4. Are the WN b stars a one-parameter family?
A classification system aims to assign stars to categories within which the spectra are "very similar". The implicit hope is that the stars producing those spectra are also "very similar" - viz. in mass, composition, age and/or history. To the extent that this is true, the spectral type alone is able to indicate the age and stage of a star in its evolution.
Our hypothesis is that the WN b and only the WN b stars correspond to the hydrogen free phase of WN evolution. Evolutionary models predict that, in this phase, the previous history of the star is unimportant and that the mass is the critical parameter defining the properties of the star. We therefore examine the dominant spectral properties of the WN b to ascertain the degree to which this group may be regarded as a one-parameter family.
4.1. EW of HeII 5411 vs. log
Fig. 6 (previous section) conforms to the primary prediction of the evolution models - the presence of a simple relationship between and . In this section, we examine the relationships between log , EW 5411, and FWHM 4686.
Fig. 7 shows the relationship between the EW of HeII 5411 and log . Note that the points in this diagram are entirely independent of the - calibration. The relationship is extremely well defined; scatter around the line is much less than the observational uncertainty in log EW (, for EW 10 Å, according to SSM96). EW 5411 increases monotonically with over subclasses WN 7b to WN 4b; the increase is more rapid in the WN 7 domain than at higher .
is derived from a model fit to HeII 5411 and HeI 5875. Schmutz et al. (1989, Fig. 6) show the contours of the two line strengths as functions of and , the transformed radius. The tight relationship in Fig. 7 reflects a restriction of the observed stars to a narrow band in the theoretically possible parameter space. The observed WN b stars follow the low- "ridge" in the contours; i.e. the observed EW's of HeII 5411 are the maximum allowed by the models at any given value of .
Fig. 8 shows the correspondingly good relationship between EW 5411 and on the assumption that the log - relationship (Sect. 3) applies to all b-stars. The EW increases as the continuum brightness decreases to hotter subclasses. For the WN 7b stars, the rate of increase is only slightly lower than for constant line-flux (indicated by the arrow in Fig. 8); i.e. these stars have nearly constant HeII 5411 flux implying that the "size" (integral ) of the atmosphere is nearly constant while the continuum brightness of hotter stars is lower. In the WN 6 to 4 domain, the rate of increase of EW 5411 with decreasing is much lower than for constant flux. That is, the flux from the atmosphere is de creasing steeply as we move to higher but the brightness of the continuum (the star) is decreasing even more steeply. This relationship is potentially useful since it allows us, in principle, to estimate the of a WN b star from the EW 5411. Its usefulness, in practice, is limited by the typical uncertainty of in log EW. The lines in Fig. 8 are:
= 3.3 EW 5411 - 11.1,
for EW 1.74
On the basis of their behaviour in , and EW 5411, the b-stars appear to be a one-parameter family in which radius , luminosity L, and line flux decrease as effective temperature and EW 5411 increase.
4.2. FWHM of HeII 4686 vs. log
In contrast to EW 5411, the behaviour of FWHM 4686 (i.e. the terminal velocity, see Fig. 1) is complex.
SSM96 have shown that, within an ionisation subclass, there is a very tight correlation between EW 5411 (i.e. , see Fig. 7) and FWHM 4686 (terminal velocity, see Fig. 1). Fig. 9 plots FWHM 4686 vs. with the ionisation subclasses distinguished by symbols. Because of the very tight EW 5411 - relationship for WN b stars, Fig. 9 corresponds to the EW 5411 vs. FWHM 4686 diagram of SSM96. In marked contrast to the tight correlation of EW 5411 and , the spread of FWHM 4686 at constant is very large and the error bars are very small.
The spread of FWHM 4686 at a given value of log indicates that a second parameter must be important in defining the velocity structure of the wind.
A clue to an explanation of the spread of comes from a comparison of Figs. 4 and 9. The stars in Fig. 4 that have significantly low HeII/I for their value of , namely WR 36, 75 and 110, are the same stars that in Fig. 9 have the largest FWHM, 45 Å or above. The second parameter involved appears to be the extent/optical thickness of the atmosphere.
Fig. 10 shows the mass loss rate, , and the surface mass flux as functions of with the lines drawn through the stars of lowest FWHM 4686 as in Fig. 9. The same three stars WR 36, 75 and 110 fall the farthest above the line in both mass loss parameters. We also note that the WN 5o star (WR 149) which has been included as a curiosity (see Sect. 3.1) is distinguished by low values of both mass loss parameters, consistent with our suspicion that it is not yet a full member of the "b" subclass but is in the process of loosing the last of its hydrogen shell and increasing its mass loss rate.
The behaviour of FWHM 4686, EW 5411, HeII/I and the mass loss parameters as functions of suggests the following:
The critical question then is: Why, at a constant mass and , does the surface mass flux and, therefore, the atmospheric opacity vary? This will be addressed in Sect. 6 after we have further discussed the evolutionary models.
The separation of the b-stars from the o and h-stars (Fig. 4) may be understood in the same fashion. The later stars have larger radii and lower due to the presence, in both subclasses, of an extended hydrogen envelope. However, the o and h-stars do not have optically thick atmospheres and, therefore, at a given value of , have a higher ratio of HeII/I.
© European Southern Observatory (ESO) 1998
Online publication: June 2, 1998