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The weak gravitational lensing distortion of distant galaxy images (definedas sources) probes the projected large-scale matter distribution in theUniverse. To improve quality in the 3D mass mapping using 3D-lensing, wecombine the lensing information with the spatial clustering of a population ofgalaxies that trace the matter density with a known galaxy bias (defined astracers). For our minimum variance estimator, merely all the second-order biasof the tracers has to be known, which can in principle be self-consistentlyconstrained in the data by lensing techniques. This synergy introduces a newnoise component because of the stochasticity in the matter-tracer densityrelation. We give a description of the stochasticity noise in the Gaussianregime, and we investigate the estimator characteristics analytically. We applythe estimator to a mock survey based on the Millennium Simulation. Theestimator linearly mixes the individual lensing mass and tracer number densitymaps into a combined smoothed mass map. The weighting in the mix depends on theS/N of the individual maps and the correlation, $r$, between the matter andgalaxy density. The weight of the tracers can be reduced by hand. For moderatemixing, 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 peakdistance ($z$-shift bias) in a lensing-only map is eliminated, even for weakcorrelations of $r\sim0.4$. If the second-order bias of tracer galaxies can bedetermined, the synergy technique potentially provides an option to improveredshift accuracy and completeness of the lensing 3D mass map. However,theestimator's performance on sub-degree, non-Gaussian scales depends on alldetails in the galaxy bias mechanism and, hence, its accuracy on the choice ofthe tracer population.[abridged]

Improving three-dimensional mass mapping with weak gravitational lensing using galaxy clustering