Observational $\Delta\nu$-$\bar\rho$ relation for $\delta$ Sct stars using eclipsing binaries and space photometry

Delta Scuti ($\delta$ Sct) stars are intermediate-mass pulsators, whose intrinsic oscillations have been studied for decades. However, modelling their pulsations remains a real theoretical challenge, thereby even hampering the precise determination of global stellar parameters. In this work, we used space photometry observations of eclipsing binaries with a $\delta$ Sct component to obtain reliable physical parameters and oscillation frequencies. Using that information, we derived an observational scaling relation between the stellar mean density and a frequency pattern in the oscillation spectrum. This pattern is analogous to the solar-like large separation but in the low order regime. We also show that this relation is independent of the rotation rate. These findings open the possibility of accurately characterizing this type of pulsator and validate the frequency pattern as a new observable for $\delta$ Sct stars.