  Galactic dynamo models sustained by supernova (SN) driven turbulence and
differential rotation have revealed that the sustenance of large scale fields
requires a flux of small scale magnetic helicity to be viable. Here we
generalize a minimalist analytic version of such galactic dynamos to explore
some heretofore unincluded contributions from shear on the total turbulent
energy and turbulent correlation time, with the helicity fluxes maintained by
either winds, diffusion, or magnetic buoyancy. We construct an analytic
framework for modeling the turbulent energy and correlation time as functions
of SN rate and shear. We compare our prescription with previous approaches that
only include rotation. The solutions depend separately on the rotation period
and the eddy turnover time and not just on their ratio (the Rossby number). We
consider models in which these two time scales are allowed to be independent
and also a case in which they are mutually dependent on radius when a radial
dependent SN rate model is invoked. For the case of a fixed rotation period (or
fixed radius) we show that the influence of shear is dramatic for low Rossby
numbers, reducing the correlation time of the turbulence, which in turn,
strongly reduces the saturation value of the dynamo compared to the case when
the shear is ignored. We also show that even in the absence of winds or
diffusive fluxes, magnetic buoyancy may be able to sustain sufficient helicity
fluxes to avoid quenching.
