Astron. Astrophys. 362, 27-41 (2000)

3. Hotspots in CSS and larger sources

The hotspots, which are the high brightness regions in the outer lobes of the high-luminosity FRII radio sources, indicate the Mach disks where the jets terminate. The hotspots usually subtend small angles in the radio cores suggesting the high degree of collimation of the jets in these sources (Bridle & Perley 1984; Bridle et al. 1994; Fernini et al. 1997). However, the jet momentum may be spread over a larger area than the cross-section of the jet itself due to the dentist-drill effect discussed by Scheuer (1982), where the end of the jet wanders about the leading contact surface drilling into the external medium at slightly different places at different times. Recent simulations of 3D supersonic jets suggest that cocoon turbulence drives the dentist-drill effect (Norman 1996).

In this section we study some of the properties of the hotspots for CSS as well as larger objects using the results from our IPS survey and also available interferometric observations of hotspots. IPS observations enable us to estimate the weighted average of the fraction of flux density in the scintillating components and their sizes. For sources larger than about 400 mas the scintillating components are usually the hotspots at the outer edges of the lobes. Since the cores in CSSs are usually weak, especially at low frequencies, the scintillating components are the hotspots in the lobes. Over the last few years the sizes of hotspots have also been determined reasonably reliably from interferometric observations for samples of compact steep-spectrum radio sources using largely VLBI and MERLIN observations, as well as for the larger objects using the VLA. Although there is no well-accepted definition of a hotspot (cf. Laing 1989; Perley 1989), we have used the following empirical definition. The hotspots are defined to be the brightest features in the lobes located further from the nucleus than the end of any jet, and in the presence of more extended diffuse emission these should be brighter by at least a factor of 4 (cf. Bridle et al. 1994). In the presence of multiple hotspots, only the primary hotspot has been considered.

In the following subsections we consider the possible dependence of the fraction of flux density from the hotspot and its size on both radio luminosity and overall projected linear size, and discuss possible constraints these might place on models of evolution of radio sources. We have excluded sources with prominent flat-spectrum nuclei, and those with a complex or core-jet morphology, and have considered only those sources where the scintillations are likely to be produced by the hotspots in the outer lobes. In the GPS sources with two outer components, we have assumed that these features are likely to be hotspots rather than being the counterparts of flat-spectrum nuclei. The compact-double structures seen in several GPS sources, lack of variability, and polarization measurements as in 2134+004 (cf. Stanghellini et al. 1998b) lend some support to such an interpretation.

3.1. Hotspot prominence and radio luminosity

The dependence of the prominence of the hotspots on radio luminosity was examined about 20 years ago (e.g. Jenkins & McEllin 1977; Kapahi 1978). Jenkins & McEllin reported a strong correlation of the prominence of the hotspots with radio luminosity for the well-studied sample of 3CR radio sources. They defined the hotspots to be features with a size less than about 15 kpc. Kapahi (1978) argued that this correlation is possibly due to the effective resolution being coarser for the higher redshift and hence higher luminosity sources. We investigate this relationship for the CSS as well as larger objects using both the IPS and interferometric measurements.

In Figs. 1a and b the scintillation visibility, µ, is plotted against the total radio luminosity at 5 GHz for the sources from our IPS observations (Table 4 and Table 5) with an LAS 400 and 1000 mas respectively. Since the effective size of the hotspots estimated from IPS observations can depend on the relative prominence of the compact and halo components as well as their separation (cf. Duffet-Smith 1980), we have examined these trends for sources 1000 mas where the blending of the two oppositely-directed hotspots is minimal. The scintillation visibility, µ, ranges from about 0.04 to 0.7 with most objects in the range of 0.1 to 0.7. The median value of µ is about 0.3. The luminosity of most objects at 5 GHz lie in the range of about to 10²⁸ W Hz^-1 sr^-1, and in further discussions in this paper we confine ourselves largely to objects in this luminosity range. The scintillation visibility µ - luminosity diagrams for all the sources in Table 1 and Table 2 with S₃₂₇ 0.5 Jy (Figs. 1a and b), show no evidence of a significant dependence on radio luminosity.

