  The kinetic Sunyaev Zel'dovich (kSZ) effect, cosmic microwave background
(CMB) anisotropies induced by scattering from free electrons in bulk motion, is
a primary target of future CMB experiments. Measurements of the kSZ effect have
the potential to address fundamental questions about the structure and
evolution of our Universe on the largest scales and at the earliest times. This
potential is unlocked by combining measurements of small-scale CMB anisotropies
with large-scale structure surveys, a technique known as kSZ tomography.
Previous work established a quadratic estimator for the remote dipole field,
the CMB dipole observed at different locations in the Universe. This previous
work did not include gravitational lensing, redshift space distortions, or
non-linear evolution of structure. In this paper, we investigate how well the
remote dipole field can be reconstructed in the presence of such effects by
using mock data from a suite of simulations. To properly model both large and
small scales, we develop a novel box-in-box simulation pipeline, where
small-scale information is obtained from N-body simulations, and large-scale
information obtained by evolving fields using linear theory and adding the
resulting corrections to the N-body particle data. This pipeline allows us to
create properly correlated maps of the primary CMB including lensing, as well
as the kSZ effect and density maps on the past light cone of an observer.
Analyzing an ensemble of mocks, we find that the dipole field can be
reconstructed with high fidelity over a range of angular scales and redshift
bins, although there is evidence of excess power from nonlinear structure. We
also analyze correlations with the primary CMB, investigating the ability of
kSZ tomography to reconstruct the intrinsic CMB dipole. Our results constitute
a proof-of-principle that kSZ tomography is a promising technique for future
datasets.
