Constraining the Matter Power Spectrum Normalization using the SDSS/RASS and REFLEX Cluster surveys

TL;DR

The paper tackles constraining the matter power spectrum normalization $\sigma_8$ as a function of $\Omega_0$ using a novel approach that bypasses the cluster $M$–$T_X$ relation. It combines the REFLEX X-ray luminosity function with a weak-lensing–calibrated $L_X$–$M$ relation derived from a SDSS/RASS cluster sample and compares this to the Jenkins et al. (2001) halo mass function to infer $\sigma_8(\Omega_0)$ via Monte Carlo propagation of uncertainties. The main result is $\sigma_8 = 0.38 \; \Omega_0^{-0.48+0.27\Omega_0}$ with ~15% 95% uncertainty, generally lower than most temperature-function based estimates, though two luminosity-subsample analyses reveal significant systematic sensitivity. The study highlights potential inconsistencies between X-ray luminosity–mass calibrations and the mass function, and emphasizes that the inferred $L_X$–$M_{500}$ slope may be steeper than previously thought, suggesting both systematic biases and the need for larger surveys (e.g., XMM-Newton) to refine the constraint.

Abstract

We describe a new approach to constrain the amplitude of the power spectrum of matter perturbations in the Universe, parametrized by sigma_8 as a function of the matter density Omega_0. We compare the galaxy cluster X-ray luminosity function of the REFLEX survey with the theoretical mass function of Jenkins et al. (2001), using the mass-luminosity relationship obtained from weak lensing data for a sample of galaxy clusters identified in Sloan Digital Sky Survey commissioning data and confirmed through cross-correlation with the ROSAT all-sky survey. We find sigma_8 = 0.38 Omega_0^(-0.48+0.27 Omega_ 0), which is significantly different from most previous results derived from comparable calculations that used the X-ray temperature function. We discuss possible sources of systematic error that may cause such a discrepancy, and in the process uncover a possible inconsistency between the REFLEX luminosity function and the relation between cluster X-ray luminosity and mass obtained by Reiprich & Bohringer (2001).