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4 Radio source asymmetries

In this section we measure the asymmetries in armlength, flux density, spectral index, etc. We compare the values and correlations we find for the GRGs with results obtained for samples of smaller-sized sources.

4.1 Morphological asymmetries

Asymmetries in the morphology of a radio source are common and may reflect asymmetries in their environment. McCarthy et al. (1991), for instance, find that in a sample of powerful 3CR radio sources there is a correlation between the side of the source with the shortest arm and the side of the source with the highest optical emission-line flux. If a larger intensity of the line emission is due to a higher amount of gas, then the advance of the radio lobe on that side of the source may have been slowed down. On the other hand, the filling factor of this gas may be too low to play an important role in the dynamical evolution of the radio lobe (e.g. Begelmann & Cioffi 1989). Also, at large distances (i.e. $\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle ... kpc) from the host galaxy and the AGN, this warm gas is difficult to detect by emission-line studies even if it were abundant, so that identifying the side with the highest gas density around the lobes becomes extremely difficult for larger sources. If line emitting gas or clouds are dynamically unimportant for large sources, then the armlength asymmetries of radio galaxies may reflect asymmetries in the distribution of the hot ($\sim 10^7$ K) diffuse IGM around the host galaxy. In principle, GRGs thus allow us to investigate the uniformity of the IGM on scales up to a few Mpc, which is well outside of the reach of current X-ray instruments, apart from a few very luminous clusters.

However, armlength asymmetries can also be a result of orientation effects (e.g. Best et al. 1995; Scheuer 1995), since the forward edges of the two lobes have different light travel times to the observer. Best et al. (1995) explain the differences in the armlength asymmetries between radio galaxies and quasars in a sample of 3CR sources with orientation differences only, although high expansion velocities of the lobes, up to 0.4c, are then required. Since Best et al. find no significant correlation between the parameters describing the arm-length asymmetry and the emission-line asymmetry, they suggest that environmental effects are not necessarily the main cause of the observed asymmetries in 3CR sources, in agreement with Begelmann & Cioffi (1989).

To investigate if the linear size of the radio source has any influence on the observed asymmetries, we have measured the armlengths of the lobes of all FRII-type sources in the 1-Jy sample. We have calculated the armlength-ratio, Q, by dividing the length of the longest arm by that of the shortest arm. This yields the fractional separation difference, x, which is defined as $x =
\frac{Q-1}{Q+1}$ (e.g. Best et al. 1995). The advantage of using x, instead of Q, is that its range is limited between 0 and 1. In Table 4 we present the armlengths, Q, x, and the references to the data used to measure these parameters.

In Fig. 3a we have plotted a histogram of the fractional separation difference of the GRGs. We have omitted the source B2043+745 from our GRG sample since it is identified with a quasar and may thus have an extreme orientation; note, however, that this source is very symmetrical ( $x=0.01 \pm 0.01$) and that including it would raise the first bin only by $\sim 0.05$.

As comparison we have plotted the armlength asymmetry distribution of z<0.3 (i.e. similar redshift range) FRII-type 3CR radio galaxies with $50\!<\!D\!<\!1000$ kpc, for which we have taken the data from Best et al. (1995). We have removed sources smaller than 50 kpc since their asymmetries, if environmental, more reflect the gas distribution inside or close to the host galaxy whereas we are interested in the large-scale environment. There are 27 sources in the 3CR subsample, as compared to 19 FRII-type GRGs.

This comparison is only meaningful if 3CR sources are in similar gaseous environments as GRGs, and will develop into GRGs provided that their nuclear activity lasts for a long enough time. As yet, there is little detailed knowledge on the difference in the environments of 3CR and GRG sources, and on the evolution of radio sources from small to large ones (e.g. Schoenmakers 1999). Radio source evolution models (e.g. Kaiser et al. 1997; Blundell et al. 1999) predict that GRGs must have been much more radio luminous when they were of smaller size, which is not inconsistent with them being 3CR galaxies at an earlier evolutionary stage (see also Schoenmakers 1999). We will therefore assume that the environments are largely similar for the >50 kpc 3CR sources and the GRGs.

Although the difference in armlength asymmetry between 3CR radio galaxies and GRGs is small and probably not significant, the GRGs tend to be biased towards higher armlength asymmetries (Fig. 3a). A Kolmogorov-Smirnoff (K-S) test shows that the two distributions are different at the 95% confidence level. Note, however, the relatively large (Poissoneous) errors in Fig. 3a, due to the small number of sources in the samples.

We have also measured the bending angle, defined as the angle between the lines connecting the core with the endpoints of the two lobes. The results are presented in Table 4. The distribution of bending angles is plotted in Fig. 3b, together with the values for the z<0.3 3CR galaxies from Best et al. (1995). The distributions are quite similar; a K-S test shows that they do not differ significantly at the 90% confidence level. Further discussion of these asymmetries will be presented in Sect. 7.3.

