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3 Data analysis

3.1 Memberships

The determination of memberships in NGC 6231 was carried out inspecting the locations of the stars in all the photometric diagrams simultaneously. From Figs. 3 and 4, the following main features can be outlined:

The two-colour diagram shows, down to $B-V \leq 0.5$ and $U-B \leq 0.4$, a well populated upper main sequence composed by OB- and early A-type stars slightly affected by differential reddening. Since these all stars have unique reddening solution their memberships can be analysed individually. There are also some stars located along the reddening path of OB-type stars that could be heavily reddened background faint stars of early types. But there is no doubt that many others are located there because of large errors in the U-B indices.

\includegraphics [clip,width=7cm]{ds1577f03a.eps}

\includegraphics [clip,width=7cm,height=9.7cm]{ds1577f03b.eps}\end{figure} Figure 3: a) The two-colour diagram of all stars observed in NGC 6231. Filled circles are likely members; filled inverted triangles are probable members; open inverted triangles are non-members. Open circles are stars for which no membership was assessed. Solid lines stand for the intrinsic line for luminosity class V stars, in its normal location (I), and displaced by 0.43 and 0.33 mag in B-V and U-B respectively (II). The path of the reddening is indicated. The location of star # 30 (HD 326338), a non-member $\delta$ Scut variable of spectral type F0III and period $P=0.0896^{\rm d}$ (Balona & Laney 1995) is shown. b) The V vs. B-V diagram. Symbols have the same meaning as in a). The solid line is the ZAMS (Schmidt-Kaler 1982) fitted to an apparent distance modulus V-MV = 12.90 and displaced by 0.43 mag in B-V
\includegraphics [clip,width=14cm,height=10cm]{ds1577f04.eps}\end{figure} Figure 4: a) The V vs. U-B diagram. Symbols have the same meaning as in Fig. 3a. The solid line is the ZAMS (Schmidt-Kaler 1982) fitted to an apparent distance modulus V-MV = 12.90 and displaced by 0.33 mag in V-B. b). The V vs. V-I diagram. Symbols as in Fig. 3a. Star # 38, ($-41^{\circ}7734$) is a probable variable $\beta$ Ceph for which our CCD measures differ by more than 0.1 in V and B-V in respect of PHC91 values. The ZAMS was derived from Cousins (1978) relation of B-V and V-I

The three colour-magnitude diagrams show a broadening of the observed sequence from $V\approx 11$ to $V\approx 13.5$ mag probably produced by contamination of non-member stars of intermediate B-types located slightly in front of or beyond the cluster that could belong to Sco OB1. This broadening ends in a well marked bend at $V\approx 13.5$ mag, longward of which the stars are mostly located in a band that shows the highest density at $\approx 
1.5$ mag above the ZAMS. That is why the Schmidt-Kaler ZAMS (1982), when fitted to an apparent distance modulus of 12.9 (see Sect. 3.3), does not coincide with the left envelope of the lower sequence.

We will return to this fact in section 4 but, in advance and without denying a sure confusion with non members, if this band is primarily composed of field stars, it draws the attention that no one is found "in the ZAMS" from V=14 to V=16 mag. In view of this, cluster memberships were only determined for stars with $B-V \leq 0.5$ and $V \leq 14$ mag. Stars above these limits were then analysed and given one of the following membership categories: likely members (stars with the highest chances), probable members (stars whose magnitudes and colours are not very well correlated in all the diagrams but with reddening solutions still acceptable) and non-members (obvious cases of inconsistency in all the diagrams). The membership category is listed in Table 1.

3.2 Reddening analysis

To get intrinsic colours we need to know the EU-B/EB-V excess relation valid in the cluster. Table 4 contains a list of the bright stars with CCD photometry whose spectral types were mostly taken from Table 3 of PHC91. This sample was used to determine the reddening curve of NGC 6231. Besides, as the list of PHC91 includes a large number of stars in Sco OB1 having spectral types and UBV photometry, we used this information to perform a more refined analysis of the reddening around the cluster too.

Table 4: CCD photometry and main characteristics of the brightest stars of NGC 6231

$\char93 $\space & $...
 ...&0.42& 0.27& 
-- &0.64 & -- & 11.92\\  

Note: Details of membership can be found in Table 1. "Seg" is for Seggewiss (1968) and "Ho" is for Houck (1956) numberings respectively. The main source of spectral types has been the PHC91 article and Levato & Morrell (1983). V0-MV column contains spectrophotometric moduli.
Remarks: v1 probable variable according to the $\Delta V$ differences with PHC91 photometry. See also Table 1.
v = variable; v? = variable?
B = binary (from PHC91)
* = binary according to Raboud (1996).

