3 Results

Assuming that the polarization is of interstellar origin, the wavelength at which maximum polarization $P_{\rm max}$ occurs can be computed by observing in several photometric bandpasses. This wavelength $\lambda _{\rm max}$ is a function of the optical properties and characteristic particle size distribution of the aligned grains (McMillan [1978]; Wilking et al. [1980]). The maximum polarization (in microns) at which $P_{\rm max}$ (in percentage) occurs has been calculated by fitting the observed interstellar polarization in the UBVRI bandpasses to the standard Serkowski polarization law (Serkowski [1973]):

$$P_{\lambda}/P_{\rm max} = \exp~[-K~\ln ^2~(\lambda_{\rm max}/\lambda)]$$ (1)

and adopting K = 1.15.

  

Table 1: Polarization results

The left side of Table 2 lists the $P_{\rm max}$ and $\lambda _{\rm max}$ values for 32 stars, excluding those from Table 1 with errors in their P _V values higher than 15 $\%$ and P _B higher than 20$\%$. If the polarization is well represented by the Serkowski relation, $\sigma_{1}$ (the unit weight error of the fit) should not be higher than 1.5 because of the weighting scheme; a higher value could indicate the presence of intrinsic polarization. The mathematical expression used to determine the individual $\sigma_{1}$ values can be found as a footnote. Excesses are taken from the works of Hillenbrand et al. ([1993]), Thé et al. ([1990]), de Winter et al. ([1997]) or they have been calculated according to Feinstein & Marraco ([1971]), using UBV colors from Hillenbrand et al. ([1993]). Star No. 313 shows indications of photometric variability, as it results from a comparison between magnitudes and colors from Thé et al. ([1990]) and from Chini & Wargau ([1990]): 13.29 (V), 0.36 (B-V) and -0.14 (U-B) versus 12.95, 0.58 and -0.19, respectively.

Following Marraco et al. ([1993]), we have intended to remove the effects on the measured polarizations of the interstellar dust located in front of the complex, leaving only the intra-cluster variations of the extinction. To do so, we adopted a more conservative approach than in Marraco et al. ([1993]) or in Vega et al. ([1994]), since in the present case the foreground absorption over the region under study is somewhat patchy and that particular situation prevents us from performing a fair modeling of the effects of the foreground dust parameters in terms of latitude and longitude.

We selected from the observed stars those which seem to be the least affected by reddening and having low values in their polarizations: stars Nos. 349, 367, 374 and 455, excluding star No. 411 by reasons discussed later. Please note that "frontside" is a concept not directly related to the conditions of "foreground" and "member". The ideal frontside star is one that has all foreground dust in front of it and all intracluster dust behind it. Sometimes this condition is met by the member stars just in front of most of intracluster dust as explained in Marraco et al. (1993). Those four already mentioned stars, which are hereinafter referred to as "frontside'' stars, are noted with asterisks in Tables 1 and 2. They will be used to subtract the effects of the foreground extinction from the light coming from any other object in the zone under study.

Figure 1: Relation between PR polarizations values for stars observed in this work (OVM) and by Carrasco et al. ([1975])

Having in mind that we are handling observed parameters of the dust we proceeded to average them instead of simply obtaining a mean value for each bandpass. Thus the weighted mean of the $\lambda _{\rm max}$ value for the "frontside'' stars is:

$$\overline{\lambda_{\rm max}}= 0.58\pm0.06 ~ \rm\mu m \, .$$

For the polarization and orientation of the electric vector ( $\theta_{ V}$) in equatorial coordinates, we get mean values:

$$\overline{P_{\rm max}} = 1.88\pm0.02\%$$

and

$$\overline{\theta_{ V}} = 75\hbox{$.\!\!^\circ$ }3\pm2\hbox{$.\!\!^\circ$ }7$$

respectively.

Now, through the use of the Serkowski relation (1), we can calculate a distribution $\overline P_{\lambda}$ for each bandpass that should characterize the "frontside'' stars, in the mean. Then, it is possible to calculate mean Stokes parameters $\overline{Q_{\lambda}}$ and $\overline{U_{\lambda}}$for the group. Subtracting these mean values from the individuals ${Q_{\lambda}}$and ${U_{\lambda}}$ for the rest of the observed members of NGC 6611 and inverting the procedure, we obtain the values $P_{\rm intracluster}({\lambda})$ and ${\theta}_{\rm intracluster}({\lambda})$, which are listed on the right side of Table 1.

