Fundamentals of Stars: A Critical Look at Mass-Luminosity Relations and Beyond

Developments on various relations among stellar variables such as the main sequence empirical mass-luminosity (MLR), mass-radius (MRR) and mass-effective temperature (MTR) relations were reviewed. Conceptual changes in their understanding and usages were discussed. After its discovery, MLR was treated as one of the fundamental secrets of the cosmos. Differences between fundamental laws and statistical relations were used to understand long-term developments of MLR, MRR and MTR. Developments show a break point, initiated by Andersen et al. (1991), in the line of progress. Before the break when reliable data were limited, MLR and MRR were calibrated using $M$, $L$, and $R$ of binary components of all kinds visual, spectroscopic, and eclipsing for two purposes: i) to obtain mean mass, mean luminosity, and mean radius, ii) to estimate $M$ and $R$ of single stars. By the time of the break, the number of solutions from detached double-lined eclipsing binaries (DDEB) giving accurate $M$ and $R$ within a few percent levels are increased. Parameters from very close, semi-detached, and contact binaries were excluded for refinement, however, MLR and MRR diagrams were found insufficient to derive MLR and MRR functions because the dispersions are not only due to random observational errors but also due to chemical composition and age differences. Then, a new trend was adopted by replacing classical MLR and MRR with empirical $M$ and $R$ predicting relations. Thus, the purpose one was suppressed also because the new trend found a fruitful application in determining $M$ and $R$ of exoplanet hosting single stars.