Subaru weak-lensing measurement of a z = 0.81 cluster discovered by the Atacama Cosmology Telescope Survey

We present a Subaru weak lensing measurement of ACT-CL J0022.2-0036, one of the most luminous, high-redshift (z=0.81) Sunyaev-Zel'dovich (SZ) clusters discovered in the 268 deg^2 equatorial region survey of the Atacama Cosmology Telescope. For the weak lensing analysis using i'-band images, we use a model-fitting (Gauss-Laguerre shapelet) method to measure shapes of galaxy images, where we fit galaxy images in different exposures simultaneously to obtain best-fit ellipticities taking into account the different PSFs in each exposure. We also take into account the astrometric distortion effect on galaxy images by performing the model fitting in the world coordinate system. To select background galaxies behind the cluster at z=0.81, we use photometric redshift (photo-z) estimates for every galaxy derived from the co-added images of multi-passband Br'i'z'Y, with PSF matching/homogenization. After a photo-z cut for background galaxy selection, we detect the tangential weak lensing distortion signal with a total signal-to-noise ratio of about 3.7. By fitting a Navarro-Frenk-White model to the measured shear profile, we find the cluster mass to be M_200\bar{\rho}_m = [7.5^+3.2_-2.8(stat.)^+1.3_-0.6(sys.)] x 10^14 M_\odot/h. The weak lensing-derived mass is consistent with previous mass estimates based on the SZ observation, with assumptions of hydrostatic equilibrium and virial theorem, as well as with scaling relations between SZ signal and mass derived from weak lensing, X-ray, and velocity dispersion, within the measurement errors. We also show that the existence of ACT-CL J0022.2-0036 at z=0.81 is consistent with the cluster abundance prediction of the \Lambda-dominated cold dark matter structure formation model. We thus demonstrate the capability of Subaru-type ground-based images for studying weak lensing of high-redshift clusters.Comment: 17 pages, 8 figure

Optimal Location of Two Laser-interferometric Detectors for Gravitational Wave Backgrounds at 100 MHz

Recently, observational searches for gravitational wave background (GWB) have been developed and given constraints on the energy density of GWB in a broad range of frequencies. These constraints have already resulted in the rejection of some theoretical models of relatively large GWB spectra. However, at 100 MHz, there is no strict upper limit from direct observation, though an indirect limit exists due to He4 abundance due to big-bang nucleosynthesis. In our previous paper, we investigated the detector designs that can effectively respond to GW at high frequencies, where the wavelength of GW is comparable to the size of a detector, and found that the configuration, a so-called synchronous-recycling interferometer is best at these sensitivity. In this paper, we investigated the optimal location of two synchronous-recycling interferometers and derived their cross-correlation sensitivity to GWB. We found that the sensitivity is nearly optimized and hardly changed if two coaligned detectors are located within a range 0.2 m, and that the sensitivity achievable in an experiment is far below compared with the constraint previously obtained in experiments.Comment: 17 pages, 6 figure

Set optimization - a rather short introduction

Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems. Extensive sections with bibliographical comments summarize the state of the art. Applications to vector optimization and financial risk measures are discussed along with algorithmic approaches to set optimization problems

Low-Temperature Properties of Quasi-One-Dimensional Molecule-Based Ferromagnets

Quantum and thermal behaviors of low-dimensional mixed-spin systems are investigated with particular emphasis on the design of molecule-based ferromagnets. One can obtain a molecular ferromagnet by assembling molecular bricks so as to construct a low-dimensional system with a magnetic ground state and then coupling the chains or the layers again in a ferromagnetic fashion. Two of thus-constructed quasi-one-dimensional bimetallic compounds are qualitatively viewed within the spin-wave treatment, one of which successfully grows into a bulk magnet, while the other of which ends in a singlet ground state. Then, concentrating on the ferrimagnetic arrangement on a two-leg ladder which is well indicative of general coupled-chain ferrimagnets, we develop the spin-wave theory and fully reveal its low-energy structure. We inquire further into the ferromagnetic aspect of the ferrimagnetic ladder numerically calculating the sublattice magnetization and the magnetic susceptibility. There exists a moderate coupling strength between the chains in order to obtain the most ferromagnetic ferrimagnet.Comment: 10 pages, 7 figures embedded, to be published in J. Phys. Soc. Jpn. Vol.70, No.5 (2001

Hunting for Primordial Non-Gaussianity in the Cosmic Microwave Background

Since the first limit on the (local) primordial non-Gaussianity parameter, fNL, was obtained from COBE data in 2002, observations of the CMB have been playing a central role in constraining the amplitudes of various forms of non-Gaussianity in primordial fluctuations. The current 68% limit from the 7-year WMAP data is fNL=32+/-21, and the Planck satellite is expected to reduce the uncertainty by a factor of four in a few years from now. If fNL>>1 is found by Planck with high statistical significance, all single-field models of inflation would be ruled out. Moreover, if the Planck satellite finds fNL=30, then it would be able to test a broad class of multi-field models using the four-point function (trispectrum) test of tauNL>=(6fNL/5)^2. In this article, we review the methods (optimal estimator), results (WMAP 7-year), and challenges (secondary anisotropy, second-order effect, and foreground) of measuring primordial non-Gaussianity from the CMB data, present a science case for the trispectrum, and conclude with future prospects.Comment: 33 pages, 4 figures. Invited review, accepted for publication in the CQG special issue on nonlinear cosmological perturbations. (v2) References added. More clarifications are added to the second-order effect and the multi-field consistency relation, tauNL>=(6fNL/5)^2

Searching for a Stochastic Background of Gravitational Waves with LIGO

The Laser Interferometer Gravitational-wave Observatory (LIGO) has performed the fourth science run, S4, with significantly improved interferometer sensitivities with respect to previous runs. Using data acquired during this science run, we place a limit on the amplitude of a stochastic background of gravitational waves. For a frequency independent spectrum, the new limit is $\Omega_{\rm GW} < 6.5 \times 10^{-5}$. This is currently the most sensitive result in the frequency range 51-150 Hz, with a factor of 13 improvement over the previous LIGO result. We discuss complementarity of the new result with other constraints on a stochastic background of gravitational waves, and we investigate implications of the new result for different models of this background.Comment: 37 pages, 16 figure