Polarization properties of synchrotron sources from simulations of relativistic magnetohydrodynamic turbulence

TL;DR

This work addresses how magnetic turbulence in relativistically hot plasmas shapes synchrotron polarization. It employs a GPU-accelerated 3D RMHD framework to simulate decaying turbulence across a range of magnetizations, then computes synthetic synchrotron emission and polarization for two geometric configurations of the mean field. The results reveal a robust Kolmogorov-like cascade in magnetic fluctuations, dissipation in thin current sheets with intermittency, and PD values that span the range observed in PWNe; crucially, an anisotropy-adjusted analytic PD model reproduces the simulation outcomes, connecting turbulence statistics to polarization signatures. The findings provide a practical link between microscopic turbulence properties and macroscopic polarization measurements, aiding the interpretation of IXPE and future high-energy polarimetry observations.

Abstract

The emission from the relativistically hot plasmas of high-energy astrophysical synchrotron sources, pulsar wind nebulae (PWNe) in particular, depends on the level of magnetic fluctuations. Recent observations by the X-ray polarimeter IXPE support the presence of turbulence, with varying conditions even in different regions of a same source. We model such emission, and in particular the degree of linear polarization, by using 3D relativistic magnetohydrodynamic (MHD) turbulence simulations for the first time. Thanks to a novel accelerated version of the ECHO code, a series of 3D relativistic MHD simulations were performed assuming a relativistically hot plasma and various degrees of magnetization, mimicking different conditions encountered in synchrotron sources. Magnetic fluctuations at random directions with respect to a background field were initialized at large scales. After the full development of the turbulent cascade, the statistical properties of the plasma and of the synchrotron emission maps were analyzed. Turbulence rapidly relaxes to a sort of Alfvénic equilibrium and a Kolmogorov cascade with a slope of $-5/3$ soon develops, with differences depending on the initial ratio, $η$, of magnetic fluctuations over the background field. Dissipation mostly occurs in thin current sheets, where (numerical) reconnection takes place and intermittency and deviation from isotropic Gaussian distributions are observed. Synthetic synchrotron maps and their statistical properties depend on $η$ too, approaching analytical estimates for large $η$. The integrated degree of linear polarization is found to cover the whole range of observed values in PWNe, and its dependence on the relative amplitude of turbulent fluctuations shows a good agreement with analytical estimates, even in the presence of anisotropy.

Figures (11)

• Figure 1: Typical output of relativistic MHD turbulence simulations obtained with the novel version of the ECHO code. Here we refer to the case described in DelZanna2024 (2D run at the resolution of $4096^2$), and we display the module of $\nabla\times\bm{B}$ parallel to the mean field.
• Figure 2: Time sequences of rms quantities for a selection of four runs, choosing a varying $\sigma_0$ while keeping $\sigma_1=0.1$ fixed. In the upper panels we show the total current density, $J=|\nabla\times\bm{B}|$, $J_\parallel$ (along $\bm{B}_0$), and $J_\perp$, whereas in the bottom ones we plot $B/\sqrt{\mathcal{E}_0}$, basically the Alfvén speed, and $v$, again total, parallel, and perpendicular components, adopting the same notations.
• Figure 3: Omnidirectional, compensated spectra of magnetic (red) and kinetic (green) energies, for the $\texttt{R08}$ run and several output times.
• Figure 4: Omnidirectional spectra, compensated by $k^{5/3}$, of magnetic (red) and kinetic (green) energies, with total (solid), parallel (dashed), and perpendicular (dotted) components. In the left panel, we show spectra for the $\texttt{R02}$ run at $t=40$, while the case $\texttt{R11}$ at $t=10$ is shown in the right panel (both times are after the peak of turbulence, see the corresponding blue curves in Fig. \ref{['fig:rms']}. Horizontal black lines indicate a $k^{-5/3}$ slope, while the kinetic spectra for $\texttt{R11}$ are better fit by a $k^{-4/3}$ slope.
• Figure 5: Statistical properties of turbulence for the same runs and output times of Fig. \ref{['fig:spectra']}. In the top panels, we plot the PDF of $\delta_x B_y$ for three different spatial separations, $l=2\pi/k$. In the bottom panels, the kurtosis, $\mathcal{K}$, is plotted against the separation scale, $l$, for$\delta_i B_y$, with $i=1,2,3$.