4 Instrumental polarization

One major goal of the new 1.4 GHz survey is the sensitive mapping of polarized emission out of the Galactic plane. However, a problem is given by the relatively high instrumental polarization mainly introduced by the cooled broad-band polarization transducer and hybrid of the L-band Effelsberg receiver. A change of the bandwidth and centre frequency has a significant effect on the instrumental U and Q components. Other instrumental effects due to the antenna and feed characteristics, residual ellipticity of the polarimeter response and variations with time add, but are too small to be separated from the main effect.

An attempt was made to minimize these instrumental effects to a residual effect of the order of 1%. We assume that the instrumental components $U_\mathrm{inst}$ and $Q_\mathrm{inst}$ scale with the total intensity I. When observing in an astronomical coordinate system the instrumental components depend on the parallactic angle $\phi$. A procedure was developed to correct for this effect. From the observations of the polarized calibration sources 3C 286 and 3C 138 at different parallactic angles, correction factors f_U and f_Q are calculated in such way that the nominal percentage polarization and the polarization angle are obtained.

The algorithm of the elimination of the instrumental effects is as follows: Suppose $U_\mathrm{act}$ and $Q_\mathrm{act}$ are the intrinsic values of a source in an astronomical coordinate system. $U_\mathrm{obs}$ and $Q_\mathrm{obs}$ are the observed values depending on the parallactic angle $\phi$. The instrumental values $U_\mathrm{inst}$ and $Q_\mathrm{inst}$are:

$$\begin{eqnarray} {U}_\mathrm{inst}(\phi) &=& {U}_\mathrm{obs}(\phi) - {U}_\math... ...\mathrm{inst}(\phi) &=& {Q}_\mathrm{obs}(\phi) - {Q}_\mathrm{act}.\end{eqnarray}$$ (1)

The instrumental polarization angle $PA_\mathrm{inst}$ and polarization intensity $PI_\mathrm{inst}$ are:

$$\begin{eqnarray} {PA}_\mathrm{inst}(\phi) & = &\frac{1}{2} \tan^{-1} \left[ \fra... ...&\sqrt{ {U}_\mathrm{inst}^2 (\phi) + {Q}_\mathrm{inst}^2 (\phi) }.\end{eqnarray}$$ (2)

The correction factors f_U and f_Q are then:

$$\begin{eqnarray} f_{U}(\phi) = \frac{\displaystyle {PI}_\mathrm{inst}(\phi)} {\... ...m{obs}} \cos \left[ 2 ({PA}_\mathrm{inst}(\phi) - \phi ) \right].\end{eqnarray}$$ (3)

In Fig. 3 we show, as an example, the data for f_U and f_Q from observations of 3C 286. f_U and f_Q are determined for each session. It is obvious that f_U and f_Q vary with parallactic angle, which needs to be taken into account when correcting a survey map. According to the introduced procedure each pixel I of a map is multiplied with the appropriate f_U and f_Q. The resulting U and Q components of the instrumental polarization are transformed into parallactic angle corrected components for each pixel of an U and Q map and subtracted from the observed U and Q. The procedure corrects for most of the instrumental effects. The corrected U and Q maps are then used to calculate the polarized intensity PI and the polarization angle PA.

  

Figure 3: Variation of the calculated fU and fQ factors with respect to the parallactic angle for 3C 286 during one observing session. Error bars are the standard deviations of the factors

It has been found that the correction effect on the large-scale polarization emission is not significant. Strong sources, however, cause distortions which are clearly minimized by the described procedure. In Fig. 4 we illustrate the effect of our correction procedure. We note that instrumental effects do not always act in a way to increase the observed polarization. Depending on the arrangement and variations in U and Q it is equally possible to observe the reverse of this effect.

  

Figure 4: A sample region to illustrate the effect of the procedure to eliminate the instrumental polarization. The upper panel displays the same region before (left) and after (right) the correction. Contours show the total intensity starting from -50 mK with 50 mK intervals. The strong source around $\ell \sim 47\hbox{$^\circ$}$ is 3C 386 with a flux density of 6.5 Jy. Its percentage polarization is 2.7% after the procedure is applied. In the lower panel the polarized intensity data of the same regions are displayed in grey scale. Contour levels run starting from 10 mK with 30 mK steps. Again the original data are at left and corrected data are at right. The plotted electric field vectors are scaled to the polarized intensity and astronomical coordinates such that 100 mK correspond to a vector of length 1$.\mkern-4mu^\prime$5