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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 Msun, and for evolutionary phases from the main sequence to the beginning of the red giant stage, the stellar flux weighted gravity, g_F ~ g/Teff^4, is tightly correlated with absolute bolometric magnitude Mbol. 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 Mbol = 9.0 mag to -8.0 mag with a scatter of 0.17 mag above Mbol = -3.0 and 0.29 mag below this value. We then test the relation with 2.2 million stars with 6.5 mag > Mbol > 0.5 mag, where 'mass-produced' but robust log g, Teff and Mbol 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 percent.