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We aim at studying the theoretical properties of the regular spacings foundin the oscillation spectra of delta Scuti stars. We performed a multi-variableanalysis covering a wide range of stellar structure and seismic properties andmodel parameters representative of intermediate-mass, main sequence stars. Thework-flow is entirely done using a new Virtual Observatory tool: TOUCAN (the VOgateway for asteroseismic models), which is presented in this paper. A linearrelation between the large separation and the mean density is predicted to befound in the low frequency frequency domain (i.e. radial orders spanning from 1to 8, approximately) of the main-sequence, delta Scuti stars' oscillationspectrum. We found that such a linear behavior stands whatever the mass,metallicity, mixing length, and overshooting parameters considered in thiswork. The intrinsic error of the method is discussed. This includes theuncertainty in the large separation determination and the role of rotation. Thevalidity of the relation found is only guaranteed for stars rotating up to 40percent of their break-up velocity. Finally, we applied the diagnostic methodpresented in this work to five stars for which regular patterns have beenfound. Our estimates for the mean density and the frequency of the fundamentalradial mode match with those given in the literature within a 20 percent ofdeviation. Asteroseismology has thus revealed an independent direct measure ofthe average density of delta Scuti stars, analogous to that of the Sun. Thisplaces tight constraints on the mode identification and hence on the stellarinternal structure and dynamics, and allows a determination the radius ofplanets orbiting around delta Scuti stars with unprecedented precision. Thisopens the way for studying the evolution of regular patterns in pulsatingstars, and its relation with stellar structure and evolution.

Measuring mean densities of delta Scuti stars with asteroseismology. Theoretical properties of large separations using TOUCAN