§33 Bent jets in powerful radio sources

We have seen in the previous section how the jets in radio trail sources can be stable against the formation of internal shock waves generated because of their bending. Most powerful double radio sources, in particular radio galaxies and quasars show almost no deflection of their jets as they propagate through the interstellar and intergalactic medium. As we saw in Chapter III, this behaviour occurs because the bulk velocity of the flow inside the jet is highly relativistic (up to $\unit{ 0.99 }{ \ensuremath{\mathsf{c}}}$ in some cases according to observations). One of the best examples of this behaviour is the radio galaxy Cygnus A, shown in fig.(I.1). As can be seen in the image, the jet has a very well defined straight structure. However, when the jet approaches half the width of the radio lobe it seems to bend through $\sim \! \unit{ 20 }{ \degree }$ and then goes on to the hotspots. In exactly the same way as it was done in the last section, the ratio $D / R$ can be calculated and the result is that $D / R \! \sim \! 0.01$. This value lies well below the curve plotted in fig.(IV.4) for a bending angle $\sim \! \unit{ 20 }{ \degree }$. This bending angle is also well below the upper limit of $\sim \! \unit{50}{\degree}$ calculated in eq.(25.7). In other words, the deflection of the western jet in Cygnus A does not generate any internal shocks.

Fig.(VI.3) shows a VLA radio map of the FR I plumed radio galaxy 3C 31. The jets have large scale arcs before they bend an angle $\sim \unit{ 30 }{ \degree }$. This angle is less than the maximum bending angle calculated in eq.(32.1) for a non-relativistic bulk motion of the flow. From the figure, the ratio $D / R \! \sim 0.1$ at the onset of the curvature, and the angle the jet bends at the onset of the curvature is $\sim \! \unit{ 30 }{ \degree }$.

Figure VI.3: Radio Image of the radio galaxy 3C 31. This radio galaxy is an FR I (plumed) galaxy at a redshift $z \! = \! 0.0169$. The left image is a VLA $\unit{ 1.4 }{ \giga \hertz }$ radio image at $\unit{ 5.5 }{ \text{arcsec} }$ resolution. This image shows a large distortion (wiggling) of both plumes of the radio jet. The right image is a VLA $\unit{ 8 }{ \giga \hertz }$ radio image of the same radio source, but zoomed about the core. This image is a VLA radio map at $\unit{0.3}{\text{arcsec} }$ resolution. Both images taken from Bridle (2000); Laing et al. (2000).

Applying the previous technique to radio quasars is somewhat more complicated due to orientation effects. According to unification models for strong radio sources, namely the 3CR radio quasars and radio galaxies (see section §3), the jets of radio quasars are observed within a cone of half-angle roughly $\unit{ 45 }{ \degree }$ to the line of sight. This means that whatever the deflection angle we observe on the plane of the sky, it would certainly differ from the real deflection. Figs.(VI.4)-(VI.5) show two radio quasars with very well defined deflections. Bearing in mind that the uncertainties in any calculation done for quasars with respect to their bending angle are most probably incorrect, in what follows, we discuss briefly the implications of this result.

In the case of the quasar 3C 175 shown in fig.(VI.4), the deflection angle is $\sim \! \unit{ 25 }{ \degree }$ which is less than the maximum bending angle $\sim \! \unit{50}{\degree}$ for relativistic flows. The ratio $D / R \! \sim \! 0.02$ and the deflection angle at the onset of the curvature is $\sim \unit{ 15 }{ \degree }$. This pair of values lie well below the curve of the appropriate diagram of fig.(IV.4). For the quasar 3C 334 the total deflection angle is $\sim \! \unit{ 40 }{ \degree }$. The ratio $D / R \! \sim \! 0.1$ and the bending angle at the onset of the curvature is $\sim \! \unit{ 10 }{ \degree }$. According to eq.(25.7) and fig.(IV.4) this means that the jet does not generate internal shocks due to its deflection.

Figure VI.4: Radio Image of the quasar 3C 175. The quasar lies at a redshift of $z \! \sim \! 0.768$. The radio image was taken with the VLA at $\unit{ 4.9 }{ \giga\hertz }$ with $\unit{ 0.35 }{ \text{arcsec} }$ resolution (Bridle, 2000; Bridle et al., 1994).

Figure VI.5: Radio Image of the quasar 3C 334. The quasar is at a redshift $z \! = \! 0.555$. This radio image was taken with the VLA at $\unit{ 4.9 }{ \giga\hertz }$ with $\unit{ 0.35 }{ \text{arcsec} }$ resolution (Bridle, 2000; Bridle et al., 1994).

