Studies in Radio Structure: II. The Relaxation of Relativistic Electron Spectra in Self-Absorbed Radio Sources

A calculation is presented of the synchrotron spectrum of self-absorbed radio sources. It is well known that electron spectra $$N(E)\propto E^{-\gamma}$$ when γ is a constant $$\gt \frac13$$ , give rise to radiation spectra whose logarithmic slope is 2.5. It is shown that other forms of N ( E ) can give rise to radiation spectra either steeper or flatter than this. Such spectra might arise when an initial power law spectrum relaxes. The nature of this relaxation is studied and is shown to depend crucially on whether γ ≷ 3. The relevance of these results to observed radio sources is discussed.