The Kinematic Sunyaev-Zel'dovich Effect with Projected Fields II:
  prospects, challenges, and comparison with simulations
  The kinematic Sunyaev-Zel'dovich (kSZ) signal is a powerful probe of the
cosmic baryon distribution. The kSZ signal is proportional to the integrated
free electron momentum rather than the electron pressure (which sources the
thermal SZ signal). Since velocities should be unbiased on large scales, the
kSZ signal is an unbiased tracer of the large-scale electron distribution, and
thus can be used to detect the "missing baryon" that evade most observational
techniques. While most current methods for kSZ extraction rely on the
availability of very accurate redshifts, we revisit a method that allows
measurements even in the absence of redshift information for individual
objects. It involves cross-correlating the square of an appropriately filtered
cosmic microwave background (CMB) temperature map with a projected density map
constructed from a sample of large-scale structure tracers. We show that this
method will achieve high signal-to-noise when applied to the next generation of
high-resolution CMB experiments, provided that component separation is
sufficiently effective at removing foreground contamination. Considering
statistical errors only, we forecast that this estimator can yield $S/N \approx
$ 3, 120 and over 150 for Planck, Advanced ACTPol, and hypothetical Stage-IV
CMB experiments, respectively, in combination with a galaxy catalog from WISE,
and about 20% larger $S/N$ for a galaxy catalog from the proposed SPHEREx
experiment. This work serves as a companion paper to the first kSZ measurement
with this method, where we used CMB temperature maps constructed from Planck
and WMAP data, together with galaxies from the WISE survey, to obtain a 3.8 -
4.5$\sigma$ detection of the kSZ$^2$ amplitude.
