Asteroseismology for “à la carte” stellar age-dating and weighing

Abstract

Context. In the context of the space missions CoRoT, Kepler, Gaia, TESS, and PLATO, precise and accurate stellar ages, masses, and radii are of paramount importance. For instance, they are crucial for constraining scenarii of planetary formation and evolution. Aims. We aim at quantifying how detailed stellar modelling can improve the accuracy and precision on age and mass of individual stars. To that end, we adopt a multifaceted approach where we carefully examine how the number of observational constraints as well as the uncertainties on observations and on model input physics affect the results of age-dating and weighing. Methods. We modelled in detail the exoplanet host-star HD 52265, a main-sequence, solar-like oscillator that CoRoT observed for four months. We considered different sets of observational constraints (Hertzsprung-Russell data, metallicity, various sets of seismic constraints). For each case, we determined the age, mass, and properties of HD 52265 inferred from stellar models, and we quantified the impact of the model input physics and free parameters. We also compared model ages with ages derived by empirical methods or Hertzsprung-Russell diagram inversion. Results. For our case study HD 52265, our seismic analysis provides an age A = 2.10−2.54 Gyr, a mass M = 1.14−1.32 M , and a radius R = 1.30−1.34 R , which corresponds to age, mass, and radius uncertainties of ∼10, ∼7, and ∼1.5 per cent, respectively. These uncertainties account for observational errors and current state-of-the-art stellar model uncertainties. Our seismic study also provides constraints on surface convection properties through the mixing-length, which we find to be 12−15 per cent lower than the solar value. On the other hand, because of helium-mass degeneracy, the initial helium abundance is determined modulo the mass value. Finally, we evaluate the seismic mass of the exoplanet to be M p sin i = 1.17−1.26 M Jupiter , much more precise than what can be derived by Hertzsprung-Russell diagram inversion. Conclusions. We demonstrate that asteroseismology allows us to substantially improve the age accuracy that can be achieved with other methods. We emphasize that the knowledge of the mean properties of stellar oscillations -such as the large frequency separation -is not enough to derive accurate ages. We need precise individual frequencies to narrow the age scatter that is a result of the model input physics uncertainties. Further progress is required to better constrain the physics at work in stars and the stars helium content. Our results emphasize the importance of precise classical stellar parameters and oscillation frequencies such as will be obtained by the Gaia and PLATO missions.

A seismic and gravitationally bound double star observed byKepler

“…Baudin et al (2012) found a similar result in a red giant star observed by CoRoT. Lebreton & Goupil (2014) examined in detail the correlation between model input parameters of the CoRoT target HD 52265. They quantified the anti-correlation of the mass with the initial helium abundance to be ΔY 0 ΔM = −0.58 and also suggested a correlation of the age with the mixing length parameter of ΔAge Δα = +0.13.…”

“…Free model, mode frequencies, and empirical surface correction (Lebreton) To model the stars we proceeded as explained in Lebreton & Goupil (2014). A Levenberg-Marquardt minimisation was used to adjust the free parameters in the modelling in order to minimise the merit functions per Eq.…”

“…In their stellar-age dating, Otí Floranes et al (2005) and Miglio & Montalbán (2005) showed that the frequency difference ratios where very powerful age indicators (See also the pioneering works of Ulrich 1986;Christensen-Dalsgaard 1988). In the case of HD 52265, Lebreton & Goupil (2014) examined different sets of seismic constraints and showed that the use of frequency ratios provide the best accuracy and precision for the age of the star. Therefore the use of method not based upon surface frequency correction should also be tested using the MESA evolution code (Verma and Ball).…”

“…A deeper analysis of the impact of all the input and optimisation parameters in a similar fashion as done by Lebreton & Goupil (2014) is indeed required and is beyond the scope of this article.…”

Asteroseismic age determination for dwarfs and giants

“…When the signal-to-noise ratios in the observations are high enough, it is possible to isolate the individual peaks in the power spectrum and perform what is known as "boutique" modelling of the targets (e.g., Lebreton & Goupil 2014;Metcalfe et al 2010;Silva Aguirre et al 2013). In these cases, instead of fitting for the global asteroseismic parameters the Bayesian schemes aim at reproducing either the individual frequencies of oscillations or combinations of them.…”