M-R-L Relation and Contraction Time Scale for Convective Stars of Low Mass.

Abstract

view Abstract Citations (3) References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS M-R-L Relation and Contraction Time Scale for Convective Stars of Low Mass. Kumar, Shiv S. ; Upton, Edward K. L. Abstract We attempt to derive a theoretical M-R-L relation for stars in the mass range 0.1 to 0.4M0, for application to main sequence structure and convective contraction. In previous work on this problem the hydrogen molecules have been neglected. Here they are included in the equation of state, and their contribution to opacity is assumed to be Rayleigh scattering only. Since the molecules are inefficient scatterers, the mass absorption coefficient is substantially lowered due to the combination of hydrogen atoms into molecules. This raises the effective temperature and luminosity for a star of given mass and radius. The lowering of the temperature gradient in the outer convection zone, through the presence of molecules, also has an effect in the same direction. Calculations have been made for the Schmidt- Kaler composition (X=0.62, Y=0.35, Z=0.03). The surface layers are represented by grey atmospheres in which, besides H and H2 scattering, H and H- opacities are included. The atmosphere is fitted to an adiabatic curve either at the point where the criterion of Hoyle and Schwarzschild is satisfied or at T =1, whichever is deeper. We have also studied the effect of fitting at T =2. The asymptotic behavior of the adiabat in the deep interior gives the scaling for representation of that region by a model of polytropic index 1.5. The theoretical M-R-L relation thus obtained gives effective temperatures on the main sequence about 15% higher than those obtained by Johnson from infrared photometry. The discrepancy may be due to errors in observational data or it may be due to molecular opacity sources such as H2- not included in the calculation. The evolutionary tracks for completely convective contraction are nearly vertical in the theoretical H-R diagram. The times required to reach the main sequence are 1.5 X 108 and 3.5 X 108 yr, for masses 0.4 and 0.1, respectively. Publication: The Astronomical Journal Pub Date: March 1963 DOI: 10.1086/108918 Bibcode: 1963AJ.....68...76K full text sources ADS |