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Astron. Astrophys. 340, 371-380 (1998)

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4. The results

4.1. Contamination by interstellar polarization

Since all objects in the sample are at high galactic latitudes ([FORMULA]), the contamination by interstellar polarization in the Galaxy is expected to be negligible. This may be verified using the Burstein & Heiles (1982, hereafter BH) reddening maps 3. The maps provide E(B-V) values from which the interstellar polarization is estimated with the relation [FORMULA] 8.3% E(B-V) (Hiltner 1956). These upper limits on [FORMULA] are reported in Table 2. All but two are smaller than 0.3%, indicating a very small contamination by the Galaxy.

Polarization of faint field stars recorded on the CCD frames may also provide an estimate of the interstellar polarization. The dispersion of their Stokes parameters (Table 1) indicates that actually both instrumental and interstellar polarization are small. This is further illustrated in Fig. 1, where the QSO polarization is compared to the field star polarization (interstellar + instrumental), and to the maximum interstellar polarization derived from the BH maps. The absence of correlation between the field star polarization and the BH interstellar polarization suggests that instrumental polarization dominates field star polarization (although one cannot exclude that a few of them are intrinsically polarized). In addition, no deviation from uniformity was found in the distribution of the acute angle between quasar and field star polarization vectors measured on the same frame. These results confirm the insignificance of interstellar polarization in our sample.

[FIGURE] Fig. 1. The QSO polarization degree [FORMULA] (in%) [[FORMULA]] is represented here as a function of the Galactic latitude of the objects ([FORMULA], in degree), together with the de-biased polarization degree of field stars [[FORMULA]] (also corrected for the small systematic trend reported in Table 1), and the maximum interstellar polarization degree [FORMULA] derived from the Burstein & Heiles (1982) reddening maps [+]

We may therefore safely conclude that virtually any quasar with [FORMULA] 0.5% (or [FORMULA] 0.6%) is intrinsically polarized (cf. Fig. 1 and Table 1), in good agreement with the results obtained by Berriman et al. (1990) for low-polarization Palomar-Green (PG) QSOs.

4.2. Polarization variability

For some BAL QSOs of our sample, previous polarimetric measurements are available in the literature, and may be used for comparison. In Table 4, we list first epoch measurements obtained in 1977-1981. For all these objects, and within the limits of uncertainty, the values of the polarization position angles are in excellent agreement with ours (Table 2).


Table 4. Previous polarimetric measurements
From Moore & Stockman 1981, 1984, and Stockman et al. 1984

On the contrary, our values of p are generally smaller than or equal to the previous ones. However variability cannot be invoked since the observed differences are most likely due to the fact that the old measurements were done in white light and using detectors more sensitive in the blue, i.e. in a wavelength range where polarization is suspected to be higher (cf. Stockman et al. 1984, and more particularly the case of 1246-0542). Note further that those objects with null polarization ([FORMULA]) are identical, except 0145+0416 which we find significantly polarized. But 0145+0416 is also the only object in our sample not far from a bright star which might contaminate the measurements. Its variability can nevertheless not be excluded.

In conclusion, we find no evidence in our sample of BAL QSOs for the strong polarization variability (in degree or angle) which characterizes blazars, confirming on a larger time-scale the results of Moore & Stockman (1981). This does not preclude the existence of small variations like those reported by Goodrich & Miller (1995) for 1413+1143.

4.3. Polarization versus QSO sub-types

Before discussing the polarization properties of the different QSO sub-types, it is important to note that our sample is quite homogeneous in redshift (as from WMFH). Therefore, the polarization we measure in the V filter roughly refers to the same rest-frame wavelength range, such that differences between quasar sub-types will not be exaggerately masked by a possible wavelength dependence of the polarization. Also, spectral lines generally contribute little to the total flux in the V filter, and our polarimetric measurements largely refer to the polarization in the continuum.

Fig. 2 illustrates the distribution of [FORMULA] for non-BAL, HIBAL and LIBAL QSOs. It immediately appears that nearly all QSOs with high polarization ([FORMULA] 1.2%) are LIBAL QSOs. Only two other objects have high polarization (cf. Table 2): 1235+0857 which is unclassified (and therefore could be a LIBAL QSO), and 0145+0416 which has uncertain measurements (cf. Sect. 4.2). Also important is the fact that not all LIBAL QSOs do have high polarization (like 0335-3339 or 1231+1320 which are bona-fide ones; cf. WMFH and Voit et al. 1993). Further, although the strongest LIBAL QSOs are all highly polarized, there is apparently no correlation between the LIBAL strength and the polarization degree (cf. 2225-0534 or 1120+0154 which are weak and marginal LIBAL QSOs, respectively). This suggests that polarization is not systematically higher in LIBAL QSOs, but that its range is wider than in other QSOs. Although less polarized, several HIBAL QSOs also have intrinsic polarization ([FORMULA] 0.5%), and apparently more often than non-BAL QSOs.

[FIGURE] Fig. 2. The distribution of the polarization degree [FORMULA] (in%) for the three main classes of QSOs. Non-BAL QSOs include the intermediate object. LIBAL QSOs contain the three sub-categories, i.e. strong, weak and marginal LIBAL QSOs

The distribution of non-BAL QSOs peaks near [FORMULA] 0% with a mean value [FORMULA] 0.4%. It is in good agreement with the distribution found by Berriman et al. (1990) for low-polarization PG QSOs. The distribution of LIBAL QSOs is wider with a peak displaced towards higher polarization ([FORMULA] 2%), and with [FORMULA] 1.5%. The distribution of HIBAL QSOs looks intermediate peaking near [FORMULA] 0.7%, and with [FORMULA] 0.7%.

