Rodolfo Barniol Duran, Ehud Nakar, Tsvi Piran
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 non-relativistic sources. Here we generalize the Newtonian equipartition theory to relativistic sources including the effect of deviation from spherical symmetry expected in such sources. We show that in the relativistic case a single epoch measurement of the synchrotron self-absorption flux and frequency is insufficient to constrain the radius and energy and at least two epochs, or knowledge of the time of the onset of the relativistic outflow, are needed. We show that like in the Newtonian case we can determine the emission radius and obtain a lower limit on the energy. We find that using the Newtonian formalism on 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.
View original:
http://arxiv.org/abs/1301.6759
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