A realistic two-dimensional model of Altair^⋆

¹ Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Bd de l’Observatoire, CS 34229, 06304 Nice Cedex 4, France
e-mail: kevin.bouchaud@oca.eu
² LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Univ. Paris Diderot, Sorbonne Paris Cité, 5 Place Jules Janssen, 92195 Meudon, France
³ Université de Toulouse, UPS-OMP, IRAP, 31028 Toulouse, France
⁴ CNRS, IRAP, 14 Avenue Édouard Belin, 31400 Toulouse, France

Received: 2 October 2019
Accepted: 3 December 2019

Abstract

Context. Fast rotation is responsible for important changes in the structure and evolution of stars and the way we see them. Optical long baseline interferometry now allows for the study of its effects on the stellar surface, mainly gravity darkening and flattening.

Aims. We aim to determine the fundamental parameters of the fast-rotating star Altair, in particular its evolutionary stage (represented here by the core hydrogen mass fraction X_c), mass, and differential rotation, using state-of-the-art stellar interior and atmosphere models together with interferometric (ESO-VLTI), spectroscopic, and asteroseismic observations.

Methods. We use ESTER two-dimensional stellar models to produce the relevant surface parameters needed to create intensity maps from atmosphere models. Interferometric and spectroscopic observables are computed from these intensity maps and several stellar parameters are then adjusted using the publicly available MCMC algorithm Emcee.

Results. We determined Altair’s equatorial radius to be R_eq = 2.008 ± 0.006 R_⊙, the position angle PA = 301.1 ± 0.3°, the inclination i = 50.7 ± 1.2°, and the equatorial angular velocity Ω = 0.74 ± 0.01 times the Keplerian angular velocity at equator. This angular velocity leads to a flattening of ε = 0.220 ± 0.003. We also deduce from the spectroscopically derived v sin i ≃ 243 km s⁻¹, a true equatorial velocity of ∼314 km s⁻¹ corresponding to a rotation period of 7h46m (∼3 cycles/day). The data also impose a strong correlation between mass, metallicity, hydrogen abundance, and core evolution. Thanks to asteroseismic data, and provided our frequencies identification is correct, we constrain the mass of Altair to 1.86 ± 0.03 M_⊙ and further deduce its metallicity Z = 0.019 and its core hydrogen mass fraction X_c = 0.71, assuming an initial solar hydrogen mass fraction X = 0.739. These values suggest that Altair is a young star ∼100 Myr old. Finally, the 2D ESTER model also gives the internal differential rotation of Altair, showing that its core rotates approximately 50% faster than the envelope, while the surface differential rotation does not exceed 6%.