A Simple Unified Spectroscopic Indicator of Stellar Luminosity: The Extended Flux-weighted Gravity-Luminosity Relationship

We show that for a wide range of stellar masses, from 0.3 to 20 M_⊙, and for evolutionary phases from the main sequence to the beginning of the red giant stage, the stellar flux-weighted gravity, g_F ≅ g/ ${T}_{\mathrm{eff}}^{4}$ , is tightly correlated with absolute bolometric magnitude ${M}_{\mathrm{bol}}$ . Such a correlation is predicted by stellar evolution theory. We confirm this relation observationally, using a sample of 445 stars with precise stellar parameters. It holds over 17 stellar magnitudes from ${M}_{\mathrm{bol}}$ = 9.0 to -8.0 mag with a scatter of 0.17 mag above ${M}_{\mathrm{bol}}$ = -3.0 and 0.29 mag below this value. We then test the relation with 2.2 million stars with 6.5 mag ≥ ${M}_{\mathrm{bol}}$ ≥ 0.5 mag, where "mass-produced" but robust $\mathrm{log}\,g$ , ${T}_{{\rm{e}}{\rm{f}}{\rm{f}}},$ and ${M}_{\mathrm{bol}}$ from LAMOST DR5 and Gaia DR2 are available. We find that the same relation holds with a scatter of ∼0.2 mag for single stars offering a simple spectroscopic distance estimate good to ∼10%.