Unexpected series of regular frequency spacing of delta Scuti stars in the non-asymptotic regime -- I. The methodology

TL;DR

This paper introduces a new sequence search method to identify regular frequency spacings in delta Scuti stars, revealing numerous independent series and potential links to stellar rotation and large separation in non-asymptotic regimes.

Contribution

The paper presents a novel sequence search methodology for analyzing frequency spacings in delta Scuti stars, applied to CoRoT data, uncovering unexpected regularities and their possible physical origins.

Findings

Detected multiple regular frequency sequences in 77 delta Scuti stars.

Found spacings shifted by twice the estimated rotational splitting frequency.

Suggested one spacing corresponds to the large separation, influenced by stellar rotation.

Abstract

A sequence search method was developed to search regular frequency spacing in delta Scuti stars by visual inspection and algorithmic search. We searched for sequences of quasi-equally spaced frequencies, containing at least four members per sequence, in 90 delta Scuti stars observed by CoRoT. We found an unexpectedly large number of independent series of regular frequency spacing in 77 delta Scuti stars (from 1 to 8 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 0.5-0.59 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 and that 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 reveal a possible explanation that one spacing is the large separation, while the other is a sum of the large separation and the rotational frequency. In CoRoT 102675756, the two spacings (2.249 and 1.977 d^{-1}) agree better with the sum of a possible 1.710 d^{-1} large separation and two or one times, respectively, the value of the rotational frequency.