We also make a comparison with other cluster surveys. We find good agreement with these previous results and show that the REFLEX II survey provides a significant reduction in the uncertainties compared to earlier measurements.

Figures (17)

• Figure 1: Effective survey volume as a function of X-ray luminosity. The survey volume has been calculated for three different cut-off redshift, $z=0.8$, $z=0.3$, $z=0.22$ for our reference cosmology ($h=0.7$, $\Omega_m = 0.3$ and $\Omega_{\Lambda}=0.7$). We have also determined the same set of curves for a cosmology with the parameters $h=0.7$, $\Omega_m = 0.26$ and $\Omega_{\Lambda}=0.74$ shown as dashed curves. Note that the difference between the set of curves has been amplified by a factor of 10, to make the offset better visible. This affects the dashed curves which are shown slightly offset from the original position.
• Figure 2: X-ray luminosity function of REFLEX II determined in four equidistant redshift shells from $z = 0$ to $z = 0.4$. Due to the flux limit of the sample the different redshift shells cover different luminosity ranges. In the overlap region the functions show no major differences.
• Figure 3: X-ray luminosity function of the REFLEX II galaxy cluster survey averaged over the survey volumes out to redshift $z = 0.1$ and $z = 0.3$. Schechter functions have been fit to the two data sets separately to visualize the potential difference of the functions. The fits were performed over the whole observed X-ray luminosity range.
• Figure 4: X-ray luminosity histogram of the REFLEX II clusters at $z \le 0.3$ (red line with error bars) compared to the best fitting Schechter function for the X-ray luminosity range $L_X \ge 0.1 \times 10^{44}$ erg s$^{-1}$. The X-ray luminosity limit is indicated by the vertical dotted line. The error bars give the Poisson uncertainty of the counts in the bins.
• Figure 5: Constraints on the Schechter parameters $\alpha$ and $L_X^{\ast}$ from the fit to the data of the X-ray luminosity function of REFLEX II for $z \le 0.3$ and luminosity range $L_X \ge 0.1 \times 10^{44}$ erg s$^{-1}$.