# Patterns, an efficient way to analyse the p-mode frequency content in rapidly rotating stars.

Abstract

The objective of this work is to apply the recent techniques used with the pulsating spectrum of A-F stars [REFS] to study non-pertubative rotating models (SCF) [REFS] and  targets. The techniques are the Fourier transform (FT, from now), the autocorrelation function (ACF, from now), the histogram of frequency differences (HFD, from now), and the Echelle diagram (ED, from now). We are looking for the best procedure to obtain a reliable mode identification.

# Introduction

Here, the intro. Yes, I propose here to include a relation of the papers we have published on this topic, including the last accepted one. Then, we should also mention the works by Lignières and Reese that are more related (e.g. those mentioning the periodic patterns predicted by non-perturbative theory)

# Model sample

To test the confidence in the tools and figure out what information we can obtain with each of them, we started the analysis of a set of rotating models. We have computed 54 SCF different models [REFS] with the following characteristics. They have 9 different rotations from $$\Omega/\Omega_{K} = 0$$ to $$\Omega/\Omega_{K} = 0.8$$. For each rotational velocity, we have two different inclination angles and three different ways of setting the mode amplitudes. In one case, the mode amplitude is given by the mode visibility; in a second case these amplitudes are multiplied by a random number comprised between 1 and 10 (the random number is uniformly distributed in a logarithmic scale); in a third case these amplitudes are multiplied by a random number comprised between 0.1 and 10 (the random number is uniformly distributed in a logarithmic scale).

The most visible modes (in terms of visibility calculations) are the island modes, then the chaotic and then the whispering gallery modes. As rotation increases the number of visible whispering gallery mode decreases while the number of chaotic mode increases (together with the number of island modes).

The other subsets of modes (mainly chaotic modes and whispering gallery modes) have a different organisation that is not fully understood yet. Nevertheless a large separation (but not half the large separation) and a spacing close to $$2\Omega$$ (between $$m=-1$$ and $$m=1$$ modes) should still be present in the chaotic mode subspectrum.

The models contain the following information:

 $$\Delta_{n}$$ $$\Delta_{\ell}$$ $$\Delta_{m}$$ $$\Omega$$ 7.1969685 3.0115791 0.23874654 0.0000000 7.1296325 2.9668959 0.14821643 0.60528506 7.0805956 2.5754183 -0.020148432 1.1861165 7.0474367 1.8731673 -0.072648819 1.7204604 6.9380044 1.1871432 -0.20184019 2.1902553 6.6969111 1.0043267 -0.63984686 2.5823731 6.2993731 1.1582393 -1.0687608 2.8913942 6.0308690 1.1349926 -1.0545724 3.1175864 5.6754183 0.84165972 -0.82021388 3.2670515