Main sequence semi-empirical effective temperature calculation metallicity relation

The classical method, which is known as calculating the effective temperatures (Teff) of main sequence stars from their masses (M) and radii (R) according to the Stephan-Boltzmann law (L=4R2T4) using the main-sequence mass-luminosity relation (MLR), is a rough computing technique, which gives results with biases. During its main-sequence lifetime, the luminosity (L) and the radius (R) of a main-sequence star increases. However, for the stars with M > 1.1 M, the increasing rate of R is higher than the increasing rate of L, thus Teff appears to decrease during the main-sequence lifetime. With a less rate of increase of R, with respect to the rate of increase of its L, the stars M ≲1.1 M compensate the difference by increasing its Teff also. In any case, classical method produce larger Teff temperatures for young stars which are close to the Zero Age Main Sequence (ZAMS) and vice versa for the older stars which are close to the terminal Age Main Sequence (TAMS) stars because of the biases involved by the classical method. In order to correct this bias and to produce true Teff temperatures, a new method, Two Uniform Contractions (TUC method) was suggested according to the TÜBİTAK Project number 114R072. The preliminary application of the TUC method accomplished by using 450 main-sequence stars by using PARSEC evolutionary models with solar metallicity (Z = 0.014). In this thesis, the TUC method was improved by including the metallicity effect by 72 main-sequence stars with measured metallicities in the range of 0.008 < Z < 0.06. It can be concluded that, the TUC method would produce up to 600 K error, which is proportional to Z, in the computed temperatures if solar metalicity (Z = 0.014) were assumed for the stars with accurate M and R while their metallicities could be different within the range 0.008 < Z < 0.06. The correctness of the results of the TUC method depends on the correct Z measurements as much as the accuracy of the M and R.