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6.1. Synchrotron Spectral Ageing

Mitton and Ryle (1969) first noted that the radio spectral index flattened towards the extremities of the radio source in Cygnus A. This flattening was confirmed in the images of Hargrave and Ryle (1974), who showed that the radio hotspots had the flattest spectra in the source (besides the core). This effect can be seen in the spectral index image of Cygnus A in Fig. 8. The hotspots have spectral indices of -0.5 between 1.5 GHz and 5 GHz, with gradual steepening of the spectra to indices leq -2 in the tails of the radio lobes.

Figure 8

Figure 8. The spectral index distribution across Cygnus A between 1.5 GHz and 5 GHz at 1.1" resolution. The grey-scale ranges from -2.4 (white) to -0.4 (black), and the contour levels are: -2.5, -2.3, -1.9, -1.7, -1.5, -1.4, -1.3, -1.2, -1.1, -1.0, -0.9, -0.8, -0.7, -0.5.

The spectral steepening seen in Cygnus A is characteristic of powerful radio galaxies in general. This effect has been explained as synchrotron radiative ageing of the relativistic electrons. Synchrotron radiation preferentially depletes the highest energy electrons, leading to a steepening in the emission spectrum at high frequencies over time (Pacholcyzk 1970, Scheuer and Williams 1968). A synchrotron-aged radio spectrum is characterized by an (assumed) low frequency power-law emission spectrum of index alphain, a `break frequency', nuB, near which the spectrum steepens from the injected power-law, and the behavior above the break, which depends on micro-physical processes such as pitch angle scattering and particle acceleration (Myers and Spangler 1985, Carilli et al. 1991a). The `injection index', alphain, relates to the energy index for the relativistic electron population, Sin, as: Sin = 2alphain - 1, where N(E) propto ES (Pacholcyzk 1970). The radiative `age' of the relativistic particle distribution, tsyn, defined as the time since the spectrum was a power-law out to infinite frequency, relates to nuB and the magnetic field, B, through: tsyn = 1610 B-3/2 nuB-1/2 Myr, with B in µG, and nuB in GHz (2).

The inference is that the electrons at the center of the source are `older' than those closer to the hotspots, i.e. that the source is expanding in time with the principal site of particle acceleration being the hotspots, in agreement with the jet model. The connection between radio spectrum and age allows for a study of the growth and evolution of the lobes by careful measurement of the spectrum throughout the length and width of the source. Extensive synchrotron `spectral ageing' studies of radio galaxies have been performed by many authors (Burch 1979, Alexander 1985, 1987, Alexander and Leahy 1987, Myers and Spangler 1985, Leahy, Muxlow, and Stevens 1989). Using minimum energy magnetic fields these studies have led to lifetimes for powerful radio galaxies between 106 and 108 yrs, and advance speeds between 0.02 and 0.2c. The validity of spectral ageing analyses is supported by the general agreement between spectral ages and upper limits to source lifetimes dictated by the space density of powerful radio galaxies (leq 108 yrs; Schmidt 1965), and upper limits to source expansion velocities set by special relativity and the statistics of arm-length asymmetries for lobes in radio galaxies (leq 0.2c; Longair and Riley 1979).

Spectral ageing studies also allow for the study of the micro-physical processes in the relativistic electrons by determining the behavior of the spectrum at frequencies higher than the break frequency (Kardashev 1962, Pacholcyzk 1970, Jaffe and Perola 1973, Eilek and Shore 1989, Carilli et al. 1991a).

Cygnus A has been the most exhaustively studied of all radio galaxies in this regard (Winter et al. 1980, Alexander et al. 1984, Roland et al. 1988, Muxlow et al. 1988, Carilli et al. 1991a). The difficulty in spectral ageing studies of radio galaxies is that the curvature in the spectrum is very gradual, requiring sensitive observations to be made over a large frequency range at matched spatial resolution. The large angular size and high flux density of Cygnus A over a wide range in frequency has allowed for the first fundamental test of synchrotron radiation theory, and we review the results herein.

2 Inverse Compton losses have been ignored. For Cygnus A the energy density in the ambient photon field is leq 1% that in minimum energy magnetic fields throughout the source. Note that in general this may not be true, in particular for low surface brightness sources, and/or for sources at high redshift, where the microwave background energy density can become substantial. Back.

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