  We aim at studying the theoretical properties of the regular spacings found
in the oscillation spectra of delta Scuti stars. We performed a multi-variable
analysis covering a wide range of stellar structure and seismic properties and
model parameters representative of intermediate-mass, main sequence stars. The
work-flow is entirely done 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 frequency domain (i.e. radial orders spanning from 1
to 8, approximately) of the main-sequence, delta Scuti stars' oscillation
spectrum. We found that such a linear behavior stands whatever the mass,
metallicity, mixing length, and overshooting parameters considered in this
work. 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
percent 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 percent of
deviation. Asteroseismology has thus revealed an independent direct measure of
the average density of delta Scuti stars, 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 a determination the radius of
planets orbiting around delta 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.
