2000MNRAS.311..825W

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(∞)=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(∞)=f_b. The X-ray surface brightness profile described by the β model and the temperature profile approximated by the polytropic model should satisfy γ~2(1-1/3β) and γ~1+1/3β for β<1 and β>1, respectively, which sets a stringent limit to the polytropic index: γ<4/3. In particular, a mildly increasing temperature with radius is required if the observationally fitted β parameter is in the range 1/3<β<2/3. It is likely that a reliable determination of the universal baryon fraction can be achieved in the small β clusters because the disagreement between the exact and asymptotic baryon fractions for clusters with β>2/3 breaks down at rather large radii (≳30r_c) where hydrostatic equilibrium has probably become inapplicable. We further explore how to obtain the asymptotic value f_b(∞) of the 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(∞): 0.094±0.035≤f_b(∞)≤0.41±0.18, corresponding to a cosmological density parameter 0.122±0.069≤Ω_M≤0.53±0.28 for H₀=50km.s^–1.Mpc^–1. An optimal estimate of f_b(∞) based on three cooling flow clusters with β<1/2 in our lensing cluster sample yields <]f_b(∞)>=0.142±0.007 or Ω_M=0.35±0.09.