Fundamental properties of two rapidly rotating stars: Rasalhague and Alkaid

The fundamental parameters of rapidly rotating stars are key quantities required to understand the impact of rotation on stellar evolution. A few nearby early-type stars offer the possibility to take precise measurements of these parameters, which helped us to constrain newly available two-dimensional models. We propose a method to retrieve the fundamental parameters of a fast-rotating star (mass, rotation rate, and age) and the inclination of its rotation axis on the line of sight using five spectrophotometric observables along with a set of steady 2D models. From two photometric indices, the temperature tIRFM derived by the infrared flux method, the projected equatorial velocity (V i), and the apparent luminosity, along with a grid of 2D steady-state models, we selected models that are compatible with all observational constraints and derived the most probable mass, rotation rate, core hydrogen mass fraction relative to that of the envelope, and inclination of the rotation axis on the line of sight of the targeted star. We applied this method to two stars: Rasalhague (α Oph, A5IV) and Alkaid (η UMa, B3V). We confirm and improve on the fundamental parameters of Rasalhague previously determined by infrared interferometry and provide a new determination of its rotation axis inclination on the line of sight, which we find to be 68.9 Concerning Alkaid, about which little is known, we infer a mass of 5.071 M_⊙ and a rotation rate of 0.413 times the critical angular velocity, corresponding to an equatorial rotation period of 14.6 hours. We also find an inclination of the rotation axis of 41.9 on the line of sight. We show that Alkaid is a very young star, presumably between 2 and 8 Myr off the zero-age main sequence. As a side result, using high resolution spectra and the Least Square Deconvolution method, we determined a precise value of the V i of Rasalhague, namely 224.3 km/s. Similarly, we find V i=154.3 km/s for Alkaid. Our results show that fundamental parameters of rapidly rotating stars can be determined (or at least bracketed) using five observable quantities that can be measured from the spectrum of the star. This is of great interest for stars that are beyond reach of interferometric observations.