Study of rotational splittings in δ Scuti stars using pattern finding techniques

Detecting and understanding rotation in stellar interiors is nowadays one of the unsolved problems in stellar physics. Asteroseismology has been able to provide insights on rotation for the Sun, solar-like stars, and compact objects like white dwarfs. However, this is still very difficult for intermediate-mass stars. These stars are moderate-to-rapid rotators. Rotation splits and shifts the oscillation modes, which makes the oscillation spectrum more complex and harder to interpret. Here we study the oscillation patterns of a sample of benchmark $\delta$~Sct stars belonging to eclipsing binary systems with the objective to find the frequency spacing related to the rotational splitting ($\delta r$). For this task, we combine three techniques: the Fourier transform, the autocorrelation function, and the histogram of frequency differences. The last two showed a similar behaviour. For most of the stars, it was necessary to determine the large separation ($\Delta\nu$) prior to spot $\delta r$. This is the first time we may clearly state that one of the periodicities present in the p~modes oscillation spectra of $\delta$~Sct stars corresponds to the rotational splitting. This is true independently of the stellar rotation rate. These promising results pave the way to find a robust methodology to determine rotational splittings from the oscillation spectra of $\delta$~Sct stars and, thus, understanding the rotational profile of intermediate-mass pulsating stars.