Parameter constraints in a near-equipartition model with multi-frequency NuSTAR, Swift and Fermi-LAT data from 3C 279

Precise spectra of 3C 279 in the 0.5-70 keV range, obtained during two epochs of \emph{Swift} and \emph{NuSTAR} observations, are analyzed using a near-equipartition model. We apply a one-zone leptonic model with a three-parameter log-parabola electron energy distribution (EED) to fit the \emph{Swift} and \emph{NuSTAR} X-ray data, as well as simultaneous optical and \emph{Fermi}-LAT $\gamma$-ray data. The Markov Chain Monte Carlo (MCMC) technique is used to search the high-dimensional parameter space and evaluate the uncertainties on model parameters. We show that the two spectra can be successfully fit in near-equipartition conditions, defined by the ratio of the energy density of relativistic electrons to magnetic field $\zeta_{\rm e}$ being close to unity. In both spectra, the observed X-rays are dominated by synchrotron-self Compton photons, and the observed $\gamma$ rays are dominated by Compton scattering of external infrared photons from a surrounding dusty torus. Model parameters are well constrained. From the low state to the high state, both the curvature of the log-parabola width parameter and the synchrotron peak frequency significantly increase. The derived magnetic fields in the two states are nearly identical ($\sim1$\ G), but the Doppler factor in the high state is larger than that in the low state ($\sim$28 versus $\sim$18). We derive that the gamma-ray emission site takes place outside the broad-line region, at $\gtrsim$ 0.1 pc from the black hole, but within the dusty torus. Implications for 3C 279 as a source of high-energy cosmic-rays are discussed.