UNEXPECTED SERIES OF REGULAR FREQUENCY SPACING OF δ SCUTI STARS IN THE NON-ASYMPTOTIC REGIME. I. THE METHODOLOGY

A sequence search method was developed to search the regular frequency spacing in δ Scuti stars through visual inspection and an algorithmic search. We searched for sequences of quasi-equally spaced frequencies, containing at least four members per sequence, in 90 δ Scuti stars observed by CoRoT . We found an unexpectedly large number of independent series of regular frequency spacing in 77 δ Scuti stars (from one to eight sequences) in the non-asymptotic regime. We introduce the sequence search method presenting the sequences and echelle diagram of CoRoT 102675756 and the structure of the algorithmic search. Four sequences (echelle ridges) were found in the 5–21 d⁻¹ region where the pairs of the sequences are shifted (between 0.5 and 0.59 d⁻¹) by twice the value of the estimated rotational splitting frequency (0.269 d⁻¹). The general conclusions for the whole sample are also presented in this paper. The statistics of the spacings derived by the sequence search method, by FT (Fourier transform of the frequencies), and the statistics of the shifts are also compared. In many stars more than one almost equally valid spacing appeared. The model frequencies of FG Vir and their rotationally split components were used to formulate the possible explanation that one spacing is the large separation while the other is the sum of the large separation and the rotational frequency. In CoRoT 102675756, the two spacings (2.249 and 1.977 d⁻¹) are in better agreement with the sum of a possible 1.710 d⁻¹ large separation and two or one times, respectively, the value of the rotational frequency.