Time-dependent lepto-hadronic modelling of the emission from blazar jets with <i>SOPRANO</i>: the case of TXS 0506 + 056, 3HSP J095507.9 + 355101, and 3C 279

ABSTRACT The observation of a very high-energy neutrino by IceCube (IceCube-170922A) and its association with the flaring blazar TXS 0506 + 056 provided the first multimessenger observations of blazar jets, demonstrating the important role of protons in their dynamics and emission. In this paper, we present SOPRANO (https://www.amsdc.am/soprano), a new conservative implicit kinetic code that follows the time evolution of the isotropic distribution functions of protons, neutrons, and the secondaries produced in photo-pion and photo-pair interactions, alongside with the evolution of photon and electron/positron distribution functions. SOPRANO is designed to study leptonic and hadronic processes in relativistic sources such as blazars and gamma-ray bursts. Here, we use SOPRANO to model the broadband spectrum of TXS 0506 + 056 and 3HSP J095507.9 + 355101, which are associated with neutrino events, and of the extreme flaring blazar 3C 279. The SEDs are interpreted within the guise of both a hadronic and a hybrid model. We discuss the implications of our assumptions in terms of jet power and neutrino flux.