Relativistic Electron Energy Spectra of Active Galactic Nuclei in the Thin Synchrotron Limit. I. The Method

Here we present a new method called "inverse synchrotron transform" (IST) to study the spectral energy distributions of active galactic nuclei. We demonstrate that it is possible to make use of Bayes Theorem for conditional probability in order to derive a unique, self-consistent solution for the electron energy spectra (EES), departing from the observed spectral energy distributions (S ED) and the assumption that the main physical process involved is the emission of thin synchrotron radiation. We show the close relationship between the EES so derived, and the electron energy distribution (EED), which in turn, does not have a unique solution, but depends on assumptions that fix the magnetic field strength. We test the IST method and find that it is capable of distinguishing between rather different EEDs that produce SEDs that are apparently very similar.