Searching rotational splittings in δ-Scuti stars using pattern finding techniques

Asteroseismology has been able to provide some information on stellar rotation for the Sun, solar-like stars, and compact objects like white dwarfs. However, this study is still rather arduous for intermediate-mass stars, which are moderate-to-rapid rotators. This is so because rotation causes splittings and shiftings in the oscillation modes, thus increasing the complexity of the oscillation spectrum and making it harder to decipher. We present a study of the oscillation patterns of a sample of benchmark $\delta$~Scuti stars that belong to eclipsing binary systems. Our objective was finding the frequency spacing related to the rotational splitting. For this task, we combined three complementary techniques: the Fourier transform, the autocorrelation function, and the histogram of frequency differences. We were able to find the rotational splittings for the majority of the stars, especially when using the last two methods (with both of them showing a similar behaviour). Hence, this is the first time we may clearly state that one of the periodicities present in the p~modes oscillation spectra of $\delta$~Scuti stars corresponds to the rotational splitting. Furthermore, we found that this is true independently of the stellar rotation rate. Additionally, for most of the stars, it was necessary to determine the large separation prior to spot the rotational splitting. These promising results pave the way to find a robust methodology to determine rotational splittings from the oscillation spectra of $\delta$~Scuti stars and, thus, to the understanding of the rotational profile of intermediate-mass pulsating stars.