Interrelated main-sequence mass–luminosity, mass–radius, and mass–effective temperature relations

Abstract

Absolute parameters of 509 main-sequence stars selected from the components\nof detached-eclipsing spectroscopic binaries in the Solar neighbourhood are\nused to study mass-luminosity, mass-radius and mass-effective temperature\nrelations (MLR, MRR and MTR). The MLR function is found better if expressed by\na six-piece classical MLR ($L \\propto M^{\\alpha}$) rather than a fifth or a\nsixth degree polynomial within the mass range of $0.179\\leq M/M_{\\odot}\\leq\n31$. The break points separating the mass-ranges with classical MLR do not\nappear to us to be arbitrary. Instead, the data indicate abrupt changes along\nthe mass axis in the mean energy generation per unit of stellar mass. Unlike\nthe MLR function, the MRR and MTR functions cannot be determined over the full\nrange of masses. A single piece MRR function is calibrated from the radii of\nstars with $M\\leq1.5M_{\\odot}$, while a second single piece MTR function is\nfound for stars with $M>1.5M_{\\odot}$. The missing part of the MRR is computed\nfrom the MLR and MTR, while the missing part of the MTR is computed from the\nMLR and MRR. As a result, we have interrelated MLR, MRR and MTR, which are\nuseful in determining the typical absolute physical parameters of main-sequence\nstars of given masses. These functions are also useful to estimate typical\nabsolute physical parameters from typical $T_{eff}$ values. Thus, we were able\nto estimate the typical absolute physical parameters of main-sequence stars\nobserved in the Sejong Open Cluster survey, based on that survey's published\nvalues for $T_{eff}$. Since typical absolute physical parameters of main\nsequence stars cannot normally be determined in such photometric surveys, the\ninterrelated functions are shown to be useful to compute such missing\nparameters from similar surveys.\n