Masamune Oguri

Revising the Halofit Model for the Nonlinear Matter Power Spectrum

Based on a suite of state-of-the-art high-resolution N-body simulations, we revisit the so-called halofit model as an accurate fitting formula for the nonlinear matter power spectrum. While the halofit model has frequently been used as a standard cosmological tool to predict the nonlinear matter power spectrum in a universe dominated by cold dark matter, its precision has been limited by the low resolution of N-body simulations used to determine the fitting parameters, suggesting the necessity of an improved fitting formula at small scales for future cosmological studies. We run high-resolution N-body simulations for 16 cosmological models around the Wilkinson Microwave Anisotropy Probe best-fit cosmological parameters (one-, three-, five-, and seven-year results), including dark energy models with a constant equation of state. The simulation results are used to re-calibrate the fitting parameters of the halofit model so as to reproduce small-scale power spectra of the N-body simulations, while keeping the precision at large scales. The revised fitting formula provides an accurate prediction of the nonlinear matter power spectrum in a wide range of wavenumbers (k ? 30 h?Mpc?1) at redshifts 0 ? z ? 10, with 5% precision for k ? 1 h?Mpc?1 at 0 ? z ? 10 and 10% for 1 ? k ? 10 h?Mpc?1 at 0 ? z ? 3. We discuss the impact of the improved halofit model on weak-lensing power spectra and correlation functions, and show that the improved model better reproduces ray-tracing simulation results.

Clustering of High Redshift (z>2.9) Quasars from the Sloan Digital Sky Survey

We study the two-point correlation function of a uniformly selected sample of 4426 luminous optical quasars with redshift 2.9 ≤ z ≤ 5.4 selected over 4041 deg2 from the Fifth Data Release of the Sloan Digital Sky Survey. We fit a power-law to the projected correlation function wp(rp) to marginalize over redshift-space distortions and redshift errors. For a real-space correlation function of the form ξ(r) = (r/r0)-γ, the fitted parameters in comoving coordinates are r0 = 15.2 ± 2.7 h-1 Mpc and γ = 2.0 ± 0.3, over a scale range 4 h-1 Mpc ≤ rp ≤ 150 h-1 Mpc. Thus high-redshift quasars are appreciably more strongly clustered than their z ≈ 1.5 counterparts, which have a comoving clustering length r0 ≈ 6.5 h-1 Mpc. Dividing our sample into two redshift bins, 2.9 ≤ z ≤ 3.5 and z ≥ 3.5, and assuming a power-law index γ = 2.0, we find a correlation length of r0 = 16.9 ± 1.7 h-1 Mpc for the former and r0 = 24.3 ± 2.4 h-1 Mpc for the latter. Strong clustering at high redshift indicates that quasars are found in very massive, and therefore highly biased, halos. Following Martini & Weinberg, we relate the clustering strength and quasar number density to the quasar lifetimes and duty cycle. Using the Sheth & Tormen halo mass function, the quasar lifetime is estimated to lie in the range ~4-50 Myr for quasars with 2.9 ≤ z ≤ 3.5, and ~30-600 Myr for quasars with z ≥ 3.5. The corresponding duty cycles are ~0.004-0.05 for the lower redshift bin and ~0.03-0.6 for the higher redshift bin. The minimum mass of halos in which these quasars reside is (2-3) × 1012 h-1 M⊙ for quasars with 2.9 ≤ z ≤ 3.5 and (4-6) × 1012 h-1 M⊙ for quasars with z ≥ 3.5; the effective bias factor beff increases with redshift, e.g., beff ~ 8 at z = 3.0 and beff ~ 16 at z = 4.5.

Gravitational Lens Time Delays: A Statistical Assessment of Lens Model Dependences and Implications for the Global Hubble Constant

Time delays between lensed multiple images have been known to provide an interesting probe of the Hubble constant, but such an application is often limited by degeneracies with the shape of lens potentials. We propose a new statistical approach to examine the dependence of time delays on the complexity of lens potentials, such as higher order perturbations, nonisothermality, and substructures. Specifically, we introduce a dimensionless reduced time delay and explore its behavior analytically and numerically as a function of the image configuration, which is characterized by the asymmetry and opening angle of the image pair. In particular, we derive a realistic conditional probability distribution for a given image configuration from Monte Carlo simulations. We find that the probability distribution is sensitive to the image configuration such that more symmetric and/or smaller opening-angle image pairs are more easily affected by perturbations on the primary lens potential. On average time delays of double lenses are less scattered than those of quadruple lenses. Furthermore, the realistic conditional distribution allows a new statistical method to constrain the Hubble constant from observed time delays. We find that 16 published time delay quasars constrain H0 to be 70 ± 6 km s-1 Mpc-1, where the value and its error are estimated using jackknife resampling. Systematic errors coming from the heterogeneous nature of the quasar sample and the uncertainty of the input distribution of lens potentials can be larger than the statistical error. After including rough estimates of important systematic errors, we find H0 = 68 ± 6(stat.) ± 8(syst.) km s-1 Mpc-1. The reasonable agreement of the value of the Hubble constant with other estimates indicates the usefulness of our new approach as a cosmological and astrophysical probe, particularly in the era of large-scale synoptic surveys.

