An extended theoretical scenario for Classical Cepheids. I. Modeling
  Galactic Cepheids in the Gaia photometric system
  We present a new extended and detailed set of models for Classical Cepheid
pulsators at solar chemical composition ($Z=0.02$, $Y=0.28$) based on a well
tested nonlinear hydrodynamical approach. In order to model the possible
dependence on crucial assumptions such as the Mass-Luminosity relation of
central Helium burning intermediate-mass stars or the efficiency of
superadiabatic convection, the model set was computed by varying not only the
pulsation mode and the stellar mass but also the Mass-Luminosity relation and
the mixing length parameter that is used to close the system of nonlinear
hydrodynamical and convective equations. The dependence of the predicted
boundaries of the instability strip as well as of both light and radial
velocity curves on the assumed Mass-Luminosity and the efficiency of
superadiabatic convection is discussed. Nonlinear
Period-Mass-Luminosity-Temperature, Period-Radius and Period-Mass-Radius
relations are also computed. The theoretical atlas of bolometric light curves
for both the fundamental and first overtone mode has been converted in the Gaia
filters $G$, $G_{BP}$ and $G_{BR}$ and the corresponding mean magnitudes have
been derived. Finally the first theoretical Period-Luminosity-Color and
Period-Wesenheit relations in the Gaia filters are provided and the resulting
theoretical parallaxes are compared with Gaia Data Release 2 results for both
fundamental and first overtone Galactic Cepheids.