Fig. 1a-c. The scintillation visibility, µ for sources a with LAS 400 mas, b LAS 1 arcsec and c the fraction of emission from the hotspots, fhs, estimated from interferometric observations by B94 and F97 are plotted against the total radio luminosity at 5 GHz. The sample of largely CSS and GPS sources (Table 1) are shown by open and filled circles for galaxies and quasars respectively, while the larger galaxies and quasars (Table 2, B94 and F97) are shown by open and filled triangles respectively.

Table 5. Observed parameters of larger sources

We have also examined this relationship using the hotspot flux densities listed by Bridle et al. (1994, hereinafter referred to B94) and Fernini et al. (1993, 1997, hereinafter referred to as F97), whose sources have a similar luminosity to those of our samples and have been observed with resolution of about a few hundred mas, which is comparable to our IPS cut-off size. A plot of the fraction of the hotspot flux densities, f_hs = (S+S)/S_total, from the two lobes against the total radio luminosity at 5 GHz for the sources from B94 and F97 are presented in Fig. 1c. The interferometric measurements also do not show a significant dependence of hotspot prominence on radio luminosity.

3.2. Hotspot prominence and linear size

We have presented the µ-linear size diagram for the IPS samples described in the earlier section in Figs. 2a and b, and the f_hs-linear size diagram for the B94 and F97 sources in Fig. 2c. The Spearman rank correlation coefficient for the IPS sample of sources with LAS 1000mas is -0.32, compared to -0.15 for the B94 and F97 sources. Again, we find no evidence of a significant dependence of either µ or f_hs on linear size for these high-luminosity objects. There is, at best, a weak anticorrelation.

Fig. 2a-c. The scintillation visibility, µ for sources a with LAS 400 mas, b LAS 1 arcsec and c the fraction of emission from the hotspots, fhs, estimated from interferometric observations by B94 and F97 are plotted against the projected linear size. The symbols have the same meaning as in Fig. 1.

A relation between the prominence of hotspots with source size, and the total luminosity can in principle provide constraints on the models of evolution of radio sources. The luminosity of the hotspot depends on the pressure in the hotspot and the size of the hotspot. Many models in the literature assume that the contribution of the hotspot to the total luminosity is negligible (Kaiser et al. 1997; Blundell et al. 1999) or do not consider the evolution of the hotspot independently (Chyzy 1997; Begelman 1996). The self-similar models assume that the pressure in the head of the jet, which is essentially the hotspot, scales with the mean cocoon pressure (Kaiser et al. 1997; Begelman 1996) by means of adjusting the size of the working surface. These models predict that the cocoon luminosity decreases as the source ages. This would suggest, in the light of our data, that the hotspot luminosity also decreases as the source grows old. Non-relativistic numerical simulations have been attempted to understand the structures of the hotspots (Wilson & Scheuer 1983; Smith et al. 1985; Norman & Balsara 1993). Although these simulations reveal dynamically varying structures of the hotspots, the luminosity evolution needs to be studied. The simulations involving relativistic electron transport with the 3D MHD simulations of jets (Jones et al. 1999a; Tregillis et al. 1999; Jones et al. 1999b) might provide better insight into the evolution of the hotspots.

3.3. Sizes of hotspots and collimation of radio jets

A study of the variation of the size of the hotspots on the overall linear size of the objects could provide useful clues on the collimation of radio jets. A plot of the size of the scintillating components for sources larger that 1000 mas, against the overall linear size of the source shows no significant dependence of the hotspot size on the overall size of the object (Fig. 3a). To examine any effect of contamination by diffuse emission around the hotspots (cf. Hewish & Readhead 1976; Duffet-Smith 1980) we have confined ourselves to objects above 1000 mas, and have also considered separately objects with 0.3 (Fig. 3b). We again find no evidence of a significant relationship. We also examine this trend using the sizes of hotspots determined by B94 and F97, which have similar luminosity to our IPS sample (Fig. 3c). The interferometric measurements for the B94 and F97 sources also suggest that the hotspot sizes do not exhibit a significant dependence on the overall linear size. The hotspot sizes remain nearly constant with a mean value of about 3 kpc although the hotspot sizes range from about 1 to 10 kpc, implying that the jets have an approximately constant mean width beyond about 20 kpc.

