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7. Membership criteria

Differentiating field stars from cluster members is crucial, but it is a quite complex problem. Tools to assist in separating them, are the E(B-V) and probabilities of membership (P) derived from proper motion studies #(Th&(Thé et al. 1990). In this study, we add the location of an object in the HRD as a criterion of membership (see Fig. 5 (click here)). This is because the assumed stellar evolutionary status for each star can be compared to the age of NGC 6611 of 5 Myr or less. The resulting probability of membership, P for most objects are listed in Table 7 (click here). Note that such values are not always indicative to distinguish between cluster members and non-members. The proper motion of a star can be influenced by nearby cluster members, binarity, or by its formation process.

In the direction of NGC 6611 a distance of 2.6 kpc implies tex2html_wrap_inline6190 (Thé et al. 1990 and Fig. 2 (click here)). A star being a cluster member must therefore have tex2html_wrap_inline6192. Background objects in the cluster field will have a larger E(B-V)-value. From Fig. 2 (click here) and from Fig. 1 (click here) of Thé et al. (1990) we take an upper limit of tex2html_wrap_inline61960tex2html_wrap6220 8. Indeed most of our objects have an E(B-V) value between tex2html_wrap_inline6202 and tex2html_wrap_inline6204, see Table 7 (click here). We refer to this group of stars as Group A.

A second group, Group B, with tex2html_wrap_inline6206 tex2html_wrap_inline6208, can be identified from the same figures. A third group, Group C, are objects which have very large E(B-V) values, up to tex2html_wrap_inline6212. Finally, we distinguish Group D as objects with tex2html_wrap_inline6214, being probably non-cluster members.

In this section, we meticulously examine Groups A-D and deduce their membership probabilities.

7.1. Stars in Group A

7.1.1. Stars with a high proper motion membership probability

From Table 7 (click here) it appears that a large number of stars having an E(B-V) value between 0tex2html_wrap6248 55 and 0tex2html_wrap6250 75 also have high proper motion membership probability. From their position in the HRD, we find that most of these objects also belong to Group I. We will consider these MS stars as confirmed cluster members and are indicated ``Y'' in Table 8 (click here). However, two stars need a closer analysis:
W266sh: it has a good E(B-V) value for membership, tex2html_wrap_inline6242, but no proper motion of this star is known. W266sh is located just above the stellar birthline (Group II) in the HRD. The shell designation is due to its IR-excess above the F8 SED. The origin of this excess remains doubtful. If it is due to CS dust then the object is a good protostar-candidate. However, the CS extinction will reduce the IS value close to a foreground value. In case of an M-companion we have no such problem. We adopt this object as a probable cluster member.

W599: is definitely not a cluster member, since it is a very bright star that lies far away to the right of the stellar birthline. It has a late spectral type (G9). It cannot be at the same time a cluster member and an evolved object. It has also a rather low E(B-V) value, tex2html_wrap_inline6246, which suggest membership. However, its location in the HRD proves it to be a foreground object.

7.1.2. Stars with a low proper motion membership probability

In Group A we have also a number of stars whose E(B-V) value indicates that they are cluster members, but their proper motion probability suggests the opposite. The objects are: W240, W299, W300, W374, W396a, W396b, W440, W455 and W494sh.

W240: E(B-V) = tex2html_wrap_inline6260, P = 0% and Sp.T. = B8. It is located low in the HRD, but still on the MS. It seems reasonable to conclude that W240 is a probable cluster member.

W299sh: E(B-V) = tex2html_wrap_inline6266, P = 0% and Sp.T. = B6. We find W299sh located next to the ZAMS (Group I) which suggests that it is probably a cluster member.

W300: shows again a good membership value E(B-V) = tex2html_wrap_inline6272. It has an early spectral type, B2. In the HRD W300 is located exactly on the MS. Although Kamp's (1974) P value is 0%, it is a possible cluster member.

W374: E(B-V) = tex2html_wrap_inline6278 is a boundary case. We have derived F2 for its spectral type. Examining the HRD, we find W374 (option: tex2html_wrap_inline6280 = 4.4) to lie close to the stellar birthline at the right side (Group II) and even on the stellar birthline when we plot W374sh. Due to the possible presence of CS dust, the IS extinction can be lower than the total value of 0tex2html_wrap6326 56. In case of anomalous extinction this value is a minimum (note that tex2html_wrap_inline6284). This indicates that we should be careful in accepting this star to be a cluster member, but if this is the case, it seems to be a very good PMS-candidate.

