Constraints on the Asymptotic Baryon Fractions of Galaxy Clusters at Large Radii

Abstract

While X-ray measurements have so far revealed an increase in the volume-averaged baryon fractions $f_b(r)$ of galaxy clusters with cluster radii $r$, $f_b(r)$ should asymptotically reach a universal value $f_b(\infty )=f_b$, provided that clusters are representative of the Universe. In the framework of hydrostatic equilibrium for intracluster gas, we have derived the necessary conditions for $f_b(\infty )=f_b$: The X-ray surface brightness profile described by the $\beta$ model and the temperature profile approximated by the polytropic model should satisfy $\gamma \approx 2(1-1/3\beta )$ and $\gamma \approx 1+1/3\beta$ for $\beta <1$ and $\beta >1$, respectively, which sets a stringent limit to the polytropic index: $\gamma <4/3$. In particular, a mildly increasing temperature with radius is required if the observationally fitted $\beta$ parameter is in the range $1/3<\beta <2/3$. It is likely that a reliable determination of the universal baryon fraction can be achieved in the small $\beta$ clusters because the disagreement between the exact and asymptotic baryon fractions for clusters with $\beta >2/3$ breaks down at rather large radii ($\ga30r_c$) where hydrostatic equilibrium has probably become inapplicable. We further explore how to obtain the asymptotic value $f_b(\infty )$ of baryon fraction from the X-ray measurement made primarily over the finite central region of a cluster. We demonstrate our method using a sample of 19 strong lensing clusters, which enables us to place a useful constraint on $f_b(\infty )$: $0.094\pm 0.035\le f_b(\infty )\le 0.41\pm 0.18$. An optimal estimate of $f_b(\infty )$ based on three cooling flow clusters with $\beta <1/2$ in our lensing cluster sample yields $<f_b(\infty )>=0.142\pm 0.007$ or ${\Omega }_M=0.35\pm 0.09$.

6 pages + 4 figures; accepted for publication in MNRAS

References in corpus (3)

• The Lx-T and Lx-sigma Relationships for Galaxy Clusters Revisited
• Outer Regions of the Cluster Gaseous Atmospheres
• The Mass Profile of the Coma Galaxy Cluster

Cited by in corpus (10)

• The Lx-T, Lx-sigma and sigma-T relations for groups and clusters of galaxies
• The Effect of radiative cooling on the scale-dependence of global stellar and gas contents of groups and clusters of galaxies
• Properties of the double beta model for intracluster gas
• Constraints on the Interaction between Dark Matter and Baryons from Cooling Flow Clusters
• Dynamical Effect of the Turbulence of IGM on the Baryon Fraction Distribution
• Strong lensing as a test for Conformal Weyl Gravity
• A serendipitous survey for galaxy clusters by the XMM-Newton Survey Science Center
• Implications of the Universal Temperature Profile for Galaxy Clusters
• Radial density and temperature profiles of the intracluster gas constructed jointly from the X-ray surface brightness measurement and the universal density profile
• Missing baryons in shells around galaxy clusters