Fig. 3a-c. The linear sizes of the scintillating components for all the objects in Table 1 and Table 2 with an LAS 1 arcsec are plotted against the total projected linear size in panel a and for those with 0.3 in panel b . In panel c the sizes of the hotspots from B94 and F97 are plotted against the projected linear sizes of these objects. The symbols have the same meaning as in Fig. 1.

Jeyakumar & Saikia (2000a,b) have earlier examined the dependence of hotspot size on projected linear size for CSS and GPS objects, and find that the hotspot size increases linearly with the total linear size, suggesting that they evolve in a self-similar way. By comparing this trend with larger objects observed with a similar number of resolution elements, they suggested that there is a flattening of the relationship beyond about 20 kpc. The plots in Fig. 3 where most of the objects are larger than about 10 kpc are consistent with this flattening.

The relationship between the hotspot sizes and the overall size of the source suggest that the jets are largely confined. The jets could be confined by the ambient pressure whose density falls with distance from the nucleus for sources less than about 20 kpc, while for larger scales the jets could be possibly magnetically confined. Numerical simulations of the propagation of jets also show that the hotspot sizes do not tend to increase with linear size as the jets propagate outwards beyond a certain distance (Sanders 1983; Wilson & Falle 1985).

The recollimation of the jet can occur if the jet pressure falls more rapidly than the ambient pressure. In such a scenario one would expect recollimation to occur at a distance where the jet pressure falls below the ambient pressure. In the model of Sanders (1983) applied to the jet in NGC 315, the reconfinement of the jet is accompanied by conical shocks which heat the jet causing it to reexpand. In this scenario, the reconfinement region beyond about 20 kpc, where the mean hotspot width has an approximately constant value of 3 kpc, requires a high ambient pressure, comparable to or larger than the jet pressure, beyond the CSS stage. On the large scales, where the ambient pressure may not be sufficient for confinement, the jet could be possibly held together by its own toroidal magnetic field (cf. Begelman et al. 1984). Magnetic collimation provides a natural explanation of the observed trend of a nearly constant width in the large sources. The mechanism of self-collimation by current-carrying jets has been examined by Appl & Camenzind (1992, 1993a,b), and the development of Kelvin-Helmholtz and current-driven instabilities in these relativistic MHD jets have been studied by Appl (1996). In this scenario, the jet is initially pressure confined and becomes self-collimated by the magetic pressure when the ambient pressure drops below the jet pressure. The width of the jet in the pressure confined regime is determined by the ambient pressure alone, where the jet current is shielded by the surface currents (Appl & Camenzind 1992). The increase in jet width with source size in this phase is due to the decrease in ambient pressure. Self-collimation becomes important when the ambient pressure falls just below the jet pressure. At this point, the current, I, is estimated to be amp where P is in units of 10^-12 dyn cm^-2 and the radius of the jet R_j is in kpc (Appl & Camenzind 1992). For a hotspot radius of 1.5 kpc, which is the mean value for our large sources, and typical jet pressure of dyn cm^-2 the current required to be carried by the jet is about 10¹⁸ amp. The variation of the sizes of the hotspots is consistent with pressure confinement in the CSS phase with the ambient pressure falling with distance from the nucleus, while at larger distances from the nucleus where the ambient pressure has fallen below the jet pressure, the jet could be possibly magnetically confined.

© European Southern Observatory (ESO) 2000

Online publication: October 30, 19100
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