Pulse-driven non-linear Alfvén waves and their role in the spectral line broadening

Abstract

We study the impulsively generated non-linear Alfv\'en waves in the solar atmosphere, and describe their most likely role in the observed non-thermal broadening of some spectral lines in solar coronal holes. We solve numerically the time-dependent magnetohydrodynamic equations to find temporal signatures of large-amplitude Alfv\'en waves in the model atmosphere of open and expanding magnetic field configuration, with a realistic temperature distribution. We calculate the temporally and spatially averaged, instantaneous transversal velocity of non-linear Alfv\'en waves at different heights of the model atmosphere, and estimate its contribution to the unresolved non-thermal motions caused by the waves. We find that the pulse-driven nonlinear Alfv\'en waves with the amplitude $A_{\rm v}$=50 km s$^{-1}$ are the most likely candidates for the non-thermal broadening of Si VIII $\lambda$1445.75 \AA\ line profiles in the polar coronal hole as reported by Banerjee et al. (1998). We also demonstrate that the Alfv\'en waves driven by comparatively smaller velocity pulse with its amplitude $A_{\rm v}$=25 km s$^{-1}$ may contribute to the spectral line width of the same line at various heights in coronal hole without any significant broadening. The main conclusion of this paper is that non-linear Alfv\'en waves excited impulsively in the lower solar atmosphere are responsible for the observed spectral line broadening in polar coronal holes. This is an important result as it allows us to conclude that such large amplitude and pulse-driven Alfv\'en waves do indeed exist in solar coronal holes. The existence of these waves and their undamped growth may impart the required momentum to accelerate the solar wind.