Halo-Galaxy Lensing: A Full Sky Approach

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 $f_{\mathrm{NL}}\sim 10$ 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.

12 pages, 4 figures

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