Can we use weak lensing to measure total mass profiles of galaxies on 20 kpc scales?

Abstract : Current constraints on dark matter density profiles from weak lensing are typically limited to radial scales greater than 50-100 kpc. In this paper, we explore the possibility of probing the very inner regions of galaxy/halo density profiles by measuring stacked weak lensing on scales of only a few tens of kpc. Our forecasts focus on scales smaller than the `equality radius' (R_eq), where the stellar component and the dark matter component contribute equally to the lensing signal. We compute the evolution of R_eq as a function of lens stellar mass and redshift and show that R_eq = 7-34 kpc for galaxies with M_* = 10^9.5-10^11.5 M_⊙. Unbiased shear measurements will be challenging on these scales. We introduce a simple metric to quantify how many source galaxies overlap with their neighbours and for which shear measurements will be challenging. Rejecting source galaxies with close-by companions results in an ∼20 per cent decrease in the overall source density. Despite this decrease, we show that Euclid and Wide Field Infrared Survey Telescope will be able to constrain galaxy/halo density profiles at R_eq with S/N >20 for M_* > 10¹⁰ M_⊙. Weak lensing measurements at R_eq, in combination with stellar kinematics on smaller scales, will be a powerful means by which to constrain both the inner slope of the dark matter density profile as well as the mass and redshift dependence of the stellar initial mass function.