Cosmological Implications of Number Counts of Clusters of Galaxies: logN-logS in X-Ray and Submm Bands

We compute the number counts of clusters of galaxies, the logN-logS relation, in several X-ray and submm bands on the basis of the Press-Schechter theory. We pay particular attention to a set of theoretical models which well reproduce the ROSAT 0.5-2 keV band logN-logS, and explore possibilities to further constrain the models from future observations with ASCA and/or at submm bands. The latter is closely related to the European PLANCK mission and the Japanese Large Millimeter and Submillimeter Array (LMSA) project. We exhibit that one can break the degeneracy in an acceptable parameter region on the $\Omega_0 - \sigma_8$ plane by combining the ROSAT logN-logS and the submm number counts. Models which reproduce the ROSAT band logN-logS will have $N(>S) \sim (150-300) (S/10^{-12} erg cm^{-2} s^{-1})^{-1.3}$ str$^{-1}$ at $S > 10^{-12} erg cm^{-2} s^{-1}$ in the ASCA 2-10 keV band, and $N(>S_\nu) \sim (10^2-10^4) (S_\nu/100 mJy)^{-1.5} str^{-1}$ at $S_\nu > 100 mJy$ in the submm (0.85mm) band. The amplitude of the logN-logS is very sensitive to the model parameters in the submm band. We also compute the redshift evolution of the cluster number counts and compare with that of the X-ray brightest Abell-type clusters. The results, although still preliminary, point to low density ($\Omega_0\sim 0.3$) universes. The contribution of clusters to the X-ray and submm background radiations is shown to be insignificant in any model compatible with the ROSAT logN-logS.Comment: 18 pages, 6 figures and 1 table. Figures revised. Accepted for publication in PAS

Monte-Carlo Modeling of Non-Gravitational Heating Processes in Galaxy Clusters

We consider non-gravitational heating effects on galaxy clusters on the basis of the Monte-Carlo modeling of merging trees of dark matter halos combined with the thermal evolution of gas inside each halo. Under the assumption of hydrostatic equilibrium and the isothermal gas profiles, our model takes account of the metallicity evolution, metallicity-dependent cooling of gas, supernova energy feedback, and heating due to jets of radio galaxies in a consistent manner. The observed properties of galaxy clusters can be explained in models with higher non-gravitational heating efficiency than that in the conventional model. Possibilities include jet heating by the Fanaroff-Riley Type II radio galaxies, and the enhanced star formation efficiency and/or supernova energy feedback, especially at high redshifts.Comment: 29 pages, 12 figures. To appear in PASJ, February 25, 200

Reliability of merger tree realizations of dark halos in the Monte-Carlo modeling of galaxy formation

We examine the reliability of the merger trees generated for the Monte-Carlo modeling of galaxy formation. In particular we focus on the cold gas fraction predicted from the merger trees with different assumptions on the progenitor distribution function, the timestep, and the mass resolution. We show that the cold gas fraction is sensitive to the accuracy of the merger trees at small-mass scales of progenitors at high redshifts. One can reproduce the Press-Schechter prediction to a reasonable degree by adopting a fairly large number of redshift bins, N_{step} ~ 1000 in generating merger trees, which is a factor of ten larger than the canonical value used in previous literature.Comment: 9 pages, 10 figures. To appear in PASJ, October 25, 200

Systematic bias in the estimate of cluster mass and the fluctuation amplitude from cluster abundance statistics

We revisit the estimate of the mass fluctuation amplitude, sigma_8, from the observational X-ray cluster abundance. In particular, we examine the effect of the systematic difference between the cluster virial mass estimated from the X-ray spectroscopy, M_{vir, spec}, and the true virial mass of the corresponding halo, M_{vir}. Mazzotta et al. (2004) recently pointed out the possibility that alpha_M = M_{vir, spec}/M_{vir} is systematically lower than unity. We perform the statistical analysis combining the latest X-ray cluster sample and the improved theoretical models and find that sigma_8 \sim 0.76 +/- 0.01 + 0.50 (1-alpha_M) for 0.5 \le alpha_M \le 1, where the quoted errors are statistical only. Thus if alpha_M \sim 0.7, the value of sigma_8 from cluster abundance alone is now in better agreement with other cosmological data including the cosmic microwave background, the galaxy power spectrum and the weak lensing data. The current study also illustrates the importance of possible systematic effects in mapping real clusters to underlying dark halos which changes the interpretation of cluster abundance statistics.Comment: 13 pages, 4 figures. To appear in PASJ, April 25, 200

