Cosmic shear results from the deep lens survey - I: Joint constraints on omega_m and sigma_8 with a two-dimensional analysis

TL;DR

<3-5 sentence high-level summary> This study presents a deep, five-field cosmic shear analysis from the Deep Lens Survey (DLS) to constrain the matter density parameter and the amplitude of matter fluctuations via a non-tomographic two-point lensing signal. The authors develop a two-stage PSF treatment based on principal component analysis for per-CCD PSFs and a stack-based reconstruction of the mosaic PSF, paired with image-simulation–driven shear calibration, and they marginalize over photo-z, shear calibration, and h while using a cosmology-dependent covariance. They find a tight DLS-alone constraint on Ω_M and σ_8, and demonstrate that combining with WMAP7 yields even stronger joint constraints; they also show that fully accounting for covariance evolution with cosmology is essential for robust inference. The methodology and results highlight the power of deep, wide-area weak-lensing surveys and set the stage for future tomographic analyses that will further break degeneracies in the Ω_M–σ_8 plane.

Abstract

We present a cosmic shear study from the Deep Lens Survey (DLS), a deep BVRz multi-band imaging survey of five 4 sq. degree fields with two National Optical Astronomy Observatory (NOAO) 4-meter telescopes at Kitt Peak and Cerro Tololo. For both telescopes, the change of the point-spread-function (PSF) shape across the focal plane is complicated, and the exposure-to-exposure variation of this position-dependent PSF change is significant. We overcome this challenge by modeling the PSF separately for individual exposures and CCDs with principal component analysis (PCA). We find that stacking these PSFs reproduces the final PSF pattern on the mosaic image with high fidelity, and the method successfully separates PSF-induced systematics from gravitational lensing effects. We calibrate our shears and estimate the errors, utilizing an image simulator, which generates sheared ground-based galaxy images from deep Hubble Space Telescope archival data with a realistic atmospheric turbulence model. For cosmological parameter constraints, we marginalize over shear calibration error, photometric redshift uncertainty, and the Hubble constant. We use cosmology-dependent covariances for the Markov Chain Monte Carlo analysis and find that the role of this varying covariance is critical in our parameter estimation. Our current non-tomographic analysis alone constrains the Omega_M-sigma_8 likelihood contour tightly, providing a joint constraint of Omega_M=0.262+-0.051 and sigma_8=0.868+-0.071. We expect that a future DLS weak-lensing tomographic study will further tighten these constraints because explicit treatment of the redshift dependence of cosmic shear more efficiently breaks the Omega_M-sigma_8 degeneracy. Combining the current results with the Wilkinson Microwave Anisotropy Probe 7-year (WMAP7) likelihood data, we obtain Omega_M=0.278+-0.018 and sigma_8=0.815+-0.020.

Figures (30)

• Figure 1: Survey area and depth of various optical surveys. The red line represents the $A \Omega t=constant$ locus, where $A$, $\Omega$, and $t$ are the primary mirror area, field of view, and exposure time, respectively. DLS is the deepest optical survey to date among the current $\gtrsim10$ sq. degree surveys. Depth is compared either in the R or i band.
• Figure 2: Example of spatial variation of DLS PSF. Although this particular pattern is observed on 24 February 2001 from the Blanco telescope, a similar degree of PSF variation complexity is commonly present in all of our DLS data. Each"whisker" shows the direction and magnitude of the stellar ellipticity at the location by its orientation and length, respectively. The red stick in the middle shows the size of 10% ellipticity [i.e., $(a-b)/(a+b)=0.1$]. The eight shaded rectangles depict the eight CCDs of the camera. Here we did not clean up outliers (e.g., cosmic-ray hit stars, binary stars, etc.), and they do not represent real PSFs. A similar degree of PSF variation complexity is commonly present in DLS data, albeit typically with a smaller amplitude.
• Figure 3: Complication in PSF modeling due to image stacking. Weak-lensing analysis is typically performed on a stacked image, which often exhibits sharp PSF discontinuities. The figure schematically shows how this complication arises. When we combine the two images in the left panel, the resulting PSF (right) possesses abrupt ellipticity changes across the boundaries of input frames.
• Figure 4: Variance vs. number of PSF basis functions (eigenPSFs). To determine the number of basis functions for a compact description of the PSF, we examine fractional data variance for different number of basis functions. For $HST$/ACS PSFs, we observe that the growth slows down notably after $\hbox{$\sim$}20$ (Jee et al. 2007). For the PSF of the 4-m Mayall/Blanco telescopes, this happens at $\hbox{$\sim$}5$. The simpler profile of the ground-based PSF (as opposed to complex, diffraction limited PSF of $HST$) requires fewer basis functions. However, because of the larger FWHM variation (i.e., atmospheric seeing), the total variance remains slightly lower than in the case of $HST$/ACS ($\hbox{$\sim$}96$% vs. $\hbox{$\sim$}99$% at 20 ). The PSF reconstruction of the Mayall/Blanco Telescopes does not show any significant difference in quality as long as the number of eigenPSFs is $\gg5$. In the current study, we choose to keep 20 eigenPSFs.
• Figure 5: Observed PSF ellipticity in the stacked image for F2. The whiskers display the ellipticity distribution of the stars directly measured from the $2\degr\times2\degr$ mosaic image. The background shade represents the weight map (darker shade indicates lower value) derived from both exposure maps and photon statistics, and illustrates the complexity of the weight distribution. PSF discontinuities occur at exposure boundaries (i.e., at discontinuities in the weight map). We did not clean up outliers (e.g., cosmic-ray hit stars, binary stars, etc.), and they do not represent real PSFs.