Main-Sequence Effective Temperatures from a Revised Mass-Luminosity Relation Based on Accurate Properties

The mass-luminosity (M-L), mass-radius (M-R) and mass-effective temperature ($M-T_{eff}$) diagrams for a subset of galactic nearby main-sequence stars with masses and radii accurate to $\leq 3\%$ and luminosities accurate to $\leq 30\%$ (268 stars) has led to a putative discovery. Four distinct mass domains have been identified, which we have tentatively associated with low, intermediate, high, and very high mass main-sequence stars, but which nevertheless are clearly separated by three distinct break points at 1.05, 2.4, and 7$M_{\odot}$ within the mass range studied of $0.38-32M_{\odot}$. Further, a revised mass-luminosity relation (MLR) is found based on linear fits for each of the mass domains identified. The revised, mass-domain based MLRs, which are classical ($L \propto M^{\alpha}$), are shown to be preferable to a single linear, quadratic or cubic equation representing as an alternative MLR. Stellar radius evolution within the main-sequence for stars with $M>1M_{\odot}$ is clearly evident on the M-R diagram, but it is not the clear on the $M-T_{eff}$ diagram based on published temperatures. Effective temperatures can be calculated directly using the well-known Stephan-Boltzmann law by employing the accurately known values of M and R with the newly defined MLRs. With the calculated temperatures, stellar temperature evolution within the main-sequence for stars with $M>1M_{\odot}$ is clearly visible on the $M-T_{eff}$ diagram. Our study asserts that it is now possible to compute the effective temperature of a main-sequence star with an accuracy of $\sim 6\%$, as long as its observed radius error is adequately small (<1%) and its observed mass error is reasonably small (<6%).