## 2. Correlations with fundamental stellar parametersIn this section we study the correlations between slopes of SPh behaviours obtained in MZH with the following stellar parameters: , (critical equatorial linear velocity of rigid rotation), T and which is used as an aspect angle indicator (see Sect. 2.3.1). In what follows, the SPh slopes are noted as: Units of slopes and
are mag dex ## 2.1. Data usedFor each studied star the slopes , , , and their respective statistical uncertainty are given in Table 1. When Be stars have two slopes corresponding to the same kind of SPh phase, they are both considered separately. The same was also done for a given star when it showed two different SPh phases.
Effective temperatures, radii and masses of our program Be stars were determined from the "photospheric" BD () and, when available, the BCD parameter. For stars without a measured parameter, we adopted the mean corresponding to its MK luminosity class. Calibrations of ( in , are from Divan & Zorec (1982), Zorec (1986). With and we determine both the stellar radius and the stellar mass using Maeder & Meynet's (1988) evolutionary tracks. The critical velocity is then derived assuming (Sackmann 1970, Bodenheimer 1971, Zorec et al. 1988). The parameters are mostly from Slettebak (1982) except for HD 37202 (Yang et al. 1990). The stellar parameters used in this work are given in Table 1. ## 2.2. ResultsInstead of considering each SPh slope individually, for they are
marred to some extent by uncertainties, we preferred to study mean
values of slopes per interval of a given stellar parameter. Mean
values are obtained independently for SPh-E and SPh-A phases. In this
way, trends indicating possible underlying parametric dependencies can
be made conspicuous more clearly. For some stars there are two slopes
in a given SPh phase. As in each of them points correspond to
different observation epochs, they were considered independently. In
the calculation of mean slopes we did not take into account those for
which the total detected variation of D was
. The sampling intervals used are:
50 km s
Results shown in Figs. 2 to 5 can be summed up as follows: ( ( ( ( ( For easy comparison of the present results with previous results dealing with SPh behaviours, we reproduce the regression lines of mean slopes , , which can be used simply as indications for possible mean dependencies on the respective stellar parameters. Regression lines for SPh-E phases are: The significance level of SPh-A mean slope regressions are too low to suggest any reliable correlation. The values of mean SPh-A slopes scatter near zero and are characterized by the following averages and dispersions: Comparing our results with those obtained in previous works, we observe that: (a) Slopes in SPh-E phases, which suggests that, as a mean, there is reddening of visible energy distribution as emission in the second BD increases. Nevertheless, two exceptions (HD 56014 and HD 91465) have been found that present some blueing as emission increases in the second BD; (b) Similarly to the findings of other authors, slopes
in SPh-E phases, which corresponds
to brightening in the (c) Comparing our results with those of Hirata (1982) and Hirata & Hubert-Delplace (1981), we see that reddening of the visible energy distribution in SPh-E phases implied by a in relations (5) or in Fig. 5 is smaller for lower effective temperatures, but that it never turns to a blueing effect for lower temperatures, as noted in Kogure & Hirata (1982). We note that blueings of photometric indices can sometimes be due to variable spectral lines produced in CE, so that they do not necessarily correspond to a temperature effect; (d) Using the transformations from UBV photometric to SPh indices obtained in MZH [cf. (1), (2) and (3)], we readily derive the following relations between photometric and SPh slopes: which allow us to compare the photometric results discussed by other authors with the SPh results used in the present work. Using the and slopes listed in Table 1 respectively in (7) and (8), we confirm the results previously obtained by Hirata (1982) and Hirata & Hubert-Delplace (1981), where it was noted that in SPh-E phases and have the same sign. However, we have found some exceptions to these rules which are observed in HD 58978, HD 63462, HD 173219 and HD 217543; (e) Introducing relation (2) for into (8), we see that is steeper when is higher as also claimed in previous works. Using now relation (5) for in (8), we can still add that is flatter when is higher; (f) Dachs et al. (1988) found that the ratio . They also found that absolute values of this slope are twice as small as those predicted theoretically. Using the a slopes given in Table 1, we find that in SPh-E phases this ratio not only has negative values as low as , but that it can also have positive values as previously also noted by Hirata (1982). ## 2.3. Correlations of SPh parameters with stellar parametersNoticeable correlations seem to exist for mean and SPh slopes with (and/or ), and . A correlation between and is not expected in a sample where stars are of different luminosity classes. Nevertheless, the regression line obtained for stars in the SPh-E phase: is obtained with a correlation coefficient . On the other hand, with is derived by using the mean values of and corresponding to the sampling intervals of Figs. 4 and 5. This shows that mixing of luminosity classes in our sample is not high enough to prevent a rather clear relation between and . This also means that correlations of and against and can be considered synonymous. ## 2.3.1. Correlations with and/orWe have just seen that for our program stars there is a well
defined relation between V and
T. On the other, as we shall see, the
"true" rotational velocity Distributions of the angular velocity ratio
(
critical angular velocity for rigid rotation) of Be stars are strongly
peaked, according to the spectral type and luminosity class, from
to
(Zorec 1986, Zorec & Briot
1997). In Fig. 6 is shown the distribution of the most numerous group
of Be stars: B2+B2.5+B3 main sequence stars, obtained from their
observed distribution of (histogram)
and corrected from errors in (Smart
1958) and random distribution of the inclination
## 2.3.2. Correlations withThe visible continuum emission is proportional to the emission measure. The latter is larger when the radius of the H-ionized region is more extended, so when is higher. It is expected then that SPh variations will also be more noticeable if stars are hotter. Such a tendency is depicted by the trends in Fig. 5 of and SPh slopes against . © European Southern Observatory (ESO) 1999 Online publication: August 25, 1999 |