Can we use Weak Lensing to Measure Total Mass Profiles of Galaxies on 20
  kiloparsec Scales?
  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 (Req)
where the stellar component and the dark matter component contribute equally to
the lensing signal. We compute the evolution of Req as a function of lens
stellar mass and redshift and show that Req=7-34 kpc for galaxies with the
stellar mass of 10^{9.5}-10^{11.5} solar masses. 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 about a 20 per cent decrease in the overall source
density. Despite this decrease, we show that Euclid and WFIRST will be able to
constrain galaxy/halo density profiles at Req with signal-to-noise ratio >20
for the stellar mass of >10^{10} solar masses. Weak lensing measurements at
Req, 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.
