Measuring mean densities ofδScuti stars with asteroseismology

Abstract

Aims. We study the theoretical properties of the regular spacings found in the oscillation spectra of δ Scuti stars. Methods. We performed a multivariable analysis that covered a wide range of stellar structure, seismic properties and model parameters that are representative of intermediate-mass, main-sequence stars. The workflow was entirely performed using a new Virtual Observatory tool: TOUCAN (the VO gateway for asteroseismic models), which is presented in this paper. Results. A linear relation between the large separation and the mean density is predicted to be found in the low-frequency domain (i.e. radial orders spanning from 1 to 8, approximately) of the main-sequence, δ Scuti stars' oscillation spectrum. We found that this linear behavior remains the same whatever the mass, metallicity, mixing length, and overshooting parameters considered. The intrinsic error of the method is discussed. This includes the uncertainty in the large separation determination and the role of rotation. The validity of the relation found is only guaranteed for stars rotating up to 40% of their break-up velocity. Finally, we applied the diagnostic method presented in this work to five stars for which regular patterns have been found. Our estimates for the mean density and the frequency of the fundamental radial mode match with those given in the literature within a 20% of deviation. Conclusions. Asteroseismology has thus revealed an independent direct measure of the average density of δ Scuti stars, which is analogous to that of the Sun. This places tight constraints on the mode identification and hence on the stellar internal structure and dynamics, and allows determining the radius of planets orbiting δ Scuti stars with unprecedented precision. This opens the way for studying the evolution of regular patterns in pulsating stars, and its relation with stellar structure and evolution.

Accurate and loggof δ Sct stars using Asteroseismology

“…Equation 1 fits those relations found in previous theoretical works, both using non-rotating models [29] and 2D models using a non-perturbative approach to compute the theoretical frequencies [27]. This relation is essentially the same obtained as that obtained in GH15, although the coefficients are slightly different.…”

“…In fact, a recent work has found a relation between this periodicity, pattern or large separation and the mean density of the star [9, from now GH15]. All these results are agree with theoretical predictions, both based on non-rotating models [29] and on 2D models using a non-perturbative approach [22,27].…”

“…A plot of the data, our fit and a comparison with the solar-like relation and the theoretical relation found by [29] can be seen in the Fig. 1.…”

“…Large separation-mean density relation obtained for the seven binary systems of our sample. A linear fit to the points is also depicted, as well as the solar-like scaling relation [30] and the theoretical scaling relation for non-rotating models of δ Sct stars [29]. Symbols are plotted with a gradient colour scale to account for the different rotation rates.…”

“…They estimated the masses, the radius and the rotational velocities of the stars and tried to place the sample over the ∆ν-ρ relation given in [29]. The conclusion was that it was necessary to assume that the periodicity was a combination of the large separation and the rotational splitting in most cases in order to put the data over the relation.…”