Detection of cosmic magnification via galaxy shear-galaxy number density correlation from HSC survey data

We propose a novel method to detect cosmic magnification signals by cross-correlating foreground convergence fields constructed from galaxy shear measurements with background galaxy positional distributions—namely, shear-number density correlation. We apply it to the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) survey data. With 27 nonindependent data points and their full covariance, χ₀²≈34.1 and χ_T²≈24.0 with respect to the null and the cosmological model with the parameters from HSC shear correlation analyses in Hamana et al. [Publ. Astron. Soc. Jpn. 72, 16 (2020), 10.1093/pasj/psz138], respectively. The Bayes factor of the two is log₁₀B_{T 0}≈2.2 assuming equal model probabilities of null and HSC cosmology, showing a clear detection of the magnification signals. Theoretically, the ratio of the shear-number density and shear-shear correlations can provide a constraint on the effective multiplicative shear bias m ¯ using internal data themselves. We demonstrate the idea with the signals from our HSC-SSP mock simulations and rescale the statistical uncertainties to a survey of 15000 deg². For two-bin analyses with background galaxies brighter than m_lim=23 , the combined analyses lead to a forecasted constraint of σ (m ¯)∼0.032 , 2.3 times tighter than that found when using the shear-shear correlation alone. Correspondingly, σ (S₈) with S₈=σ₈(Ω_m/0.3 )0.⁵ is tightened by ∼2.1 times. Importantly, the joint constraint on m ¯ is nearly independent of cosmological parameters. Our study therefore points to the importance of including the shear-number density correlation in weak lensing analyses, which can provide valuable consistency tests of observational data, and thus to solidify the derived cosmological constraints.