In this work, after improving the formulation of the model on particle transport within astrophysical plasma outflows and constructing the appropriate algorithms, we test the reliability and effectiveness of our method through numerical simulations on well-studied galactic microquasars as the SS 433 and the Cyg X-1 systems. Then, we concentrate on predictions of the associated emissions, focusing on detectable high-energy neutrinos and γ-rays originated from the extragalactic M33 X-7 system, which is an X-ray binary discovered in 2006, located in the neighboring galaxy Messier 33, and has not yet been modeled in detail. The particle and radiation energy distributions, produced from magnetized hadronic astrophysical jets in the context of our method, are assumed to originate from decay and scattering processes taking place among the secondary particles created when hot (relativistic) protons of the jet scatter on thermal (cold) ones (p-p interaction mechanism inside the jet). These distributions are computed by solving the system of coupled integrodifferential transport equations of multiparticle processes (reactions chain) following the inelastic proton-proton (p-p) collisions. For the detection of such high-energy neutrinos as well as multiwavelength (radio, X-ray, and gamma-ray) emissions, extremely sensitive space telescopes and other γ-ray and neutrino detection instruments are in operation or have been designed like the CTA, IceCube, ANTARES, KM3NeT, and IceCube-Gen-2.
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