The radio galaxy 3C 34 at redshift $z \! = \! 0.69$ shown in fig.(VI.6) is very peculiar. Best et al. (1997) suggested that the western radio jet of this source has undergone a collision with a galaxy giving rise to a jet-galaxy interaction. In the top panel of fig.(VI.6), the emission regions labelled as n and s represent two hot spots in the western lobe of the source and the region a is what the authors identified as a galaxy which was assumed to be at the same redshift as 3C 34. The idea that object a is an ordinary galaxy in the cluster containing 3C 34 is very natural. First of all, this object presents an elongated structure along what appears to be one of the axes of the radio source (blue line in fig.(VI.6)). Secondly, the deep radio map (bottom map on fig.(VI.6)) shows an enhanced region of radio emission located to the north of object a. The radio spectral index of this area increases away from the hotspot and it is not as steep as the rest of the radio lobe. This means that this region shows a back flow emanating from the hotspot n (Blundell, 1994). This back flow seems to pass around the object a rather than through it, which is consistent with the idea that object a is in the same cluster of galaxies as the one 3C 34 belongs to.

Figure VI.6: Optical image of the radio galaxy 3C 34 with VLA radio contours superimposed. Top: Image at $\unit{545} {\nano\meter}$ taken with the Hubble Space Telescope with overlaid radio contours at $\unit{8.4} {\giga\hertz}$ taken with the VLA A-Array. The contour levels are $\unit{120} {\micro Jy} \times \left(2, 4, 8, 16\right)$. Bottom: HST image at $\unit{865} {\nano\meter}$ with overlaid contours of the radio emission at $\unit{5}{\giga\hertz}$ as seen using the B and C arrays of the VLA. The contour levels are $\unit{120} {\micro Jy} \times \left(1, 2, 4, 8, 16, 32, 64, 128\right)$. Both images from Best et al. (1997). The blue line is what seems to be the old axis of the radio galaxy. The green one is what appears to be its current axis. The red line shows what the path of the west jet will be if a deflection of the jet would have been caused by the collision with the galaxy underlying the emission labelled a.

The $\unit{1.4-5} {\giga\hertz}$ spectral indices of hotspots s and n are $0.83 \pm 0.03$ and $0.92 \pm 0.03$ respectively. Since the spectral index is flatter for hotspot s, this suggests that it is younger as compared to hotspot n. For comparison, it is important to note that the spectral index of the eastern hotspot is $0.82 \pm 0.03$.

Cox et al. (1991) showed that a steadily precessing jet could initially make an impact on the wall of the cocoon producing a jet curvature as it feeds its primary hot spot. As the precession continues, the jet then interacts with the cocoon at a very sharp angle and it is then able to produce a new -primary- hotspot while still feeding the old -secondary- hotspot which is now located downstream. This scenario could be the explanation of the observed features in the radio galaxy 3C 34. With this model, the double hot spot and the difference in ages of their electron populations is automatically satisfied. This means also that the radio jet of 3C 34 was previously lying in the direction of the blue axis of fig.(VI.6) and that it is currently aligned with the green axis. The collision of the radio jet of 3C 34 with the galaxy underlying object a occurred when the jet was aligned with the blue axis and star formation was induced due to this interaction.

However, there is another scenario which could well explain the features observed in 3C 34. If the west radio jet collides with the galaxy underlying object a, this interaction could deviate the jet from its original trajectory, as it is pictorially represented by the red curved line in fig.(VI.6). The appearance of a double hot spot could then be explained as follows: originally, the western jet was lying along the blue line of fig.(VI.6) and the proper motion of the orbital companion object a in the cluster resulted in it intersecting the path of the jet which made it follow a curved trajectory such as that shown by the red line. It could also have been that the precession of the jet eventually interacted with object a giving rise to the observed deflection. No radio jet has been observed, but the narrow width of the object a would be consistent with values of $D / R \lesssim 0.01$.

If the jet in 3C 34 was bent because of the interaction with a typical galaxy for which its gas is in pressure equilibrium with a dark matter halo, then we can use the standard values presented in section §21. First of all, the western jet in 3C 34 has a bending angle $\theta \sim \unit{ 10 }{ \degree }$, so that the deflection angle $\psi \sim \unit{ 170 }{ \degree }$. If we assume that the flow inside the jet moves with a velocity $\ensuremath{v}= 0.99 \ensuremath{\mathsf{c}}$, it follows from the bottom diagram in fig.(III.8) that $\sin \varphi_0 \sim 0.3$, or $\varphi_0 \sim \unit{ 17 }{ \degree }$. On the other hand, the value $\theta \sim \unit{ 10 }{ \degree }$ is well below the upper limit of $\sim \unit{ 50 }{ \degree }$ calculated in eq.(25.7), so that at least no terminal shock will be produced by the deflection of the jet. From the bottom plot of fig.(IV.4) and because the angle $\theta_\star \! \ll \! 1$ for a high relativistic flow, it follows that if the trajectory of the jet in 3C 34 is circular, then in order not to produce an internal shock at the onset of the curvature, the ratio $D / R$ has to be less than $\sim \! 0.08$.