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4. Spectral energy distribution

Using the stellar spectral types and the photometric observations made through the different pass-bands, we can draw spectral energy distributions (SEDs). By fitting the SED to a Kurucz (1991) model, with solar abundances, appropriate to the MK-type of the star, we obtain information concerning the correct spectral classification, the extinction at the different wavelengths and a possible IR-excess. Below we will discuss briefly the fitting procedure, the selection of the photometric data and the estimation of the Kurucz parameters.

In most cases the value tex2html_wrap_inline3992 = 3.1 can be used to correct for the extinction due to the interstellar medium. However, we have encountered objects which, after correction with tex2html_wrap_inline3994 = 3.1, show SEDs with a small near-infrared excess. Taking into account previous studies of NGC 6611 and the characteristics of PMS stars, we assume that the existence of an infrared excess is caused, either by anomalous extinction towards the star, or, when no extinction law can be fitted easily, by the presence of circumstellar dust.

The observed magnitudes are first corrected assuming a normal interstellar extinction law. The resulting extinction-free SED is then compared with the theoretical SED model of Kurucz (1991), appropriate to the MK type of the star. When an infrared excess remains, an tex2html_wrap_inline3996 value of one tenth higher is applied. If the infrared excess still exists, the same procedure is repeated until a best fit between the observed extinction-free SED and the Kurucz model is obtained according to the tex2html_wrap_inline3998-test. The tex2html_wrap_inline4000 value of the best fit is then adopted. The extinction laws used in this procedure are those of Steenman & Thé (1991).

The tex2html_wrap_inline4002-test is applied to the difference between the extinction-free SED and the Kurucz model for all pass bands with wavelengths between the B passband at 0.434 tex2html_wrap_inline4004m and the near-IR K passband at 2.2 tex2html_wrap_inline4008m. The errors in the observed data (Koulis 1993) are taken into account in the tex2html_wrap_inline4010-test procedure. For a better accuracy, especially around the Balmer jump, we have integrated over the response curve of each filter instead of using monochromatic fluxes.

4.1. Selection of the photometric data

From Tables 1-3 we see that in most cases multiple sets of photometric data are available. In addition, several stars display the typical HAeBe characteristic of photometric variability. The ones with a visual variability range significantly more than 0tex2html_wrap4106 2 are marked with a star in Table 7 (click here).

Because of the large amount of data that had slowly accumulated and because the differences in most of the tex2html_wrap_inline4014, Walraven and JHKLM data sets are only small, we have decided to average the data sets that appeared to be compatible, preferably with the highest intensity to acquire data at maximum light. The agreements of so many data sets indicate that we are working with reliable photometric observations. The increase of accuracy in the various photometric colours implies a more accurate determination of the colour excess, the photometric spectral type, and consequently the (possibly anomalous) extinction.

Table 5:
Systematic differences of stellar UBV and JHK(L) data in NGC 6611 for the observations taken in our programme minus those of other authors. n indicates the number of available datasets

The photometric data were selected using the following criteria:
For the Walraven data in the visual we have first calculated the corresponding Johnson visual magnitudes tex2html_wrap_inline4080, using the relation (Pel 1987):
When a tex2html_wrap_inline4084 agrees with the V in the tex2html_wrap_inline4088 system, it is considered eligible for further use.

We used a maximum of 5 sets of UBV data per star. For some stars we had only one set of Johnson tex2html_wrap_inline4092 and/or Cousins tex2html_wrap_inline4094 as noted in Table 2. Of the available UBVRI data sets we only used the ones that are in mutual agreement, and for which the relative differences of the colours are minimal. A similar procedure was applied to the JHK(L) data sets, but with 3 data sets per star at most.

Before averaging the selected data sets used for the SEDs, we must note that, when averaging data of different authors, i.e. taken during different observational periods with different telescopes, different sets of filters etc., one has to take into account the systematic differences that may arise between the various observing runs. Therefore we first must correct the data from all authors with respect to our data, references 1a-c in Table 2, by adding an average systematic difference. The systematic differences, as given in Table 5 (click here), are taken from Thé et al. (1990) and Hillenbrand (1993), except for Chini & Wargau's data for which we calculated the correction ourselves. We also estimated the average systematic differences for the JHK(L) colours. The Walraven and tex2html_wrap_inline4102 data did not need a correction as they were made in one system. The same applies to the tex2html_wrap_inline4104 data of Chini & Wargau (1990).

All corrected and averaged magnitudes and colours are given in Appendix C of Koulis (1993). Table 6 lists the accordingly derived photometric data sets which were used to construct the SED of each star.

4.2. Estimate of the Kurucz parameters

To fit the selected photometry to a Kurucz (1991) model, we first need to consider the best tex2html_wrap_inline4112, E(B-V) and log g for each object in order to select its appropriate model.

