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Register a new userThe integrated 3-point correlation function of cosmic shear
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We present the integrated 3-point shear correlation function $izeta_{pm}$ -- a higher-order statistic of the cosmic shear field -- which can be directly estimated in wide-area weak lensing surveys without measuring the full 3-point shear correlation function, making this a practical and complementary tool to 2-point statistics for weak lensing cosmology. We define it as the 1-point aperture mass statistic $M_{mathrm{ap}}$ measured at different locations on the shear field correlated with the corresponding local 2-point shear correlation function $xi_{pm}$. Building upon existing work on the integrated bispectrum of the weak lensing convergence field, we present a theoretical framework for computing the integrated 3-point function in real space for any projected field within the flat-sky approximation and apply it to cosmic shear. Using analytical formulae for the non-linear matter power spectrum and bispectrum, we model $izeta_{pm}$ and validate it on N-body simulations within the uncertainties expected from the sixth year cosmic shear data of the Dark Energy Survey. We also explore the Fisher information content of $izeta_{pm}$ and perform a joint analysis with $xi_{pm}$ for two tomographic source redshift bins with realistic shape-noise to analyse its power in constraining cosmological parameters. We find that the joint analysis of $xi_{pm}$ and $izeta_{pm}$ has the potential to considerably improve parameter constraints from $xi_{pm}$ alone, and can be particularly useful in improving the figure of merit of the dynamical dark energy equation of state parameters from cosmic shear data.
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We constrain cosmological parameters from a joint cosmic shear analysis of peak-counts and the two-point shear correlation functions, as measured from the Dark Energy Survey (DES-Y1). We find the structure growth parameter $S_8equiv sigma_8sqrt{Omega_{rm m}/0.3} = 0.766^{+0.033}_{-0.038}$, which at 4.8% precision, provides one of the tightest constraints on $S_8$ from the DES-Y1 weak lensing data. In our simulation-based method we determine the expected DES-Y1 peak-count signal for a range of cosmologies sampled in four $w$CDM parameters ($Omega_{rm m}$, $sigma_8$, $h$, $w_0$). We also determine the joint covariance matrix with over 1000 realisations at our fiducial cosmology. With mock DES-Y1 data we calibrate the impact of photometric redshift and shear calibration uncertainty on the peak-count, marginalising over these uncertainties in our cosmological analysis. Using dedicated training samples we show that our measurements are unaffected by mass resolution limits in the simulation, and that our constraints are robust against uncertainty in the effect of baryon feedback. Accurate modelling for the impact of intrinsic alignments on the tomographic peak-count remains a challenge, currently limiting our exploitation of cross-correlated peak counts between high and low redshift bins. We demonstrate that once calibrated, a fully tomographic joint peak-count and correlation functions analysis has the potential to reach a 3% precision on $S_8$ for DES-Y1. Our methodology can be adopted to model any statistic that is sensitive to the non-Gaussian information encoded in the shear field. In order to accelerate the development of these beyond-two-point cosmic shear studies, our simulations are made available to the community upon request.
The nature of dark energy and the complete theory of gravity are two central questions currently facing cosmology. A vital tool for addressing them is the 3-point correlation function (3PCF), which probes deviations from a spatially random distribution of galaxies. However, the 3PCFs formidable computational expense has prevented its application to astronomical surveys comprising millions to billions of galaxies. We present Galactos, a high-performance implementation of a novel, O(N^2) algorithm that uses a load-balanced k-d tree and spherical harmonic expansions to compute the anisotropic 3PCF. Our implementation is optimized for the Intel Xeon Phi architecture, exploiting SIMD parallelism, instruction and thread concurrency, and significant L1 and L2 cache reuse, reaching 39% of peak performance on a single node. Galactos scales to the full Cori system, achieving 9.8PF (peak) and 5.06PF (sustained) across 9636 nodes, making the 3PCF easily computable for all galaxies in the observable universe.
