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

Constraints on the warm dark matter model from gravitational lensing

Formation of sub-galactic halos is suppressed in warm dark matter (WDM) model due to thermal motion of WDM particles. This may provide a natural resolution to some puzzles in standard cold dark matter (CDM) theory such as the cusped density profiles of virialized dark halos and the overabundance of low mass satellites. One of the observational tests of the WDM model is to measure the gravitationally lensed images of distant quasars below sub-arcsecond scales. In this Letter, we report a comparison of the lensing probabilities of multiple images between CDM and WDM models using a singular isothermal sphere model for the mass density profiles of dark halos and the Press-Schechter mass function for their distribution and cosmic evolution. It is shown that the differential probability of multiple images with small angular separations down to 10 milliarcseconds should allow one to set useful constraints on the WDM particle mass. We discuss briefly the feasibility and uncertainties of this method in future radio surveys (e.g. VLBI) for gravitational lensing.Comment: 3 pages, 1 figure, accepted for publication in ApJ Let

Artificial-Noise-Aided Physical Layer Phase Challenge-Response Authentication for Practical OFDM Transmission

Recently, we have developed a PHYsical layer Phase Challenge-Response Authentication Scheme (PHY-PCRAS) for independent multicarrier transmission. In this paper, we make a further step by proposing a novel artificial-noise-aided PHY-PCRAS (ANA-PHY-PCRAS) for practical orthogonal frequency division multiplexing (OFDM) transmission, where the Tikhonov-distributed artificial noise is introduced to interfere with the phase-modulated key for resisting potential key-recovery attacks whenever a static channel between two legitimate users is unfortunately encountered. Then, we address various practical issues for ANA-PHY-PCRAS with OFDM transmission, including correlation among subchannels, imperfect carrier and timing recoveries. Among them, we show that the effect of sampling offset is very significant and a search procedure in the frequency domain should be incorporated for verification. With practical OFDM transmission, the number of uncorrelated subchannels is often not sufficient. Hence, we employ a time-separated approach for allocating enough subchannels and a modified ANA-PHY-PCRAS is proposed to alleviate the discontinuity of channel phase at far-separated time slots. Finally, the key equivocation is derived for the worst case scenario. We conclude that the enhanced security of ANA-PHY-PCRAS comes from the uncertainty of both the wireless channel and introduced artificial noise, compared to the traditional challenge-response authentication scheme implemented at the upper layer.Comment: 33 pages, 13 figures, submitted for possible publicatio

Applications of graph theory in protein structure identification

There is a growing interest in the identification of proteins on the proteome wide scale. Among different kinds of protein structure identification methods, graph-theoretic methods are very sharp ones. Due to their lower costs, higher effectiveness and many other advantages, they have drawn more and more researchers’ attention nowadays. Specifically, graph-theoretic methods have been widely used in homology identification, side-chain cluster identification, peptide sequencing and so on. This paper reviews several methods in solving protein structure identification problems using graph theory. We mainly introduce classical methods and mathematical models including homology modeling based on clique finding, identification of side-chain clusters in protein structures upon graph spectrum, and de novo peptide sequencing via tandem mass spectrometry using the spectrum graph model. In addition, concluding remarks and future priorities of each method are given

A comparison of different cluster mass estimates: consistency or discrepancy ?

Rich and massive clusters of galaxies at intermediate redshift are capable of magnifying and distorting the images of background galaxies. A comparison of different mass estimators among these clusters can provide useful information about the distribution and composition of cluster matter and their dynamical evolution. Using a hitherto largest sample of lensing clusters drawn from literature, we compare the gravitating masses of clusters derived from the strong/weak gravitational lensing phenomena, from the X-ray measurements based on the assumption of hydrostatic equilibrium, and from the conventional isothermal sphere model for the dark matter profile characterized by the velocity dispersion and core radius of galaxy distributions in clusters. While there is an excellent agreement between the weak lensing, X-ray and isothermal sphere model determined cluster masses, these methods are likely to underestimate the gravitating masses enclosed within the central cores of clusters by a factor of 2--4 as compared with the strong lensing results. Such a mass discrepancy has probably arisen from the inappropriate applications of the weak lensing technique and the hydrostatic equilibrium hypothesis to the central regions of clusters as well as an unreasonably large core radius for both luminous and dark matter profiles. Nevertheless, it is pointed out that these cluster mass estimators may be safely applied on scales greater than the core sizes. Namely, the overall clusters of galaxies at intermediate redshift can still be regarded as the dynamically relaxed systems, in which the velocity dispersion of galaxies and the temperature of X-ray emitting gas are good indicators of the underlying gravitational potentials of clusters.Comment: 16 pages with 7 PS figures, MNRAS in pres