|Annu. Rev. Astron. Astrophys. 1988. 36:
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5.2. Extended Lobes
The advancing working surface inflates a "cocoon" in the intergalactic medium (IGM) surrounded by a bow shock enveloping the jet channel. The pressure distribution between hot spots and the leading bow shock drives a flow pattern sideways and backward along the jet. The bow shock permits the internal jet pressure and external IGM pressure to balance through appropriate gradients in their macroscopic quantities. In fact, the cocoon wraps the entire radio source (Begelman & Cioffi 1989). Therefore, the cocoon's width is determined by the drive of its internal pressure expanding in the external medium at sonic speeds (its length is given by the hot spots' advancement).
This situation has been modeled by Begelman & Cioffi (1989), Cioffi & Blondin (1992); Figure 7 is a cartoon drawn from these references. The head of the bow shock can have a cross section Ah Aj if the jet direction fluctuates on short time scale; in this case, the advancement velocity vh , as determined by the modified balance Equation 20, becomes the following for light jets (vj >> vh):
The cocoon pressure Pc drives a sideways shock into the IGM at a speed vc that is fixed by the balance of Pc and ram pressure e vc2; in the approximation that the cocoon inflates at constant Lj and vh, Pc ~ Lj T / Ac vh, where Ac is the cocoon's cross section. Then,
until it decreases below the speed of sound cs in the IGM. The cocoon is elongated, vh vc, when Lj e vj3 Ah3 / Ac2, where Ac is the cocoon cross section. The whole body of the radio galaxy becomes embedded in an overpressured region, and this makes the jet collimation easier: Observationally, we cannot measure the gas pressure in the cocoons owing to the limited angular resolution of X-ray telescopes, but jet confinement may actually come from the regions of the cocoon at the interface of the flow. In addition, the transverse dimensions of lobes are due to the bow shock expansion and are made wide through wave propagation.
Figure 7. Schematic diagram of overpressured cocoons around jets (Begelman & Cioffi 1989).