Kavli Affiliate: Masahiro Takada
| First 5 Authors: Taisei Terawaki, Taisei Terawaki, , ,
| Summary:
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, $C_rm gE(ell)$, 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.
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