Particle acceleration and pitch-angle evolution in relativistic turbulence

Abstract

Synchrotron radiation detected from relativistic astrophysical objects such as pulsar-wind nebulae and {jets from active galactic nuclei} depends on the magnetic fields and the distribution functions of energetic electrons in these systems. Relativistic magnetically dominated turbulence has been recognized as an efficient mechanism for structure formation and non-thermal particle acceleration in these environments. Recent numerical simulations of relativistic turbulence have provided insights into the energy distribution functions of accelerated electrons. Much less is currently understood about their {pitch angle distributions}, which are crucial for accurately interpreting the spectra of synchrotron radiation. {We perform a detailed case study of} the pitch angle distributions formed during the process of turbulent acceleration {for $B_0/δB_0 = 10$ and $\tildeσ_0 \sim 40$, where $B_0$ is the uniform component of the magnetic field, $δB_0$ is the fluctuating component, and $\tildeσ_0$ is the plasma magnetization based on the magnetic fluctuations. We find that even minimal numerical noise can cause substantial pitch angle scattering, but we demonstrate techniques for overcoming the numerical challenges associated with the evolution of very small pitch angles. Our numerical results are consistent with the phenomenological model found in \cite[][]{vega2024b,vega2025}.}

Figures (14)

• Figure 1: Electron energy distribution functions in Runs I, II, and III.
• Figure 2: Pitch angle distributions corresponding to different energy intervals of accelerated particles, measured in Runs I, II, and III. The pitch angle is calculated in the local plasma frame, which is co-moving with the local "$E\times B$" velocity.
• Figure 3: Compressed-exponential fit to the tail of the self-similar angular distribution function, with empirically fitted parameters $\delta\approx 1.38$, $\lambda \approx 161$, and $A \approx 3.86$ (Eq. \ref{['compexp_eq']}). The argument in the angular distribution function corresponding to $20<\gamma <30$ is rescaled according to $\sin\theta\to (\sin\theta)/1.6$, to overlap with the case of the larger $\gamma$.
• Figure 4: Pitch angle distribution for particles accelerated in static fields. Particles were traced over the time interval of $c\Delta t/l=2$. The pitch angles are calculated in local plasma frames, co-moving with the local "$E\times B$" velocities. The distributions for different $\gamma$ exhibit a self-similar nature.
• Figure 5: Pitch angle distribution for particles accelerated in static fields. The curves are rescaled to overlap with the case of the lowest $\gamma$ value, according to the theoretically motivated $\sin \theta\sim 1/\gamma$ rescaling symmetry. Particles were traced over the time interval of $c\Delta t/l=2$. The pitch angles are calculated in local plasma frames, co-moving with the local "$E\times B$" velocities. Increasing deviations from theory (i.e., imperfect overlap) are present for higher $\gamma$ values.