Analysing Turbulent Energy Cascade in a Coronal Mass Ejection using Empirical Mode Decomposition

Abstract

Coronal mass ejections (CMEs) are large-scale expulsions of plasma and magnetic flux from the Sun's corona into the heliosphere. In interplanetary space they are referred to as interplanetary CMEs (ICMEs), often characterised by a shock, a sheath, and in some cases a magnetic cloud, and are capable of triggering geomagnetic storms. We apply empirical mode decomposition (EMD) in conjunction with Hilbert spectral analysis (HSA) to investigate turbulence characteristics at different stages of an ICME event observed on 27 June 2013 by the MAG instrument onboard NASA's ACE spacecraft. The event is divided into four regions: (i) preceding solar wind, (ii) sheath, (iii) magnetic cloud, and (iv) trailing solar wind. The magnetic field components (Bx, By, Bz) are decomposed into intrinsic mode functions using EMD, and instantaneous frequencies and amplitudes are derived via HSA. Spectral slopes in the inertial range are calculated from the second-order marginal Hilbert spectra. The preceding solar wind shows a slope near the Kolmogorov value (α_HHT \approx -1.68), indicating fully developed turbulence at 1 AU. Clear steepening is observed in the sheath and trailing solar wind (α_HHT \approx -1.78 and -1.79), consistent with enhanced intermittency and non-linear activity from shock compression and solar wind-ICME interactions. Within the magnetic cloud the exponent is slightly less steep (α_HHT \approx -1.71), suggesting the effects driving steepening are less prevalent inside the flux rope. ICME passage thus modifies the turbulent energy distribution across scales, and the EMD-HSA method provides smoother and more stable spectral estimates than conventional Fourier approach.

Figures (6)

• Figure 1: Magnetic field data recorded by NASA's MAG instrument onboard ACE. The subplots represent the signal for the field magnitude $|B|$ and the component vectors $B_{x}$, $B_{y}$, and $B_{z}$ in the GSE coordinate system. The red vertical line denotes the shock arrival resulting in the ICME sheath indicated by the orange-shaded region. This is followed by the MC, shown as violet-shaded region. The onset of the sheath and the end of the MC spans the entire ICME event.
• Figure 2: IMFs obtained for the magnetic field components $B_{x}$, $B_{y}$, and $B_{z}$ for the ICME sheath. The y-axis represents the magnitude (nT) and the x-axis denotes the time duration of the interval.
• Figure 3: Instantaneous frequency distribution for each IMF for all the magnetic field components ($B_{x}$, $B_{y}$ and $B_{z}$), across different ICME regions. The instantaneous frequencies are binned into 2160 equally spaced logarithmic bins ranging from 0 to 0.5 Hz. Each IMF order is represented by a distinct colour to enhance clarity and differentiation.
• Figure 4: Hilbert spectra for magnetic field components across different ICME regions. From left to right: regions corresponding to the preceding solar wind, sheath, magnetic cloud and trailing solar wind. From top to bottom: magnetic field components for $B_{x}$, $B_{y}$, and $B_{z}$. The y-axis is represented on the logarithmic scale up to 0.032 Hz to visually emphasise the contribution of the dominating low frequencies.
• Figure 5: Marginal Hilbert spectra for each IMF representing the total amplitude contribution across the frequency domain. Each IMF order is depicted using a distinct colour for clarity. The black curve in each subplot represents the total marginal spectrum obtained by summing the marginal spectra of each IMF order. The vertical magenta and green dashed lines mark the spacecraft gyrofrequency and proton gyrofrequency, respectively.