We develop a novel method of measuring the lensing distortion profiles of clusters with stacking the scaled amplitudes of background galaxy ellipticities as a function of the scaled centric radius according to the NFW prediction of each cluster, base
d on the assumption that the different clusters in a sample follow the universal NFW profile. First we demonstrate the feasibility of this method using both the analytical NFW model and simulated halos in high-resolution $N$-body simulations. We then apply, as a proof of concept, this method to the Subaru weak lensing data and the XMM/Chandra X-ray observables for a sample of 50 massive clusters in the redshift range $0.15le zle 0.3$, where their halo masses range over an order of magnitude. To estimate the NFW parameters of each cluster, we use the halo mass proxy relation of X-ray observables, based on either the hydrostatic equilibrium or the gas mass, and then infer the halo concentration from the model $c(M)$ relation. We evaluate a performance of the NFW scaling analysis by measuring the scatters of 50 cluster lensing profiles relative to the NFW predictions over a range of radii, $0.14le R/[h^{-1}{rm Mpc}]le 2.8$. We found a 4 - 6$sigma$ level evidence of the universal NFW profile in 50 clusters, for both the X-ray halo mass proxy relations, although the gas mass appears to be a better proxy of the underlying true mass. By comparing the measurements with the simulations of cluster lensing taking into account the statistical errors of intrinsic galaxy shapes in the Subaru data, we argue that additional halo mass errors or intrinsic scatters of $sigma_{ln M_{500c}}sim 0.2$ - $0.3$ could reconcile a difference between the measurements and the simulations.
Cosmological weak lensing is the powerful probe of cosmology. Here we address one of the most fundamental, statistical questions inherent in weak lensing cosmology: whether or not we can recover the initial Gaussian information content of large-scale
structure by combining the weak lensing observables, here focused on the weak lensing power spectrum and bispectrum. To address this question we fully take into account correlations between the power spectra of different multipoles and the bispectra of different triangle configurations, measured from a finite area survey. In particular we show that super-survey modes whose length scale is larger than or comparable with the survey size cause significant sample variance in the weak lensing correlations via the mode-coupling with sub-survey modes due to nonlinear gravitational clustering -- the so-called super-sample variance. In this paper we discuss the origin of the super-sample variance and then study the information content inherent in the weak lensing correlation functions up to three-point level.
We develop a novel abundance matching method to construct a mock catalog of luminous red galaxies (LRGs) in SDSS, using catalogs of halos and subhalos in N-body simulations for a LCDM model. Motivated by observations suggesting that LRGs are passivel
y-evolving, massive early-type galaxies with a typical age >5Gyr, we assume that simulated halos at z=2 (z2-halo) are progenitors for LRG-host subhalos observed today, and we label the most tightly bound particles in each progenitor z2-halo as LRG ``stars. We then identify the subhalos containing these stars to z=0.3 (SDSS redshift) in descending order of the masses of z2-halos until the comoving number density of the matched subhalos becomes comparable to the measured number density of SDSS LRGs, n=10^{-4} (h/Mpc)^3. Once the above prescription is determined, our only free parameter is the number density of halos identified at z=2 and this parameter is fixed to match the observed number density at z = 0.3. By tracing subsequent merging and assembly histories of each progenitor z2-halo, we can directly compute, from the mock catalog, the distributions of central and satellite LRGs and their internal motions in each host halo at z=0.3. While the SDSS LRGs are galaxies selected by the magnitude and color cuts from the SDSS images and are not necessarily a stellar-mass-selected sample, our mock catalog reproduces a host of SDSS measurements: the halo occupation distribution for central and satellite LRGs, the projected auto-correlation function of LRGs, the cross-correlation of LRGs with shapes of background galaxies (LRG-galaxy weak lensing), and the nonlinear redshift-space distortion effect, the Finger-of-God effect, in the angle-averaged redshift-space power spectrum.
Nonlinear redshift-space distortions, the Finger-of-God (FoG) effect, can complicate the interpretation of the galaxy power spectrum. Here, we demonstrate the method proposed by Hikage et al. (2012) to use complimentary observations to directly const
rain this effect on the data. We use catalogs of Luminous Red Galaxies (LRGs) and photometric galaxies from the SDSS DR7 to measure the redshift-space power spectrum of LRGs, the cross-correlation of LRGs with the shapes of background photometric galaxies (galaxy-galaxy weak lensing), and the projected cross-correlation of LRGs with photometric galaxies having similar photometric redshifts to the LRG spectroscopic redshift. All of these measurements use a reconstructed halo field. While we use the position of each LRG for single LRG systems, we compare the measurements using different halo-center proxies for multiple-LRG systems (4.5 per cent of all the halos): the brightest LRG position (BLRG), the faintest LRG position (FLRG) and their arithmetical mean position (Mean), respectively, in each system. We find significant differences in the measured correlations of different centers, showing consistent off-centering effects in the three observables. By comparing the measurements with a halo model that treats the satellite photometric galaxies as being distributed according to a generalized NFW profile, we find that about 40 (70) per cent of BLRGs (FLRGs) are off-centered satellite galaxies in the multiple-LRG systems. The satellite LRGs have typical off-centering radius of about 400 kpc/h, and velocity dispersion of about 500 km/s in host halos with a mean mass of 1.6x10^14 Ms/h. We show that, if LRGs in the single LRG systems have similar offsets, the residual FoG contamination in the LRG power spectrum can be significant at k>0.1 h/Mpc, which may cause a bias in cosmological parameters such as the neutrino mass.