Systematic Errors in the Hubble Constant Measurement from the Sunyaev-Zel'dovich effect

The Hubble constant estimated from the combined analysis of the Sunyaev-Zel'dovich effect and X-ray observations of galaxy clusters is systematically lower than those from other methods by 10-15 percent. We examine the origin of the systematic underestimate using an analytic model of the intracluster medium (ICM), and compare the prediction with idealistic triaxial models and with clusters extracted from cosmological hydrodynamical simulations. We identify three important sources for the systematic errors; density and temperature inhomogeneities in the ICM, departures from isothermality, and asphericity. In particular, the combination of the first two leads to the systematic underestimate of the ICM spectroscopic temperature relative to its emission-weighed one. We find that these three systematics well reproduce both the observed bias and the intrinsic dispersions of the Hubble constant estimated from the Sunyaev-Zel'dovich effect.Comment: 26 pages, 7 figures, accepted for publication in ApJ, Minor change

On the Design Rationale of SIMON Block Cipher: Integral Attacks and Impossible Differential Attacks against SIMON Variants

SIMON is a lightweight block cipher designed by NSA in 2013. NSA presented the specification and the implementation efficiency, but they did not provide detailed security analysis nor the design rationale. The original SIMON has rotation constants of $(1,8,2)$, and Kölbl {\it et al}.~regarded the constants as a parameter $(a,b,c)$, and analyzed the security of SIMON block cipher variants against differential and linear attacks for all the choices of $(a,b,c)$. This paper complements the result of Kölbl {\it et al}.~by considering integral and impossible differential attacks. First, we search the number of rounds of integral distinguishers by using a supercomputer. Our search algorithm follows the previous approach by Wang {\it et al}., however, we introduce a new choice of the set of plaintexts satisfying the integral property. We show that the new choice indeed extends the number of rounds for several parameters. We also search the number of rounds of impossible differential characteristics based on the miss-in-the-middle approach. Finally, we make a comparison of all parameters from our results and the observations by Kölbl {\it et al}. Interesting observations are obtained, for instance we find that the optimal parameters with respect to the resistance against differential attacks are not stronger than the original parameter with respect to integral and impossible differential attacks. We also obtain a parameter that is better than the original parameter with respect to security against these four attacks

Extracting Galaxy Cluster Gas Inhomogeneity from X-ray Surface Brightness: A Statistical Approach and Application to Abell 3667

Our previous analysis indicates that small-scale fluctuations in the intracluster medium (ICM) from cosmological hydrodynamic simulations follow the lognormal distribution. In order to test the lognormal nature of the ICM directly against X-ray observations of galaxy clusters, we develop a method of extracting statistical information about the three-dimensional properties of the fluctuations from the two-dimensional X-ray surface brightness. We first create a set of synthetic clusters with lognormal fluctuations. Performing mock observations of these synthetic clusters, we find that the resulting X-ray surface brightness fluctuations also follow the lognormal distribution fairly well. Systematic analysis of the synthetic clusters provides an empirical relation between the density fluctuations and the X-ray surface brightness. We analyze \chandra observations of the galaxy cluster Abell 3667, and find that its X-ray surface brightness fluctuations follow the lognormal distribution. While the lognormal model was originally motivated by cosmological hydrodynamic simulations, this is the first observational confirmation of the lognormal signature in a real cluster. Finally we check the synthetic cluster results against clusters from cosmological hydrodynamic simulations. As a result of the complex structure exhibited by simulated clusters, the empirical relation shows large scatter. Nevertheless we are able to reproduce the true value of the fluctuation amplitude of simulated clusters within a factor of two from their X-ray surface brightness alone. Our current methodology combined with existing observational data is useful in describing and inferring the statistical properties of the three dimensional inhomogeneity in galaxy clusters.Comment: 34 pages, 17 figures, accepted for publication in Ap