4 Results

4.1 Average radial velocity of the cluster

To compute the average radial velocity of NGC 6231, we have included the five stars with constant velocities plus the seven binary systems with orbits. The weighted mean is $<V_{\rm r}>$ = -30.7 $\pm$ 0.9 (3.1 rms) km s^-1. This result is in good agreement with the value computed by Raboud (1996): -29.2 km s^-1, and more precise than that derived by LM83 from 8 stars: $<V_{\rm r}>$ = -27.3 $\pm$ 3.5 km s^-1 .

4.2 New orbital elements

The new orbital elements based on combination of the literature radial velocities and our new observations are given in Table 3. For each element, Table 3 lists on the first line its values, and on the second line its errors. The orbital elements for S289 (353) and S306 (858) are first, somewhat preliminary, determinations. The radial-velocity curves are displayed in Fig. 1.

Contrary to what is observed for solar-type stars, the eccentricities are all larger than 0.10 although the orbital periods are shorter than 8 days. Similar results were obtained by Mermilliod (1996) on the basis of a larger sample of 24 O- and early B-type spectroscopic binaries in open clusters. Eccentric orbits are observed even for periods as short as 2 days.

Figure 2: H$_{\gamma }$ profiles at various phases for S2. The double lines are evident at phase 0.371

Figure 3: H$_{\gamma }$ profiles at various phases for S224. Asymetric wings are observed at phases 0.356 and 0.613

Figure 4: H$_{\gamma }$ profiles at various phases for S254. The change in radial velocity is quite clear, but the presence of the secondary component is not obvious

Figure 5: H$_{\gamma }$ profiles at various phases for S290

Figure 6: H$_{\gamma }$ profiles at various phases for S291. The double-lined nature is especially evident

4.3 Percentage of binaries

The binary frequency can be estimated only on the basis of the stars in the central part of the cluster, because we have only one radial velocity per star for 9 corona candidates, which were obtained to check their membership. Indeed two are probable non-members.

Therefore, in Table 1, we count 42 member stars brighter than V = 10.50, i.e. V₀ = 8.90. But, we do not have radial-velocity observations for 8 stars, which leaves 34 stars. Among them we find 14 SB2 (8 + 6), 14 SB1 (10 + 4), 6 constant. The global binary frequency for stars mostly earlier than B1.5V is than 82% (28/34).

We have 14 O-type stars, including the brightest B0 Iab supergiant, and count 11 spectroscopic binaries, with 8 stars with confirmed double-lined spectra. The rate for the O-type stars is 79%. Star S293 (O9 Ib CNO) shows intrinsic line variability (Levato et al. 1988) and has not be included in the binary sample.

Our binary frequency is larger than that computed by LM83 (>41%) and by Raboud (1996), 52% for the stars later than B2V. However, Raboud's simulations demonstrated that the theoretical detection percentage of about 55% of binary stars with 2 observations, separatelly 744 days; but raises to 67%, if we consider three observations, and reaches 71% with four. The large number of observations obtained so far on the brightest stars explained the larger number of confirmed spectroscopic binaries. Further observations are needed to complete the survey of stars later than B0. Eight O-type stars (S2, 161, 220, 254, 290, 291, 306, 338) have been observed with the CHARA speckle camera (Mason et al. 1998) and a companion has been detected only for S291. The comparison of the location of the stars in the colour-magnitude diagram confirm in most cases the spectroscopic binary identification. We are aware of the work by Gies (1987) who showed that some O-type stars display line-profile variability due to non-radial pulsations; these variations produce apparent changes in the line profiles and radial velocities. An analysis of variance test for the interline variation could be applied to decide on the reality of the duplicity of dubious cases as Levato et al. (1988) did. But this statistical technique requires larger numbers of observations than we presently have.

4.4 Axial rotation

For those stars later than O9, and of luminosity classes III, IV and V, we derived the $V\sin i$ values. If we compare the results with the average $V\sin i$ for the field stars of the same types (Sletteback 1970; Abt 1970), the results will be a ratio $< V \sin i >$/ $< V \sin i>_{\rm FS}$ = 0.67 $\pm$ 0.04, in the new Sletteback system, in agreement with Levato & Morrell (1983).

Fom this result, there is no doubt that the axial rotation is lower between the members of the binary systems, and NGC 6231 results in a good example due the great incidence of binary stars. Another cluster with similar characteristics is NGC 6193 (Arnal et al. 1988), with 72% of probable binary stars, and a projected axial rotation refered to field stars of similar types, of 0.67 $\pm$ 0.08.

4.5 Colour-magnitude diagram

The Geneva colours of Raboud et al. (1997) have been used to plot the (V₀, X) colour magnitude diagram (Fig. 7). X is a good temperature indicator for early-type stars, presents an interesting range and is corrected for interstellar reddening. The various symbols denote the different binaries: filled squares for SB2 and open circles for SB1. Binarity is now pretty well known down to V₀ = 8 ( $V\,\sim 9.5$) and much more work remains to be done for fainter stars. The position of the double-lined binaries in the CM diagram is in good agreement with the presence of a bright companion. We note that there are only seven stars which define the single star locus, both from the photometry and spectroscopy ($V_{\rm r}$ = cte).

Figure 7: Colour-magnitude diagram for observed stars in NGC 6231. Symbols are as follows: filled squares: SB2, open circles: SB1, dots: "single'' stars, cross: no spectroscopic information, filled triangles: corona stars

 

 

Table 4: Binary frequency of clusters $N_{{\rm O\, star}} >$ 5

	Number of
Cluster	O-stars	SBs	Frequency
IC 1805	10	8	0.80
NGC 6231	14	11	0.79
NGC 2244	6	3	0.50
IC 2944	16	7	0.44
NGC 6611	12	5	0.42
Tr 16	20	7	0.35
Cr 228	21	5	0.24
Tr 14	7	1	0.14