2013AJ....146..148M

α¹ Her is the second closest asymptotic giant branch (AGB) star to the Sun, and the variable luminous M5 Ib-II member of a triple-stellar system containing G8 III and A9 IV-V components. However, the mass of this important star was previously uncertain, with published values ranging from ∼2-15 M_☉. As shown by this study, its fortuitous membership in a nearby resolved triple-star system makes it possible to determine its fundamental properties including its mass and age. We present over 20 years of VRI photometry of α¹ Her as well as Wing intermediate-band near-IR TiO and NIR continuum photometry. We introduce a new photometry-based calibration technique and extract the effective temperature and luminosity of α¹ Her, in agreement with recent interferometric measures. We find average values of T_eff= 3280±87 K and log (L/L_☉) = 3.92±0.14. With the MESA code, we calculate a dense grid of evolutionary tracks for Galactic low- to intermediate-mass (1.3 to 8 M_☉) rotating stars from the pre-main sequence phase to the advanced AGB phase. We include atomic diffusion and rotation mechanisms to treat the effects of extra elemental mixing. Based on the observed properties of the α Herculis stars, we constrain the age of the system to lie in the range 0.41 to 1.25 Gyr. Thus, the mass of α¹ Her lies in the range 2.175 ≤ M/M_☉ ≤ 3.250. We compare our model-based age inference with recent tracks of the Geneva and STAREVOL codes, and show their agreement. In the prescribed mass range for α¹ Her, the observed ¹²C/¹³C and ¹⁶O/¹⁷O ratios are consistent (within 2σ) with the ratios predicted by the MESA, Geneva, and STAREVOL codes.