Cascade Processes of Strong and Weak MHD Turbulence

TL;DR

The paper investigates strong and weak relativistic force-free MHD turbulence using high-resolution RMHD simulations, revealing that magnetic spectra follow $E(k) \propto k^{-5/3}$ in strong and $E(k) \propto k^{-2}$ in weak regimes, while perpendicular cascades dominate energy transfer and scale-dependent anisotropy follows $\ell_{\parallel} \propto \ell_{\perp}^{2/3}$. It shows distinct intermittency signatures, with strong turbulence exhibiting MB-like 2D-sheet structures and weak turbulence showing SL-like 1D filaments, and finds that Alfvén and fast modes share similar spectral slopes but with smaller energy in fast modes, especially as turbulence weakens. The results are applied to neutron-star magnetospheres, where the turbulent cascade luminosity $L_{\rm cas}$ can account for the Vela pulsar’s X-ray emission under strong or moderately weak turbulence ($\chi \sim 1.0$ to $0.5$), implying a key role for force-free turbulence in energy transfer and particle acceleration in extreme environments. Overall, the study advances understanding of energy cascade, magnetic-field evolution, and radiative signatures in magnetically dominated relativistic plasmas.

Abstract

On the framework of relativistic force-free magnetohydrodynamic (MHD) turbulence, we explore the fundamental properties of strong and weak turbulent cascades using high-resolution numerical simulations in the presence of a uniform background magnetic field. We find that (1) power spectra and scale-dependent anisotropies both for the strong and weak turbulence resemble those observed in the non-relativistic MHD turbulence; (2) intermittency of magnetic fields in strong turbulence is stronger than that in the weak one; (3) generated Alfvén modes show similar energy spectra and scale-dependent anisotropies to those of non-relativistic case; (4) generated fast modes present a power spectrum similar to that of Alfvén modes, with a strong (for strong turbulence) or weak (for weak turbulence) scale-dependent anisotropy, which are significantly different from non-relativistic turbulence; and (5) applications of our numerical results to neutron star magnetospheres show that the strong (or moderately weak) turbulent cascade can explain the X-ray radiation of the Vela pulsar. Our study is of great significance for understanding energy transfer, magnetic field evolution, and particle acceleration mechanisms in extreme astrophysical environments.

Figures (9)

• Figure 1: Comparison of magnetic field power spectrum with different numerical resolutions at $t \sim 5.86$ for $\chi \sim 1.0$.
• Figure 2: The time-dependent evolution of magnetic field power spectrum for the cases of $\chi \sim 1.0$ (panel (a)), 0.5 (panel (b)) and 0.25 (panel (c)).
• Figure 3: The probability distribution function of the magnetic field for $\chi \sim 1.0$ (red), 0.5 (blue), and 0.25 (orange). Gaussian fitting results with the mean value $\mu$ and standard deviation $\sigma$ are plotted as dashed lines in the corresponding colors. $\xi$ and $\zeta$ represent higher-order statistical measurements -- skewness and kurtosis, respectively.
• Figure 4: The overall (panel (a)), perpendicular (panel (b)) and parallel (panel (c)) power spectra of the magnetic field.
• Figure 5: Scale-dependent anisotropy of the magnetic field. The coordinates $\ell_{\perp}$ and $\ell_{\parallel}$ represent the perpendicular and parallel scales of the eddies along the local magnetic field, respectively. The colored lines are the corresponding linear fitting.