THE LOW-MASS DOUBLE-LINED ECLIPSING BINARY CM DRACONIS: A TEST OF THE PRIMORDIAL HELIUM ABUNDANCE AND THE MASS-RADIUS RELATION NEAR THE BOTTOM OF THE MAIN SEQUENCE

摘要

CM Dra is the least massive main-sequence eclipsing double-lined spectroscopic binary currently known. Consequently, this system offers a unique opportunity to test stellar structure models near the bottom of the main sequence. The orbital solution of Lacy (1977) established the masses and radii of the two components with uncertainties of a few percent, but these errors are too large to distinguish between competing models. We present a new double-lined orbital solution based on 233 echelle spectra obtained with the CfA Digital Speedometers over the past 10 yr. Radial velocities for both components were determined using TODCOR, a two-dimensional correlation technique. Using Lacy's (1977) value for orbital inclination, we derive individual masses of M_A = 0.2307 ± 0.0010 and M_B = 0.2136 ± 0.0010 solar mass and a mass ratio of q = 0.9260 ± 0.0026. Using Lacy's light-curve solution and our spectroscopic orbit we derive individual radii of R_A = 0.2516 ± 0.0020 and R_B = 0.2347 ± 0.0019 solar radius. When plotted on a mass-radius diagram, the slope defined by the two components of CM Dra agrees well with the predictions of recent models. The ability to distinguish between models is limited by the uncertainties in the radii and the metal abundance. Following the analysis of Paczynski & Sienkiewicz (1984), we derive bulk helium abundances for the two components of Y_A = 0.32 and Y_B = 0.31. The uncertainty in the difference of these two helium abundances, Y_A — Y_B, is ± 0.02 and depends only on the uncertainty in the ratios of the masses and radii. The uncertainty in the absolute value of these helium abundances set by the uncertainties in the luminosity (including parallax and bolometric correction), radii, ages, and masses is ±0.04. CM Dra, appears to be a member of Population II. Thus there is some promise that it will be able to provide a useful test of the primordial helium abundance.