A Self-Consistent Framework for Synchrotron Equipartition Analysis

Determining the energy, size, and velocity of synchrotron-emitting outflows is essential for testing models of their formation and evolution, but these quantities are often poorly constrained by observations alone. Equipartition analysis, therefore, provides a widely used framework for estimating these properties. Prior works have developed refinements to account for additional physical effects and other sources of energy (e.g., self-absorption, hot protons, and deviations from strict equipartition); however, these corrections are typically applied independently of one another, resulting in internal inconsistencies. In this work, we derive a self-consistent equipartition framework that accounts for the interdependence of various correction factors for Newtonian outflows and on- and off-axis relativistic jets. We implement our framework in an easy-to-use, publicly available code and apply it to study the tidal disruption events ASASSN-19bt and AT2019dsg, fast X-ray transient EP240414a, and active galactic nucleus J0231-0433. The interdependence of the corrections can increase energy estimates by a factor of 5, suggesting that the energies of other synchrotron sources may be similarly underestimated in the literature. These results indicate that simultaneously incorporating these correction factors is essential for determining accurate outflow properties and constraining launch mechanisms.