To see whether these differences are statistically significant, a two-sample Kolmogorov-Smirnov (K-S) statistical test (from Press et al. 1989) has been used to compare the observed distributions of [FORMULA]. In Table 5, we give the probability that the distributions of two sub-samples are drawn from the same parent population, considering various combinations. We also include a comparison with the polarization of PG QSOs (after de-biasing the polarization degrees as described in Sect. 2). The number of objects involved in the sub-samples ([FORMULA] and [FORMULA]) are given in the table. The difference between LIBAL and non-BAL QSOs appears significant ([FORMULA] 0.01) as well as the difference between LIBAL and HIBAL QSOs. However, no significant difference between HIBAL and non-BAL QSOs can be detected. Comparison with PG QSOs confirms these results. It also suggests that the distributions of non-BAL, HIBAL, and PG QSOs do not significantly differ, although the latter objects have much lower redshifts and were measured in white light (any marginal difference with HIBAL QSOs is due to the polarization of 0145+0416, which is uncertain).


Table 5. Comparison of [FORMULA] for various pairs of samples
The PG QSO sample is from Berriman et al. (1990), Seyfert galaxies and BAL QSOs excluded. HIBAL- refers to the HIBAL QSOs of our sample minus 0145+0416

These results suggest that the polarization of LIBAL QSOs definitely differs from that of non-BAL and HIBAL QSOs, showing a distribution significantly extended towards higher polarization. On the contrary, no significant difference is found between HIBAL and non-BAL QSOs. The difference, if any, is small and would require a larger sample and more accurate measurements to be established.

Finally, no polarization difference was found when comparing the gravitationally lensed QSOs to other non-BAL or BAL QSOs. When polarized, their polarization is essentially related to their BAL nature. Small variations due to microlensing in either component can nevertheless be present (Goodrich & Miller 1995).

4.4. BAL QSO polarization versus spectral indices

The previous results suggesting a different behavior of LIBAL QSOs, it is important to recall that these QSOs also differ by the strength of their high-ionization features and the slope of their continuum (WMFH, Sprayberry & Foltz 1992). This is clearly seen in Fig. 3, using our newly determined continuum slopes. LIBAL QSOs (including several marginal ones) appear to have the highest balnicity indices and the most reddened continua. These differences are significant: the probability that the distribution of BI (resp. [FORMULA]) in HIBAL and LIBAL QSOs is drawn from the same parent population is computed to be [FORMULA] = 0.008 (resp. 0.002). In addition BI and [FORMULA] seem correlated. Possible correlations may be tested by computing the Kendall ([FORMULA]) and the Spearman ([FORMULA]) rank correlation coefficients (Press et al. 1989; also available in the ESO MIDAS software package). The probability [FORMULA] that a value more different from zero than the observed value of the Kendall [FORMULA] statistic would occur by chance among uncorrelated indices is [FORMULA] = 0.003, for n = 29 objects. The Spearman test gives [FORMULA] = 0.001. This indicates a significant correlation between BI and [FORMULA] in the whole BAL QSO sample.

[FIGURE] Fig. 3. The correlation between the balnicity index BI (in 103 km s-1) and the slope of the continuum [FORMULA] for all BAL QSOs of our sample

Possible correlations between the polarization degree [FORMULA] and the various spectral indices were similarly searched for by computing the Kendall [FORMULA] and the Spearman [FORMULA] statistics. The resulting probabilities [FORMULA] and [FORMULA] are given in Table 6, for the whole BAL QSO sample and for LIBAL QSOs only. Note that similar results are obtained when using p instead of [FORMULA]. From this table, it appears that the polarization degree is significantly correlated with the slope of the continuum [FORMULA], and with the line profile detachment index DI.


Table 6. Analysis of correlation between [FORMULA] and various indices

The correlation with [FORMULA] disappears when considering LIBAL QSOs only, although [FORMULA] and [FORMULA] still span a large range of values. Most probably, this correlation is detected in the whole BAL QSO sample as a consequence of the different distributions of both [FORMULA] and [FORMULA] in the LIBAL and HIBAL QSO sub-samples (Figs. 2 and 3).

On the contrary, the correlation with the detachment index holds for the whole BAL QSO sample as well as for the LIBAL QSO sub-sample. It is illustrated in Fig. 4. In fact, the correlation appears dominated by the behavior of LIBAL QSOs. HIBAL QSOs roughly follow the trend, but their range in DI is not large enough to be sure that they behave similarly 4. It is interesting to remark that the observed correlation is stable - and even slightly better - if we assume that the polarization degree increases towards shorter wavelengths, i.e. if [FORMULA] is redshift-dependent. This is as illustrated in Fig. 5 for the LIBAL QSO sub-sample, assuming a reasonable [FORMULA] dependence (e.g. Cohen et al. 1995). In this case, [FORMULA] = 0.0006 and [FORMULA] = 0.0003.

[FIGURE] Fig. 4. The correlation between the polarization degree [FORMULA] (in%) and the line profile detachment index DI for all BAL QSOs of our sample. Symbols are as in Fig. 3. The correlation is especially apparent for the QSOs of the LIBAL sample

[FIGURE] Fig. 5. The correlation between the redshift-corrected polarization degree [FORMULA] (in%) and the line profile detachment index DI for LIBAL QSOs only. We assume [FORMULA], i.e. a [FORMULA] dependence of [FORMULA]. Symbols are as in Fig. 3

No other correlation of [FORMULA], namely with the balnicity index, or with emission line indices is detected.

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© European Southern Observatory (ESO) 1998

Online publication: November 9, 1998