Abstract
According to the standard cold dark matter (CDM) cosmology, the structure of dark halos including those of galaxy clusters reflects their mass accretion history. Older clusters tend to be more concentrated than younger clusters. Their structure, represented by the characteristic radius r s and mass M s of the Navarro–Frenk–White (NFW) density profile, is related to their formation time. In this study, we showed that r s , M s , and the X-ray temperature of the intracluster medium (ICM), T X , form a thin plane in the space of ( log r s , log M s , log T X ) . This tight correlation indicates that the ICM temperature is also determined by the formation time of individual clusters. Numerical simulations showed that clusters move along the fundamental plane as they evolve. The plane and the cluster evolution within the plane could be explained by a similarity solution of structure formation of the universe. The angle of the plane shows that clusters have not achieved “virial equilibrium” in the sense that mass/size growth and pressure at the boundaries cannot be ignored. The distribution of clusters on the plane was related to the intrinsic scatter in the halo concentration–mass relation, which originated from the variety of cluster ages. The well-known mass–temperature relation of clusters ( M Δ ∝ T X 3 / 2 ) can be explained by the fundamental plane and the mass dependence of the halo concentration without the assumption of virial equilibrium. The fundamental plane could also be used for calibration of cluster masses.
Highlights
Clusters of galaxies are the most massive objects in the Universe
Cold dark matter (CDM) cosmology predicts that more massive halos form later
The halo structure represented by the characteristic radius rs, and mass Ms is related to the formation time of the halo
Summary
Clusters of galaxies are the most massive objects in the Universe. Since the fraction of baryons in clusters is not much different from the cosmic mean value, dark matter accounts for most of the mass of clusters (∼84%) [1,2]. The mass profile of the NFW profile is written as Another commonly defined characteristic radius of clusters is that based on the critical density ρc ; it is represented by r∆ , which is the radius of a sphere of mean interior density ρ∆ ≡ ∆ρc , where ∆ is the constant. Navarro et al [4] pointed out that the characteristic parameters of the NFW profile (e.g., ρs and c∆ ) reflect the density of the background universe when the halo was formed. ∼ rs ) is formed in the subsequent “slow-rate growth” phase in which halos grow slowly through moderate matter accumulation During this phase, the inner region is almost preserved.
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