5 Discussion

5.1 Morphology and core identification

All the resolved sources have a FRII double morphology, with hot-spots at the extremity of the radio source. A few sources, such as 1558-003, have multiple hot-spots connecting the core to the outermost components, typically on only one side. There are 8 small sources that can be classified as compact steep spectrum (CSS) sources, having linear (projected) sizes smaller than about 20 kpc (e.g. Fanti et al. 1990). Of these, 3 are unresolved (1017-220 and 1132+37 and 2224-273, with sizes less than 0.2''), one is barely resolved (0011-023, which is sightly elongated in the 4.7 GHz maps) and another 4 (0152-209, 1019+053, 1204+401 and 1357+007) appear as small FRII radio galaxies. The percentage of CSS sources is 29%, significantly higher than found in similar samples observed at the same frequencies and VLA array configuration: 14% of small sources in the sample of Carilli et al. (1997), which included 38 HzRGs; 13% in the sample of Athreya et al. (1997), which included 15 HzRGs, some of which also belonged to the previous sample. The only difference between our sample and the previous ones, is the slightly lower average optical magnitude of the radio galaxies selected here, but it is unclear how this should influence the average size of the sources. Interestingly the percentage of CSS sources in this study is more similar to that found by Lonsdale et al. (1993) in a sample of steep spectrum radio loud quasars at $z\ge 1.5$ (27% of CSS sources).

In Table 2 we tabulate the characteristics (coordinates, flux density, spectral index, and core fraction) of the cores. We can identify the radio cores in less than half of the resolved radio sources (11 out of 24): the cores are identified as the unresolved component with the relatively flattest spectral index, which are not polarized. The percentage of identified cores is lower that the identification rate of Carilli et al. (1997) (75%).

In the source 1202+527 there is a component with very flat spectral index (-0.1), but given that it is polarized and that its position would imply a highly asymmetric morphology, we consider it to be a hot-spot, and tabulate its characteristics in Table 3 instead of Table 2. In the highest redshift radio source of the sample, 1338-19 at z=4.11, the core is the faint component just below the northern hot-spot, and appears only in the high frequency map (Fig. 18b). Despite its steep spectrum ($\alpha=-1$) and the high resulting asymmetry of the radio sources we are confident about its identification given its proximity to the host galaxy (de Breuck et al. 1999).

As previously mentioned, in general the radio cores are identified as the flat spectrum components: however in 5 radio galaxies the cores have very steep spectra (spectral index equal or steeper than -1). While it could be that in some cases the nucleus is not correctly identified or is blended with a steep spectrum component (this could be the case of 1019+681), most should be true unresolved cores.

Steep core spectra have previously been found in many high redshift radio galaxies by Carilli et al. (1997) and Athreya et al. (1997). Athreya et al. suggest that the rest frame frequencies at which these cores are observed (15 to 30 GHz, depending on redshift) are higher than the turn over frequency due to synchrotron self-absorption. They suggest that the cores of radio sources exhibit synchrotron self-absorption turn over at 20 GHz in the rest frame of the emitting plasma, and that the spectra will appear steep above that frequency. They also explain the difference between the galaxy cores and quasars cores (which exhibit steepening at a much higher frequency) with the fact that the turn over frequency appears blue-shifted in the relativistically beamed quasar core and redshifted in the galaxy cores. They predict that the size of the dominant core component should be less than 1 mas.

In Col. 5 of Table 2 we list the core factions, calculated at a rest-frame frequency of 20 GHz: for those sources where the core is undetected we give an upper limit, assuming that the core flux is less than 3 times the rms noise of the map. Core fractions vary from less than 0.05% to few %, a range that is typical for radio galaxies. The only exception is the CSS source 1357+007 that has a core contributing for 27% of the total flux. The median core fraction is 0.6%.

