Foreseeing the era of high spatial resolution measurements of the Sunyaev-Zel'dovich effect (SZE) in clusters of galaxies, we present a prototype analysis of this sort combined with Chandra X-ray data. It is applied specifically to RX J1347-1145 at z = 0.451, the most X-ray-luminous galaxy cluster known, for which the highest resolution SZE and X-ray images are currently available. We demonstrate that the combined analysis yields a unique probe of complex structures in the intracluster medium, offering determinations of their temperature, density, and line-of-sight extent. For a subclump in RX J1347-1145, previously discovered in our SZE map, the temperature inferred after removing the foreground and background components is well in excess of 20 keV, indicating that the cluster has recently undergone a violent merger. Excluding the region around this subclump, the SZE signals in submillimeter to centimeter bands (350, 150, and 21 GHz) are all consistent with those expected from Chandra X-ray observations. We further present a temperature deprojection technique based on the SZE and X-ray images, without any knowledge of spatially resolved X-ray spectroscopy. The methodology presented here will be applicable to a statistical sample of clusters available in the future SZE surveys.

A mechanism leading to the spin-triplet superconductivity is proposed based on the antiferromagnetic spin fluctuation. The effects of anisotropy in spin fluctuation on the Cooper pairing and on the direction of d vector are examined in the one-band Hubbard model with RPA approximation. The gap equations for the anisotropic case are derived and applied to Sr2RuO4. It is found that a nesting property of the Fermi surface together with the anisotropy leads to the triplet superconductivity with the d =ẑ(sin kx ± i sin ky), which is consistent with experiments.74. 74.20Mn, 74.25Dw Since the discovery of superconducting phase in Sr 2 RuO 4 [1], much effort has been paid for understanding its exotic properties. Among several interesting natures, the most fascinating one is that it is a spintriplet superconductor confirmed by NMR experiment [2]. While most superconductors found during several decades are singlet, the only exceptions were 3 He and UPt 3 . Therefore the fact that the triplet pairing is realized in Sr 2 RuO 4 has attracted much attention. While UPt 3 , the second example of spin-triplet superconductor, has a complicated electronic structure, Sr 2 RuO 4 has a rather simple electronic state [1]. Thus clarifying the microscopic mechanism of superconductivity in Sr 2 RuO 4 is very important for understanding the triplet superconductors in general.In 3 He, Cooper pairs are formed due to ferromagnetic spin fluctuations peaked at q = 0 [3,4]. Therefore it is natural to expect the origin of the triplet pairing in Sr 2 RuO 4 is also ferromagnetic spin fluctuation [5,6]. This assumption has been believed to be justified by NMR experiments [7][8][9]. However the recent neutron scattering experiment has shown that there exists a significant peak near q 0 = (±2π/3, ±2π/3) and no sizable ferromagnetic spin fluctuation [10]. Thus it is difficult to assume that the spin fluctuation near q 0 plays no role in the Cooper pairing in Sr 2 RuO 4 . (In the following discussion we call this fluctuation as antiferromagnetic (AF) spin fluctuation, for simplicity.) However this AF fluctuation leads to the singlet superconductivity rather than * e-mail address: t-kuwabara@bea.hi-ho.ne.jp † Address from April 2000, Dept. of Physics, Univ. of Tokyo, Hongo, Bunkyo-ku 113-0033 Tokyo the triplet superconductivity as expected in analogy to high-T c cuprates [5].In this paper we propose a mechanism which gives the triplet pairing even if the spin fluctuation is AF. We find that the characteristic features of Sr 2 RuO 4 are twofold: One is the anisotropy of the spin fluctuation found in NMR experiments [8,9], and the other is a nesting property with momentum q 0 of the two-dimensional Fermi surface. We show that these two features explain the pairing in Sr 2 RuO 4 .In addition to the competition between singlet and triplet pairing, the direction of the d vector, which is the order parameter of triplet superconductivity, is another interesting problem. We show that the anisotropy of the spin fluctuation also explains the experimental fact...

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We derive the pairwise peculiar velocity distribution function of dark matter particles applying the dark matter halo approach. Unlike the previous work, we do not assume a Gaussian velocity distribution function of dark matter in a single halo, but compute it self-consistently with the assumed density profile for dark matter halo. The resulting distribution function is well approximated by an exponential distribution which is consistent with the previous observational, numerical and theoretical results. We also compute the pairwise peculiar velocity dispersion for different density profiles, and provide a practical fitting formula. We apply an empirical biasing scheme into our model and present prediction for pairwise peculiar velocity dispersion of galaxies, and reproduce the previous results of simulations using our semi-analytical method.