3 The results

The observed UBV polarimetric results are given in Table 1 (available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5)). The columns of this Table contain the following data:

Column 1: star identification in the Knude's catalogue;

Column 2: HD number, when available;

Column 3: right ascension for the equinox 1900.0;

Column 4: declination for the equinox 1900.00;

Column 5: galactic longitude;

Column 6: galactic latitude;

Column 7: computed V magnitude on the Johnson system (Knude 1977);

Column 8: measured polarization in the UBV bands in per cent, the respective estimated uncertainty is given between parenthesis;

Column 9: galactic position angle. This angle is measured relative to the galactic north pole in the direction of increasing longitude;

Column 10: equatorial position angle. This angle is measured relative to the celestial north pole in the direction of increasing right ascension. The respective estimated uncertainty is given between parenthesis;

Column 11: estimated colour excess (E(b-y)) (Knude 1978);

Column 12: estimated distance in parsecs (Knude 1978).

The measured polarizations are plotted in galactic coordinates in Fig. 1. The lines represent the $\vec E$-vectors of the linearly polarized starlight. The lines are centered in the observed star's position. The length of each line is proportional to the percentage polarization and the angle at which each line is drawn relative to the galactic north pole in the direction of the increasing longitude is given by $\theta_{\rm gal}$.

 

Table 2: Comparison between the polarization introduced in this work with previous measurements

 

Table 3: Results obtained for the polarized standard stars

 

Figure 3: The distribution of the observed stars as a function of the distance. Nineteen stars are located beyond the distance interval represented in this histogram

 

Figure 4: The normalized wavelength dependence of the interstellar linear polarization derived from the 40 stars showing degree of polarization greater than 0.5% in all the observed passbands. The solid line represents the Serkowski's empirical formula relating the ratio ${P}/{P}_{\rm max}$ to the corresponding ratio $\lambda_{\rm max}/\lambda$. The bars indicate the observed uncertainties for HD79936 and HD80085 (see text). The U, B, and V colours are represented by open circles, filled squares and open squares, respectively

 

Figure 5: The distribution of the obtained $\lambda_{\rm max}$ values for the 40 stars showing degree of polarization greater than 0.5% in all the observed passbands

The estimated average uncertainties of the polarimetric measurements are: $\overline{\sigma_{U}} = 0.048 \%$, $\overline{\sigma_{B}} = 0.031 \%$, and $\overline{\sigma_{V}} = 0.058 \%$, respectively for the U, B, and V bands. Figure 2 displays the obtained uncertainties for the B-band as a function of the stellar magnitude. For bright stars () the uncertainty is mainly determined by atmospheric scintillation, and the mean uncertainty is about $\pm 0.01 \%$. For fainter stars, the uncertainty is dominated by photon shot noise, and since it has been used the same integration time to collect the measurements, the uncertainty increases as a function of the stellar magnitude.

Among the observed stars, 5 were found in the literature having previous polarimetric measurements. Table 2 gives a comparison between the polarization introduced in this work with the values found in the literature. Within the observational errors, a good agreement is obtained for the two unpolarized stars. The degree of polarization obtained for the remaining polarized stars seems to be systematically smaller than the value found in the literature. In special, a rather large discrepancy was observed for the polarized star 414 (HD 99545). Such discrepancy requires a more careful analysis. In order to test the accuracy of our measurements for the polarized stars, we have compared the observed polarizations obtained for the standard stars used to determine the zero point of polarization angles with the standard values.

Table 3 gives a comparison between the results obtained from our measurements and the standard values. The maximum polarization ($P_{\rm max}$) and the wavelength $\lambda_{\rm max}$ were obtained as described in the next section. The agreement between our results and the standard ones is very good. Except for the case of HD147084, the difference for the maximum polarizations is smaller than 0.1%. An analysis of the measurements obtained for HD147084 showed that the observed discrepancy is mainly caused by a difference in the polarization observed for the V channel, as compared to the value obtained by Serkowski et al.(1975).

An idea of the stellar distance distribution of the observed sample can be obtained by the histogram given in Fig. 3. Almost 70% of the stellar sample is closer than 200 pc. There are 19 stars located beyond the distance interval represented in this figure.

 

Figure 6: The polarization in the B-band versus E(b-y). (left) All observed stars. The solid line represents optimum alignment efficiency (P(%) = 12.1 $\times$ E(b-y); E(b-y) = 0.74 E(B-V)). (right) Expanded view for the low reddening part of the diagram

 

Figure 7: (upper) The polarization in the B-band versus distance. (lower) E(b-y) versus distance. Although polarization is a positive quantity, the vertical axis of the upper diagram has been extended to negative values in order to make easier the comparison between both diagrams. It is remarkable, nevertheless the positive bias, the small degree of the observed linear polarization showed by stars up to $\protect\approx 100$ pc