According to evolutionary models of radio sources (e.g. Kaiser et al. 1997), as a radio source grows older and expands, its lobe radio luminosity declines, whereas the core flux remains constant. Therefore the prediction is that larger radio sources, which on average should be older, should also have higher core fractions. To test this model, in Fig. 1a we have plotted the core fractions of the radio sources in this sample, augmented by the sample of Carilli et al. (1997), versus their radio sizes in kpc. We do not detect any increase in the average core fractions with increasing radio size: on the contrary we see the opposite effect, i.e. a slight decrease in the core fraction, from a median value of 1.5% for sources smaller than 50 kpc, to 1.2% for sources between 50 and 100, to 0.8% for sources larger than 100 kpc, with a large scatter around these median values at any given size (note that using the median value is a better estimate, expecially when dealing with upper limits).

These trends should be interpreted with caution since the sizes of HzRGs range only from 10 to less than 500 kpc and there are very few large sources. For example the only two sources larger than 400 kpc have relatively large core fractions. Therefore if the effect predicted by Kaiser et al. sets in only at rather large sizes (of few hundreds of kpc), we would not observe it given our limited number of large sources.

The core fractions of HzRGs tend to be higher than those of matched luminosity 3CR galaxies (Laing et al. 1983) at redshift $z\sim 1$. Best et al. (1999) show that for these radio galaxies the median core fraction at a rest frame frequency of 16 GHz is 0.2-0.3% and does not depend on radio sources size for a large range of sizes (from 10 to 1000 kpc. The slight difference in rest-frame frequency (we use 20 GHz instead of 16 GHz) should not be important. Therefore the core fractions at z > 2 are $\sim 4$ times larger that at $z\sim 1$. This could indicate that either at high redshift there are intrinsically stronger cores, or that the beaming factor is higher at earlier epochs. Alternatively, if the core fraction really depends on radio sources sizes as predicted by Kaiser et al. (1997), the difference between the high and low redshift samples could be due to different average sizes of the two samples considered. A full discussion of this issue is beyond the scope of this paper.

In Fig. 1b we present also a plot of core fraction versus power. Although we sample only about one order of magnitude in power, we see no significant correlation between these two quantities. This is in agreement with previous results at lower redshift (Best et al. 1999).

Figure 1: Left: A log-log plot of the core fraction at rest frame frequency of 20 GHz versus linear radio size in kpc (arrows represent upper limits). Right: The core fraction plotted versus the radio luminosity at a rest-frame frequency of 178 MHz

5.2 Radio source distortion

Several sources in our sample show "distorted" morphologies, with multiple hot-spots which are often not aligned (e.g. 1908+722). Following previous authors (e.g. Barthel & Miley 1988), we measure this non-linearity of a radio source with a "bending angle", which is defined as 180$^{\circ}$ minus the angle between the lines joining the core to opposite hot-spots on either side of the source. The bending angles for objects in our sample range from 0$^{\circ}$ to 22$^{\circ}$. Note that many sources such as 1908+722 and 1039+681 show multiple bends, therefore the bending angle as defined above only measures the overall bends as defined by the outer extremities.

In Fig. 2a we present the distribution of the bending angles of our present sample, with the addition of data for objects in Carilli et al. (1997), supplemented by data on a few radio sources from the literature (Carilli et al. 1994). This larger sample is homogeneous, i.e. all the galaxies have been observed at the same resolution and frequencies. The distribution of bending galaxies is basically flat from 0$^{\circ}$ to 20$^{\circ}$, with an average of 12.3$^{\circ}$. We compare this distribution with that of the 3CR radio sources which are matched in luminosity and have redshifts between 0.6 and 1.6 (Fig. 2b reproduced from Athreya 1996). The difference is striking: not only is the average bending angle at redshift greater than 2 more than double that at $z\sim 1$, but also the distribution is different. Barthel & Miley (1988) first pointed out the increasing distortion in the appearance of radio sources at high redshift, although the angles involved for quasars are larger, due to larger projection angles (e.g. Kaphai 1990). This is in agreement with the predictions of unification schemes based on orientation. The increase with redshift of asymmetries in the morphology of powerful radio galaxies was also noted by McCarthy et al. (1991) for low redshift 3CR radio sources, comparing two samples of z < 0.2 and 2.5> z > 0.7 radio galaxies.

