Updated theoretical Period-Age and Period-Age-Color relations for
  Galactic Classical Cepheids: an application to the Gaia DR2 sample
  Updated evolutionary and pulsational model predictions are combined in order
to interpret the properties of Galactic Classical Cepheids in the Gaia Data
Release 2. In particular, the location of the instability strip boundaries and
the analytical relations connecting pulsation periods to the intrinsic stellar
parameters are combined with evolutionary tracks to derive reliable and
accurate period-age, and the first theoretical period-age-color relations in
the Gaia bands for a solar chemical abundance pattern ($Z$=$0.02$, $Y$=$0.28$).
The adopted theoretical framework takes into account possible variations in the
mass-luminosity relation for the core helium-burning stage as due to changes in
the core convective overshooting and/or mass loss efficiency, as well as the
impact on the instability strip boundaries due to different assumptions for
superadiabatic convection efficiency. The inferred period-age and
period-age-color relations are applied to a selected sample of both fundamental
and first overtone Gaia Cepheids, and individual ages for the various adopted
theoretical scenarios are derived. The retrieved age distributions confirm that
a variation in the efficiency of superadiabatic convection in the pulsational
model computations has a negligible effect, whereas a brighter Mass-Luminosity
relation, as produced by mild overshooting, rotation or mass loss, implies
significantly older age predictions. Moreover, older Cepheids are found at
larger Galactocentric distances, while first overtone Cepheids are found to be
systematically older than the fundamental ones. The comparison with independent
age distribution analysis in literature supports the predictive capability of
current theoretical framework.