Once more, the maximum wavelength (in $\rm\mu m$) at which $P_{\rm max}$ occurs has been calculated by fitting the intra-cluster polarization in the five bandpasses to the standard Serkowski polarization law for the "non-frontside'' stars. The results are presented on the right side of Table 2, together with their correspondent $\lambda _{\rm max}$ values.

From their intra-cluster polarization values 8 objects (stars Nos. 150, 166, 251, 259, 275, 297, 311 and 401) have a value for the intracluster unit weight error of the fit ( $\sigma_{1}$) above 1.5. Such value may be considered as a limit due to the weighting scheme, that is: a higher value could be indicative of the presence of intrinsic polarization. Stars 175, 275 (recently mentioned), 306 and 406 have their fitted $\lambda _{\rm max}$ shorter than the average general value for the interstellar medium (0.55 $\rm\mu m$). This second rejection criterion usually gives another clue to intrinsic polarization. Star 197 stands out as a polarimetric variable as it results from comparing P _R observations from Carrasco et al. ([1975]) and this work, see Fig.  1.

Some objects falling into this two criteria display emission-lines spectra: Nos. 251 and 311 (B2 Ve and B2.5 Ve, respectively; Hillenbrand et al. [1993]), Nos. 297 and 306 (B0.5 Ve and B2-B3e, respectively; de Winter et al. [1997]), Star 175 has spectral type O5.5 V ((f)) (Hillenbrand et al. [1993]). The fitting of the Serkowski's law to star No. 313 gives an abnormal value of 1.24 $\rm\mu m$ on the right side of Table 2. This star has been mentioned earlier as a visual variable star. The most notable $P_\lambda$ and $\theta_\lambda$ vs. $\lambda$ plots are shown in Fig.  2, where the solid curve denotes the Serkowski polarization relation for the general interstellar medium. In particular, the plot for star 275 resembles that for star 109 in the polarimetric study of IC 2944 (Vega et al. [1994]), and also the stars in Table 4 (Figs. 4 and 5) in Waldhausen & Marraco ([1982]), perhaps denoting the presence of circumstellar scattering.

Figure 2: Intracluster polarization and position angle dependence with wavelength for some of the stars with indications of intrinsic polarization (mismatch between observations and Serkowski's curve fit and/or variable position angle). In the case of star 411, both plots correspond to observed values

In order to disentangle the relationship between the reddening and the polarization produced by the dust along the line of sight, the upper plot of Fig.  3 examines the relation between $P_{\rm max}$ and color excess E _B-V for the observed stars in NGC 6611. Objects shown as open circles indicate our "frontside'' stars. Most objects are located to the right of the interstellar maximum line:

$$P_{\rm max} < ~3~A_{ V}~\simeq~3~R_{ V}~E_{ B-V}$$ (2)

which is derived for the interstellar dust particles (Hiltner [1956]). For comparison purposes this relation is also shown in the plot adopting two different values of R _V: 3.1, the "normal'' value for the interstellar medium; and 3.75, the most frequent value in the work of Hillenbrand et al. ([1993]). The only star located to the left of both relations is No. 411. This object has been classified as a K5 III star by de Winter et al. ([1997]). It is considered to be a nonmember of NGC 6611, with an E _B-V= 0.10 mag. Polarimetrically, it shows a $P_{\rm max}$ value of $1.93 \pm 0.41\%$ (for $\lambda_{\rm max}= 0.58\pm 0.03 ~ \mu\rm m$), which is relatively high when related to its excess. Its observed plots have been included in Fig.  2, where an abnormal curve can be seen that reflects more than one origin: interstellar plus circumstellar.

Figure 3: Polarization efficiency diagrams for observed (upper plot) and intracluster parameters (lower plot). Using R V = 3.1, the line of maximum efficiency is drawn in both diagrams. The same line but for R V = 3.75, is also shown. Open circles are used for our "frontside'' stars

For the interstellar medium, Serkowski et al. ([1975]) have found a value of 5.03 for the ratio $P_{\rm max} / E_{ B-V}$. In the case of NGC 6611 the stars in the upper plot seem to cluster around 4.2, a value equal to the sample of Carrasco et al. ([1975]) for NGC 6611. This situation denotes a mean polarization efficiency coming from a combined effect of intracluster and foreground material. Although the observed ratio $P_{\rm max} / E_{ B-V}$ may depend on several elements, mainly on the alignment efficiency, the magnetic field strength and the angle between the magnetic field and the line of sight, in this case it shows the depolarization due to radiation crossing at least two dust clouds with different field directions.

