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 ($Delta u$) 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.
Download