A source can be distorted due to interaction between the radio jets and the ambient medium: one example is the radio galaxy 1138-262 (Pentericci et al. 1998), which shows clear signs of interaction between the western jet and the emission line gas, and has large velocity gradients at the location where the radio jet sharply bends. Therefore denser and clumpier environment at high redshift could also explain the increase of distortion with redshift. Indeed optical and narrow band observations have shown that also the stars and gas distribution of HzRGs appear extremely clumpy and asymmetric at high redshift, on a scale comparable or larger than that of the radio emission (e.g. Pentericci et al. 1999).

The increase of ambient density with redshift has also been invoked to explain the decrease in average source size, at a fixed radio power, observed by many groups, although there is still disagreement on the exact shape of the distance-redshift relationship (see references in Blundell et al. 1999).

Figure 2: Right: the distribution of the bending angles for the sample of HzRGs that includes all the sources presented in this paper plus those from Carilli et al. (1997). Left, the analogous distribution for the 3CR sources (figure from Athreya 1997)

5.3 Polarization properties

In most sources one or more components are polarized at both frequencies; typical polarization levels are on the order of less than 10% at 4.5 GHz and up to 20% at 8.2 GHz. In many case there are large differences in polarization between the hot-spots, which could be due to asymmetric properties in the environment.

In Figs. 6-32c we present the polarization maps at 4.5 GHz with superimposed vectors representing the direction and strength of the magnetic field (corrected for Faraday rotation). The electric field is oriented perpendicular to these vectors.

In about half the sources the hot-spots magnetic fields are oriented perpendicular to the jet direction, a common characteristic of the hot-spots of powerful radio sources (e.g. Muxlow & Garrington 1991). However there are several cases, such as 1357+007 where the magnetic field vectors are parallel to the jet direction, and in many sources both parallel and perpendicular fields are present (e.g. 2211-251).

A possible reason is that these components are not true outer hot-spot but are associated with jets or oblique shocks. The magnetic field is parallel in the jets, and perpendicular to the jet axis in the hot-spots, while in the radio bridges it wraps around the the edges around the hot-spots, hence being parallel to the radio axis (Saikia & Salter 1988). Therefore if the knots we observe are not real hot-spots but consist of different unresolved structures, there can be intermediate direction or even parallel B field.

The strength of the magnetic field in each hot-spot can be calculated by making the standard minimum energy conditions (Miley 1980): the resulting magnetic fields range from 160 to 700 $\mu$G.

5.4 Faraday rotation

In Table 3 we list the observed values of Faraday rotation for those regions of the radio galaxies that produce enough polarized signal to allow a determination of the angle of polarization (see Sect. 2). In Fig. 3 we show several plots of the polarization position angles (in radians) versus wavelength squared for the components of three HzRGs. The lines represent the best linear fit to the data points, given by the AIPS task RM.

If the Faraday screen is located at a redshift $z_{\rm F}$, then the intrinsic value of $RM_{\rm intr}$ is related to the observed value $RM_{\rm obs}$ as:

$$RM_{\rm intr} =RM_{\rm obs} \times(1+z_{\rm F})^2.$$

For the radio galaxies, it is most probable that the Faraday screen that produces the RM is located at the same redshift of the radio sources. We can exclude a Galactic origin for the Faraday rotation since at latitudes $b > 20^{\circ }$ the contribution of the Galactic screen is of order of 10 rad m^-2 with RM gradients of <<10 rad m^-2 over 1'' (e.g. Leahy 1987) while we observe much larger gradients between the two (or more) hot-spots of each radio source. For example in the radio galaxy 1202+527 there is a gradient of more than 300 rad m^-2 with a sign reversal, over only 4''. Contribution from intervening structures such as galaxies and clusters, which have $\mu$G magnetic fields correlated over kpc or 10ns of kpc scales, or absorption line systems, can be also ruled out on the basis of small probability (e.g. Athreya et al. 1998).

Therefore if the RM screen is in the vicinity of the radio source, the values listed in Table 3 have to be multiplied by a factor of 10 to 20 (depending on redshift), implying RMs of the order of several 100 rad m^-2 for most sources and in excess of 1000 rad m^-2 for 8 sources, with a maximum of 3100 rad m^-2 for the radio source 0930+389.