The lower plot in Fig.  3 shows the situation for the same group of stars when we subtract the effects of polarization and reddening due to the material in front of the cluster. Open circles indicate, again, the "frontside'' stars. No. 411 has been excluded from this plot and also from the intra-cluster values in Tables 1 and 2. In this plot, only two stars are located to the left of the maximum line (2): No. 245 is a visual variable, of spectral type B6e and with suspected circumstellar material as noted by de Winter et al. ([1997]); and No. 280 being a fast rotation variable emission line star (Hillenbrand et al. [1993]). From this plot we infer that most of the stars apparently are not strongly affected by intrinsic polarization. The dominant mechanism of polarization in the observed section of NGC 6611 is, therefore, supposed to be the alignment of grains by a magnetic field, in a similar way as that found in the general interstellar medium, with relatively good efficiency.

Figure  4 includes the plot of $P_{\lambda }/P_{\rm max}$ vs. $\lambda/\lambda_{\rm max}$ for those stars not excluded from any of the criteria explained in the previous paragraphs showing that their polarization is fully of interstellar origin. Only these stars will be used to test the canonical relations hereinafter. Star 503 was not included because it is a Herbig Ae/Be. It will be mentioned again later.

Figure 4: $P_{\lambda }/P_{\rm max}$ vs. $\lambda _{\rm max}/\lambda$ plot for the observed stars not excluded from any of the explained criteria

Figure 5: E V-K/EB-V vs. $\lambda _{\rm max}$ plots for stars belonging toNGC 6611 (upper), Tr 14/16-Cr 228 (middle) and Tr 15 (lower). In the upper plot, the vectors intend to show the first order results of a mean particle size increase

Figure 6: Observed (upper plot) and intracluster (lower plot) polarization vectors and their orientations for stars belonging to NGC 6611. The length of each vector is proportional to the percentage polarization

For member stars in NGC 6611, individual (V-K) values have been taken from the works of Hillenbrand et al. ([1993]) and Chini & Wargau ([1990]); the excesses E _V-K were calculated from the relationships (Johnson [1966]):

E_V-K = (V-K) - (V-K)₀

where

(V-K)₀ = 1.05  Q

and

$$Q = (U-B) - \alpha (B-V)$$

where $\alpha$ takes values in the range 0.69 to 0.72. As for the particular case of NGC 6611, we have adopted $\alpha = 0.72$ in the calculations of the Q parameter. This procedure is justified by the fact that it is the same one used by Hillenbrand et al. ([1993]) and subsequently by Belikov et al. ([1999]). At the same time, this value is also very similar to the one quoted by Turner ([1976]) for the cluster, namely $\alpha = 0.74$.

In order to check the canonical relationship between R _V and $\lambda _{\rm max}$for the interstellar dust we have plotted in the upper panel of Fig.  5 only those stars not suspected of having some kind of intrinsic polarization. For comparison purposes we have also plotted stars from the open clusters Tr 14/16 and Cr 228, embedded within the Carina Nebula (an H II region similar to M 16), in the middle panel; and from the open cluster Tr 15, to the north of the other two clusters but just outside the H II region, in the lower panel. The $\lambda _{\rm max}$ data for these two plots come from Marraco et al. ([1993]) and the infrared photometry is from Tapia et al. ([1988a]). The plot for Tr 14/16-Cr 228 is identical to the upper panel in Fig. 3 of Marraco et al. ([1993]). The canonical relation of $E_{V-K} / {E_{ B-V}}= 5.09 \lambda_{\rm max}$ is drawn in the three panels as a solid line.

The dashed line in the upper panel was fitted to the 18 observed stars in NGC 6611 giving $E_{V-K} / {E_{ B-V}} = 5.6 ~\lambda_{\rm max}$. This means that if we adopt A _V / E_V-K = 1.12 we get

$$R_{ V} = 6.3~ \lambda_{\rm max}$$ (3)

in comparison with a canonical value for the constant in (3) of 5.5.

