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.