Astrophysical jets

The origin of cosmic rays (CRs) with >EeV energies is one of the most important outstanding mysteries in high-energy astrophysics. Simple energetic arguments based on Hillas criterion (the figure on the right), indicate that Active Galactic Nucleii (AGNs) and Gamma-ray Bursts (GRBs) are realistically viable candidates for acceleration of these Ultra-High-Energy Cosmic Rays (UHECRs). Recent analysis of UHECR data from the Pierre Auger Observatory indicates that Centaurus A may be the dominant source for the observed CR anisotropy signal (The Pierre Auger collaboration, 2023, arXiv:2305.16693), while the acceleration mechanism is still unclear. As the jet velocity of Centaurus A is only mild relativistic ~0.5c, and no clear evidence of strong recollimation or termination shocks has been found in the jet of Centaurus A, we propose that shear acceleration is the mechanism to accelerate UHECR and validate this through relativistic magnetohydrodynamic (MHD) simulations and test-particle simulations.

Shear acceleration is a special Fermi-II acceleration mechanism, where particles can gain energy by scattering on the turbulence embedded in the velocity-shear flows. We performed relativistic MHD simulations using the PLUTO code to study the formation of a spine-sheath jet and its properties. We found that a velocity-shearing sheath can be generated mainly via Kelvin-Helmholtz instability in the interface between a relativistic spine and a static cocoon, and that turbulence is developed in both the spine and the sheath with spectra mostly consistent with a Kolmogorov scaling, which facilitates shear acceleration. The GIF figure on the right illustrates how it evolves. The self-generation of a sheath indicates that shear acceleration is unavoidable in jet.

Wang et al., 2023, MNRAS, 519, 1872. https://ui.adsabs.harvard.edu/abs/2023MNRAS.519.1872W/abstract

The figure on the right shows an example of the simutaneous relativistic MHD and test-partice simulation to study this mechanism. The top color bar is for the jet velocity in units of speed of light. The bottom color bar shows the magnitude of the magnetic field (streamlines) with code units. The jet with a helical magnetic field is injected along the $Y$-axis with a periodic boundary condition. The interaction between the high-velocity spine and static cocoon generates a velocity-shearing sheath with a turbulent field. The black arrows represent the test particles with larger arrow sizes for higher energy particles. The simulation is run with high resolution to avoid sub-grid physics for test particles. The two figures on the lower left are the test-particle trajectories in a regular magnetic field (initial setup of our simulation) projected in 2D to illustrate the drift effect due to the gradient of magnetic field. The right two figures are particles in a turbulent spine-sheath, so that particles have scattering with MHD turbulence, which faciliate acceleration. The colorbar below each figure is for the particle Lorentz factor.
Wang J.-S., Reville B., Rieger F.~M., Aharonian F.~A., 2024, ApJL, 977, L20.
https://ui.adsabs.harvard.edu/abs/2024ApJ...977L..20W/abstract

The features of turbulence and shear acceleration are presented below.
Wang J.-S., Reville B., Rieger F.~M., Aharonian F.~A., 2024, ApJL, 977, L20.
https://ui.adsabs.harvard.edu/abs/2024ApJ...977L..20W/abstract

The HD/MHD turbulence spectra of different simulations, which is consistent with Kolmogorov type over a large dynamical range. The verticle dashed lines indicate the gyro scale of injected particles.

A example of particle trajectories for shear acceleration. The blue curves are the velocity profiles at different time steps. The particles scatter back and forth in the velocity shearing region and get accelerated.

The acceleration rate and average radial position of particles.

The particle spectra for different simulations. The verticle dashed lines indicate the Hillas limit of the system.

To bridge between theory and observations, we provided a simple general solution for shear acceleration by solving the steady-state Fokker-Planck-type equation and found that the accelerated particles have a power-law spectrum with an exponential-like cut-off, where the power-law index is determined by the MHD turbulence spectrum and the radial velocity profile of the jet. We applied our solution to model the multi-wavelength spectrum of kilo-parsec-scale X-ray jet. The origin of the X-ray emission in these jets from radio galaxies has been actively debated in the past twenty years. We found that shear acceleration can provide a natural explanation for their multi-wavelength spectral energy distribution, such as the prominent FR I radio galaxy Centaurus A (the figure on the right) and the FR II radio galaxies such as 3C 273 and Pictor A.

Wang et al., 2021, MNRAS, 505, 1334

https://ui.adsabs.harvard.edu/abs/2021MNRAS.505.1334W/abstract

He, Sun, & Wang et al., 2023, MNRAS, 525, 5298 https://ui.adsabs.harvard.edu/abs/2023MNRAS.525.5298H/abstract

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