W396: we have to consider both options with P = 0%: W396a (Sp.T. = F9, E(B-V) = tex2html_wrap_inline6290) and W396b (Sp.T. = G2, E(B-V) = tex2html_wrap_inline6294). We find both options located to the right of the stellar birthline (Group II) in the HRD. In both cases, the position in the HRD and the late spectral types suggest that the star is a very young object. The alternative would be that W396 is a foreground object. This seems to be unlikely if we consider the derived E(B-V) values and the presence of anomalous extinction.

W440(1): with E(B-V) = tex2html_wrap_inline6300, P = 0% and spectral type G9, it is located in the HRD far away and above the stellar birthline. Because of this and its late spectral type it cannot be an evolved cluster members, see Fig. 9 (click here). Together with the fact that we found a normal extinction law, tex2html_wrap_inline6304 = 3.1, we conclude that this star is not a cluster member as is the case for most of such objects, see Fig. 4 (click here).

W455: E(B-V) = tex2html_wrap_inline6308, P = 7% and Sp.T. = B7. In the HRD W455 is located between the stellar birthline and the MS-curve (Group I), which makes it very possibly a cluster member, although the SED fit shows a depletion in the near-IR.

W494sh: has a tex2html_wrap_inline6312 membership probability
according to its proper motion E(B-V) = tex2html_wrap_inline6316 and its spectral type is B6. Examining the star's location in the HRD, we find it is located just above the MS. We can likely assume that this star is a cluster member
and most probably a good PMS-star candidate due to the presence of CS dust.

7.2. Stars in Group B

As far as their E(B-V) is concerned, this group is located at the border of the ``back'' side of NGC 6611. However, if we consider that the extinction consist of an IS, CS and intracluster (IC) value, they could be very well cluster members. Group B consists of W213(2), W245sh, W297, W306, W406 and W611.

W213: we have two options with unknown probability of membership: W213(1), with E(B-V) = tex2html_wrap_inline6342 and spectral type A7 (this option belongs strictly speaking to Group C but we also consider it here); and W213(2), with E(B-V)= tex2html_wrap_inline6346 and spectral type F9. Comparing the two obtained SED fits, we concluded that option W213(2) is better. In the HRD, W213(1) lies isolated, quite high and to the right of the stellar birthline. W213(2) is located somewhat lower than W213(1) in the HRD, but also to the right of the stellar birthline. W213(2) appears to belong to Group II. The HRD positions of W213(1) and W213(2) and the SED fits permit us to discard option W213(1) and only to consider W213(2) from now on. W213(2) is probably a very young object and probably a cluster member.

W245sh: shows evidence for CS dust, it has: E(B-V) = tex2html_wrap_inline6350, P = 0% and spectral type B6. In the HRD we find W245sh reasonably close to the ZAMS (Group I). This star could be a suitable HAeBe candidate and considered to be a probable cluster member as we have no contradictory proof.

W297: E(B-V) = tex2html_wrap_inline6356, P = 0% and spectral type B1. Based on its location in the HRD (Group I), the presence of an anomalous extinction law and the E(B-V) of the star, it is highly probable that {W297 is a cluster member.

W306: it has E(B-V) = tex2html_wrap_inline6364, P = 89% and spectral type B2. W306 belongs to Group I and we assume that it is a cluster member.

W406: E(B-V) = tex2html_wrap_inline6370, spectral type K0 III and P = 0%. In the HRD W406 is seen as a very bright star that lies far to the right of the stellar birthline (Group III). We conclude, therefore, that W406 is not a cluster member and most probably a background object.

W611: E(B-V) = tex2html_wrap_inline6376, spectral type is G8 and P = 13%, is located above and far away to the right of the stellar birthline in the HRD. {W611 is therefore a Group III object and probably no cluster member. As for {W406 the extinction law is normal, we therefore must conclude that it is a background object.

7.3. Stars in Group C

Stars in this group are expected to be background objects or objects that are located in a dark region (high IC extinction) or with a considerable amount of CS material in the line of sight (high CS extinction). Stars that exhibit an E(B-Vtex2html_wrap_inline6396 tex2html_wrap_inline6398 or more, are: W188, W202, W213(1), discussed above, W339(2), and W556.

