Halo-galaxy lensing: A full sky approach

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, counterintuitively, errors in the conventionally used flat-sky approximation remain at a percent 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 percent level at the baryonic acoustic oscillation scales for lensing halos of z∼0.2, and comparable with the effect of primordial non-Gaussianity with f_NL∼10 at large separations. Our results allow one 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.