Carilli et al. (1994) were the first to point out the existence of very large Faraday rotation in HzRGs. In the previous VLA observational study similar to this, they found that about 20% of radio galaxies had intrinsic RM in excess with 1000 rad m^-2, while Athreya et al. (1998) found high RM in 4 out of 15 radio galaxies. Both these results are in agreement with the results from the present sample.

At low redshift most powerful radio galaxies show rotation measures of only several 10 s rad m^-2 which arise in the interstellar medium (ISM) of our Galaxy. However few radio galaxies have a RM in excess of 1000 rad m^-2 (Taylor et al. 1994): these are either compact (sub galactic in size) radio sources or are radio galaxies located in X-rays cooling flow clusters. In fact Taylor et al. (1994) found that the strength of the cooling flow (or alternatively the core density of the cluster) directly correlates with the rotation measure. An important point is that the above relation is independent of radio source luminosity and morphological class: since FRI and FRII type galaxies have very different physical interactions, this suggests that the Faraday rotation is most likely a probe of cluster properties and not radio source properties. The physical conclusion is that for those sources located in clusters, the RM arises in the dense X-ray emitting gas which is substantially magnetized.

Figure 3: Polarization position angles versus $\lambda ^2$ (in cm) for the lobes of some HzRGs in our sample: upper panels are the components of 0930 north (left) and south (right). The lower panels are 1425 north (left) and 1988 north (right)

5.4.1 Does Faraday rotation depend on radio source properties?

To determine the nature of the Faraday screen at high redshift we first investigated whether the Faraday rotation is significantly correlated with the radio source morphology or other properties. As mentioned in the previous section, at low redshift Faraday rotation does not depend on radio source morphology or luminosity: this might not be the case at high redshift, where it is believed that the interactions of the radio jets with the host galaxies and the ambient medium are much stronger, as shown for example by the increasing distorted morphology of radio sources discussed in Sect. 5.2.

From the combined sample of about 70 radio galaxies at z > 2 with homogeneous high resolution radio polarimetric VLA observations (Carilli et al. 1994 and 1997; Athreya et al. 1998 and this paper), we selected all HzRGs with observed RM larger than 40 rad m^-2 (lower observed values might be effected by relatively larger errors). The total number of selected HzRGs is 37, of which 23 have intrinsic RM larger than 1000 rad m^-2.

Figure 4: The maximum Faraday rotation observed in high redshift radio galaxies, plotted against different energetic and morphological properties of the radio sources (see text)

To characterize a radio source we used the following parameters: (a) the monochromatic power at a rest-frame frequency of 178 MHz; (b) the total extent of the radio source; (c) the integrated spectral index between 8.2 and 4.5 GHz (observed frequencies); (d) the core fraction at a rest-frame frequency of 20 GHz; (e) the number of hot-spots defined as the number of separate emission peaks in the 8.2 GHz maps and (f) the bending angle. Assuming orientation unification models (e.g. Barthel 1989) the core fraction allows us study line-of sight effects, knowing that radio sources in general have a smaller core fraction (typically 1-2%) than radio loud quasars and therefore those with higher core fractions will be in the transition zone between radio galaxies and quasars. The total length of the source is used to see if Faraday rotation is related to the inner region of the galaxy, and hence is shown only by radio sources whose size is comparable to the galaxy, like the CSS sources that have sizes of less than 20 kpc, or is a larger scale effect. Finally parameters such as the number of hot-spot and the bending angle, give us information on the distortion of the radio sources, which is probably related to the density of the near environment of the object (e.g. Barthel & Miley 1988).

In Fig. 4 we present the results of these investigations: we do not see any significant dependence of the Faraday rotation on any of above parameters. Therefore we conclude that, at high redshift, Faraday rotation is independent of radio source luminosity and morphology, and is probably not the probe of radio sources properties but of their environment.

Drawing the analogy with lower redshift sources having extreme RM, the conclusion is that also the HzRGs with large Faraday rotation might reside in dense, proto-cluster environment. Indeed selecting the HzRGs with highest known Faraday rotation (6600 rad m^-2) our group has detected possibly extended X-ray emission around the radio galaxy 1138-262 at a redshift of 2.2 (Carilli et al. 1998). If confirmed (time has been allocated at the Chandra X-ray observatory to re-observe the source with a much higher spatial resolution), this would be the highest redshift X-ray cluster known to date.

