  We present a new method to measure the redshift-dependent galaxy bias by
combining information from the galaxy density field and the weak lensing field.
This method is based on Amara et al. (2012), where they use the galaxy density
field to construct a bias-weighted convergence field kg. The main difference
between Amara et al. (2012) and our new implementation is that here we present
another way to measure galaxy bias using tomography instead of bias
parameterizations. The correlation between kg and the true lensing field k
allows us to measure galaxy bias using different zero-lag correlations, such as
<kgk>/<kk> or <kgkg>/<kgk>. Our method measures the linear bias factor on
linear scales under the assumption of no stochasticity between galaxies and
matter. We use the MICE simulation to measure the linear galaxy bias for a
flux-limited sample (i < 22.5) in tomographic redshift bins using this method.
This paper is the first that studies the accuracy and systematic uncertainties
associated with the implementation of the method, and the regime where it is
consistent with the linear galaxy bias defined by projected 2-point correlation
functions (2PCF). We find that our method is consistent with linear bias at the
percent level for scales larger than 30 arcmin, while nonlinearities appear at
smaller scales. This measurement is a good complement to other measurements of
bias, since it does not depend strongly on sigma8 as the 2PCF measurements. We
apply this method to the Dark Energy Survey Science Verification data in a
follow-up paper.
