Numerical simulations of waves and turbulence in coronal loops: Observables and spectra

Context. Coronal loops are often regarded as the building blocks of the solar corona; however, the heating mechanism and complex dynamics resulting from the turbulent nature of the plasma and the presence of waves are still unclear. Aims. We numerically investigated the time evolution of velocity and magnetic field fluctuations in a coronal loop, focusing on the dynamics due to both phase mixing and turbulent cascades. We synthesized the intensity, Doppler velocity, and nonthermal broadening from numerical results to assess whether the upcoming Multi-slit Solar Explorer (MUSE) mission can reveal the presence of those phenomena in the solar corona through its unprecedented high-resolution spectroscopic observations. Methods. We studied the time evolution of velocity and magnetic field fluctuations in coronal loops using numerical 3D magnetohydrodynamics (MHD) simulations. The loop is represented by a cylindrical, pressure-balanced magnetic structure with a transverse density and magnetic field inhomogeneity. The initial perturbation is a superposition of a torsional Alfv & eacute;n wave and a transverse turbulent component with different, tunable weights. We included heating effects due to viscous and resistive dissipation. To reconstruct plasma emission features, we calculated moments of the Fe IX 171 & Aring; spectral line, synthesized from the simulations. We calculated 2D maps obtained by integrating the emission along the assumed line of sight for the emission intensity I-0, the Doppler shift I-1, and the nonthermal broadening I-2 as functions of time for several values of the model parameters. Finally, we simulated the MUSE spectrograph by considering a resolution of 312 km & times; 312 km. Results. We observe that intensity maps show the formation of longitudinal threads during the time evolution. The generation of small-scale fluctuations takes place mainly in the inhomogeneity region at the loop boundary, where the effects of phase mixing and nonthermal broadening are stronger. In these regions the presence of transverse oscillations is clearly visible in I-1 and I-2 maps. We calculated 1D power spectra of intensity and Doppler shift maps and compared them with the corresponding spectra of density and the line-of-sight velocity component. At large spatial scales (i.e., between 300 km and 3000 km) the spectral indexes of density and intensity spectra are very similar, while the spectrum of I-1 is steeper. Conclusions. We discuss these results in the context of forward modeling of observations of fluctuation dynamics in coronal loops, in particular with the MUSE spectrograph. The resolution attained by MUSE will allow us to obtain power spectra of coronal loops with a resolution never achieved before. The agreement observed between the spectral indices of the intensity power spectra at MUSE resolution and those computed from the full 3D density field indicates that the spectra of I0 can be used to infer information about the spectra of density fluctuations inside a loop.