Astron. Astrophys. 324, 566-572 (1997)

5. Discussion

The new Doradus variable, HD 108100, shows normal narrowband photometric values for its class: = 0.234, = 0.161, = 0.639. A new value (2.705 0.008) has been obtained by one of us (GH) as part of a larger, presently unpublished program. The calibrations for F stars by Crawford (1975) give = 2.38 with zero reddening. The value of 0.012 indicates normal, solar abundances. The photometric calibration of Moon & Dworetsky (1985) gives 6890 K, = 3.93. In the H-R Diagram, HD 108100 lies on the main sequence, just to the cool side of the instability strip border. This position is typical for a Doradus variable.

The values of the pulsation constants Q can be estimated from the following equation:

Based on the results obtained for other Doradus stars (see Sect. 1), we interpret the variability in terms of nonradial, g-mode pulsation. We note, however, that for this star the spot model cannot be ruled out as an explanation for the variability.

The Q values of the two pulsation frequencies become 0.27 0.03 d, and 0.29 0.03 d. The uncertainties are estimated from the uncertainties of the photometric quantities and calibrations used. The Q values of HD 108100 are too high by a factor of at least 8 for the variability to be caused by p modes, since for these stars the fundamental radial mode has a Q value of 0.033 d. The most promising interpretation is in terms of high-order g modes.

Garrido et al. (1990) have shown that the phase shifts between the light curves in V and provide excellent indicators of the pulsational values. The observed values are shown in Table 3. The listed uncertainties are estimates calculated by dividing the available data in two halves and examining the agreement between the derived parameters.

Table 3. Amplitude Ratios and Phase Shifts for HD 108100

However, the results listed by Garrido et al. are not fully applicable to HD 108100, because the large value of the pulsation constant, Q, derived for HD 108100, dramatically changes the expected amplitude, phase diagrams for the different values. Following the approach of Garrido et al., we have recomputed the expected phase shifts and amplitude ratios for Q  = 0.27 d, 6850 K, = 3.9. Because of the small pulsational amplitude in HD 108100, the adopted linear approximation used in these calculations should be valid.

Fig. 4 shows the loci where and . We refer to Garrido et. al. (1990) for details. The results show that it is possible to distinguish between = 1 and = 2 on the basis of phase differences. At least for one of the two detected pulsation modes, both the observed phase difference and amplitude ratio agree with = 1. The second pulsation mode shows a slightly higher than predicted amplitude ratio, but we consider the disagreement to be minor, since the calculated amplitude ratio (but not the phase difference) is sensitive to the adopted atmospheric parameters.

Fig. 4. Phase shifts versus amplitude ratios for 6850 K, = 3.9, Q = 0.27 d. The computed loci for = 1 and 2 are indicated (see text). The observed points are plotted together with their uncertainties

We conclude that the observed phase shifts are in agreement with those expected for g modes with = 1, while = 2 is improbable.

The Q value can be used to estimate the radial overtones of the excited g modes. We have used an equilibrium model kindly supplied by A. Claret (see Claret 1995). This model (Table 4) corresponds to a slightly evolved star with 1.6 , = 0.896, = 4.03, and . Nonradial g-modes were computed using a numerical code written by RG and is based on the formulation given in Unno et al. (1989). All the periods were calculated in the quasi-adiabatic aproximation, which gives values similar to those obtained by non-adiabatic calculations. The numerical values in Table 4 reach the asymptotic value () of

where N is the Brunt-Väisälä frequency and a constant value depending on the stellar structure.

Table 4. A g-mode model ( = 1) for HD 108100

The comparison of the observed periods with the model shows a good agreement near a radial order, 20, while the Q values indicate 18. The small difference is caused by the fact that the model parameters are not exactly identical to the values derived above for HD 108100. These uncertainties are within those of the photometric calibrations used. Furthermore, the observed difference in period between the two modes corresponds to the expected difference of two successive radial orders of the model.

© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998

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