Constraints on hadronic emission from microquasars detected by LHAASO

Recently, the Large High-Altitude Air Shower Observatory (LHAASO) collaboration reported ultrahigh-energy (UHE; $>$100 TeV) gamma rays from five microquasars. In all five sources, the emission extends beyond 100 TeV, making microquasars promising candidates for Galactic PeVatrons. We investigated whether gamma rays around 100 TeV originate from hadronic interactions of accelerated cosmic rays with the ambient medium, and we estimated the contribution of these sources to the measured cosmic-ray proton spectrum around the knee. We also derived upper limits on the contribution from the seven additional microquasars in the LHAASO field of view, from which no UHE emission was detected. We considered a cosmic-ray transport scenario in which particle propagation in the source vicinity is diffusion-dominated, with a diffusion coefficient largely suppressed with respect to the average Galactic value, while, at large distances from the source, the diffusion coefficient matches the Galactic value. In addition, we assumed continuous injection over timescales of t_ age =0.1-1 Myr. Using available measurements of the gas density in the emission region, we find that hadronic interactions alone cannot fully account for the observed emission for any of the detected sources. However, in the case of GRS 1915+105 and MAXI J1820+070, the hadronic scenario may still be valid when considering acceleration efficiency higher than 10%. We subsequently derived upper limits on the hadronic contribution to the observed gamma-ray flux. We estimate that the detected sources contribute at most sim4% of the Galactic cosmic-ray spectrum at 1 PeV for an injection timescale of 0.1 Myr and a cosmic-ray acceleration efficiency of 10 %. When adopting the maximum acceleration efficiency allowed by the gamma-ray observations, instead, the contribution of these microquasars to the Galactic cosmic-ray spectrum at PeV energies rises to 37%. Longer injection timescales (∼ 1 Myr) lead to contributions exceeding the observational constraints. For sources not detected at UHE, we obtain a maximum contribution of ∼ 17%, achieved assuming continuous injection over 1 Myr.