As previously suggested for Carina by Tapia et al. ([1988b]) and subsequently confirmed by Marraco et al. ([1993]), Fig. 5 clearly demonstrates that the canonical relation between E_V-K/E _B-V and $\lambda _{\rm max}$ is not valid for stars belonging to dusty H II regions, as is the case for M 16 and the Carina Nebula, but remains in use for Tr 15, located well outside the H II region.

Figure 7: Polarization vectors and their orientations for stars from the catalog of Axon & Ellis (1976) in the neighborhood of NGC 6611. The length of each vector is proportional to the percentage polarization. The approximate position of the cluster in the region is indicated with a square whose borders are those of Fig.  6

Chini & Wargau ([1990]) have attempted to model the NGC 6611 dust properties in order to fit the extinction curves obtained with their UBVRIJHKL photometry. Using the MRN graphite-silicate dust model (Mathis et al. [1977]; Chini & Krugel [1983]), they obtained a close fit by increasing (in relation with the model representing the standard ISM) the mean graphite grain size by a factor of 2, while the mean size of silicate grains was increased slightly by a factor of $1.20\pm 0.09$. As it is widely known (Whittet [1996]; Li & Greenberg [1998]), the polarization is accounted for only by silicate grains because graphites are difficult to align. Our mean intracluster $\lambda _{\rm max}$ is $0.62\pm0.10~\rm\mu m$ and, if we adopt for the ISM a $\overline{\lambda_{\rm max}}$value of $0.55\pm 0.05~ \rm\mu m$, we find that the mean size of the particles responsible for the polarization within the observed region in NGC 6611 is increased by a factor of $1.13\pm0.09$ relative to the general ISM, in general agreement with the ideas of Chini & Wargau ([1990]). Returning to Fig.  5 we are able to understand now that the canonical relationship between R _V and $\lambda _{\rm max}$ is expected to follow the extinction in the standard ISM where the shape of the extinction curve (R _V) is mainly accounted for the mean silicate grain size. In dusty H II regions, as it is the case of this paper and Tr14/16-Cr 228, variations in R _V are also due to changes in mean graphite grain size. In both cases, standard ISM and dusty H II regions, $\lambda _{\rm max}$ varies along with mean silicate grain size. The vectors inserted in the upper panel of Fig. 5 intend to show the first order results of a mean particle size increase. This is the reason why our polarization observations of NGC 6611 and also those of the $\eta$ Carinae nebula do not follow the canonical relationship between R _V and $\lambda _{\rm max}$ of the general interstellar medium. McMillan ([1978]) concluded that an unimodal size distribution of dielectric particles could not account for the position of 3 Orion stars observed by Breger ([1977]) in the R _V vs. $\lambda _{\rm max}$ diagram. This further points to graphite grain growth as an important factor in changing the shape of the interstellar extinction curve in the direction of dusty H II regions.

Figure 6 depicts the polarization vectors and their orientations for observed and intra-cluster values (upper and lower plots, respectively).

The foreground polarization has an average direction in galactic coordinates of 131 $\hbox{$.\!\!^\circ$ }2\pm7\hbox{$.\!\!^\circ$ }2$ (69 $\hbox{$.\!\!^\circ$ }7$ in equatorial coordinates), while the intra-arm polarization amounts to 117 $.\!\!^\circ$$1\pm18$ $.\!\!^\circ$7 (55 $.\!\!^\circ$6 in equatorial coordinates); that is, the projected magnetic field interior to the cluster is somewhat different from the foreground field. As mentioned earlier, star No. 503 with an ${\vec e}$-vector of $\theta_{ V}$ = 157 $\hbox{$.\!\!^\circ$ }4$, deviates significantly from the average direction, as other stars from the group with suspected circumstellar dust shells do. Figure 7 shows the observed polarizations in the cluster area from the catalog of Axon & Ellis ([1976]). The line of sight to M 16 looks into the Sagittarius arm; in spite of this situation, no alignment of the e-vector of the observed field stars polarization is apparent. To conclude neither the field nor the intracluster polarization are particularly aligned, but the later is closer to the direction of the magnetic field that runs along the arm ( $\theta_{\rm G}$ = 90$^\circ$).