W188: has the largest E(B-V) value of our sample: tex2html_wrap_inline6402. Its membership probability
is 87%. It has been classified as B0. In the HRD we find W188 next to the ZAMS, which makes it acceptable to presume that W188 is a cluster member. This is supported by the small anomalous extinction.

W202: E(B-V) = tex2html_wrap_inline6406, spectral type B3 and P = 0%. In the HRD we find W202 located next to the ZAMS. This implies that W202 is a probable cluster member.

W339(2): E(B-V) = 1tex2html_wrap6428 08, spectral type B3 and proper motion not known. Furthermore we obtained two fits. In the HRD W339(2) (tex2html_wrap_inline6414 = 3.9) is located between the ZAMS and the stellar birthline (Group I). The other fit (W339(2)sh), in which a dust shell was fitted, is located much closer to the ZAMS. Although this fit is not as good as that for W339(2) it must be considered because it makes a good HAeBe candidate. However, note that for W339(2) the IR-excess can be explained by an M-type companion also. For both options we conclude that this star is most probably a cluster member.

{W556: E(B-V) = tex2html_wrap_inline6418, P = 93% and spectral type B2. In the HRD we note that W556 is the brightest star of our sample and it lies somewhat above, although in the proximity of, the MS. W556 appears to be a cluster member, and is probably evolving away from the MS.
All of these three objects have a slightly anomalous extinction, indicating that they are located in or behind a region with larger average dust grains than that of the IS material. The objects seem to be cluster members but located in regions with high IC absorption.

7.4. Stars in Group D

Stars in this group are considered to be foreground objects as they have very low E(B-V) values (tex2html_wrap_inline6434). Most of these objects, W103, W232, W349, W402, W411, W525, W534, W605, W606 and W617, belong to Group III, have a high membership probability
according to their proper motion, but are located high and/or far to the right of the upper stellar birthline in the HRD. We therefore discard W349, W402, W411, W525, W534, W606 and W617 as cluster members. They are rated ``N'' in Col. 2 of Table 8 (click here). We discuss the objects W103, W232 and W605 as their location in the HRD does not permit us to draw a direct conclusion.

W103: E(B-V) = tex2html_wrap_inline6438, P = 90% and spectral type B9. Although there is an IR-depletion in the SED fit, W103 is located between the ZAMS and the stellar birthline in the HRD which would indicate it to be a cluster member with a luminosity class V. Perhaps the depression in the IR-photometry is due to absorption lines. Probably W103 is a foreground object. Otherwise, it could be a PMS star.

W232: E(B-V) = tex2html_wrap_inline6444, spectral type F8 and no known proper motion. It is located below the stellar birthline in the HRD. No definite conclusions can be made on whether this is a cluster member or not. Its E(B-V) value clearly suggests that it is a foreground object, but the presence of anomalous extinction and traces of emission lines indicate it could be young. In case it is a cluster member it could be a PMS candidate of which the E(B-V) is strongly affected by the anomalous extinction or the detected variability.

W605sh: E(B-V) = tex2html_wrap_inline6452, P = 92% and spectral type G2. In the HRD, we locate W605sh on the right side close to the stellar birthlineWe conclude that this star is probably a foreground object surrounded by a dust shell, which would make it a very interesting object to study, or it could have a background IR-source.
The membership probabilities
discussed in this section are listed in Table 8 (click here). In Fig.5 (click here) we make a comparison of the membership probabilities of an object and its location in the HRD. From this figure it is evident that most of the Group III stars are foreground objects, as confirmed before. W599 has an E(B-V)-value close to the foreground one, and W611 has a low probability of membership, both probably being foreground stars. The Group I and Group II objects contain both populations. This makes it clear that it is best to discuss each star individually, as done above.

Figure 5: The tex2html_wrap_inline6458, tex2html_wrap_inline6460 diagram for our programme stars in NGC 6611 that have different probabilities of membership. The stars being probably nonmembers are indicated as a tex2html_wrap_inline6462 in case tex2html_wrap_inline6464, or as tex2html_wrap_inline6466 when tex2html_wrap_inline646810%. The remaining cases, probably being cluster members, are noted as  tex2html_wrap_inline6470

Table 8: Membership probabilities, Col. 2, of the programme stars in NGC 6611 as discussed in the text. Typical Herbig Ae/Be characteristics are also given. The abbreviations used are: P = probably; Y = yes; N = not; d = dust; M-C= M-Companion

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