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4. Discussion

4.1. Fractional polarization and depolarisation

Following Garrington et al. (1991), we have measured for each source (and for each component in the source) the mean scalar polarization, m', defined as the integrated polarization flux over the total intensity. For the lobes, typical values of m' (at 6 cm) range from 10% to 30%, with a median value tex2html_wrap_inline2578. The m' values of the two lobes are rather similar, contrary to what was found at 20 cm (see Paper I), where the lobe containing the brighter jet was significantly more polarized than the other lobe.

The old maps at 20 cm and the new at 6 cm have been analysed to determine the depolarization, tex2html_wrap_inline1836, between these two frequencies. The depolarization is defined as the ratio of the mean scalar fractional polarization, m', at 20 cm over that at 6 cm: tex2html_wrap_inline2586. The m' values we find at 6 cm are larger than the values of m'20, implying depolarization between the two frequencies.

The values of tex2html_wrap_inline1836 are presented in Col. 10 of Table 3 (click here). They are peaked around 0.7 and extend down to tex2html_wrap_inline2594. Only about 25% of the objects show little or no depolarization (tex2html_wrap_inline2596). Head-tail sources seem to be more depolarized, although the statistics is small.

4.2. Rotation angles

The differences between the position angle of the polarization at 6 and 20 cm (tex2html_wrap_inline1838) are presented in Col. 12 of Table 3 (click here). The values obtained cover a broad range with a number of sources showing little or no rotation between the two wavelengths. We used the component polarization position angles to derive two-point Faraday rotation measures (RMs). Since position angles are ambiguous by tex2html_wrap_inline2602, the calculated RMs are ambiguous by tex2html_wrap_inline2604. In practice we have:
displaymath2598
with tex2html_wrap_inline1838 in degrees.

For 22 sources the integrated polarization data in Parma & Weiler (1981) at 2.7 GHz and of Mack et al. (1994) at 10.8 GHz were used to resolve the ambiguity (see Appendix). We find n= 0 in 13 sources (0034+25, 0828+32, 0836+29, 1102+30, 1113+29, 1122+39, 1141+35, 1243+26, 1316+29, 1322+36, 1357+28, 1422+26, 1455+28), tex2html_wrap_inline2636 in seven cases and n= 2 in two cases (see Appendix). In this subsample, which we consider free of ambiguity, two thirds of the sources have RMs less than 50 rad tex2html_wrap_inline2640. These figures are mostly consistent with Faraday rotation in the galactic foreground screen (Simard-Normandin et al. 1981).

We note that of the three sources with tex2html_wrap_inline2642 larger than 100 rad tex2html_wrap_inline2640, two (1254+27 and 1626+39) are in rich Abell clusters and the third (2116+26) is at low galactic latitude (tex2html_wrap_inline2646).

For the remaining sources for which we do not have additional data we choose the n value which minimizes the absolute value of RM. For them we expect, statistically, a comparable fractional number of ambiguities.

We have compared the RMs of the two lobes for the double sources (38 objects). Following the result of Conway et al. (1983), we assume that the differences in RM (tex2html_wrap_inline2650) are free of ambiguity. The rms difference is tex2html_wrap_inline2652. About two thirds of the sources have tex2html_wrap_inline2654, in agreement with what Simonetti & Cordes (1986) found. Only in three cases did we find differences in the rotation angles of the two lobes above tex2html_wrap_inline2656, implying RM differences above 20 rad tex2html_wrap_inline2640. These few cases are mentioned in the Notes on individual sources in the Appendix.

As for the sample of PRG studied by Garrington et al. (1991), we do not find any correlation between rotation measure and depolarization.

4.3. Magnetic field geometry

On the basis of the obtained RM, we conclude that the polarization position angle at 6 cm is within tex2html_wrap_inline2660 of the intrinsic position angle and we derive the magnetic field projected geometry from the maps at this wavelength by a rotation of tex2html_wrap_inline2662.

In the double sources, the magnetic field appears in general very well oriented along the outer borders of the component, in agreement with earlier findings (e.g. Bridle et al. 1991). The best examples of this geometry are: 0755+37, 0828+32, 1141+37, 1322+36, 1441+26, 1455+28, 1658+30.

In general the direction of the magnetic field in jets is perpendicular to the jet orientation, in agreement with what found in Bridle & Perley (1984), for the typical range of radio powers of our sample. In a number of double sources the jet shows up in the polarisation map for its magnetic field orientation which contrast with that of the radio lobes (see, for example, 0755+37, 1322+36, 1613+27, 1658+30). In some double sources the jet, which is not well distinguished from the lobe in the total-intensity map, emerges clearly in the polarization map (0828+32, 1457+29 1609+31).

There are, however, situations where we see a parallel magnetic field. The first is at the jet sides, as in 1357+28 and, most notably, in 1553+24. This characteristic has already been found in 3C 31 (R.A. Laing et al. in preparation). The second is in the final part of the jets, in sources dominated by jet emission (see 0915+32 and 1243+26).

For the hot-spots the situation is not very clear. In general we find low fractional polarization and an unclear field geometry. We believe that the generally inadequate resolution of our observations mixes regions with different field geometry and causes beam depolarization.

In the head-tail sources the magnetic field tends to run parallel to the tail.

4.4. The depolarizing halo

As discussed in Laing (1988) and Garrington & Conway (1991), the depolarization observed in PRG is likely to be caused by an inhomogeneous, unresolved, foreground Faraday screen, which rotates the polarization position angle randomly across the observing beam. The more depolarized lobe is, therefore, the lobe seen through a larger halo depth. The depolarization ratio tex2html_wrap_inline2666 is related to the standard deviation of the Faraday depth, tex2html_wrap_inline2668, by the relation
displaymath2664
where K= 0.81, tex2html_wrap_inline2668 is in units of tex2html_wrap_inline2674 and tex2html_wrap_inline2676 and tex2html_wrap_inline2678 are in metres (Garrington & Conway 1991).

From this we derive for each source the lobes' Faraday dispersion parameters, tex2html_wrap_inline2680 and tex2html_wrap_inline2682 corresponding to the lobe with higher and lower depolarization, respectively. The values we find range mostly from 4 to tex2html_wrap_inline2684. These values are similar to those of the low redshift (z < 0.2) sources of the Garrington & Conway (1991) sample, and are much lower than the values of the sources at high redshift. For each source with lobes, we have also estimated tex2html_wrap_inline2688 defined as the ratio of the highest to the lower depolarization (tex2html_wrap_inline2690). Using this parameter, we have searched for correlation between tex2html_wrap_inline2688 and source size. Although we find a marginal tendency for large tex2html_wrap_inline2688 in large sources, no obvious relation has been found between tex2html_wrap_inline2688 and source size.

In their work on PRG, Garrington & Conway (1991) conclude that the major contribution to depolarization arises from a halo of hot gas surrounding the radio source. By using a Montecarlo simulation, we have derived the parameters of such a halo. From the distributions of the tex2html_wrap_inline2688 and of the ratio tex2html_wrap_inline2700 we find the following parameters:


eqnarray605
where B0 and n0 are the halo's central magnetic field and density. These parameters agree well with those found by Garrington & Conway (1991) for the low redshift (z < 1) radio galaxies.

A discussion on the depolarization asymmetry in the source components is presented in a companion paper (Morganti et al. 1996).


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