A method of weak lensing reconstruction through cosmic magnification with multi-band photometry information

Weak gravitational lensing induces flux dependent fluctuations in the observed galaxy number density distribution. This cosmic magnification (magnification bias) effect in principle enables lensing reconstruction alternative to cosmic shear and CMB lensing. However, the intrinsic galaxy clustering, which otherwise overwhelms the signal, has hindered its application. Through a scaling relation found by principal component analysis of the galaxy clustering in multi-band photometry space, we design a minimum variance linear estimator to suppress the intrinsic galaxy clustering and to reconstruct the lensing convergence map. In combination of the CosmoDC2 galaxy mock and the CosmicGrowth simulation, we test this proposal for a LSST-like galaxy survey with $ugrizY$ photometry bands. The scaling relation holds excellently at multipole $\ell<10^3$, and remains reasonably well to $\ell\sim 3000$. The linear estimator efficiently suppresses the galaxy intrinsic clustering, by a factor of $\sim 10^2$. For galaxies in the photo-z range $0.8<z_\kappa<1.2$, the reconstructed convergence map is cosmic variance limited per $\ell$ mode at $\ell<10^2$, and shot noise limited at $\ell>= 200$. Its cross-correlation with cosmic shear of galaxies can achieve $S/N >= 200$. When the source redshift of cosmic shear galaxies $z_\gamma<z_\kappa$, the systematic error is negligible at all investigated scales ($\ell<3000$). When $z_\gamma\geq z_\kappa$, the systematic error caused by the residual intrinsic galaxy clustering becomes non-negligible. We discuss possible mitigation of the residual intrinsic galaxy clustering required for accurate measurement at $\ell>10^3$. This work further demonstrates the potential of lensing measurement through cosmic magnification to enhance the weak lensing cosmology.