5.2. The Filaments
Filamentary structure in the radio lobes of Cygnus A was discovered in the high dynamic range VLA images by Perley et al. (1984). Since then filamentary structure has been seen in most extragalactic radio sources observed with sufficient sensitivity and resolution (Hines et al. 1990, Fomalont et al. 1989, Dreher and Feigelson 1984, Clarke et al. 1992).
An important question raised when filamentary structure was first observed in radio galaxies was whether the volume filling factor for radio emitting fluid in the lobes could be very low. Perley et al. (1984) estimate that the volume filling for the lobes of Cygnus A could be between 0.03 and 0.3. On the other hand, detailed analysis of surface brightness profiles of the lobes shows that there is a space filling diffuse component (Carilli 1989, Leahy 1991). Although noticeable to the eye, the surface brightness contrast between the filaments and the background is typically 20% at 4.5 GHz, with a few filaments contrasting by up to 50%. If the filaments are rope-like (one dimensional) their minimum pressures are typically about a factor four larger than their environments, while if they are sheet-like (two dimensional) they are only over-pressured by 30% or so.
Many explanations have been considered for filaments in radio sources, including cooling instabilities (Eilek 1989), regions of anomalous resistive reconnection (Eilek 1989, Hines et al. 1990, Christiansen 1989), turbulent vortices in back-flow in the radio lobe (Norman et al. 1982), and weak shocks, or non-linear (Mach 1) acoustic waves driven by the pressure difference between the hotspots and lobes (Carilli 1989).
The most recent and convincing explanation of filamentary structure in radio galaxies is that coming from the 3D simulations of Clarke (1992) which include passive magnetic fields. He finds the natural development of rope-like filaments in radio lobes corresponding to regions of enhanced, or `bundled' magnetic field. Importantly, he notes no evidence for enhanced thermal densities or pressures in these regions. The intermittent bundles of enhanced field occur in regions of large velocity shear implying a simple kinematic dynamo process as the origin for the enhanced (although still dynamically weak) field regions. The polarization characteristics of these filaments are consistent with that observed for Cygnus A (high fractional polarization with longitudinal fields).
A possible physical diagnostic for filamentary structure in radio lobes is the power spectrum. Carilli (1989) measured a power-law power spectrum of the form: P(k) k-2.6, on spatial scales (= 1/k) between 0.7" and 8". Eilek (1989) shows that an observed power-spectrum of index -3 might result from isotropic, weak-field Kolmogorov turbulence.
DeGraff (1992) has performed a fractal analysis of the filaments in Cygnus A. He obtains a fractal dimension between 0.4 and 1.2, consistent with the elongated appearance of the structures. DeGraff and Christiansen (1996) show that the fractal spectra of the filamentary structure in the lobes of Cygnus A are best reproduced with turbulent models involving spatial variations in both the fields and the relativistic particles.