On collective nature of nonlinear torsional Alfv\'en waves

Abstract

Torsional Alfv\'en waves in coronal plasma loops are usually considered to be non-collective, i.e. consist of cylindrical surfaces evolving independently, which significantly complicates their detection in observations. This non-collective nature, however, can get modified in the nonlinear regime. To address this question, the propagation of nonlinear torsional Alfv\'en waves in straight magnetic flux tubes has been investigated numerically using the astrophysical MHD code Athena++ and analytically, to support numerical results, using the perturbation theory up to the second order. Numerical results have revealed that there is radially uniform induced density perturbation whose uniformity does not depend on the radial structure of the mother Alfv\'en wave. Our analysis showed that the ponderomotive force leads to the induction of the radial and axial velocity perturbations, while the mechanism for the density perturbation is provided by a non-equal elasticity of a magnetic flux tube in the radial and axial directions. The latter can be qualitatively understood by the interplay between the Alfv\'en wave perturbations, external medium, and the flux tube boundary conditions. The amplitude of these nonlinearly induced density perturbations is found to be determined by the amplitude of the Alfv\'en driver squared and the plasma parameter $\beta$. The existence of the collective and radially uniform density perturbation accompanying nonlinear torsional Alfv\'en waves could be considered as an additional observational signature of Alfv\'en waves in the upper layers of the solar atmosphere.