Main sequence mass-luminosity relation and a problem of temperature accuracy

In this thesis, the classical method, which is defined as computing effective temperatures of stars from its mass (M) and radius (R) using a mass-luminosity relation (MLR) according to the Stefan-Boltzmann law, were studied and the sources of the large uncertainty of computed effective temperatures were investigated. Different forms and evolution of MLR, which was discovered for main-sequence stars in early XXth Century, was summarized. Contributions to the uncertainty of the computed effective temperatures by the classical method are not due to only observational random errors. Actually, the main contribution comes from varying chemical compositions and evolutionary status of the stars. Unlike observational random errors, which are random, the uncertainty contributions originating from metallicity and evolution are systematic. First computing, and later correcting of the systematic errors due to metalicity and evolution are the main problems of this study. A semi-empirical method, which were called Two Uniform Contractions (TUC), were developed and applied to 450 main sequence stars with most reliable M and R values. The method requires a mass-luminosity relation (MLR) and theoretical predictions of radius (R) and effective temperature (Teff) for a star both at zero age main sequence (ZAMS) and at terminal age main sequence (TAMS). The introduced method (TUC) is independent of the MLR used, but strongly model dependent. Therefore, the stellar structure and evolution models of Bressan et al. (2012) were used to obtain for the theoretical predictions of R and Teff at both ZAMS and TAMS together with the MLR's of Eker et al.(2015). The MLRs, which act as a catalyst, are necessary but have no effect on the final results. The introduced method, in this thesis, is not only useful to provide reliable effective temperatures and luminosities but also useful to test stellar structure and evolution models. The present sample of main-sequence stars in the solar neighborhood, which are chosen from the "The Catalog of Stellar Parameters from the Detached Double-Lined Eclipsing Binaries in the Milky Way" of Eker et al. (2014), has an error histogram for the observed effective temperatures with a peak at 2-3%. The errors of the refined effective temperatures by the present method are the propagated errors of the observed masses and radii. That is, the refined temperatures and associated errors are both independent of the observational temperatures and their associated errors. The histogram of the refined temperature errors (450 stars) shows a peak at less than 1%. A refined sample of stars with masses and radii accurate up to 3% and their refined effective temperatures has been used in this study to improve the classical MLRs. One may prefer, however, to use improved classical MLRs, which allows one to compute effective temperatures available as accurate as 3.5%. As a result, a new method of computing more reliable effective temperatures, which was called TUC, and new improved MLRs were presented.