Gravitationally lensed quasars and supernovae in future wide-field optical imaging surveys

Cadenced optical imaging surveys in the next decade will be capable of detecting time-varying galaxy-scale strong gravitational lenses in large numbers, increasing the size of the statistically well-defined samples of multiply-imaged quasars by two orders of magnitude, and discovering the first strongly-lensed supernovae. We carry out a detailed calculation of the likely yields of several planned surveys, using realistic distributions for the lens and source properties and taking magnification bias and image configuration detectability into account. We find that upcoming wide-field synoptic surveys should detect several thousand lensed quasars. In particular, the Large Synoptic Survey Telescope (LSST) should find more than some 8000 lensed quasars, some 3000 of which will have well-measured time delays. The LSST should also find some 130 lensed supernovae during the 10-year survey duration, which is compared with � 15 lensed supernovae predicted to be found by a deep, space-based supernova survey done by the Joint Dark Energy Mission (JDEM). We compute the quad fraction in each survey, predicting it to be � 15% for the lensed quasars and � 30% for the lensed supernovae. Generating a mock catalogue of around 1500 well-observed double-image lenses, as could be derived from the LSST survey, we compute the available precision on the Hubble constant and the dark energy equation parameters for the time delay distance experiment (assuming priors from Planck): the predicted marginalised 68% confidence intervals are σ(w0) = 0.15, σ(wa) = 0.41, and σ(h) = 0.017. While this is encouraging in the sense that these uncertainties are only 50% larger than those predicted for a space-based type-Ia supernova sample, we show how the dark energy figure of merit degrades with decreasing knowledge of the the lens mass distribution.

Hyper Suprime-Cam

Hyper Suprime-Cam (HSC) is an 870 Mega pixel prime focus camera for the 8.2 m Subaru telescope. The wide field corrector delivers sharp image of 0.25 arc-sec FWHM in r-band over the entire 1.5 degree (in diameter) field of view. The collimation of the camera with respect to the optical axis of the primary mirror is realized by hexapod actuators whose mechanical accuracy is few microns. As a result, we expect to have seeing limited image most of the time. Expected median seeing is 0.67 arc-sec FWHM in i-band. The sensor is a p-ch fully depleted CCD of 200 micron thickness (2048 x 4096 15 μm square pixel) and we employ 116 of them to pave the 50 cm focal plane. Minimum interval between exposures is roughly 30 seconds including reading out arrays, transferring data to the control computer and saving them to the hard drive. HSC uniquely features the combination of large primary mirror, wide field of view, sharp image and high sensitivity especially in red. This enables accurate shape measurement of faint galaxies which is critical for planned weak lensing survey to probe the nature of dark energy. The system is being assembled now and will see the first light in August 2012.

Direct measurement of dark matter halo ellipticity from two-dimensional lensing shear maps of 25 massive clusters★

We present new measurements of dark matter distributions in 25 X-ray luminous clusters by making a full use of the two-dimensional (2D) weak-lensing signals obtained from high-quality Subaru/Suprime-Cam imaging data. Our approach to directly compare the measured lensing shear pattern with elliptical model predictions allows us to extract new information on the mass distributions of individual clusters, such as the halo ellipticity and mass centroid. We find that these parameters on the cluster shape are little degenerate with cluster mass and concentration parameters. By combining the 2D fitting results for a subsample of 18 clusters, the elliptical shape of dark matter haloes is detected at 7σ significance level. The mean ellipticity is found to be (e) = 〈1 ― b/a〉 = 0.46 ± 0.04 (1σ), which is in excellent agreement with a theoretical prediction based on the standard collisionless cold dark matter model. The mass centroid can be constrained with a typical accuracy of ∼20 arcsec (∼50 h ―1 kpc) in radius for each cluster. The mass centroid position fairly well matches the position of the brightest cluster galaxy, with some clusters showing significant offsets. Thus, the 2D shear fitting method enables us to assess one of the most important systematic errors inherent in the stacked cluster weak-lensing technique, the mass centroid uncertainty. In addition, the shape of the dark mass distribution is found to be only weakly correlated with that of the member galaxy distribution or the brightest cluster galaxy. We carefully examine possible sources of systematic errors in our measurements including the effect of substructures, the cosmic shear contamination, fitting regions and the dilution effect, and find none of them to be significant. Our results demonstrate the power of high-quality imaging data for exploring the detailed spatial distribution of dark matter, which should improve the ability of future surveys to conduct cluster cosmology experiments.

