## 5. DiscussionWe should summarize what we know about the 10 pulsational frequencies of Tucanae. For better understanding we reproduce here (Fig. 7) the schematic frequency spectrum of Tucanae published in Paper I. The extremely high regularity of frequency spacing is obvious. The spectrum is dominated by groups of closely spaced frequencies. The groups seem to be equally spaced and are divided by single frequencies.
According to we distinguish three groups in the present investigation. The middle group on Fig. 7 corresponds to Group I. The (right side) higher frequency group and the single frequency correspond to Group II. Group III consists of the (left side) lower frequency group and the single frequency. Modes in Group III have speciality in Concerning the special behaviour of modes in Group III it would be a logical conclusion that these modes are excited in the secondary component of higher temperature in the binary system. Unfortunately, no spectral type has been obtained for the secondary component. However, the low mass obtained from spectroscopy (Sterken et al. 1997) seems to exclude Scuti type pulsation in the secondary. Furthermore, the similar regularity in frequency spacing to the other modes would be a hard job to explain if we do not involve a very severe tidal synchronization in the oscillation. If these modes belong to Tuc,
serious questions can be raised. Can we find a region of excitation
with higher temperature and/or nonadiabacity (larger
) what we need to explain the higher
amplitude ratio of modes in Group
III? According to the present theoretical point of view the region of
excitation is indifferent in respect of the observable behaviour of
modes. A new investigation of the location of theoretical modes on the
traditional comparison plane based on the actual model atmospheres has
been recently published by Garrido (2000). For In fact, the behaviour of the 10 pulsational modes on the levels seems to be unified. The modes in Group III join the same levels as the other modes. Not all modes in a group belong to the same level. This is a normal behaviour if we see groups connected to the radial overtones. According to the modelling of Tucanae by Templeton et al. (2000) the frequency distances between the consecutive low radial orders of the radial modes are 2.9 c/d for most of the models. However, the distances between the non-radial consecutive radial orders show variety of values from 2.9-1.6 cycles/day for Models 1-3 and 2.85-0.55 cycles/day for the Model 4. In the observation the dominant frequency spacing is 2.2 c/d. In our view the sign of is
opposite to the sign of . As a first
approximation, the first level with
mean value is regarded as the location of radial modes However, such an explanation creates some problem. There are pairs
of modes with the same radial quantum number situated on the same
level. It is obvious, especially for the closely spaced frequencies,
that such a simple interpretation does not work. These modes may not
be consecutive radial orders with the same In the first explanation
the duplicating of modes with the same radial and horizontal quantum
numbers are caused by rotational splitting. In this case the member of
pairs have different azimuthal quantum number ( The pair of 20.11 and 20.28 c/d should be separately mentioned
since it is connected to a unique effect. On the upper panel of
Fig. 8 in the paper by De Mey et al. (1998) a In the second explanation
we suppose that the levels give information only for the even
(including zero) and odd consecutive The third level is connected to a hitherto not mentioned but interesting fact. The unusually behaving modes according to on Fig. 3 (marked by asterisk in Table 6) are situated on three different levels and are different overtones. Two of them represent the single modes between groups in Fig. 7. The role of these modes is not clear. However, the frequency at 19.02 c/d exhibit strong g-mode type behaviour according to Templeton et al. (2000).
The following principles can help in the interpretation of the
radial order. According to the asymptotic theory
According to the logical-theoretical calibration of Fig. 6 the possible schematic identification of modes are given in Table 6. , , and mean consecutive radial orders, and are different azimuthal order of rotationally splitted modes. The first column gives the frequencies. The 2 and 3 columns (marked as ) give the result of the first explanation, the 4 and 5 columns (marked as ) give the possible solution of the second explanation in general. If we accept the The exact calibration of the observational guidelines obtained in
this investigation is definitely needed. How general the regularities
are for other stars we do not know at this moment. How these
regularities would be confirmed or modified by regularities in
Grouping in modes of FG Vir according to the
parameter has been published by
Viskum et al. (1998). The modes in a group are interpreted as
modes with the same Only a few published examples are mentioned but in the near future another Scuti star (38 Eri) is going to be investigated by one of the authors (MP) following the concept of the present investigation. The high level systematic behaviour of the observational facts in Tucanae concerning both the regularities in frequency spacing, in grouping according to amplitude ratios and in leveling according to phase differences, give high probability to reduce the number of suitable models to a unique solution. The observational guidelines, hopefully, can serve as key to the mystic mode selecting and/or amplitude limiting mechanism in low amplitude Scuti stars. © European Southern Observatory (ESO) 2000 Online publication: October 30, 19100 |