Covariances for cosmic shear and galaxy–galaxy lensing in the response approach

Abstract

In this study, we measure the response of matter and halo projected power spectra P 2D XY (k) (X, Y are matter and/or halos), to a large-scale density contrast, δ b , using separate universe simulations. We show that the fractional response functions, i.e., d ln P 2D XY (k)/dδ b , are identical to their respective three-dimensional power spectra within simulation measurement errors. Then, using various N-body simulation combinations (small-box simulations with periodic boundary conditions and sub-volumes of largebox simulations) to construct mock observations of projected fields, we study how super-survey modes, in both parallel and perpendicular directions to the projection direction, affect the covariance matrix of P 2D XY (k), known as super-sample covariance (SSC). Our results indicate that the SSC term provides dominant contributions to the covariances of matter-matter and matter-halo spectra at small scales but does not provide significant contributions in the halo-halo spectrum. We observe that the large-scale density contrast in each redshift shell causes most of the SSC effect, and we did not observe a SSC signature arising from large-scale tidal field within the levels of measurement accuracy. We also develop a response approach to calibrate the SSC term for cosmic shear correlation function and galaxy-galaxy weak lensing, and validate the method by comparison with the light-cone ray-tracing simulations. Our method provides a reasonably accurate, albeit computationally inexpensive, way to calibrate the covariance matrix for clustering observables available from wide-area galaxy surveys.

Cosmological inference from emulator based halo model I: Validation tests with HSC and SDSS mock catalogs

“…expected to arise from the four-point correlation among super-and sub-survey modes [112,113], and the recent simulations have shown that the SSC in the halo-matter cross correlation becomes important only at 1 h −1 Mpc [114]. At the scale of R ∼ 1 h −1 Mpc, the statistical uncertainties in our lensing analyses are mostly determined by the shot noise terms.…”

Perturbation theory approach to predict the covariance matrices of the galaxy power spectrum and bispectrum in redshift space

“…The situation becomes worse in the joint analysis of the power spectrum and the bispectrum, because it requires about 10 or 20 times larger number of data bins than the power spectrum only analysis (Sugiyama et al 2019), substantially increasing the required number of independent realizations. To reduce the computational cost of mock generation, various other approaches have been proposed for the power spectrum analysis (Hamilton et al 2006;Pope & Szapudi 2008;Schneider et al 2011;Paz & Sanchez 2015;Pearson & Samushia 2016;Padmanabhan et al 2016;O'Connell et al 2016;Howlett & Percival 2017;Escoffier et al 2016;Takahashi et al 2018). Second, aforementioned fast mock generation schemes are typically designed to only reproduce the observed 2-point function for a target galaxy sample, and hence it is not entirely clear if they can reproduce the 3-point functions at the same time.…”

“…In the case of the two-point statistics, the analytical expression in the Gaussian limit was first shown in e.g., Feldman et al (1994); subsequently, perturbation theory was often adopted to assess the impact of the non-Gaussian term (the trispectrum) on the matter (halo) power spectrum covariances (Meiksin & White 1999;Eisenstein & Zaldarriaga 2001;Smith 2009;Carron et al 2015;Bertolini et al 2016;Mohammed et al 2017; Barreira & Schmidt 2017a,b;Howlett & Percival 2017) and the weak lensing power spectrum covariances (Scoccimarro et al 1999b;Reischke et al 2017; Barreira et al 2018). In addition, the halo model approach (for a review, see Cooray & Sheth 2002) has been used to estimate the covariance matrix for the matter (halo) (Neyrinck et al 2006;Neyrinck & Szapudi 2007;Wu & Huterer 2013;Mohammed & Seljak 2014;Ginzburg et al 2017;Takada & Hu 2013) and weak lensing power spectra (Cooray & Hu 2001;Takada & Bridle 2007;Takada & Jain 2009;Takahashi et al 2018). Since these analytical models are unable to capture full non-linear gravitational effects on small scales, one also often uses N-body simulations for a better understanding of the non-Gaussian effect and for testing the validity of these models Neyrinck & Szapudi 2008;Takahashi et al 2009Takahashi et al , 2011Sato et al 2009;Ngan et al 2012;de Putter et al 2012;Blot et al 2015Blot et al , 2016Blot et al , 2018.…”

The mass–richness relation of optically selected clusters from weak gravitational lensing and abundance with Subaru HSC first-year data

“…The covariance consists of shape noise covariance from the finite number of lens-source pairs, Poisson noise for the abundance from the finite number of the clusters, and sample covariance from an imperfect sampling of the fluctuations in large-scale structure within a finite survey volume (e.g.,Hu & Kravtsov 2003;Takada & Bridle 2007;Oguri & Takada 2011;Takada & Hu 2013;Hikage & Oguri 2016;Takahashi et al 2018;…”