4 The colour-magnitude diagram of NGC 6231

We have said above that the most noticeable feature of the colour-magnitude diagram is the bend at $V \approx$ 13.5 mag followed by a star band 2 mag broad located 1.5 mag above the ZAMS, approximately. For us, the ZAMS sector for 14 < V < 16 mag with almost no stars on it cannot be explained by anomalies in the B-V indices since the V, V-I diagram shows a similar picture. The respective diagrams of SBL98 and, less notoriously, those of Seggewiss (1968), Balona & Laney (1995) and RCB97 confirm this feature.

A rough way to prove whether such a distribution of faint stars is intrinsic to NGC 6231, is to compute the number of field stars expected in this diagram and subtract them from our observations. Cluster stars together with field stars of a variety of absolute magnitudes, different colour indices, located all at different distances and distinctly reddened, are expected to be included in our photometry. Making an arbitrary subdivision of the observed colour-magnitude diagram, say into cells of size $\Delta V=1.0$ and $\Delta (B- V)=0.25$, the removal of expected field stars can be easily performed.

The contribution of field stars within each cell was estimated adding the stars distributed in layers of thickness $\Delta r$ at distance r within the solid angle d$\omega$, subtended by the effective cluster area covered by our survey, using the function:

$\psi (M_V, ST, r, \Delta r) = \Psi (M_V,ST) {\Delta r} {{\rm d}\omega} r^{2}$.

where $\Psi (M_V,ST)$ is the number of stars per cubic parsec of magnitude absolute M_V and spectral type ST as currently tabulated (see Scalo 1986). As faint cluster stars do not have spectral types but only colour indices and apparent magnitudes, the function $\Psi (M_V,ST)$ had to be transformed adopting $V=M_V-5+5 \log r +A_{V}(r)$, $A_{V}(r) = 3.2 \times E_{B-V}$ and the relation of spectral types and intrinsic colour indices. Stars of all luminosity classes were considered in the calculation. A_V(r) was taken from Sect. 3.2. It was also assumed that the function $\Psi (M_V,ST)$ should not change significantly along the plane of the Galaxy and would remain valid over large distances (Mihalas 1967). The total contribution of field stars was estimated integrating in layers of $\Delta r = 100$ pc up to a distance of 5 Kpc.

Figure 9 shows, in the form of a contour map, the result of subtracting the expected stars in each cell. The map confirms the existence of a 2 magnitudes broad band rising above the ZAMS at $V\approx 14$ including a density peak at 16.5<V<17.5 and 1.0 <B-V<1.5. In any case, the excess of stars that are defining the level curves is larger than the uncertainty of the counts, assuming the uncertainty in a count N is $\sqrt{N}$. Longward of $V\approx 16$ mag, along the ZAMS, the expected numbers of stars largely surpass the observed ones producing negative counts (not shown in the map) while to the right side of the band, there is no difference between the expected and observed numbers of stars. In a simple way, Fig. 9 provides a rough evidence of an excess of faint stars in NGC 6231; but it is not indicating by itself that the stars lying in the band are all cluster members. Indeed, many of them are likely to be of types A, F and G surely related to the cluster, while others may be reddened field stars, even of type B.

A dozen of PMS stars and seven PMS candidates were found by SBL98 in this cluster using a criterion based in H$\alpha$ emission. Our survey includes none of their PMS candidates and only 7 out of 12 of their PMS stars. Whereas these 7 stars are all well located in the red extreme of our band, it seems that more PMS should have been detected by SBL98 between $0.5 \leq B-V \leq 1.2$. They had already noticed this deficiency arguing that their criterion, based on H$\alpha$ emission, does not work in all the cases, especially when the material surrounding some PMS stars could have been swept away by stellar winds from massive stars or some supernova event. These authors justified this assumption by a hole seen in the reddening material near the centre of NGC 6231. Whatever the reason in the failure to detect PMS stars, it seems that the UBV photometry can still provide indirect evidences of their presence here.

  

Figure 9: The contour map of the zone of NGC 6231 after the subtraction of field stars. Solid lines are the density constant loci for 3, 10, 20 and 30 stars. Dotted lines are the PMS evolutionary tracks from Bernasconi & Maeder (1996). The isochrones are indicated with dashed lines and the ZAMS (Schmidt-Kaler 1982) is also shown. Squares and triangles are PMS stars and PMS candidates from SBL98

More information can come from this PMS zone if we superimpose in Fig. 9 the PMS evolutionary models developed under canonical assumptions by Bernasconi & Maeder (1996) and the isochrones derived from them. Here we see how the PMS star region is enclosed by the isochrones of $6 \ 10^{5}$ and 10⁷ yr approximately, and masses from 3-5 ${\cal M_{\odot}}$ for the most massive PMS star to about 1 ${\cal M_{\odot}}$ for the less massive ones are observed. This suggests the existence of an age scatter of 10⁷ yr among faint stars which confirms the results from SBL98. All this acts against coevality as the evidences favour that massive and less massive stars formed in different events, the most massive ones being the youngest generation.

4.1 The cluster luminosity function

The luminosity function, LF, is defined as:

where is the of the number of stars having absolute magnitudes $M_V \pm {\rm d}M_V/2$.

Let us briefly comment some factors that may influence the LF reliability:

1.- Data completeness: this is usually the most important one, but according to the M_V range of likely members, the LF will be computed within the range -7.5 < M_V < 1.5 mag where we are immune to it.

