Mode Identification

Abstract

AbstractThe basic data for asteroseismology are the pulsation frequencies, and we have just shown in Chapter 6 how those are derived from the observations. But before the frequencies can be used for detailed modelling, it is imperative to know what pulsation mode gives rise to each frequency. Determining this is called mode identification. The reason it is so important can easily be seen in Fig. 1.7 in Chapter 1 for p modes. The frequency of pulsation is a measure of the sound travel time along the ray path for p modes, and that is determined by the variable sound speed and the length of the ray path itself. It is thus critical to know the ray path, and that is specified by the pulsation mode geometry. The situation is similar for g modes (see Fig. 1.8). Mode-identification techniques assign values to the discrete spherical harmonic quantum numbers (l, m) of each of the detected oscillation modes. The amount of astrophysical information that can be derived from the observed pulsations depends directly on the number of successfully identified modes. Therefore, great effort is put into mode identification in any seismic analysis.For oscillations in the asymptotic frequency regime, the derivation of frequency or period spacings often suffices to identify the modes for slowly rotating pulsators. This can be achieved for the Sun, for solar-like oscillators and for white dwarfs (Chapter 7). However, when only a limited number of modes is excited to observable amplitudes, or when the modes do not follow particular frequency patterns, or whenever a very dense frequency spectrum is predicted, the frequency values alone are insufficient to derive the (l, m, n). In this case, one cannot proceed with seismic modelling considering all values for (l, m, n) for any of the detected frequencies. In order to limit the computation time of such forward modelling, the values of the degree l are usually limited from arguments of partial cancellation. As we will show later on in this chapter (see Fig. 6.4), the observed photometric amplitude of modes with l ≥ 3 are a factor five to ten less than those of modes with l < 3 having the same intrinsic amplitude, as first demonstrated by Dziembowski (1977b) and already emphasized in Chapter 1. It is then customary to consider modes with l ≤ 2 and to assume m = 0 when no obvious evidence for rotational splitting is found in the Fourier transform of the time series.