2014A&A...563A...7S

We study the theoretical properties of the regular spacings found in the oscillation spectra of δ Scuti stars. 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. 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. 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.