\end{figure} Figure 3: Plots of the distribution of the fractional separation difference, x (top), and the bending angle, $\theta $ (bottom), of the FRII-type GRGs (hatched area) and of z<0.3 and 50 < D < 1000 kpc powerful 3CR sources from Best et al. (1995; area under dashed line). The error bars assume a poisson distribution of the number of sources in a bin

Table 4: Morphological parameters of the radio lobes. Column 1 gives the name of the source. Column 2 indicates which side of the source is named A and B in this table ("N'' stands for north, etc.). Columns 3 to 6 give the angular size and the physical size of the lobes. Column 7 gives the asymmetry parameter, Q, defined as ratio of the length of the longest lobe to that of the shortest. Column 8 gives the fractional separation parameter, x, defined as x = (Q-1)/(Q+1). Column 9 gives the bending angle, $\theta $, of the radio source, defined as the angle between the radio axes of the two lobes

\begin{displaymath}\begin{tabular}{l c r@{$\,\pm\,$}r r@{$\,\pm\,$}r r@{$\,\pm\,...
... 0.03 & 0.05 & 0.01 & 11 & 2 \\
\hline \hline\\

4.2 Flux density and spectral index asymmetries

We have measured the flux density asymmetry, R, of the radio lobes and the spectral index difference, $\Delta\alpha$, between the two lobes. We have defined these parameters such that they increase monotonically with increasing asymmetry, i.e. R is the 325-MHz flux density of the brightest lobe divided by that of the weakest lobe and $\Delta\alpha$ is the spectral index of the lobe with the flattest spectrum minus the spectral index of the lobe with the steepest spectrum, measured between 325 MHz and 10.5 GHz. We have searched for correlations between these parameters and the armlength asymmetry parameter x using Spearman rank correlation tests. To avoid spuriously significant correlations as a result of single outliers in the parameter space under investigation, we have omitted, for each of the two parameters being tested, the source with the highest value of that parameter. The results of the correlation tests are presented in Cols. 1-3 of Table 5. We find that the only significant correlation is that between x and $\Delta\alpha$, i.e. when a radio source is more asymmetric in armlength, then also the spectral index difference between the lobes is systematically larger. We find that in 15 out of 20 sources the radio lobe with the shortest arm preferentially has a steeper spectrum, although the difference in spectral index between the two sides is $\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle ... for almost all sources (see Fig. 4).

The lobe flux density asymmetry, R, is not significantly correlated with either x or $\Delta\alpha$. Still, we find that in 13 out of 20 sources (i.e. 65%) the most luminous radio lobe has the shortest armlength. This is a similar percentage as found in the sample of 3CR sources studied by McCarthy et al. (1991, but see Best et al. 1995) which suggests that this trend does not occur by chance, only.

Since the luminosity of a radio lobe is the lobe volume integrated emissivity, it is perhaps preferable to compare R and $\Delta\alpha$with the asymmetry in the estimated volume of the radio lobes. Also, if the asymmetries are caused by large-scale environmental inhomogeneities, this will probably affect the dynamical evolution of the lobe as a whole, and not only its forward advance. Therefore, we have investigated the correlation of R and $\Delta\alpha$ with QV, the ratio of the volume of the largest lobe to that of the smallest. See Sect. 6.1 for the method used to estimate the lobe volumes.

The results are presented in the last three columns of Table 5. Although the correlation analysis gives significant results for both $\Delta\alpha$ and R with QV, indicating a correlated increase in asymmetry for these parameters, these results are not very meaningful. We find that in only 12 out of 20 sources the lobe which is smallest in estimated volume has the steepest spectrum. Also, in only 11 out of 20 sources we find that the largest lobe is the brightest. This indicates that the relative volume of a radio lobe has less influence on its relative spectral index than the armlength of the lobe. We will discuss this in more detail in Sect. 7.3.

\end{figure} Figure 4: The difference in spectral index between the longest and the shortest lobe against the armlength asymmetry parameter x of the GRGs. The source with the largest side-to-side difference in spectral index ( $\Delta \alpha \approx -0.4$) is B0136+396

Table 5: Spearman rank correlation tests between the asymmetry parameters of the GRGs. See the text for details on the definition of the parameters. Columns 1 and 4 give the parameters being tested. Columns 2 and 5 give the correlation coefficients, $r_{\rm s}$. Columns 3 and 6 give the significance, s, of the correlation. The probability of the correlation occurring by chance is 1-s

\begin{displaymath}\begin{tabular}{r r r r r r}
\hline \hline\\ [-1ex]
...lpha - R$ & 0.333 & 0.809 \\
\hline \hline \\

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