In Table 4 there are a number of spectral types that have been derived from the photometric and spectroscopic data of each star which were already in close agreement with each other. As we want one final spectral type for each star we averaged those spectral types, giving a weight of 2 to the averaged spectral type deduced spectroscopically and 1 to the averaged photometric spectral type.

Although the spectral types and therefore the tex2html_wrap_inline4118's are accurately known, an SED fit of the Kurucz model to the selected photometry can reveal some small modifications needed to find the correct Kurucz model. In these cases we determined a more exact tex2html_wrap_inline4120 in an iterative way.

By this final check of the stellar spectral type we determined the tex2html_wrap_inline4122 value from Schmidt-Kaler (1989). The E(B-V) is then the difference between this tex2html_wrap_inline4126 value and the (B-V) used in the SED.

Note that a wrong predetermination, á priori or iteratively, of the spectral type or tex2html_wrap_inline4130, could make a foreground object seem to be a cluster member and vice versa. In NGC 6611, cluster members should have tex2html_wrap_inline4132.

A third but also very important parameter is the star's luminosity class. Although, varying the spectral type within a luminosity class will not alter the log g values very much, changing the log g implicitly affects the tex2html_wrap_inline4138 and therefore the E(B-V) values of the star. This parameter can, therefore, affect the cluster membership probability of a star in two different ways: (1) because it influences its E(B-V), it could drop below tex2html_wrap_inline4144, and (2) the star's position in the HRD.

4.3. The fits to the SEDs

Adopting the average of the selected photometric data, listed in Table 6, the average spectral type, listed in Table 4, and the above mentioned determination of the E(B-V) value, we are able to fit the SED for each programme star to a Kurucz model SED. Because of the unknown luminosity class for most objects we adopted log g = 4.0 (luminosity class IV or V). The observed magnitudes are first corrected assuming a normal extinction law (tex2html_wrap_inline4154 = 3.1). The extinction-free SED is then plotted. A comparison is finally made with the theoretical SED model of Kurucz (1991), appropriate to the MK type of the star.

Although in many cases the SED can be satisfactorily fitted, several cannot. We made the next modifications to

improve the latter fits:

  1. In case the WULBV and UBVRI photometry did not fit well, especially around the Balmer jump, we altered the temperature tex2html_wrap_inline4160 of the star.
  2. If the fit was still not adequate and we noted a depletion in the JHK(LM) bands, we changed the luminosity class to III, II or I, which means that we lower the values of log g. Varying log g of Kurucz models will only cause significant changes for late, G-M, type objects.
  3. In those cases where the SED fit still show a discrepancy in the near-IR we applied the tex2html_wrap_inline4168-fitting procedure in order to test the presence of anomalous extinction.
  4. Some stars show a large IR-excess that can not be corrected with any reasonable anomalous extinction law. In these cases we fit a Planckian curve. If we assume circumstellar dust to be responsible for the excess, the wavelength at which the fitted Planckian-curve reaches its maximum indicates the temperature of the dust (Sect. 5.3). Note that for very high tex2html_wrap_inline4170 values a too strong correction of the extinction in the blue and near-UV pass-bands will cause a depletion of the for extinction corrected observed SED compared to the Kurucz model fitted to the optical datapoints.

For some stars, we have to discard certain data sets which are not in mutual agreement, and reduce the reliability of the SED fitting results:
For W213(1) and W494 the WULBV data;
For W525 we only use the Walraven passbands W and U;
For W617 we discard the Walraven W band and the UBV reference 1b data;
For W213(2) and W267 we discard the tex2html_wrap_inline4182 and tex2html_wrap_inline4184 data;
For W245 both the tex2html_wrap_inline4186 and tex2html_wrap_inline4188 have to be omitted;
For W400 we discard the tex2html_wrap_inline4190 and the Walker (1961) U because it differed too much from other U observations;
For W349 and W402 tex2html_wrap_inline4196 have to be ignored;
For W455 tex2html_wrap_inline4198 is not used;
For W300 and W406 we do not use the JHK observations as they appeared to lie far above or below the best-fit Kurucz model.

All the resulting plots are presented in Fig. 3 (click here). The final astrophysical parameters as derived and checked by the SED fits are given in Table 7 (click here).

Table 7: Physical data of stars in NGC 6611. Objects indicated by a star (tex2html_wrap_inline4202) show a visual variability range significantly larger than 0tex2html_wrap4954 2. In the last column the probability of membership is given by the value P from Thé et al. (1990) and references therein, the values of Kamp (1974) are given between parentheses. Note that several spectral types have been adjusted to their SED fits. The luminosities given in Col. 11 are those obtained from tex2html_wrap_inline4208, whereas those in Col. 12 are obtained from an integration over the SED (see text)

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