4 The results

Table 3 lists the QSO position-name (B1950 or J2000), its redshift z, the date of observation (dd-mm-yy), the filter used, the QSO normalized Stokes parameters q and u, the uncertainty $\sigma$ of the Stokes parameters, as well as the field star normalized Stokes parameters $q_{\star}$ and $u_{\star}$ and the associated uncertainty $\sigma_{\star}$. The normalized Stokes parameters are given in the equatorial reference frame. Objects marked with an asterisk are BAL QSOs (cf. Brotherton et al. 1998; Green et al. 1997; Korista et al. 1993; Schmidt & Hines 1999; Stocke et al. 1992; Hewitt & Burbidge 1993 and references therein).

The final values of the QSO normalized Stokes parameters q and u, corrected for the residual systematic instrumental polarization (cf. Table 2) are given in Table 4. Then, from these values, the polarization degree is evaluated with p = (q²+u²)^1/2. The error on the polarization degree is estimated by $\sigma_p = (\sigma^2 + \overline{\sigma}^2_{\star})^{1/2}$ taking into account the values of Table 2. Note that the complex statistical behavior of the polarization degree should be kept in mind (Serkowski 1962; Simmons & Stewart 1985). Indeed, since p is always a positive quantity, it is biased at low signal-to-noise ratio. A reasonably good estimator of the true polarization degree, noted p₀, is computed from p and $\sigma_{p}$ using the Wardle & Kronberg (1974) method (Simmons & Stewart 1985). The polarization position angle $\theta$ is obtained by solving the equations $q = p \cos 2\theta$ and $u = p \sin 2\theta$, while the uncertainty of the polarization position angle $\theta$ is estimated from the standard Serkowski (1962) formula where p₀ is used instead of p to avoid biasing, i.e. $\sigma_{\theta} = 28\hbox{$.\!\!^\circ$ }65\, \sigma_p / p_0$. All these quantities are given in Table 4. Note that due to the HWP chromatism over the V band, an additional error on $\theta \leq 2-3\hbox{$^\circ$ }$ should probably be accounted for (cf. the wavelength dependence of the polarization position angle offset in di Serego Alighieri 1998).

Since nearly all objects in the sample are at high galactic latitudes ( $\vert b_{\scriptscriptstyle \rm II}\vert > 30\hbox{$^\circ$ }$, except B1451-3735), the contamination by interstellar polarization in the Galaxy is expected to be small. This may be verified using the Burstein & Heiles (1982) reddening maps. The maps provide E(B-V) values from which the interstellar polarization is estimated with the relation $p_{\scriptscriptstyle \rm ISM}\leq$ 8.3% E(B-V) (Hiltner 1956). These upper limits on $p_{\scriptscriptstyle \rm ISM}$ are reported in Table 4. All but four are smaller than 0.3%, indicating a negligible contamination by the Galaxy. Polarization of faint field stars recorded on the CCD frames also provide an estimate of the interstellar polarization. The dispersion of their Stokes parameters (Table 2) indicates that actually both the instrumental and interstellar polarization are small. This is 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 Burstein & Heiles maps. We may therefore safely conclude that virtually any QSO with $p_0 \geq$ 0.6% is intrinsically polarized, in good agreement with our previous results (Hutsemékers et al. 1998), and with those of Berriman et al. (1990) obtained for low-polarization Palomar-Green QSOs. Note that several objects with p₀ < 0.6% have a polarization position angle similar to that of field stars, indicating that contamination is probably real at these low polarization levels (while no deviation from uniformity is found in the distribution of angle difference for objects with $p_0 \geq$ 0.6%).

For some QSOs of our sample (B0059-2735, B1157-2354, B1429-0053, B2240-3702), polarimetric measurements have been obtained at different epochs with the same filter and instrumentation (cf. Hutsemékers et al. 1998). The agreement is generally excellent, providing no evidence for polarization variability. Only the polarization degree of B1429-0053is marginally different, possibly in relation with its suspected gravitationally lensed nature.