Constraining the Thin Disc Initial Mass Function using Galactic
  Classical Cepheids
  Context: The Initial Mass Function (IMF) plays a crucial role on galaxy
evolution and its implications on star formation theory make it a milestone for
the next decade. It is in the intermediate and high mass ranges where the
uncertainties of the IMF are larger. This is a major subject of debate and
analysis both for Galactic and extragalactic science. Aims: Our goal is to
constrain the IMF of the Galactic thin disc population using both Galactic
Classical Cepheids and Tycho-2 data. Methods: For the first time the
Besan\c{c}on Galaxy Model (BGM) has been used to characterise the Galactic
population of the Classical Cepheids. We have modified the age configuration in
the youngest populations of the BGM thin disc model to avoid artificial
discontinuities in the age distribution of the simulated Cepheids. Three
statistical methods, optimized for different mass ranges, have been developed
and applied to search for the best IMF that fits the observations. This
strategy allows us to quantify variations in the Star Formation History (SFH),
the stellar density at Sun position and the thin disc radial scale length. A
rigorous treatment of unresolved multiple stellar systems has been undertaken
adopting a spatial resolution according to the catalogues used. Results: For
intermediate masses, our study favours a composite field-star IMF slope of
$\alpha=3.2$ for the local thin disc, excluding flatter values such as the
Salpeter IMF ($\alpha=2.35$). Moreover, a constant Star Formation History is
definitively excluded, the three statistical methods considered here show that
it is inconsistent with the observational data. Conclusions: Using field stars
and Galactic Classical Cepheids, we have found, above $1M_\odot$, an IMF
steeper than the canonical stellar IMF of associations and young clusters. This
result is consistent with the predictions of the Integrated Galactic IMF.
