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The spectroscopic Hertzsprung-Russell diagram

The Hertzsprung-Russell diagram is an essential diagnostic diagram for stellar structure and evolution, which has now been in use for more than 100 years. Our spectroscopic Hertzsprung-Russell (sHR) diagram shows the inverse of the flux-mean gravity versus the effective temperature. Observed stars whose spectra have been quantitatively analyzed can be entered in this diagram without the knowledge of the stellar distance or absolute brightness. Observed stars can be as conveniently compared to stellar evolution calculations in the sHR diagram as in the Hertzsprung-Russell diagram. However, at the same time, our ordinate is proportional to the stellar mass-to-luminosity ratio, which can thus be directly determined. For intermediate- and low-mass star evolution at constant mass, we show that the shape of an evolutionary track in the sHR diagram is identical to that in the Hertzsprung-Russell diagram. We also demonstrate that for hot stars, their stellar Eddington factor can be directly read off the sHR diagram. For stars near their Eddington limit, we argue that a version of the sHR diagram may be useful where the gravity is exchanged by the effective gravity. We discuss the advantages and limitations of the sHR diagram, and show that it can be fruitfully applied to Galactic stars, but also to stars with known distance, e.g., in the LMC or in galaxies beyond the Local Group.