Generalized equipartition method from an arbitrary viewing angle

TL;DR

This paper extends the equipartition method to analyze relativistic sources viewed off-axis, revealing degeneracies in parameters and applying it to TDE radio observations to infer jet properties.

Contribution

It introduces a generalized equipartition analysis for off-axis relativistic emitters, highlighting parameter degeneracies and applying it to real TDE data.

Findings

Off-axis relativistic sources can mimic Newtonian appearances.

The method estimates a jet kinetic energy of about 10^{53} erg for AT 2018hyz.

Degeneracy between Lorentz factor and viewing angle along minimal energy solutions.

Abstract

The equipartition analysis yields estimates of the radius and energy of synchrotron self-absorbed radio sources. Here we generalize this method to relativistic off-axis viewed emitters. We find that the Lorentz factor $\Gamma$ and the viewing angle $\theta$ cannot be determined independently but become degenerate along a trajectory of minimal energy solutions. The solutions are divided into on-axis and off-axis branches with the former reproducing the classical analysis. A relativistic source viewed off-axis can be disguised as an apparent Newtonian one. Applying this method to radio observations of several tidal disruption events (TDEs), we find that the radio flare of AT 2018hyz which was observed a few years after the optical discovery could have been produced by a relativistic off-axis jet with kinetic energy of $\sim10^{53}\,\rm erg$ that was launched around the time of discovery.