The Masses and Radii of the Eclipsing Binary F Aurigae

Abstract

We present a full determination of the fundamental stellar and orbital parameters of the eclipsing binary ζ Aurigae (K4 Ib + B5 V) using recent observations with the Hubble Space Telescope Goddard High Resolution Spectrograph (GHRS) and the Mark III long-baseline optical interferometer. The information obtained from spectroscopic and interferometric measurements is complementary, and the combination permits a complete determination of the stellar masses, the absolute semimajor axis of the orbit, and the distance. A complete solution requires that both components be visible spectroscopically, and this has always been difficult for the ζ Aur systems. The ζ Aur K star primary presents no difficulty, and accurate radial velocities are readily obtainable in the optical. However, the B star secondary is more problematic. Ground-based radial velocity measurements are hampered by the difficulty of working with the composite spectrum in the blue-violet region, the small number of suitable lines in the generally featureless optical spectrum of the B star, and the great width of the few available lines (the Balmer lines of hydrogen and a few weak He I lines) due to rapid rotation. We avoid the worst of these problems by using GHRS observations in the ultraviolet, where the K star Flux is negligible and the intrinsic B star spectrum is more distinctive, and obtain the most accurate determination of the B star radial velocity amplitude to date. We also analyze published photometry of previous eclipses and near-eclipse phases of ζ Aur in order to obtain eclipse durations, which fix the length of the eclipse chord and therefore determine the orbit inclination. The long-baseline interferometry (LBI) yields, in conjunction with the spectroscopic solution, the distance to the system and thus the absolute stellar radius of the resolved K supergiant primary star, ζ Aur A. The secondary is not resolved by LBI, but its angular (and absolute) radius is found by Fitting the model stellar flux plus an interstellar extinction model to the flux-calibrated GHRS data. We Find MK = 5.8 ± 0.2 M☉, MB = 4.8 ± 0.2 M☉, RK = 148 ± 3 R☉ and RB = 4.5 ± 0.3 RB for the masses and radii of the ζ Aur stars. We determine the distance to ζ Aur to be 261 ± 3 pc. Additionally, we refine the stellar parameters of the B star secondary presented in the 1995 spectroscopic study of Bennett, Brown, & Linsky. We also determine the effective temperature of the K star primary using values of the bolometric flux, angular diameter, and interstellar extinction derived in this study. The positions of the ζ Aur stars on the theoretical H-R diagram are compared to current evolutionary model tracks, and the resulting good agreement provides a strong check of the internal self-consistency of this analysis and the accuracy of the theoretical models. The ζ Aurigae stars are confirmed to be coeval with an age of 80 ± 15 Myr.