On The Mass-Luminosity Relation

Abstract

The new Hipparcos parallaxes and photometry are used to determine individual masses and absolute (bolometric) magnitudes for the components of nearby visual binaries with good to very good orbits. The impact on the mass-luminosity relation (MLR) in the range 0 < MBol< +7.5 mag is then evaluated.We selected 335 visual binaries within 50 pc (σπ/π < 10%) for a full error analysis of their orbits by computing the covariance matrix of the orbital elements with Pourbaix’(1994) algorithm. Using ΔHp and π, we estimated fractional and component masses as well as absolute magnitudes with theirrespective errors: 52 binary systems have relative mass errors smaller than 15%. Lutz and Kelker (1973) corrections have been applied to both datatypes. A new relation BC(Hp) as a function of Teff was obtained for the conversion to bolometric magnitudes. A doubly weighted linear regression model was applied next (Babu and Feigelson, 1996): we derived a ”mean” slope 3.82 ± 0.07 and zero point 4.94 ± 0.03 for the MLR, assuming a linear relationship.Conclusions: a) the improvement of the data on masses by Hipparcos is largely quantitative; b) not all systems agree: small fluctuations from a ”mean” MLR are found as expected from evolutionary or abundance effects; c) the break in the slope of the MLR near MBol = +7 cannot be assessed due to a lack of low-mass binaries in our sample.