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

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 $\beta1$, 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 $\beta = 0.142\pm0.007$ or $\Omega_M = 0.35\pm0.09$.Comment: 6 pages + 4 figures; accepted for publication in MNRA

Document generality: its computation for ranking

The increased variety of information makes it critical to retrieve documents which are not only relevant but also broad enough to cover as many different aspects of a certain topic as possible. The increased variety of users also makes it critical to retrieve documents that are jargon free and easy-to-understand rather than the specific technical materials. In this paper, we propose a new concept namely document generality computation. Generality of document is of fundamental importance to information retrieval. Document generality is the state or quality of docu- ment being general. We compute document general- ity based on a domain-ontology method that analyzes scope and semantic cohesion of concepts appeared in the text. For test purposes, our proposed approach is then applied to improving the performance of doc- ument ranking in bio-medical information retrieval. The retrieved documents are re-ranked by a combined score of similarity and the closeness of documents’ generality to that of a query. The experiments have shown that our method can work on a large scale bio-medical text corpus OHSUMED (Hersh, Buckley, Leone & Hickam 1994), which is a subset of MEDLINE collection containing of 348,566 medical journal references and 101 test queries, with an encouraging performance