A Method of Improving Standard Stellar Luminosities with Multiband Standard Bolometric Corrections

Standard luminosity ($L$) of 406 main-sequence stars with the most accurate astrophysical parameters are predicted from their absolute magnitudes and bolometric corrections at Johnson $B,V$, and Gaia EDR3 $G$, $G_{BP}$, $G_{RP}$ filters. Required multiband $BC$ and $BC-T_{eff}$ relations are obtained first from the parameters of 209 DDEB (Double-lined Detached Eclipsing Binaries) with main-sequence components and Gaia EDR3 parallaxes. A simplified SED is formulated to give filter dependent component light contributions and interstellar dimming, which are essential in computing $BC$ of a component virtually at any filter. The mean standard $L$ of a star is calculated from the mean $M_{Bol}$ which is a mathematical average of independent $M_{Bol}$ values predicted at different filters, while the uncertainty of $L$ is the uncertainty propagated from the uncertainty of the mean $M_{Bol}$. The mean standard $L$ of the sample stars are compared to the corresponding $L$ values according to the Stefan-Boltzmann law. A very high correlation ($R^2>0.999$) is found. Comparing histogram distributions of errors shows that uncertainties associated with the mean standard $L$ (peak at $\sim2.5$ per cent) are much smaller than the uncertainties of $L$ (peak at $\sim8$ per cent) by the Stefan-Boltzmann law. Increasing the number of filters used in predicting the mean $M_{Bol}$ increases the accuracy of the standard stellar luminosity. Extinction law, color-color relations and color excess - color excess relations for Gaia passbands are demonstrated for main-sequence stars for the first time.