Figure 5 shows the EU-B, EB-V diagram for 43 stars in NGC 6231 taken from Cols. 8 and 9 of Table 4. The same was done for 130 stars in Sco OB1 whose values were not listed for saving space. In both cases, colour excesses were obtained from the Schmidt-Kaler (1982) calibration of intrinsic colours and spectral types. Although most of the stars follow the standard reddening relation $E_{U-B}/E_{B-V} = 0.72 + 0.05\times E_{B-V}$, it is evident that both excesses are not only widely scattered but also biased towards large values, especially the EU-B. The influence of large EU-B excesses is better understood in Fig. 6 where we see how the distribution of the EU-B/EB-V ratios is biased towards values higher than 0.72. There are two reasons to think this colour excess scatter is intrinsic to the stars themselves and not produced by systematic and/or random errors of our CCD photometry: a) our data show high EU-B excesses exactly as PHC91 photoelectric measures of Sco OB1 stars do (both techniques imply different instrumental errors assuming CCD photometry is more accurate) and b) PHC91 stellar data are mainly averages of many photometric measures taken from several observers. Therefore, any unusual photometric value of a given star should have been smoothed and no large colour excess scatter should be seen in Fig. 5 among Sco OB1 stars.

\includegraphics [clip,width=8cm]{ds1577f05.eps}\end{figure} Figure 5: The EU-B vs. EB-V diagram. Open and filled circles stand for stars in the field of the Sco OB1 and member stars of NGC 6231 respectively. The line is the normal EU-B/EB-V excess relation. Some foreground stars show very anomalous excess relations. Stars # 41 and 148 are probable variables. # 38 is a probable $\beta$ Ceph and # 131 is a binary according to Raboud (1996)

The EU-B/EB-V ratios in NGC 6231, listed in Col. 11 of Table 4, show some anomalous values. If, instead of using our CCD data, we consider the Seggewiss (1968) photometry, the anomalies are confirmed in all the cases (except star # 25). Using PHC91 and SBL98 data also yield a similar result. It is interesting that several of these stars are, in addition, binaries or variables, the part of this scatter could be related to this feature as well. Another source of the scatter seen in Figs. 5 and 6 could be related to the interstellar material since Santos & Bica (1993) found that 0.20 mag out of the total reddening affecting NGC 6231 originates in intracluster dust (this would explain the differential reddening seen in the colour-colour diagram too). There is also a nearby molecular cloud in front of Sco OB1 (Dame et al. 1987) while Crawford (1990) reports strong variations in the CN density in the cluster direction.

Averaging the data of Col. 11 in Table 4 it was found $<E_{U-B}/E_{B-V}\gt = 
0.75 \pm 0.19$ (sd) (rejecting stars with very extreme values) while for association stars it was found $<E_{U-B}/E_{B-V}\gt = 0.75 \pm0.13$ (excluding 31 stars). These two mean values do not differ from each other significantly neither from the standard slope of 0.72 given above. But, in view of the numerous facts that distort the colour excess ratios, intrinsic colours of likely members without spectral classification were computed through the standard excess relation given above (described in Vázquez et al. 1996). As it is only valid for stars with $B-V \leq 0.5$ and $U-B \leq 0.4$, a few detected probable members (late B- and early A-types) were corrected for average reddenings $<E_{B-V}\gt = 0.43\pm 0.04$ and $<E_{U-B}\gt = 0.33\pm 0.09$ computed with the data of Table 4.

The R value, AV/EB-V, that allows to correct visual magnitudes according to $V_0 = V-R \times E_{B-V}$, was estimated from the individual EV-I/EB-V ratios listed in Col. 12 of Table 4. The EV-I excesses were obtained with a calibration of spectral types and (V-I)0 from Cousins (1978). These number ratios average $1.38 \pm 0.19$ that leads to $R\approx3.5$, similar to 3.6 derived by Johnson (1968) and not far from 3.3 $\pm\ 0.1$ found by SBL98. We recall that a number ratio of 1.24 is expected for normal absorbing material having R=3.1-3.2 according to Dean et al. (1978). As it is not clear if this large R is due to some of the facts discussed above (including variability and binarity) or to all of them together, we will adopt R = 3.2.

\includegraphics [clip,width=8cm]{ds1577f06.eps}\end{figure} Figure 6: The EUB/EB-V distributions for Sco OB1 stars (clean histogram) and cluster stars (hatched histogram)

To finish this part of the analysis, we re-estimated the absorption AV(r) in the direction of NGC 6231 using all the stars located within a ring of 25 arcmins radius around it. The photometry and spectroscopy of these stars, outside the area of our survey, were taken from Table 3 of PHC91. Their individual absorption AV and distances r were computed and plotted in Fig. 7. The structure of AV (r) seen in this figure is more complex than that shown by Neckel & Klare (1980) constructed with samples of OB-type stars. As OB stars are commonly far from the Sun, their sampling does not inform much about local variations of the absorption. After making some attempts, we found that AV(r) is better described by:

A_{V}(r) =\left\{ \begin{array}
 -1.65+0.93 {\times} \l...
 ... 4$~Kpc} \\  3 & \mbox{ ${ r} \gt 4$~Kpc.}\\ \end{array}\right.\end{displaymath}

for r in parsecs. Within the small volume of the cluster the second value of the array remains the same from 1.8 to 2.7 Kpc in agreement with PHC91. The third value was obtained making a straight fit from 2.7 Kpc to 4 Kpc whereupon we adopted the extinction curve proposed by Seggewiss (1968).

