Improving three-dimensional mass mapping with weak gravitational lensing
  using galaxy clustering
  The weak gravitational lensing distortion of distant galaxy images (defined
as sources) probes the projected large-scale matter distribution in the
Universe. To improve quality in the 3D mass mapping using 3D-lensing, we
combine the lensing information with the spatial clustering of a population of
galaxies that trace the matter density with a known galaxy bias (defined as
tracers). For our minimum variance estimator, merely all the second-order bias
of the tracers has to be known, which can in principle be self-consistently
constrained in the data by lensing techniques. This synergy introduces a new
noise component because of the stochasticity in the matter-tracer density
relation. We give a description of the stochasticity noise in the Gaussian
regime, and we investigate the estimator characteristics analytically. We apply
the estimator to a mock survey based on the Millennium Simulation. The
estimator linearly mixes the individual lensing mass and tracer number density
maps into a combined smoothed mass map. The weighting in the mix depends on the
S/N of the individual maps and the correlation, $r$, between the matter and
galaxy density. The weight of the tracers can be reduced by hand. For moderate
mixing, the S/N in the mass map improves by a factor $\sim2-3$ for
$r\gtrsim0.4$; the systematic offset between a true and apparent mass peak
distance ($z$-shift bias) in a lensing-only map is eliminated, even for weak
correlations of $r\sim0.4$. If the second-order bias of tracer galaxies can be
determined, the synergy technique potentially provides an option to improve
redshift accuracy and completeness of the lensing 3D mass map. However,the
estimator's performance on sub-degree, non-Gaussian scales depends on all
details in the galaxy bias mechanism and, hence, its accuracy on the choice of
the tracer population.[abridged]
