Abstract
ApJ, 772, 78 (2013) A measurement of the synchrotron self-absorption flux and frequency provides
tight constraints on the physical size of the source and a robust lower limit
on its energy. This lower limit is also a good estimate of the magnetic field
and electrons' energy, if the two components are at equipartition. This
well-known method was used for decades to study numerous astrophysical sources
moving at non-relativistic (Newtonian) speeds. Here we generalize the Newtonian
equipartition theory to sources moving at relativistic speeds including the
effect of deviation from spherical symmetry expected in such sources. Like in
the Newtonian case, minimization of the energy provides an excellent estimate
of the emission radius and yields a useful lower limit on the energy. We find
that the application of the Newtonian formalism to a relativistic source would
yield a smaller emission radius, and would generally yield a larger lower limit
on the energy (within the observed region). For sources where the
Synchrotron-self-Compton component can be identified, the minimization of the
total energy is not necessary and we present an unambiguous solution for the
parameters of the system.