Discriminating Weak Lensing from Intrinsic Spin Correlations Using the Curl-Gradient Decomposition

By Robert G. Crittenden, P. Natarajan, Ue-Li Pen, Tom Theuns. 2000

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The distortion field defined by the ellipticities of galaxy shapes as projected on the sky can be uniquely decomposed into a gradient and a curl component. If the observed ellipticities are induced by weak gravitational lensing, then the distortion field is curl-free. Here we show that, in contrast, the distortion field resulting from intrinsic spin alignments is not curl-free. This provides a powerful discriminant between lensing and intrinsic contributions to observed ellipticity correlations. We also show how these contributions can be disentangled statistically from the ellipticity correlations or computed locally from circular integrals of the ellipticity field. This allows for an unambiguous detection of intrinsic galaxy alignments in the data. When the distortions are dominated by lensing, as occurs at high redshifts, the decomposition provides a valuable tool for understanding properties of the noise and systematic errors. These techniques can be applied equally well to the polarization of the microwave background, where it can be used to separate curl-free scalar perturbations from those produced by gravity waves or defects.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/a32c68a81ea2c5bc80d701f508ccd42854a43af3

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Citations in the corpus

The Intrinsic Alignment of Galaxies and its Impact on Weak Gravitational Lensing in an Era of Precision Cosmology (2014, background): “y E-modes to ﬁrst-order in the deﬂection angle while the intrinsic alignment of galaxies (II) produces both E- and B-modes. This decomposition thus allows one to discriminate between the two signals (Crittenden et al., 2002) (see also Sec. 6.6.1). 40 As described in Crittenden et al. (2002), the E- ”
The skewness of the aperture mass statistic (2003, methodology): “However, we find that calculation of the three-point statistic is significantly easier using the form introduced by Crittenden et al. (2002).”
The Shear Testing Programme – I. Weak lensing analysis of simulated ground-based observations (2005, methodology): “Implementing diagnostic statistics that decompose cosmic shear signals into their lensing E-modes and non-lensing B-modes (Crittenden et al. 2002; Schneider et al. 2002; Brown et al. 2003) immediately alerts us to the presence of systematic error within our data set.”
The Shear TEsting Programme 2: Factors affecting high precision weak lensing analyses (2006, methodology): “Other systematics can be checked for in real data via correlation of the galaxies and the PSF, or via an E − B decomposition (Crittenden et al. 2002; Schneider, Van Waerbeke & Mellier 2002; Schneider & Kilbinger 2007).”
Cosmological constraints from the 100-deg2 weak-lensing survey (2007, methodology): “Following Crittenden et al. (2001, 2002), we define ξ ′(θ ) = ξ−(θ ) + 4 ∫ ∞ θ dϑ ϑ ξ−(ϑ) − 12θ 2 ∫ ∞ θ dϑ ϑ3 ξ−(ϑ).”
Fast estimation of polarization power spectra using correlation functions (2003, methodology): “The correlation-function based approach we develop here, motivated by Crittenden et al. (2002), has a significant feature in that, with a little post-processing of the correlation functions, leakage between E and B can be eliminated in the mean, even for observations covering only a small part of…”
Potential sources of contamination to weak lensing measurements: constraints from N-body simulations (2006, methodology): “Crittenden et al. (2002) show that the correlation functions can be decomposed into the followingE- and B-type correlators, ξE(θ) = ξ+(θ) + ξ ′(θ) 2 ξB(θ) = ξ+(θ) − ξ ′(θ) 2 (7) where, in this case, ξ±(θ) = 〈etet〉θ ± 〈erer〉θ, (8) and ξ′(θ) = ξ−(θ) + 4 ∫ ∞ θ dϑ ϑ ξ−(ϑ) − 12θ 2 ∫ ∞ θ dϑ ϑ3 ξ−(ϑ).”
Evidence of the accelerated expansion of the Universe from weak lensing tomography with COSMOS (2009, unknown): “Crittenden et al. (2002) show thatξ± can be decomposed into E- and B-modes as ξE/B(θ) = ξ+(θ) ± ξ′(θ) 2 , (8) with ξ′(θ) = ξ−(θ) + 4 ∫ ∞ θ dϑ ϑ ξ−(ϑ) − 12θ2 ∫ ∞ θ dϑ ϑ3 ξ−(ϑ) .”
Ray-tracing through the Millennium Simulation: Born corrections and lens-lens coupling in cosmic shear and galaxy-galaxy lensing (2008, background): “These artifacts can be avoided by using aperture masses to quantify the shear E- and B-mode contributions (Crittenden et al. 2002; Schneider et al. 2002).”
Combining Lens Distortion and Depletion to Map the Mass Distribution of A1689 (2007, unknown): “To do this, we utilize the relation between the gradients of κ and γ (Kaiser 1995; Crittenden et al. 2002), △κ(θ) = ∂α∂βΓαβ(θ) = 2D̂∗γ(θ) (6) where D̂ is the complex differential operator D̂ = (∂21 − ∂22)/2 + i∂1∂2.”
Gravitational lensing analysis of the Kilo-Degree Survey (2015, unknown): “Crittenden et al. (2002) show that the shear correlation functions, estimated in equation (26), can be decomposed into the E- and B-type correlators ξE(θ ) = ξ+(θ ) + ξ ′(θ ) 2 and ξB(θ ) = ξ+(θ ) − ξ ′(θ ) 2 , (27) where ξ ′(θ ) = ξ−(θ ) + 4 ∫ ∞ θ dϑ ϑ ξ−(ϑ) − 12θ2 ∫ ∞ θ dϑ ϑ3 ξ−(ϑ) .”
Very weak lensing in the CFHTLS Wide: Cosmology from cosmic shear in the linear regime (2007, unknown): “Crittenden et al. (2002) and Pen et al. (2002) derived an analogous decomposition for the shear correlations, which is also used in this work: ξE,B(θ) = ξ+(θ) ± ξ′(θ) 2 , (8) where the definition of ξ′ is also given in Schneider et al. (2002b) ξ′(θ) = ξ−(θ) + ∫ ∞ θ dϑ ϑ ξ−(θ) ( 4 − 12 ( θ ϑ )2) .”