Figure 5: The fraction of powerful radio galaxies with Faraday rotation in excess of 1000 rad m-2 as a function of redshift; the horizontal error bars indicate the redshift range for each bin

Including the new sources presented in this paper, there are now a total of 23 HzRGs with Faraday rotation exceeding 1000 rad m^-2, with redshift ranging from 2.2 to 3.8 (for a complete list see Pentericci 1999). Of these, 3 are CSS sources for which the origin of the Faraday rotation could be the local ISM, given that the radio sources are completely embedded within the host galaxies. The remaining 20 are excellent targets when searching for the most distant (proto)clusters in the early Universe.

5.4.2 Comparison with low redshift radio galaxies

To investigate whether the fraction of galaxies with extreme RM changes as a function of redshift, we gathered data from the literature for a sample of powerful radio galaxies at low and intermediate redshift to be compared to our sample. We selected all objects from the 3CR catalogue (Laing et al. 1983) having a monochromatic power at 178 MHz (rest-frame frequency) of $\log P_{178} >34.8$ (with P₁₇₈ in units of erg s^-1 Hz^-1) an arbitrary value chosen in order to have relatively powerful radio sources, with still a considerable number of low redshift sources. We added these sources to the sample of radio galaxies at $z \ge 2$. We then eliminated the CSS sources from the resulting list: in these galaxies the radio source is generally completely embedded within the host galaxy, so the RM is due to the local magnetized ISM. CSS sources generally have very high Faraday rotation, therefore if distribution of CSS sources with redshift is different from that of large radio sources (e.g. O'Dea 1998), this will modify the final result. The final sample contains $\sim 90$ radio galaxies spanning a redshift range from z=0.015 (Cygnus A) to z=3.8(4C41.17).

We then searched for Faraday rotation measurements for the 3CR galaxies: all of the values were taken from Tabara & Inoue (1980) and Inoue et al. (1995), with the exception of the radio galaxy Cygnus A for which much more detailed studies have been carried out (Carilli & Barthel 1996). The results are presented in Fig. 5, where we plot the fraction of galaxies with RMs above 1000 rad m^-2 as a function of redshift, for four redshift intervals. The fraction of galaxies with RMs above the line clearly increases with z: $9\pm 4\%$ at z <1, $16\pm 5\%$ at 1< z <2, $37 \pm 5 \%$at 2< z <3 and $80 \pm 15 \%$ at z>3 (although in the last redshift bin there are only 6 galaxies and therefore the statistics is very low).

Some care has to be taken when considering this result, given the following limitations to our analysis: (i) first, most high redshift radio galaxies were found by selecting ultra steep spectrum radio sources (radio spectral index $\alpha <-1$, where $S_{\it\nu} \propto \nu^{\alpha}$, with $S_{\it\nu}$ the flux density and $\nu$ the frequency). This means that if Faraday rotation depends on spectral index (but in the previous section we showed that this is not the case, at least for a limited range of $\alpha$), then our results will be biased; (ii) the quality of the different radio observations is not matched in resolution: since one always measures the average RM within the beam size, having a large beam size implies measuring lower values of RM; (iii) finally, and most important, the various sets of observations have different wavelength coverage, which determines the highest and lowest values of RM observable. Note that the resolution effect (ii) would tend to decrease the correlation found, since at higher redshift the beam size in kpc will tend to be larger. Furthermore, within our sample (redshift z > 2), the physical resolution is nearly constant, but we still detect the correlation between redshift and Faraday rotation.

Despite the above limitations, we regard the effect apparent in Fig. 5 to be real, namely that the fraction of powerful radio galaxies with high Faraday rotation increases with redshift. If high Faraday rotation is an indication of dense environment, this result is consistent with the fact that the average environment of powerful radio sources becomes denser with increasing redshift (e.g. Hill & Lilly 1991). At low redshift most powerful radio sources (FRII type) reside in sparse environment with few exceptions (e.g. Cygnus A), while at earlier epochs more and more radio galaxies reside in dense environments (e.g. Roche et al. 1998).