Modeling blazar broadband emission with convolutional neural networks -- II. External Compton model

In the context of modeling spectral energy distributions (SEDs) for blazars, we extend the method that uses a convolutional neural network (CNN) to include external inverse Compton processes. The model assumes that relativistic electrons within the emitting region can interact and up-scatter external photon originating from the accretion disk, the broad-line region, and the torus, to produce the observed high-energy emission. We trained the CNN on a numerical model that accounts for the injection of electrons, their self-consistent cooling, and pair creation-annihilation processes, considering both internal and all external photon fields. Despite the larger number of parameters compared to the synchrotron self-Compton model and the greater diversity in spectral shapes, the CNN enables an accurate computation of the SED for a specified set of parameters. The performance of the CNN is demonstrated by fitting the SED of two flat-spectrum radio quasars, namely 3C 454.3 and CTA 102, and obtaining their parameter posterior distributions. For the first source, the available data in the low-energy band allowed us to constrain the minimum Lorentz factor of the electrons, $\gamma_{\rm min}$, while for the second source, due to the lack of these data, $\gamma_{\rm min} = 10^2$ was set. We used the obtained parameters to investigate the energetics of the system. The model developed here, along with one from B\'egu\'e et al. (2023), enables self-consistent, in-depth modeling of blazar broadband emissions within leptonic scenario.