[en] The fragmentation of the hydronium cation H₃O⁺ after photoabsorption at 13.5 nm has been investigated with a crossed-photon-and-ion-beams experiment making pulsing and trapping techniques available for fragment momentum imaging at the intense Free-electron LASer in Hamburg. The observed photofragmentation patterns demonstrate that the photolysis of H₃O⁺ proceeds by valence ionization into H₃O²⁺ which subsequently fragments to mainly OH+2H⁺ and H₂O⁺+H⁺ with a branching ratio of up to 0.6:1 and with different degrees of excitation of the molecular fragment. The cross section for fragmentation into OH+2H⁺ is found to be (0.37±0.18)x10^-18 cm², while the total photoabsorption cross section is estimated to be greater than 0.95x10^-18 cm². The data suggest that ionization mainly occurs from the 3a₁ and 1e valence orbitals and that initial ionization from 3a₁ mainly leads to fragmentation into H₂O⁺(A ²A₁)+H⁺ while initial ionization from the 1e orbital predominantly populates the H₂O⁺(B ²B₂)+H⁺ and OH(X²Π)+2H⁺ channels. The results are of significance for astrophysical models of gas clouds in the vicinity of hot radiating objects and for models of the chemistry of planetary and lunar ionospheres under solar irradiation.