2.- Binarity or stellar duplicity: these effects that produce a less steep slope remain still unknown factors in NGC 6231 although estimates from Levato & Morrell (1983) and Raboud (1996) indicate minimum binarity percentages of 41% and 52% respectively. Trying to reduce the influence of known binaries we corrected by $\Delta M_{V}=0.75$ mag when both components have similar spectral types and 0.50 mag when no information other than binarity was available.

3.- Photometric errors: they normally act raising the magnitude distribution giving thus a steep slope. Their influence on the present case is a negligible effect of less than 1%, even assuming variable errors (magnitude dependent) like those shown in Fig. 2.

Since we know from previous sections that stars with $V \geq 13.5$mag might be in a different evolutionary status, where the hydrogen burning phase has not started yet, they were not considered for computing the LF. But the evolved members were all included, in principle, because their stage of evolution is not so advanced to exclude them.

  

Table 5: The luminosity and mass functions of NGC 6231

Note 1: Case 1, the entire $\Delta M_{V}$ range is used to the fitting. Case 2, the first three brightest bins are excluded. Case 3, as in Case 2 but excluding the last bin too.
Note 2: the lowest mass bin was not used to compute the IMF.

The stars were distributed into bins of $\Delta M_{V} =1$ mag (using $\Delta M_{V}=0.5$ does not modify the result at all) as indicated in Table 5. The WR-type star, HD 152270, the most evolved cluster member, was included in the highest $\Delta M_{V}$ bin.

Three cases were chosen to assess $\gamma$. In first term, we used the entire range of M_V, this is -7.5 < M_V < 1.5. Next, we excluded the first three bins that contain evolved stars. And finally, we ignore, in addition, the lowest M_V bin which is supposed to be affected of incompleteness due to our arbitrary choice of colour and magnitude limits up to which memberships were estimated.

A weighted fit of the data in Table 5 gives slope values of the LF which in no case are larger than 0.20 (assuming uncertainties in each luminosity bin proportional to $\sqrt{N}$). These values disagree with Perry & Hill (1992) who found $\gamma = 0.32$, a discrepancy that could hardly stem from a different fitting procedure despite they made an unweighted fitting (without quoting the slope error). Probably, this discrepancy has an explanation in the fact that Perry & Hill obtained a LF mixing stars of NGC 6231 and stars of Sco OB1. Raboud (1998) covered an area larger than ours but smaller than that of Perry & Hill, obtaining also a flat slope of the LF in this cluster.

4.2 The initial mass function

The term "initial mass function", IMF, is not strictly applicable in this cluster since it requires that all stars were formed at a same time in a same point. As it was said above, the presence of probable contracting stars gives hints against coevality. But if we only consider the likely and probable members, the cluster mass spectrum could still be seen as the cluster initial mass function. On this ground, the slope of the IMF is defined as:

where the IMF is assumed to be a power law.

Individual stellar masses of members were computed through an interpolation procedure among evolutionary tracks computed with mass loss and overshooting (Schaller et al. 1992). M_V, (B-V)₀ and (U-B)₀ values were converted to and via a relation between effective temperatures, spectral types, colour indices and bolometric corrections given by Schmidt-Kaler (1982). In this plane, the stellar path from the point a star evolved off the ZAMS was reconstructed with the theoretical parameters of the two adjacent evolutionary tracks and the initial mass was then obtained. The WR star (HD 152270) was given a mass similar to the highest stellar mass found in NGC 6231 as we assumed it has evolved the first. Like in the precedent subsection and before computing their masses, binaries were treated introducing $\Delta M_{V}$ corrections already explained.

Stellar masses were included into the mass range indicated in Table 5 and a weighted fit was then made (uncertainties in each mass bins proportional to $\sqrt{N}$). Two values of x, depending on whether binarity is taken into account or not, are shown at the bottom of the same table and the corresponding data fits are shown in Fig. 10. Evidently, binary corrections introduce no appreciable differences in the resulting slopes (1.14 or 1.06) and, according to the errors, at $2\sigma$ level, they still approximate the Salpeters (1955) law slope.

SBL98 determined the cluster IMF finding a slope of $1.2\pm 0.4$ and a turnover at = 0.4. We found a similar turnover chiefly stated by means of an arbitrary choice of membership and the presence of the bend in the colour-magnitude diagrams instead of the decrease in the number of low mass stars as SBL98 did. For this reason the last mass bin of Table 5 was not used to compute the IMF but it is gratifying the coincidence with SBL98s turnover. They also mention a probable flattening of the IMF for $\log \cal{M} \geq$ 1.2 which is weakly evident too in Fig. 10 for $\log \cal{M} \geq$ 1.4 when no binarity correction is adopted. But the same figure shows that this effect, disappears immediately after such correction is done.

SBL98 did not correct their data for binarity and found a IMF slope of 1.21. In our case of no binarity correction, we found a slope of 1.06. It would be easy to assume this difference is produced by a different statistical treatment, but no more than half of it could be explained this way. It seems more realistic to resort to a primordial radial mass segregation effect (Raboud & Mermilliod 1998) where the less massive stars tend to lie outside the cluster centre. In this case, the slope of the mass function is strongly dependent of the area under analysis and the photometric limit. Our area of observation is $\approx 100$ square minutes while the field analyzed by SBL98 is $\approx 400$ square minutes. Within our area the number of stars with $\log \cal{M} \geq$ 0.4 used to compute the IMF is $\approx$ 121 out of 136 stars while SBL98 used $\approx$ 190 out of 204 stars. Most of the $\approx 70$ stars in excess contained in the sample of SBL98 are less massive stars what supports the idea of radial mass segregation.

  

Figure 10: The Initial Mass Function of likely members in NGC 6231. Dotted line and open triangles represent the case of binarity correction. Long dashed line and filled circles are for no correction