We present measurements of cosmic shear two-point correlation functions (TPCFs) from Hyper Suprime-Cam Subaru Strategic Program (HSC SSP) first-year data, and derived cosmological constraints based on a blind analysis. The HSC first-year shape catalog is divided into four tomographic redshift bins ranging from $z=0.3$ to 1.5 with equal widths of $Delta z =0.3$. The unweighted galaxy number densities in each tomographic bin are 5.9, 5.9, 4.3, and 2.4 arcmin$^{-2}$ from lower to higher redshifts, respectively. We adopt the standard TPCF estimators, $xi_pm$, for our cosmological analysis, given that we find no evidence of the significant B-mode shear. The TPCFs are detected at high significance for all ten combinations of auto- and cross-tomographic bins over a wide angular range, yielding a total signal-to-noise ratio of 19 in the angular ranges adopted in the cosmological analysis, $7<theta<56$ for $xi_+$ and $28<theta<178$ for $xi_-$. We perform the standard Bayesian likelihood analysis for cosmological inference from the measured cosmic shear TPCFs, including contributions from intrinsic alignment of galaxies as well as systematic effects from PSF model errors, shear calibration uncertainty, and source redshift distribution errors. We adopt a covariance matrix derived from realistic mock catalogs constructed from full-sky gravitational lensing simulations that fully account for survey geometry and measurement noise. For a flat $Lambda$ cold dark matter model, we find $S_8 equiv sigma_8sqrt{Omega_m/0.3}=0.804_{-0.029}^{+0.032}$, and $Omega_m=0.346_{-0.100}^{+0.052}$. We carefully check the robustness of the cosmological results against astrophysical modeling uncertainties and systematic uncertainties in measurements, and find that none of them has a significant impact on the cosmological constraints.
The growth history of large-scale structure in the Universe is a powerful probe of the cosmological model, including the nature of dark energy. We study the growth rate of cosmic structure to redshift $z = 0.9$ using more than $162{,}000$ galaxy redshifts from the WiggleZ Dark Energy Survey. We divide the data into four redshift slices with effective redshifts $z = [0.2,0.4,0.6,0.76]$ and in each of the samples measure and model the 2-point galaxy correlation function in parallel and transverse directions to the line-of-sight. After simultaneously fitting for the galaxy bias factor we recover values for the cosmic growth rate which are consistent with our assumed $Lambda$CDM input cosmological model, with an accuracy of around 20% in each redshift slice. We investigate the sensitivity of our results to the details of the assumed model and the range of physical scales fitted, making close comparison with a set of N-body simulations for calibration. Our measurements are consistent with an independent power-spectrum analysis of a similar dataset, demonstrating that the results are not driven by systematic errors. We determine the pairwise velocity dispersion of the sample in a non-parametric manner, showing that it systematically increases with decreasing redshift, and investigate the Alcock-Paczynski effects of changing the assumed fiducial model on the results. Our techniques should prove useful for current and future galaxy surveys mapping the growth rate of structure using the 2-dimensional correlation function.
We measure the cosmic shear power spectrum on large angular scales by cross-correlating the shapes of ~9 million galaxies measured in the optical SDSS survey with the shapes of ~2.7x10^5 radio galaxies measured by the overlapping VLA-FIRST survey. Our measurements span the multipole range 10 < l < 130, corresponding to angular scales 2deg < {theta} < 20deg. On these scales, the shear maps from both surveys suffer from significant systematic effects that prohibit a measurement of the shear power spectrum from either survey alone. Conversely we demonstrate that a power spectrum measured by cross-correlating the two surveys is unbiased. We measure an E-mode power spectrum from the data that is inconsistent with zero signal at the 99% confidence (~2.7{sigma}) level. The odd-parity B-mode signal and the EB cross- correlation are both found to be consistent with zero (within 1{sigma}). These constraints are obtained after a careful error analysis that accounts for uncertainties due to cosmic variance, random galaxy shape noise and shape measurement errors, as well as additional errors associated with the observed large-scale systematic effects in the two surveys. Our constraints are consistent with the expected signal in the concordance cosmological model assuming recent estimates of the cosmological parameters from the Planck satellite, and literature values for the median redshifts of the SDSS and FIRST galaxy populations. The cross-power spectrum approach described in this paper represents a powerful technique for mitigating shear systematics and will be ideal for extracting robust results, with the exquisite control of systematics required, from future cosmic shear surveys with the SKA, LSST, Euclid and WFIRST-AFTA.
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