The Subaru Prime Focus Spectrograph (PFS) is a massively-multiplexed fiber-fed optical and near-infrared 3-arm spectrograph (N_fiber=2400, 380<lambda<1260nm, 1.3 degree diameter FoV), offering unique opportunities in survey astronomy. Here we summari
ze the science case feasible for a survey of Subaru 300 nights. We describe plans to constrain the nature of dark energy via a survey of emission line galaxies spanning a comoving volume of 9.3 (Gpc/h)^3 in the redshift range 0.8<z<2.4. In each of 6 redshift bins, the cosmological distances will be measured to 3% precision via BAO, and redshift-space distortions will be used to constrain structure growth to 6% precision. In the GA program, radial velocities and chemical abundances of stars in the Milky Way and M31 will be used to infer the past assembly histories of spiral galaxies and the structure of their dark matter halos. Data will be secured for 10^6 stars in the Galactic thick-disk, halo and tidal streams as faint as V~22, including stars with V < 20 to complement the goals of the Gaia mission. A medium-resolution mode with R = 5000 to be implemented in the red arm will allow the measurement of multiple alpha-element abundances and more precise velocities for Galactic stars, elucidating the detailed chemo-dynamical structure and evolution of each of the main stellar components of the Milky Way Galaxy and of its dwarf spheroidal galaxies. For the extragalactic program, our simulations suggest the wide avelength range will be powerful in probing the galaxy population and its clustering over a wide redshift range. We propose to conduct a color-selected survey of 1<z<2 galaxies and AGN over 16 deg^2 to J~23.4, yielding a fair sample of galaxies with stellar masses above ~10^{10}Ms at z~2. A two-tiered survey of higher redshift LBGs and LAEs will quantify the properties of early systems close to the reionization epoch.
We study the spherical, top-hat collapse model for a mixed dark matter model including cold dark matter (CDM) and massive neutrinos of mass scales ranging from m_nu= 0.05 to a few 0.1eV, the range of lower- and upper-bounds implied from the neutrino
oscillation experiments and the cosmological constraints. To develop this model, we properly take into account relative differences between the density perturbation amplitudes of different components (radiation, baryon, CDM and neutrinos) around the top-hat CDM overdensity region assuming the adiabatic initial conditions. Furthermore, we solve the linearized Boltzmann hierarchy equations to obtain time evolution of the lineariezed neutrino perturbations, yet including the effect of nonlinear gravitational potential due to the nonlinear CDM and baryon overdensities in the late stage. We find that the presence of massive neutrinos slows down the collapse of CDM (plus baryon) overdensity, however, that the neutrinos cannot fully catch up with the the nonlinear CDM perturbation due to its large free-streaming velocity for the ranges of neutrino masses and halo masses we consider. We find that, just like CDM models, the collapse time of CDM overdensity is well monitored by the linear-theory extrapolated overdensity of CDM plus baryon perturbation, smoothed with a given halo mass scale, if taking into account the suppression effect of the massive neutrinos on the linear growth rate. Using these findings, we argue that the presence of massive neutrinos of mass scales 0.05 or 0.1eV may cause a significant decrease in the abundance of massive halos compared to the model without the massive neutrinos; e.g., by 25% or factor 2, respectively, for halos with 10^15Ms and at z=1.
