In this work, at first we present a model of studying astrophysical flows of binary systems and microquasars based on the laws of relativistic magnetohydrodynamics. Then, by solving the time independent transfer equation, we estimate the primary and secondary particle distributions within the hadronic astrophysical jets as well as the emissivities of high energy neutrinos and γ-rays. One of our main goals is, by taking into consideration the various energy-losses of particles into the hadronic jets, to determine through the transport equation the respective particle distributions focusing on relativistic hadronic jets of binary systems. As a concrete example we examine the extragalactic binary system LMC X-1 located in the Large Magellanic Cloud, a satellite galaxy of our Milky Way Galaxy.

Recently, microquasar jets have aroused the interest of many researchers focusing on the astrophysical plasma outflows and various jet ejections. In this work, we concentrate on the investigation of electromagnetic radiation and particle emissions from the jets of stellar black hole binary systems characterized by the hadronic content in their jets. Such emissions are reliably described within the context of relativistic magneto-hydrodynamics. Our model calculations are based on the Fermi acceleration mechanism through which the primary particles (mainly protons and electrons) of the jet are accelerated. As a result, a small portion of thermal protons of the jet acquire relativistic energies, through shock-waves generated into the jet plasma. From the inelastic collisions of fast (non-thermal) protons with the thermal (cold) ones, secondary charged and neutral particles (pions, kaons, muons, η-particles, etc.) are created, as well as electromagnetic radiation from the radio wavelength band to X-rays and even very high energy gamma-rays. One of our main goals is, through the appropriate solution of the transport equation and taking into account the various mechanisms that cause energy losses to the particles, to study the secondary particle concentrations within hadronic astrophysical jets. After assessing the suitability and sensitivity of the derived (for this purpose) algorithms on the Galactic MQs SS 433 and Cyg X-1, as a concrete extragalactic binary system, we examine the LMC X-1 located in the Large Magellanic Cloud, a satellite galaxy of our Milky Way Galaxy. It is worth mentioning that, for the companion O star (and its extended nebula structure) of the LMC X-1 system, new observations using spectroscopic data from VLT/UVES have been published a few years ago.

In this work, after testing the reliability of our algorithms through numerical simulations on the well-studied SS 433 Galactic microquasar, we focus on neutrino and γ-ray emissions from the extragalactic M33 X-7 system. This is a recently discovered X-ray binary system located in the neighbouring galaxy Messier 33 which has not yet been modelled in detail. The neutrino and γ-ray energy spectra, produced from the magnetized astrophysical jet of M33 X-7, in the context of our method are assumed to originate from the decay (and scattering) processes taking place among the secondary particles produced assuming that, first, hot (relativistic) protons of the jet scatter on thermal ones (p-p interaction mechanism).