Spectra of relativistic electrons and synchrotron radiation of an expanding source with continuous injection

Astronomy and Astrophysics – Astronomy

Scientific paper

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Gas Expansion, Plasma Clouds, Power Spectra, Radio Sources (Astronomy), Radio Spectra, Relativistic Electron Beams, Synchrotron Radiation, Analysis (Mathematics), Flux Density, Mathematical Models, Spectral Energy Distribution

Scientific paper

The spectra of relativistic electrons and the synchrotron radiation of an expanding source are formulated and computed, where continuous injections, synchrotron losses and expansion losses of relativistic electrons take place simultaneously. The plasma clouds, injected continuously and steadily into a source, contain relativistic electrons, magnetic fields and thermal matter. The magnetic fields are frozen into the plasma. The plasma has a linear size R0 when it is injected; at time t, the size becomes R-tilde = R0 + V(t - t-tilde) due to expansion. V is the expansion velocity and t-tilde is the injection time. The source consists of a continuous series of plasma clouds with sizes from R = R0 + Vt to R0, corresponding to an injection time from t-tilde = 0 to t-tilde = t. The spectrum of an entire source is obtained by summing up the spectrum of each plasma cloud. It turns out that the total energy of relativistic electrons of the source is carried by lower-energy electrons, and that the power of synchrotron radiative is due to higher energy electrons. The prominent characteristic is that the synchrotron power saturates when the size of the initially injected plasma cloud becomes about 2R0. The spectrum of synchrotron radiation shows various shapes depending on the physical parameters of the source. Using the results mentioned above, we determine the magnetic-field strength of the lobe of Cygnus A. The result is in close agreement with the value determined from the minimum-energy argument.

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