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

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

1999-09-13

arxiv.org/abs/astro-ph/9909205v1

Astronomy and Astrophysics

Astrophysics

6 pages + 4 figures; accepted for publication in MNRAS

Scientific paper

10.1046/j.1365-8711.2000.03087.x

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 $\gamma\approx2(1-1/3\beta)$ and $\gamma\approx1+1/3\beta$ 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 $f_b(\infty)$: $0.094\pm0.035 \leq f_b(\infty) \leq 0.41\pm0.18$. An optimal estimate of $f_b(\infty)$ based on three cooling flow clusters with $\beta<1/2$ in our lensing cluster sample yields $ = 0.142\pm0.007$ or $\Omega_M = 0.35\pm0.09$.

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