5 Procedure for the absolute polarization adjustment

As was mentioned earlier the large-scale information in the polarization maps is lost due to the baseline fitting procedure. In addition, residual ground radiation effects may show up in view of the large sizes of the observed maps. As in the case of total power maps, the polarization emission needs to be adjusted to an absolute level. However, there exists no complete and regularly gridded low resolution polarization survey which is absolutely calibrated. Fortunately, a large set of linear polarization observations at 1.4 GHz obtained with the Dwingeloo 25-m telescope exists (Brouw & Spoelstra 1976). These data are absolutely calibrated and corrected for all kinds of instrumental effects and therefore match the requirements for this task. However, the data are not on a regular grid and are significantly undersampled. This data set has to be regridded to be used to adjust our polarization measurements. The polarized intensity and polarization angle data from the Dwingeloo survey have been provided by Dr. Spoelstra in digitized form.

Using the PI and PA values from this measurements we calculated U and Q values and regridded the undersampled Dwingeloo data on the grid of the Effelsberg maps. However, in some regions data points are too separated ($2\hbox{$^\circ$}$ or more) for an absolute calibration, and in other weakly polarized regions an S/N-ratio of 2 or less does not allow a proper adjustment.

We tried two methods to interpolate the Dwingeloo data on the same grid as the Effelsberg maps. One way to do this is an interpolation between the data points using a "cubic-spline interpolation''. However, we found that a cubic-spline interpolation introduces distortions at the corners of the maps and data from a much larger area must be used to avoid this problem. Moreover, a single high intensity data point affects surrounding low intensity data up to a large distance. Data points must be weighted with respect to the distance. Hence, we found that a cubic-spline interpolation is inadequate for most of our regions.

A successful method is to weigh data points by their distances to the required map element. We used the approach $\exp(-\alpha~{\cal R})$ in which $\alpha$ is a constant. We calculate for each pixel of an Effelsberg map the Dwingeloo U and Q data within a radius, ${\cal R}$, contributing with a weight as given above. For our case we found a value of $6\hbox{$^\circ$}$ for ${\cal R}$ with $\alpha=1$ to be satisfactory.

The reconstructed U, Q and PI Dwingeloo maps of a test region at the $4\hbox{$^\prime$}$ grid of the Effelsberg maps are given in Fig. 5.

  

Figure 5: Polarization maps reconstructed from the Dwingeloo data as explained in the text. The panels, from top to bottom, display the Stokes U and Q maps and polarization intensity, respectively. The area marked with dashed lines is the region observed with the Effelsberg telescope and used to demonstrate the method of absolute calibration for the polarization data

Figure 6 shows the U and Q maps of the original Effelsberg measurements of an area, which is a small section of the Dwingeloo map shown in Fig. 5. In the higher resolution Effelsberg maps numerous small-scale polarization structures are visible, which are smoothed out by the large Dwingeloo beam.

  

Figure 6: Polarization U and Q maps from the Effelsberg 1.4 GHz survey. Contours are plotted starting from the lowest value of the wedge and in steps of 30 mK $T_\mathrm{B}$. Contours starting from zero are plotted in white with the same steps

The two data sets are combined as follows: The Effelsberg map is convolved to the Dwingeloo beam (36$\hbox{$^\prime$}$) and subtracted from the Dwingeloo map. The difference is added to the original Effelsberg map. Figure 7 and Fig. 8 show the combination for U and Q and the corresponding PI map. In these figures the small-scale structures are much less pronounced due to the addition of the strong large-scale polarized emission which varies in the range from 200 mK to 800 mK across the map (Fig. 5).

The absolutely calibrated U and Q maps may be decomposed into small-scale and large-scale features by standard methods for total intensity maps and relative PI maps can be calculated. Some examples have been given by Uyaniker (1997).

Plots of the polarization vectors demonstrate the effect of adjusting the Effelsberg data to an absolute level. The polarization angle maps are presented as vector plots in Fig. 9. Numerous small-scale structures are visible in the original Effelsberg map. The polarization angle varies largely across the maps. However, the electric field vectors are almost constant in the combined Effelsberg-Dwingeloo map. The data of this map are the same as those for Fig. 8, but grey-scale representation is much more sensitive to small variations.

  

Figure 7: Polarization U and Q maps after calibrating the Effelsberg polarization maps to absolute temperature scale. Contours are plotted starting from the lowest value of the wedge and in steps of 30 mK $T_\mathrm{B}$. For U map the contours starting at 200 mK $T_\mathrm{B}$ and for the Q map the contours starting at 400 mK $T_\mathrm{B}$ are plotted in white. Contour steps are always 30 mK $T_\mathrm{B}$

  

Figure 8: Polarization intensity maps before (top) and after (bottom) calibrating the Effelsberg polarization maps to absolute temperature scale. Contours are plotted starting from the lowest value of the wedge and in steps of 30 mK $T_\mathrm{B}$. For the upper panel contours starting at 120 mK $T_\mathrm{B}$ and for the lower panel contours starting at 450 mK $T_\mathrm{B}$ are plotted in white

  

Figure 9: Electric field vectors before (top) and after (bottom) calibrating the Effelsberg polarization maps to absolute temperature scale. The lower panel is essentially the same as Fig. 8. Due to the high polarization intensity of background polarization small-scale variations from the Effelsberg observations are hidden. Electric field vectors are scaled to the polarized intensity such that 100 mK correspond to a vector of length 3$\hbox{$^\prime$}$ for the upper panel and 1$\hbox{$^\prime$}$ for the lower panel