A gravitationally lensed quasar with quadruple images separated by 14.62 arcseconds.

Gravitational lensing is a powerful tool for the study of the distribution of dark matter in the Universe. The cold-dark-matter model of the formation of large-scale structures (that is, clusters of galaxies and even larger assemblies) predicts the existence of quasars gravitationally lensed by concentrations of dark matter so massive that the quasar images would be split by over 7 arcsec. Numerous searches for large-separation lensed quasars have, however, been unsuccessful. All of the roughly 70 lensed quasars known, including the first lensed quasar discovered, have smaller separations that can be explained in terms of galaxy-scale concentrations of baryonic matter. Although gravitationally lensed galaxies with large separations are known, quasars are more useful cosmological probes because of the simplicity of the resulting lens systems. Here we report the discovery of a lensed quasar, SDSS J1004 + 4112, which has a maximum separation between the components of 14.62 arcsec. Such a large separation means that the lensing object must be dominated by dark matter. Our results are fully consistent with theoretical expectations based on the cold-dark-matter model.

Quasars Probing Quasars. I. Optically Thick Absorbers near Luminous Quasars

With close pairs of quasars at different redshifts, a background quasar sight line can be used to study a foreground quasars environment in absorption. We search 149 moderate-resolution background quasar spectra from Gemini, Keck, the MMT, and the SDSS to survey Lyman limit systems (LLSs) and damped Lyα systems (DLAs) in the vicinity of 1.8 1019 cm-2. The covering factor of N > 1019 cm-2 absorbers is thus ~50% (4/8) on these small scales, whereas 2% would have been expected at random. There are many cosmological applications of these new sight lines: they provide laboratories for studying fluorescent Lyα recombination radiation from LLSs; they constrain the environments, emission geometry, and radiative histories of quasars; and they shed light on the physical nature of LLSs and DLAs.

Comparison of Cluster Lensing Profiles with ΛCDM Predictions

We derive lens distortion and magnification profiles of four well-known clusters observed with Subaru. Each cluster is very well fitted by the general form predicted for cold dark matter (CDM) dominated halos, with good consistency found between the independent distortion and magnification measurements. The inferred level of mass concentration is surprisingly high, 8 < cvir < 15 ( cvir = 10.39 ± 0.91), compared to the relatively shallow profiles predicted by the ΛCDM model, cvir = 5.06 ± 1.10 (for Mvir = 1.25 × 1015 M☉ h−1). This represents a 4 σ discrepancy, and includes the relatively modest effects of projection bias and profile evolution derived from N-body simulations, which oppose each other with little residual effect. In the context of CDM-based cosmologies, this discrepancy implies that clusters collapse earlier (z ≥ 1) than predicted (z < 0.5), when the universe was correspondingly denser.

ARC STATISTICS IN TRIAXIAL DARK MATTER HALOS: TESTING THE COLLISIONLESS COLD DARK MATTER PARADIGM

Statistics of lensed arcs in clusters of galaxies serve as a powerful probe of both the nonsphericity and the inner slope of dark matter halos. We develop a semianalytic method to compute the number of arcs in triaxial dark matter halos. This combines the lensing cross section from the Monte Carlo ray-tracing simulations and the probability distribution function of the axis ratios evaluated from cosmological N-body simulations. This approach enables one to incorporate both asymmetries in the projected mass density and elongations along the line of sight analytically for the first time in cosmological lensed arc statistics. As expected, triaxial dark matter halos significantly increase the number of arcs relative to spherical models; the difference amounts to more than 1 order of magnitude, while the value of enhancement depends on the specific properties of density profiles. Then we compare our theoretical predictions with the observed number of arcs from 38 X-ray-selected clusters. In contrast to previous claims, our triaxial dark matter halos with inner density profile ρ ∝ r-1.5 in a Λ-dominated cold dark matter (CDM) universe reproduce observations well. Since both the central mass concentration and triaxial axis ratios (minor-to-major axis ratio ~ 0.5) required to account for the observed data are consistent with cosmological N-body simulations, our result may be interpreted to lend strong support to the collisionless CDM paradigm at the mass scale of clusters.