  We present a novel framework for jointly modelling the weak lensing source
galaxy redshift distribution and the intrinsic alignment of galaxies via a
shared luminosity function (LF). Considering this framework within the context
of a Rubin Observatory's Legacy Survey of Space and Time (LSST) Year 1 and Year
10 cosmic shear analysis, we first demonstrate the substantial impact of the LF
on both source galaxy redshift distributions and the intrinsic alignment
contamination. We establish how the individual parameters of a Schechter LF
model impact the redshift distribution of a magnitude-limited sample, and we
demonstrate the effect of marginalising over the LF parameters as incorporated
in the intrinsic alignment modelling of a standard cosmic shear analysis
set-up. We forecast the impact of our joint modelling framework on cosmological
parameter constraints. Our preliminary results are promising, indicating that
this framework can yield cosmological constraints consistent with those
expected from standard analyses, enhanced by the flexibility of not fixing LF
parameters. We plan to further validate these findings with comprehensive
Markov chain Monte Carlo simulations to robustly quantify bias avoidance and
underscore the framework's efficacy. Taking advantage of our forecasting
results and the parameter degeneracies, we identify the specific impact of the
shape of the LF of source galaxies on the cosmic shear data vector. We also
discuss the potential of this method in providing a way to model generic
selection functions in redshift distribution estimation, as well as its
possibilities for extension to a 3x2pt analysis, particularly with respect to
incorporating galaxy bias in this luminosity-function-based framework. Although
we consider the context of LSST cosmic shear in this work, the proposed joint
modelling framework is generically applicable to weak lensing surveys.
