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

In this study, we measure the response of matter and halo projected power spectra P-XY(2D)(k) (X, Y are matter and/or haloes) to a large-scale density contrast, delta b, using separate universe simulations. We show that the fractional response functions, i.e. d In P-XY(2D)(k)/d delta(b), are identical to their respective 3D power spectra within simulation measurement errors. Then, using various N-body simulation combinations (small-box simulations with periodic boundary conditions and sub-volumes of large-box simulations) to construct mock observations of projected fields, we study how supersurvey modes, in both parallel and perpendicular directions to the projection direction, affect the covariance matrix of P-XY(2D)(k), known as supersample 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 an SSC signature arising from the large-scale tidal field within the levels of measurement accuracy. We also develop a response approach to calibrate the SSC term for the 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.