Signatures of Damping Nonlinear Oscillations by KHI-induced Turbulence in Synthetic Observations

TL;DR

The paper investigates observational signatures of nonlinear damping of large-amplitude transverse (kink) oscillations in solar coronal loops driven by Kelvin-Helmholtz instability (KHI)–induced turbulence. It extends a turbulence-damping framework by performing 3D MHD simulations across parameter ranges and applying FoMo forward modelling to generate synthetic EUV observations in multiple AIA channels, revealing time-varying damping, frequency drift, and excitation of higher-order modes. Bayesian analysis shows robust constraints on the initial displacement and kink period, but strong degeneracy among damping-related parameters ($C_1/R$, $ ho_T$, and $ frac{ ho_T- ho_e}{ ho_i- ho_e}$) necessitating additional observables for reliable seismology. The forward-modeled images demonstrate channel- and LoS-dependent damping and width variations, with higher spatial resolution required to resolve KHI structures, providing a quantitative basis for identifying nonlinear damping and KHI turbulence in transverse loop oscillations.

Abstract

Large-amplitude decaying kink oscillations of coronal loops are strongly influenced by nonlinear processes, such as Kelvin-Helmholtz instability (KHI) and turbulence, though comprehensive theory and observational confirmation remain limited. Building on the recently developed theory on nonlinear damping by KHI-induced turbulence in impulsively driven transverse loop oscillations, we investigate its observational signatures using 3D magnetohydrodynamic simulations and forward-modelled EUV images. The simulated oscillations exhibit time-varying frequency shifts and damping rates, which are broadly consistent with nonlinear turbulence-damping theory. Additionally, they exhibit excitation of higher-order modes, slightly increased periods relative to the linear kink period, and reduced displacement amplitudes. These features are generally preserved in synthetic observations, though resolving higher-order modes requires higher spatial resolution than currently available. For loops embedded in a hotter background, hotter channels (e.g., 193 Angstroms) are more sensitive to boundary dynamics, thus their oscillations decay faster with smaller displacements and larger phase shifts than those in cooler channels (e.g., 171 Angstroms). Comparisons of simulated and synthetic oscillations show close agreement at the early stage. At later times, synthetic oscillations exhibit smaller displacements and larger phase shifts, due to turbulence-induced asymmetry in the loop cross-section. Bayesian fitting shows that the initial oscillation amplitude and kink period are robustly constrained, whereas parameters controlling the damping profile are degenerate, indicating that additional observables would aid reliable seismological inference. These results provide a quantitative basis for identifying nonlinear damping and detecting KHI-driven turbulence in transverse loop oscillations.

Figures (13)

• Figure 1: The loop in the 3-dimensional (3D) simulation domain $[x,y,z]$ (purple box) and FoMo setting (the whole box, resulting from mirroring the simulation box in the $y$-direction). The loop is set to have a higher density ($\rho_i$, in blue colour) than the surroundings ($\rho_e=1$). The blue arrow indicates the transverse oscillation direction. The dashed rectangle outlines the slice of emissivity across the loop's cross-section. The orange arrows indicate the LoS directions, with their length indicating the integration path to calculate the emission. The $\theta$ denotes the LoS angle with respect to the $y$-axis.
• Figure 2: Transverse profile of density, pressure, temperature and synthetic emissivity in AIA EUV channels across the loop with different density contrasts when the turbulent layer reaches a height of 0.8$R$. Left: average transverse density (black), pressure (blue) and temperature (red) across the loop. The solid curves represent the case with $T_i/T_e=1/2$ while the dashed curves with $P_i/P_e=3/2$. Middle: contribution function $G(n_{e},T)$ in 131 Å, 171 Å, 193 Å, and 211 Å of AIA, overlaid with the corresponding loop transverse profile determined by density and temperature on the left column. Right: transverse emissivity across the loop in four channels of AIA. The dotted vertical lines from left to right indicate the location of the upper limit of the turbulent layer, defined by the density threshold $\rho_T=0.9\rho_i$, and where two channels have equal emissivity, respectively. These lines are duplicated in the left panels for reference.
• Figure 3: Amplitude-dependent oscillation period deviation from the linear kink period $\rm P_{\rm k}$ (a--c) and amplitude discrepancy (d) measured in simulation data. The dotted curves are a standard stationary sine wave for reference. (a--b): Time series of displacement amplitude $\xi_{\rho\geq0.9\rho_i}$ measured in two sets of simulations: $T_i/T_e=1/2$ (a) and $P_i/P_e=3/2$ (b). (c): The ratio of measured base period ($\rm P$) and linear kink period ($\rm P_{\rm k}$) as a function of nonlinearity parameter. Different colours indicate different density contrasts ($\zeta$). The filled symbols indicate data measured from the high-resolution simulations, otherwise from low-resolution simulations taken from 2025ApJ...991..208Z. (d): The comparison of centre-of-mass velocity $V_{\rm CoM,~{\rho\geq0.9\rho_i}}$ measured in simulation (solid) and in theory (dotted) for the case of $\rho_i=3$ shows the former has a lower amplitude than expected. The theoretical curves are computed using our turbulence-damping theory (Eq.12 of 2025ApJ...991..208Z) with input parameter values measured in the simulations.
• Figure 4: Corner plot showing the posterior distributions of the parameters in the nonlinear model (Eq.\ref{['eq:com_fit']}). The diagonal panels display the posterior distributions for individual parameters, with the black vertical lines marking the best-fitted values. The panels below the diagonal show the joint posterior distributions, highlighting correlations between parameter pairs. The data are obtained via MCMC sampling for the case $\zeta=3,T_i/T_e=0.5,V_0=0.15$ with full time series. Elongated contours indicate strong correlations, while circular or rectangular contours suggest weak or no correlation. The unit of ${\rm P_k}$ ('' ut'') is the unit time of simulation.
• Figure 5: Synthetic image of the cross-section of the loop apex in 171 Å channel and transverse intensity profile in different LoS at different spatial resolutions to show the existence of high-order modes ($m\geq2$) generated by nonlinearity. First row (a--d): synthetic data in original simulation resolution. The dotted circle indicate the initial loop's cross-section. The profiles are extracted at three time frames: initial (t0), the first oscillation crest (t1) and the second crest (t2). The dotted curves are the intensity profile in corresponding colours shifted back to the initial location for comparison. Second row (e--h): similar to (a--d), but are degraded into AIA resolution. Deformation of the loop cross-section, manifested as the loop width variation, is invisible in low resolution. Third rows (i--m): The effect of velocity perturbation at t1 in different resolutions, from original, AIA (440 km/pixel), 200 km/pixel to 120 km/pixel. The transverse intensity is normalised (denoted by "N.I.") for comparison.