Measuring the Density Fluctuation from the Cluster Gas Mass Function

Abstract

We derive the gas mass function of clusters of galaxies in order to measure the density fluctuation spectrum on cluster scales. The baryon abundance confined in rich clusters is computed from the gas mass function and compared with the mean baryon density in the universe predicted by big bang nucleosynthesis. This baryon fraction and the slope of the gas mass function put constraints on σ8, the rms linear fluctuation on scales of 8 h-1 Mpc, where h is the Hubble constant in units of 100 km s-1 Mpc-1, and on the slope of the fluctuation spectrum. Adopting the density parameter of baryons ΩB0 h2=0.0175±0.0075 (errors are at 1 σ levels), we find (σ8, n)=(0.64+ 0.18−0.09, -1.6+ 1.1−0.4) for h = 0.5 and (σ8, n)=(0.73+ 0.27−0.11, -1.5+ 1.2−0.4) for h = 0.8. A higher h gives a higher σ8, while a higher ΩB0 gives a lower σ8. The errors in σ8 and n contain the 1 σ errors in ΩB0 and in the observed gas mass function. We assume that the density spectrum is approximated by a power law on cluster scales, σ(r) ∝ r-(3 + n)/2. Our value of σ8 is independent of the density parameter, Ω0, and thus we can estimate Ω0 by combining the value of σ8 obtained in this study with those from other, Ω0-dependent analyses to date. We find that σ8(Ω0) derived from cluster abundance, such as the temperature function, gives Ω0 ~ 0.7, while σ8(Ω0) measured from the peculiar velocity field of galaxies gives Ω0 ~ 0.3-1.3, depending on the technique used to analyze the peculiar velocity data. Constraints are also derived for three sets of cold dark matter models and a set of cold + hot dark matter models.