How do jet-head shocks shape the kinetic and magnetic energy spectra of relativistic active galactic nucleus jets?

Abstract

In this letter, three-dimensional relativistic magnetohydrodynamic simulations of ultra-relativistic jets from an active galactic nucleus (AGN) are performed using the PLUTO code (A. Mignone et al., “Pluto: A numerical code for computational astrophysics,” Astrophys. J. Suppl. Ser. , vol. 170, 2007, Art. no. 228) to investigate large-scale energy injection at jet heads. Spectral analyses of kinetic and magnetic energies reveal distinct shock-dominated spectral behaviors. The compensated kinetic energy spectrum exhibits an approximate k ⁻² scaling, which is consistent with the shock-dominated compressible dynamics of the jet-head region, where discontinuity-like structures and compressive motions contribute to the observed spectral behavior. The magnetic energy spectrum exhibits an approximate k ^−9/5 -like scaling over the resolved spectral range (J. R. Beattie, C. Federrath, R. S. Klessen, S. Cielo, and A. Bhattacharjee, “The spectrum of magnetized turbulence in the interstellar medium,” Nat. Astron. , pp. 1–11, 2025), representing an empirical spectral behavior obtained from the present three-dimensional ideal-RMHD simulations. This behavior is interpreted in terms of the combined influence of compressive magnetic amplification and velocity-driven field-line stretching rather than as a theoretically derived universal scaling law. The scale-dependent energy ratio remains much less than unity across all resolved scales, demonstrating the kinetic dominance of the relativistic bulk flow while not excluding localized magnetic amplification in intermittent structures. The observed spectral characteristics remain insensitive to the toroidal-to-poloidal magnetic field distribution at fixed total magnetization.