2. Polarimetric observations and data reduction
The polarimetric observations were carried out on March 14-17 and September 3-6, 1994, at the European Southern Observatory (ESO La Silla, Chile), using the 3.6m telescope equipped with the EFOSC1 camera and spectrograph. The detector was a 512512 TeK CCD (ESO#26) with a pixel size of 27 µm corresponding to 0605 on the sky.
With EFOSC1, polarimetry is performed by inserting in the parallel beam a Wollaston prism which splits the incoming light rays into two orthogonally polarized beams. Each object in the field has therefore two images on the CCD detector, separated by about and orthogonally polarized. To avoid image overlapping, one puts at the telescope focal plane a special mask made of alternating transparent and opaque parallel strips whose width corresponds to the splitting. The object is positioned at the centre of a transparent strip which is imaged on a region of the CCD chosen as clean as possible. The final CCD image then consists of alternate orthogonally polarized strips of the sky, two of them containing the polarized images of the object itself (Melnick et al. 1989, di Serego Alighieri 1989).
In order to derive linear polarization measurements, i.e. the two normalized Stokes parameters q and u, frames must be obtained with at least two different orientations of the Wollaston prism. This was done by rotating the whole EFOSC1 instrument by (usually at the adapter angles and ). For each object, two frames are therefore obtained. Typical exposure times are around 600s per frame, generally split into two shorter exposures. All observations were done with the Bessel V filter (ESO#553). The seeing was typically between and , and the nights were photometric most of the time. Note that the polarization measurements do not depend on variable transparency or seeing since the two orthogonally polarized images of the object are simultaneously recorded. Finally, polarimetric calibration stars were observed (HD90177, HD161291, and HD164740; Schwarz 1987) in order to unambiguously fix the zero-point of the polarization position angle and to check the whole observing and reduction process.
Considering the two frames obtained with the instrument rotated at and , the normalized Stokes parameters are given by
where and respectively refer to the intensities integrated over the two orthogonally polarized images of the object, background subtracted (Melnick et al. 1989). At this stage, the sign of q and u is arbitrary. It is clear from these relations that intensities must be determined with the highest accuracy. For this, the data were first corrected for bias and dark emission, and flat-fielded. A plane was locally fitted to the sky around each object image, and subtracted from each image individually. Since it appeared that standard aperture photometry was not accurate enough due to the rather large pixel size, we have measured the object center at subpixel precision by fitting a 2D gaussian profile and integrated the flux in a circle of same center and arbitrary radius by taking into account only those fractions of pixels inside the circle. With this method, the Stokes parameters may be computed for any reasonable radius of the aperture circle. They were found to be stable against radius variation, giving confidence in the method. In order to take as much flux as possible with not too much sky background, we finally fixed the aperture radius at 2.5 HW, where HW is the mean half-width at half-maximum of the gaussian profile. Note that in the few cases where the objects are resolved into multiple components, we use the smallest square aperture encompassing all the components. The whole procedure has been implemented within the ESO MIDAS reduction package. Applied to calibration stars, it provides polarization measurements in good agreement with the tabulated values. The zero-point of the polarization position angle is also determined from these stars, and the sign of q and u accordingly fixed. The uncertainties and are evaluated by computing the errors on the intensities and from the read-out noise and from the photon noise in the object and the sky background (after converting the counts in electrons), and then by propagating these errors in Eq. 1. Uncertainties are typically around 0.15% for both q and u.
Since on most CCD frames field stars are simultaneously recorded, one can in principle use them to estimate the instrumental polarization, and to correct frame-by-frame the quasar Stokes parameters, following a method described by di Serego Alighieri (1989). However, the field stars (even when combined in a single "big" one per frame) are often fainter than the quasar, and a frame-by-frame correction introduces uncertainties on the quasar polarization larger than the instrumental polarization itself. Therefore, we tried to empirically correlate the instrumental polarization with observational parameters like the observing time or the position of the telescope, in order to check for possible variation and/or to derive a useful relation. Since no significant variation was found, we have finally computed the weighted average and dispersion of the normalized Stokes parameters of field stars (a single "big" one per frame) considering all frames obtained during a given run. These values are given in Table 1. They indicate that the instrumental polarization is small. We take it into account in a rather conservative way by subtracting the systematic and from the quasar q and u, and by adding quadratically the errors. The final, corrected, values of the normalized Stokes parameters q and u are given in Table 2, together with the uncertainties. Note that possible contamination by interstellar polarization is included in the uncertainties (see also Sect. 4.1).
Table 1. Instrumental polarization
Table 2. Polarimetric results
Then, from these values, the polarization degree is evaluated with , while the polarization position angle is obtained by solving the equations and . The error on the polarization degree is estimated by , although 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 , is computed from p and using the Wardle & Kronberg (1974) method (Simmons & Stewart 1985). Finally, the uncertainty of the polarization position angle is estimated from the standard Serkowski (1962) formula where is used instead of p to avoid biasing, i.e. . All these quantities are given in Table 2. Also reported are the redshift z of the objects, the quasar sub-type (cf. Sect. 3.1), and , an upper limit to the galactic interstellar polarization along the object line of sight (cf. Sect. 4.1)
© European Southern Observatory (ESO) 1998
Online publication: November 9, 1998