Halo-Galaxy Lensing: A Full Sky Approach

TL;DR

This paper reformulates halo-galaxy lensing in harmonic space, revealing that flat-sky approximation errors are significant at large angles, impacting high-precision measurements in upcoming wide-area surveys.

Contribution

It introduces a full-sky harmonic space formulation of halo-galaxy lensing, quantifies errors in flat-sky approximation, and provides corrections for future high-precision lensing analyses.

Findings

Flat-sky approximation errors are a few percent at BAO scales.

Errors increase at larger angles and lower redshifts.

Full-sky correction enables more accurate shear profile measurements.

Abstract

The halo-galaxy lensing correlation function or the average tangential shear profile over sampled halos is a very powerful means of measuring the halo masses, the mass profile, and the halo-mass correlation function of very large separations in the linear regime. We reformulate the halo-galaxy lensing correlation in harmonic space. We find that, counter-intuitively, errors in the conventionally used flat-sky approximation remain at a % level even at very small angles. The errors increase at larger angles and for lensing halos at lower redshifts: the effect is at a few % level at the baryonic acoustic oscillation scales for lensing halos of $z\sim 0.2$, and comparable with the effect of primordial non-Gaussianity with $f_{\rm NL}\sim 10$ at large separations. Our results allow to readily estimate/correct for the full-sky effect on a high-precision measurement of the average shear profile available from upcoming wide-area lensing surveys.