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Astron. Astrophys. 334, 845-856 (1998)

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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 [FORMULA]

Fig. 6 (previous section) conforms to the primary prediction of the evolution models - the presence of a simple relationship between [FORMULA] [FORMULA] and [FORMULA]. In this section, we examine the relationships between log [FORMULA], EW 5411, and FWHM 4686.

Fig. 7 shows the relationship between the EW of HeII 5411 and log [FORMULA]. Note that the points in this diagram are entirely independent of the [FORMULA] - [FORMULA] calibration. The relationship is extremely well defined; scatter around the line is much less than the observational uncertainty in log EW ([FORMULA], for EW [FORMULA] 10 Å, according to SSM96). EW 5411 increases monotonically with [FORMULA] over subclasses WN 7b to WN 4b; the increase is more rapid in the WN 7 domain than at higher [FORMULA].

[FORMULA] 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 [FORMULA] and [FORMULA], 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- [FORMULA] "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 [FORMULA].

Fig. 8 shows the correspondingly good relationship between EW 5411 and [FORMULA] on the assumption that the log [FORMULA] - [FORMULA] 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 [FORMULA]) 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 [FORMULA] is much lower than for constant flux. That is, the flux from the atmosphere is de creasing steeply as we move to higher [FORMULA] 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 [FORMULA] of a WN b star from the EW 5411. Its usefulness, in practice, is limited by the typical uncertainty of [FORMULA] in log EW. The lines in Fig. 8 are:

[FORMULA] = 3.3 [FORMULA] EW 5411 - 11.1, for [FORMULA] EW [FORMULA] 1.74
[FORMULA] = 15 [FORMULA] EW 5411 - 31.4, for 1.74 [FORMULA] [FORMULA] EW [FORMULA] 1.95

On the basis of their behaviour in [FORMULA], [FORMULA] and EW 5411, the b-stars appear to be a one-parameter family in which radius [FORMULA], luminosity L, and line flux decrease as effective temperature [FORMULA] and EW 5411 increase.

4.2. FWHM of HeII 4686 vs. log [FORMULA]

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. [FORMULA], see Fig. 7) and FWHM 4686 (terminal velocity, see Fig. 1). Fig. 9 plots FWHM 4686 vs. [FORMULA] [FORMULA] with the ionisation subclasses distinguished by symbols. Because of the very tight EW 5411 - [FORMULA] 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 [FORMULA], the spread of FWHM 4686 at constant [FORMULA] is very large and the error bars are very small.

[FIGURE] Fig. 9. Relationship between FWHM 4686 and [FORMULA] [FORMULA] with the ionisation subclasses distinguished by symbols. The sloping dashed lines give near separation of the ionisation subclasses, corresponding to the EW-FWHM correlations found by SSM96 within each subclass. The dashed line at FWHM = 30 Å indicates the lower limit for b-star classification. The solid line passes through (to observational accuracy) the stars of lowest FWHM. Its significance is discussed below in relation to later diagrams.

The spread of FWHM 4686 at a given value of log [FORMULA] 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 [FORMULA] comes from a comparison of Figs. 4 and 9. The stars in Fig. 4 that have significantly low HeII/I for their value of [FORMULA], 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, [FORMULA], and the surface mass flux as functions of [FORMULA] 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.

[FIGURE] Fig. 10. Relationships of [FORMULA], and surface mass flux to [FORMULA]. The points are from HKW95 (corrected for the change in the [FORMULA] - [FORMULA] relationship). The lines pass through the stars of lowest FWHM 4686, as in Fig. 9. The stars with high [FORMULA] and surface mass flux for their value of [FORMULA] also have low HeII/I (Fig. 4) and large FWHM 4686 (Fig. 9) i.e. large terminal velocity.

The behaviour of FWHM 4686, EW 5411, HeII/I and the mass loss parameters as functions of [FORMULA] suggests the following:

  • The tight correlation between EW 5411 and [FORMULA] results from a Strömgren sphere, ionisation-limitation of the HeII region of the atmosphere. [FORMULA] is essentially a Zanstra temperature.
  • The extent of the HeI region (beyond the HeII zone) is controlled by the surface mass flux.
  • At a given [FORMULA], both [FORMULA] and surface mass flux have a significant range. Those stars with higher surface mass flux have a larger HeI region (at constant [FORMULA] and EW 5411) resulting in a lower ratio of HeII/I and an increased optical thickness of the atmosphere.
  • Opposing effects of increasing [FORMULA] (which increases EW HeII 5411 and increases the HeII/I ratio) and increasing extent of the HeI region (which increases EW HeI 5875 and decreases the HeII/I ratio) leads to the scatter and to the sloped subclass divisions in the HeII/I - [FORMULA] plane (Fig. 4).
  • Increasing opacity of the atmosphere correlates with increasing width of HeII 4686 (Fig. 9).

The critical question then is: Why, at a constant mass and [FORMULA], 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 [FORMULA] 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 [FORMULA], have a higher ratio of HeII/I.

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© European Southern Observatory (ESO) 1998

Online publication: June 2, 1998