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
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
using the Wardle &
Kronberg (1974) method (Simmons & Stewart 1985). The polarization
position angle
is obtained by solving the equations
and
,
while the uncertainty of the
polarization position angle
is estimated from the standard
Serkowski (1962) formula where p0 is used instead of p to avoid
biasing, i.e.
.
All these
quantities are given in Table 4. Note that due to the HWP chromatism
over the V band, an additional error on
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
(
,
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
8.3% E(B-V) (Hiltner 1956).
These upper limits on
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
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
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.
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