We show that for a wide range of stellar masses , from 0.3 to 20 M _ { \odot } , and for evolutionary phases from the main sequence to the beginning of the red giant stage , the stellar flux weighted gravity , g _ { F } \equiv 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 mag 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 \geq M _ { \mathrm { bol } } \geq 0.5 mag , where ’ mass-produced ’ but robust \log g , T _ { \mathrm { eff } } and M _ { \mathrm { bol } } from LAMOST DR5 and Gaia DR2 are available .
We find that the same relation holds with a scatter of \sim 0.2 mag for single stars offering a simple spectroscopic distance estimate good to \sim 10 % .