Credit: Puzzoni et al. 2026 (submitted)

Sub-sonic compressible magnetohydrodynamic turbulence I. Alfvénic and fast-magnetosonic injection, amplitude dependence, and compressibility effects

The dependence of magnetohydrodynamic (MHD) turbulence on key physical parameters at injection scales remains an open question. This has relevant implications in various astrophysical contexts, in particular for cosmic-ray (CR) transport in the Galaxy. We investigate how properties of sub-sonic compressible MHD turbulence that are relevant for cosmic-ray transport are affected by the nature and amplitude of initial fluctuations, and by the plasma compressibility (via the β parameter, i.e., the ratio between the thermal and magnetic pressure). Particular attention is devoted to assess the role of fast-magnetosonic versus Alfvénic fluctuations. We perform 3D simulations of decaying compressible ideal-MHD turbulence at 1024³ resolution with the PLUTO code. The level of density fluctuations δρrms/ρ0 in fully developed turbulence is insensitive to whether this state is reached starting from Alfvénic or fast-magnetosonic perturbations, being only determined by the initial fluctuation amplitude and plasma β. Fast-magnetosonic injection is indeed characterized by an early phase of rapid shock dissipation, followed by a turbulence dominated decay with a rate comparable to that of the Alfvénic case. In addition, the contribution of fast-magnetosonic fluctuations to the total energy budget in fully developed turbulence remains relevant (∼30-50%) only when the initial injection consists exclusively of fast modes, while becoming negligible (≲10%) for other types of injection. Large-amplitude turbulence (δB/B0 > 1) is characterized by a nearly isotropic Kolmogorov (∝ k⁻⁵ᐟ³) or Iroshnikov-Kraichnan (∝ k⁻³ᐟ²) spectrum for Alfvénic or fast-magnetosonic injection, respectively. However, Alfvénic turbulence with δB/B0∼1 already develops a small degree of anisotropy with ∝ k⊥⁻³ᐟ² and ∝ kz⁻⁵ᐟ³ power-law spectra. At low amplitudes (δB/B0 ≪1), both initial Alfvénic and mixed-wave perturbations lead to strongly anisotropic turbulence with a perpendicular spectrum ∝ k⊥⁻⁵ᐟ³ and a parallel spectrum roughly ∝ k⁻²  (becoming significantly steeper at β ≫1), while initializing only fast-magnetosonic perturbations produces a turbulent state populated by (weak) shocks and characterized by a nearly isotropic k⁻² spectrum. The statistics of magnetic-field curvature K∥ = |( b·∇)b| and of magnetic-mirror structures (quantified through a “mirroring curvature” KM = |b·∇ ln B|) is strongly sensitive to the initial fluctuation amplitude and to the plasma β, exhibiting broader distributions and harder (i.e., shallower) power laws as either parameter increases. The predicted PDF(K∥) ∝K∥⁻²·⁵ power-law scaling emerges only in the large-amplitude regime and at low plasma compressibility (i.e., high β). This work highlights that features of sub-sonic compressible MHD turbulence that may affect CR transport are sensitive to large-scale conditions and to the plasma β. Their effect on CR diffusion and field-line random walk is the object of Paper II.

Credit: Puzzoni et al. 2026 (submitted)