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A measurement of the synchrotron self-absorption flux and frequency providestight constraints on the physical size of the source and a robust lower limiton its energy. This lower limit is also a good estimate of the magnetic fieldand electrons' energy, if the two components are at equipartition. Thiswell-known method was used for decades to study numerous astrophysical sourcesmoving at non-relativistic (Newtonian) speeds. Here we generalize the Newtonianequipartition theory to sources moving at relativistic speeds including theeffect of deviation from spherical symmetry expected in such sources. Like inthe Newtonian case, minimization of the energy provides an excellent estimateof the emission radius and yields a useful lower limit on the energy. We findthat the application of the Newtonian formalism to a relativistic source wouldyield a smaller emission radius, and would generally yield a larger lower limiton the energy (within the observed region). For sources where theSynchrotron-self-Compton component can be identified, the minimization of thetotal energy is not necessary and we present an unambiguous solution for theparameters of the system.

Radius constraints and minimal equipartition energy of relativistically moving synchrotron sources