Aims. 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. Methods. 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. Results. 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.
Zanna et al. (Fri,) studied this question.