\includegraphics [clip,width=8cm]{ds1577f07.eps}\end{figure} Figure 7: The line is the path of AV(r) in the direction to NGC 6231. Open circles are stars located within a circle of 25 arcmin radius around NGC 6231 which data are from PHC91; filled circles are likely cluster members. Stars with peculiar distance modulus are indicated (see details in Table 4)

Figure 7 confirms thus, that most of the absorption in the direction of NGC 6231 takes place in the solar neighbourhood as stated by van Genderen et al. (1984) and PHC91. RCB97 have also arrived to the same conclusion by investigating the absorption within fields extending $\pm10 ^{\circ}$ and $\pm 2 
^{\circ}$ relative to the cluster finding, in addition, that some matter is present at the cluster distance. Like in the earlier works of Shobbrook (1983), Massa & Fitzpatrick (1986) and Balona & Laney (1995), the area covered in our survey is small enough to notice a variation of the reddening across the cluster surface. However, as RCB97 demonstrated (confirmed latterly by SBL98), that is the reddening across NGC 6231 is variable and increases towards its southern part.

3.3 The cluster distance and age

Regarding the cluster distance modulus of NGC 6231 the literature reports values ranging from 10.2 (Kholopov 1980) to 11.6 (Garrison & Schild 1979).

Individual distance moduli listed in Col. 13 of Table 4 were obtained here from a calibration of spectral types and MV (Schmidt-Kaler 1982). They average $11.7 \pm 0.4$ (sd). This high standard deviation is likely to be produced by factors such as the intrinsic scatter among the MVs of early type stars (Conti 1988) and the numerous known binaries and variables populating the upper main sequence of this cluster.

Another distance estimate, not much affected by binarity, stems from fitting the Schmidt-Kaler (1982) ZAMS in both, the V0 vs. (B-V)0 and V0 vs. (U-B)0 diagrams constructed only with likely members. This fitting yields $V_0-M_V=11.45 \pm 0.2$ (error from inspection) but we adopted a final value of $V_0-M_V=11.5\pm 0.25$ corresponding to a distance $d=1990 \pm200$ pc. The fitting of the ZAMS is shown in the MV vs. (B-V)0 diagram of Fig. 8, along with the envelope of binaries 0.75 mag above it. Curiously some likely members remain above this envelope as if they were binaries but two of them, # 93 (Segg 278) and 95 (Segg 199), were also investigated by Raboud (1996) who did not find any evidence of binarity.

PHC91 found a distance modulus of 11.50 that agrees with ours, but SBL98 found 11.0 while Balona & Laney (1995) and van Genderen et al. 1984 found 11.08 and 11.0 respectively. In the last two cases, part of the disagreement originates in the use of distinct ZAMSs (they used the Balona & Shobbrook's 1984), but also because they attempted to fit the faint stars which are clearly located above the ZAMS. If we had tried the same procedure here, we would have obtained a distance modulus reduced by 0.6 mag. In turn, SBL98 obtained 11.0 using the ZAMS of Mermilliod (1981) which being hotter than the Schmidt-Kaler's (1982) yields thus smaller distances.

\includegraphics [clip,width=7cm]{ds1577f08.eps}\end{figure} Figure 8: The MV vs. (B-V)0 diagram of the brightest stars in NGC 6231. The solid line is the Schmidt-Kaler (1982) ZAMS fitted to V0-MV = 11.5; the binary envelope, 0.75 mag above the ZAMS, is the dotted-dashed line and the isochrones of $ \log (\tau)=6.6$ and 6.5 from Schaller et al. (1992) are shown with dashed lines. HD numbers and our star designation are indicated along with the meaning of the symbols. Filled circles are for stars without known peculiarity

To estimate the age of NGC 6231 we used the isochrones from evolutionary models computed by Schaller et al. (1992) including mass loss and overshooting and solar metallicity. We assumed that solar metallicity models are applicable in this case although Kilian et al. (1994) indicate that the metallicity of NGC 6231 is lower than solar (but higher than in other clusters). Except the star HD 152233, a single variable star, all the stars with $M_V \leq 
-4.5$ are binaries. Above this magnitude the sequence is vertical, so by removing binarity, the only appreciable effect is a decrease in the magnitudes of the evolved stars HD 152234 and 152249 that leads to a larger age of the cluster. Given the combined effects of binarity and variability, is not simple to find the best isochrone fitting but if we neglect the even more uncertain location of the WR star HD 152270, the age of the cluster is between 3 and $5\ 10^{6}$ yr. This range of age is in close agreement with the cluster age given by Santos & Bica (1993), RCB97 and SBL98.

NGC 6231 contains several $\beta$ Ceph indicated in Fig. 8 and Table 4 which are located 1 mag below the cluster turn-off ($\approx M_V=-4$). The discussion of these stars is out of the scope of our work but in principle there is no conflict with the cluster age and the location in the sequence of these stars as it has been already accepted that they are not necessarily at the end of the core hydrogen burning phase and can display the $\beta$ Cepheid feature even before reaching that phase (Balona & Shobbrook 1983; Jerzykiewicz et al. 1996).

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