The flux-weighted gravity-luminosity relation of Galactic classical
  Cepheids
  The flux-weighted gravity-luminosity relation (FWGLR) is investigated for a
sample of 477 classical Cepheids (CCs), including stars that have been
classified in the literature as such but are probably not. The luminosities are
taken from the literature, based on the fitting of the spectral energy
distributions (SEDs) assuming a certain distance and reddening. The
flux-weighted gravity (FWG) is taken from gravity and effective temperature
determinations in the literature based on high-resolution spectroscopy.
  There is a very good agreement between the theoretically predicted and
observed FWG versus pulsation period relation that could serve in estimating
the FWG (and $\log g$) in spectroscopic studies with a precision of 0.1~dex.
  As was known in the literature, the theoretically predicted FWGLR relation
for CCs is very tight and is not very sensitive to metallicity (at least for
LMC and solar values), rotation rate, and crossing of the instability strip.
The observed relation has a slightly different slope and shows more scatter
(0.54~dex). This is due both to uncertainties in the distances and to the
pulsation phase averaged FWG values.
  Data from future Gaia data releases should reduce these errors, and then the
FWGLR could serve as a powerful tool in Cepheid studies.
