Constraints on the asymptotic baryon fractions of galaxy clusters at largeradii

While X-ray measurements have so far revealed an increase in the volume-ave raged baryon fractions f(b)(r) of galaxy clusters with cluster radii r, f(b )(r) should asymptotically reach a universal value f(b)(infinity) = f(b), p rovided that clusters are representative of the Universe. In the framework of hydrostatic equilibrium for intracluster gas, we have derived the necess ary conditions for f(b)(infinity) = f(b). The X-ray surface brightness prof ile described by the beta model and the temperature profile approximated by the polytropic model should satisfy gamma approximate to 2(1 - 1/3 beta) a nd gamma approximate to 1 + 1/3 beta for beta < 1 and beta > 1, respectivel y, which sets a stringent limit to the polytropic index: gamma < 4/3. In pa rticular, a mildly increasing temperature with radius is required if the ob servationally 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 (greater than or similar to 30r(c)) where hydros tatic equilibrium has probably become inapplicable. We further explore how to obtain the asymptotic value f(b)(infinity) of the baryon fraction from t he X-ray measurement made primarily over the finite central region of a clu ster. We demonstrate our method using a sample of 19 strong lensing cluster s, which enables us to place a useful constraint on f(b)(infinity): 0.094 /- 0.035 less than or equal to f(b)(infinity) less than or equal to 0.41 +/ - 0.18, corresponding to a cosmological density parameter 0.122 +/- 0.069 l ess than or equal to Ohm(M) less than or equal to 0.53 +/- 0.28 for H-0 = 5 0 km s(-1) Mpc(-1). An optimal estimate of f(b)(infinity) based on three co oling flow clusters with beta < 1/2 in our lensing cluster sample yields [f (b)(infinity)] = 0 142 +/- 0.007 or Ohm(M) = 0.35 +/- 0.09.