All-flavour neutrino luminosity as a function of proton luminosity for two different values of the optical depth to photo-pion interactions f_pπ. The red solid (dashed) line gives the neutrino luminosity corresponding to 1 muon neutrino in IceCube from 3HSP J095507.9+355101 if the neutrino emission lasted 250 days (10 yr). The blue horizontal solid (dashed) line gives the upper limit to the neutrino luminosity implied by the Fermi-LAT 250-day (long-term average) spectrum. The green line shows the upper limit to the proton luminosity implied by the Eddington luminosity of the 3 × 10⁸ M_⊙ black hole, assuming Γ = 20, proton spectral index −2, and maximum proton energy 10¹⁸ eV.