THE AGE AND MASS OF THE α HERCULIS TRIPLE-STAR SYSTEM FROM A MESA GRID OF ROTATING STARS WITH 1.3 ⩽<i>M</i>/<i>M</i>_☉⩽ 8.0

Abstract

\\alpha^1 Her is the second closest Asymptotic Giant Branch (AGB) star to the\nSun, and the variable luminous M5 Ib-II member of a triple stellar system\ncontaining G8 III and A9 IV-V components. However, the mass of this important\nstar was previously uncertain with published values ranging from ~2 - 15 Msun.\nAs shown by this study, its fortuitous membership in a nearby resolved triple\nstar system, makes it possible to determine its fundamental properties\nincluding its mass and age. We present over twenty years of VRI photometry of\n\\alpha^1 Her as well as Wing intermediate-band near-IR TiO and NIR continuum\nphotometry. We introduce a new photometry-based calibration technique, and\nextract the effective temperature and luminosity of \\alpha^1 Her, in agreement\nwith recent interferometric measures. We find, Teff=3280 +/- 87 K and\nlog(L/Lsun)=3.92 +/- 0.14.\n With the MESA code, we calculate a dense grid of evolutionary tracks for\nGalactic low- to intermediate-mass (1.3 to 8 Msun) rotating stars from the\npre-main sequence phase to the advanced AGB phase. We include atomic diffusion\nand rotation mechanisms to treat the effects of extra elemental mixing. Based\non the observed properties of the \\alpha Herculis stars, we constrain the age\nof the system to lie in the range 0.41 to 1.25 Gyr. Thus, the mass of \\alpha^1\nHer lies in the range 2.175 &lt;= M/Msun &lt;= 3.250. We compare our model-based age\ninference with recent tracks of the Geneva and STAREVOL codes, and show their\nagreement. In the prescribed mass range for \\alpha^1 Her, the observed 12C/13C\nand 16O/17O ratios are consistent (within 2\\sigma) with the ratios predicted by\nthe MESA, Geneva and STAREVOL codes.\n