Most of the hadronic jet models for quasars (QSOs) and microquasars (MQs) found in literature represent beams of particles (e.g. protons). These particles interact with the matter in the stellar wind of the companion star in the system or with crossing clouds, generating gamma-rays via proton-proton processes. Our aim is to derive the particle distribution in the jet as seen by the observer, so that proper computation of the $γ$-ray and neutrino yields can be done. We use relativistic invariants to obtain the transformed expressions in the case of a power-law and power-law with a cutoff particle distribution in the beam. We compare with previous expressions used earlier in the literature. We show that formerly used expressions for the particle distributions in the beam as seen by the observer are in error, differences being strongly dependent on the viewing angle. For example, for $Γ=10$ ($Γ$ is the Lorentz factor of the blob) and angles larger than $\sim 20^o$, the earlier-used calculation entails an over-prediction (order of magnitude or more) of the proton spectra for $E>Γmc^2$, whereas it always over-predicts (two orders of magnitude) the proton spectrum at lower energies, disregarding the viewing angle. All the results for photon and neutrino fluxes in hadronic models in beams that have made use of the earlier calculation are affected. Given that correct gamma-ray fluxes will be in almost any case significantly diminished in comparison with published results, and that the time of observations in Cherenkov facilities grows with the square of the flux-reduction factor in a statistically limited result, the possibility of observing hadronic beams is undermined.
Epicyclic oscillations in spinning particle motion around Kerr black hole applied in models fitting the quasi-periodic oscillations observed in quasars and microquasars
Constraints on Hadronic Emission from Microquasars Detected by LHAASO
INAF Osservatorio Astrofisico di Arcetri（意大利国家天体物理研究所阿切尔西天文台）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交大凌波书院）；Université Paris Cité, CNRS, AstroParticule et Cosmologie（巴黎西岱大学法国国家科学研究中心粒子与宇宙学实验室）
Instituto de Física. Universidad Nacional Autónoma de México（墨西哥国立自治大学物理研究所）；Instituto de Astronomía. Universidad Nacional Autónoma de México（墨西哥国立自治大学天文研究所）；Instituto de Radioastronomía y Astrofísica. Universidad Nacional Autónoma de México（墨西哥国立自治大学射电天文学与天体物理研究所）
Hadronic Emissions from the Microquasar V4641 Sgr, SS433, and its implications in the Diffuse Galactic Emission
Presidency University（总统大学）；Gran Sasso Science Institute（格兰萨索科学研究所）；INFN/Laboratori Nazionali del Gran Sasso（意大利国家核物理研究所/格兰萨索国家实验室）；Aryabhatta Research Institute of Observational Sciences (ARIES)（阿亚巴哈观测科学研究所）；University of Johannesburg（约翰内斯堡大学）；Central University of Kashmir（克什米尔中央大学）
The unidentified PeV source LHAASO J2108+5157: A microquasar remnant?
Universidad de Jaén（哈恩大学）；Instituto Argentino de Radioastronomía (CCT La Plata, CONICET（阿根廷射电天文研究所）；CICPBA（拉普拉塔国立大学天文与地球科学学院）；UNLP)（巴塞罗那大学）；Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata；Universitat de Barcelona
Particle acceleration at recollimation shocks in sub-relativistic jets. A model for jets in Seyfert Galaxies, Microquasars and Protostellar Systems
INAF, Istituto Nazionale di Astrofisica（意大利国家天体物理研究所）；Universite Paris Cité（巴黎西岱大学）；Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange（法国蔚蓝海岸大学，蔚蓝海岸天文台，法国国家科学研究中心，拉格朗日实验室）；University of Pisa（比萨大学）；Institute of Nuclear Physics Polish Academy of Sciences（波兰科学院核物理研究所）
