Quadratic estimators for unwindowed power spectrum of galaxy-galaxy weak lensing and its application to $P_{\rm gm}(k)$ estimation

Abstract

Galaxy-galaxy weak lensing provides a powerful means of measuring the average matter distribution around lens galaxies -- i.e., the galaxy bias relation. Properly accounting for the spin-2 nature of weak lensing distortions, we develop a quadratic estimator for measuring the $E$- and $B$-mode angular power spectra from galaxy-galaxy weak lensing, correcting for survey window effects arising from, for example, survey geometry and bright star masks. The estimator can be implemented efficiently by adopting FFTs on pixelized maps of the lens galaxy distribution and source galaxy ellipticities, under the flat-sky approximation. Using simulated weak lensing fields and halo catalogs in the light-cone ray-tracing simulations, we show that the estimator can recover the underlying $E$-mode power spectrum, $C_{{\rm g}E}(\ell)$, to within a few percent in fractional error, while minimizing the leakage of $E$-mode into the $B$-mode power spectrum, in each multipole bin over the wide range of multipoles (up to $\ell \sim 3000$ studied in this paper). We then discuss that the estimator can be used to estimate the 3D galaxy-matter power spectrum, $P_{\rm gm}(k)$, by dividing lens galaxies into multiple redshift slices. We also derive an optimal weighting for each lens redshift slice in the shot noise-limited regime for the estimation of $P_{\rm gm}(k)$, which reduces the statistical errors by up to $\sim$20\% compared to the case without weighting.