We develop a maximum likelihood based method of reconstructing band powers of the density and velocity power spectra at each wavenumber bins from the measured clustering features of galaxies in redshift space, including marginalization over uncertain
ties inherent in the Fingers-of-God (FoG) effect. The reconstruction can be done assuming that the density and velocity power spectra depend on the redshift-space power spectrum having different angular modulations of mu with mu^{2n} (n=0,1,2) and that the model FoG effect is given as a multiplicative function in the redshift-space spectrum. By using N-body simulations and the halo catalogs, we test our method by comparing the reconstructed power spectra with the simulations. For the spectrum of mu^0 or equivalently the density power spectrum P_dd(k), our method recovers the amplitudes to a few percent accuracies up to k=0.3 h/Mpc for both dark matter and halos. For the power spectrum of mu^2, which is equivalent to the density-velocity spectrum P_dv(k) in the linear regime, our method can recover the input power spectrum for dark matter up to k=0.2 h/Mpc and at both z=0 and 1, if using the adequate FoG model. However, for the halo spectrum, the reconstructed spectrum shows greater amplitudes than the simulation P_dv(k). We argue that the disagreement is ascribed to nonlinearity effect that arises from the cross-bispectra of density and velocity perturbations. Using the perturbation theory, we derive the nonlinear correction term, and find that the leading-order correction term is proportional to mu^2 and increases the mu^2-power spectrum amplitudes at larger k, at lower redshifts and for more massive halos. We find that adding the nonlinearity correction term to the simulation P_dv(k) can fairly well reproduce the reconstructed P_dv(k) for halos up to k~0.2 h/Mpc.
(Abridged) We use Subaru data to conduct a detailed weak-lensing study of the dark matter distribution in a sample of 30 X-ray luminous galaxy clusters at 0.15<z<0.3. A weak-lensing signal is detected at high statistical significance in each cluster,
the total detection S/N ranging from 5 to 13. In this paper we concentrate on fitting spherical models to the tangential distortion profiles of the clusters. When the models are fitted to the clusters individually, we are unable to discriminate statistically between SIS and NFW models. However when the tangential distortion profiles of the individual clusters are combined, and models fitted to the stacked profile, the SIS model is rejected at 6- and 11-sigma, respectively, for low- and high-mass bins. We also use the individual cluster NFW model fits to investigate the relationship between cluster mass (M_vir) and concentration (c_vir), finding an anti-correlation of c_vir and M_vir. The best-fit c_vir-M_vir relation is: c_vir(M_vir) propto M_vir^{-alpha} with alpha=0.41+/-0.19 -- i.e. a non-zero slope is detected at 2sigma significance. We then investigate the optimal radius within which to measure cluster mass, finding that the typical fractional errors are improved to sigma(M_Delta)/M_Delta ~ 0.1-0.2 for cluster masses at higher over-densities Delta=500-2000, from 0.2-0.3 for the virial over-density (~110). Further comparisons between mass measurements based on spherical model fitting and the model-independent aperture mass method reveal that the 2D aperture mass enclosed within a cylinder of a given aperture radius is systematically greater than the 3D spherical mass obtained from NFW model fitting: M_2D/M_3D= 1.34 and 1.40 for Delta=500 and 110, respectively. The amplitude of this effect agrees well with that predicted by integrating the NFW model along the line-of-sight.
The weak lensing (WL) distortions of distant galaxy images are sensitive to neutrino masses by probing the suppression effect on clustering strengths of total matter in large-scale structure. We use the latest measurement of WL correlations, the CFHT
LS data, to explore constraints on neutrino masses. We find that, while the WL data alone cannot place a stringent limit on neutrino masses due to parameter degeneracies, the constraint can be significantly improved when combined with other cosmological probes, the WMAP 5-year (WMAP5) data and the distance measurements of type-Ia supernovae (SNe) and baryon acoustic oscillations (BAO). The upper bounds on the sum of neutrino masses are m_tot = 1.1, 0.76 and 0.54 eV (95% CL) for WL+WMAP5, WMAP5+SNe+BAO, and WL+WMAP5+SNe+BAO, respectively, assuming a flat LCDM model with finite-mass neutrinos. In deriving these constraints, our analysis includes the non-Gaussian covariances of the WL correlation functions to properly take into account significant correlations between different angles.
The weak lensing power spectrum carries cosmological information via its dependence on the growth of structure and on geometric factors. Since much of the cosmological information comes from scales affected by nonlinear clustering, measurements of th
e lensing power spectrum can be degraded by non-Gaussian covariances. Recently there have been conflicting studies about the level of this degradation. We use the halo model to estimate it and include new contributions related to the finite size of lensing surveys, following Rimes and Hamiltons study of 3D simulations. We find that non-Gaussian correlations between different multipoles can degrade the cumulative signal-to-noise for the power spectrum amplitude by up to a factor of 2 (or 5 for a worst-case model that exceeds current N-body simulation predictions). However, using an eight-parameter Fisher analysis we find that the marginalized errors on individual parameters are degraded by less than 10% (or 20% for the worst-case model). The smaller degradation in parameter accuracy is primarily because: individual parameters in a high-dimensional parameter space are degraded much less than the volume of the full Fisher ellipsoid; lensing involves projections along the line of sight, which reduce the non-Gaussian effect; some of the cosmological information comes from geometric factors which are not degraded at all. We contrast our findings with those of Lee & Pen (2008) who suggested a much larger degradation in information content. Finally, our results give a useful guide for exploring survey design by giving the cosmological information returns for varying survey area, depth and the level of some systematic errors.
