5. Variations of the stellar parameters
If we interprete the variations of the integrated quantity introduced in Sect. 4.1as radius variations, the peak-to-peak amplitude would be of the order of 10% of the stellar radius. This leads to an amplitude in gravity of . The extreme stages of the star would be cool and big versus hot and small.
The photometry for Sco obtained by the LTPV program (Sterken 1983, Sterken et al. 1995, Manfroid et al. 1995) provides the possibility to check the range of the variations of the stellar parameters that were estimated spectroscopically. We used only photometry points obtained with the Danish 50-cm telescope at La Silla after since this is a homogeneous set of data. The variations observed in the Strömgren spectral indices of Sco are displayed in Fig. 11. The lines are linear fits to the data.
We calculated theoretical Strömgren indices for a grid of atmospheres from and from . Assuming amplitudes of the theoretical amplitudes agree, within the scatter of the data, well with the observed ones In Table 5 the theoretical amplitudes for models of in the bright stage and in the faint stage are compared with the observations.
Table 5. Observed and calculated variation amplitudes and mean reddening-free indices of the photometry. The observed amplitudes are derived from the linear fits in Fig. 11. The slopes of these fits and their uncertainties are shown in the lower rows
The stellar luminosity in this scenario is varying from in the bright and respectively 6.06 in the faint stage. Assuming , the variation amplitude for would be about 7%. However, the apparent strength of the line emission over the continuum depends not only on , but also on [Eq. 9, below] and . We have calculated theoretical profiles for both stages (see Sect. 6). The modeled emission strength varies by only about 2%.
The mean values for the theoretical pulsation were fixed using from Table 3, while the value was chosen to fit the mean observed most accurately.
The spectral indicators for the temperature like the SiIV /SiIII or the HeI /SiIII ratio show no significant correlation with the integrated radius difference. The SiIV /SiIII ratio is too noisy to show such small variations, while the HeI /SiIII ratio is disturbed by the wind variability.
From a typical radial-pulsation pattern one would expect stability over more than a few cycles. Although this is not the case in our program stars, an analysis of our data shows a period of in the radial-velocity pattern of the photospheric lines for Sco. This period is always present. The -emission variability in this star shows this period together with a longer one of about , which is slightly varying from year to year.
The positions of our program stars in the Hertzsprung-Russell diagram are quite close to the Humphreys-Davidson Limit (Humphreys 1989). This coincides with the region where Kiriakidis et al. (1993) have predicted "strange-mode oscillations". Their eigenfrequencies strongly depend on .
© European Southern Observatory (ESO) 1997
Online publication: July 3, 1998