Low-Mass Stars. II. The Core Mass--Luminosity Relations for Low-Mass Stars

Details Low-Mass Stars. II. The Core Mass--Luminosity Relations for Low-Mass Stars Low-Mass Stars. II. The Core Mass--Luminosity Relations for Low-Mass Stars

May 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988apj...328..641b&link_type=abstract

Astrophysical Journal v.328, p.641

Astronomy and Astrophysics

Astronomy

107

Mass-Luminosity Relation, Stars: Evolution, Stars: Interiors, Stars: Late-Type

Scientific paper

It was investigated whether the core mass-luminosity (Mc-L) relation that had been established in the literature for intermediate-mass stars (3 Msun < M < 9 Msun) can be extended to low-mass stars (0.8 Msun< Msun < 3 Msun), where many of the observations take place. Stars were evolved from the main sequence up the red giant branch, through the helium core flash and the horizontal branch phase, up to the asymptotic giant branch where helium shell flashes were followed. Two types of Mc-L relations were obtained, one for the red giant branch (when a single hydrogen-burning shell surrounds a degenerate helium core), and another one for the asymptotic giant branch (when two burning shells, of helium and hydrogen respectively, surround a degenerate carbon-oxygen core). Detailed calculations were carried out for a metal-poor case (Z = 0.001) for stars of initial masses 1.0 Msun, 1.2 Msun, 2.0 Msun, and 3.0 Msun and for a metal-rich case (Z= 0.02) for stars of initial masses 1.2 Msun and 3.0 Msun. The latest nuclear reaction rates were used, as well as the latest opacities (including some molecular opacities) and mass loss via a Reimers-type wind. The dependence of the relation on chemical composition was investigated. For the red giant branch, the relation for the metal- rich case (Z = 0.02, µ ≍ 0.624) was L = (6.86 Mc)7 for 0.3 Msun < Msun< 0.45 Msun, where all units are in solar units; the composition dependence was L ∝ µ 7(ZCNO)1/12 (µ is the envelope mean molecular weight, including free electrons). For the asymptotic giant branch, the Mc-L relation for the metal-rich case (Z = 0.02, µ ≍ 0.618) was L = 52,000 (Mc - 0.456) for 0.52 Msun < Mc < 0.7 Msun; the composition dependence was L ∝ µ 3(ZCNO)1/25. The Mc-L relation obtained for the low-mass asymptotic giant branch stars drops less steeply than would be expected from the previous higher Mc work; the difference is large at low core masses. Because of luminosity variations over the flash cycle, observers will see stars that do not lie on the Mc-L relation; the probability and extent of these deviations was described. The fortunate circumstance was established that, for the Mc relation of low-mass stars, (i) changes in the hydrogen-burning reaction rate have only a very minor effect; (ii) uncertainties in the convective mixing length have negligible effect; and (iii) there is no evidence that the star's total mass has any appreciable effect.

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