Abstract
Context. Magnetohydrodynamic (MHD) waves play an important role in the dynamics and heating of the solar corona. Their investigation also reveals information about the local conditions. Transverse (Alfvénic) oscillations of loops commonly occur in response to solar eruptions. It has been shown that these oscillations elicit an acoustic response through wave coupling at the footpoint and the pondermotive force. Aims. We extend the modelling of wave coupling between a transverse loop oscillation and slow magnetoacoustic waves through line-tied footpoint boundary conditions by considering the effect of transverse loop structuring and non-linearity. Methods. We combine analytical wave modelling with fully non-linear MHD simulations to study the wave field of propagating slow waves in a two-dimensional slab loop (arcade) model. Results. We demonstrate that transverse loop oscillations generate propagating slow waves from the footpoints with the same periodicity but shorter wavelength determined by the local sound speed. The degree of wave coupling is proportional to the square root of the plasma-β. The slow wave field is anti-symmetric in the direction of transverse wave polarisation. We show through synthetic diagnostics that this has important consequences for their observability in terms of the orientation of the loop with respect to the observer. We also show that for the interpretation of intensity oscillations associated with typical loop oscillations the ponderomotive response also needs to be taken into account. The modelling presented here allows for the successful identification of the slow waves and pondermotive response in a previous observational study.
Highlights
In the last few decades, with the development of high spatial resolution telescopes in the extreme ultraviolet and x-ray regime, we have been able to resolve a variety of magnetohydrodynamic (MHD) waves in structures in the solar corona (De Moortel & Nakariakov 2012; Liu & Ofman 2014; Roberts 2019)
Terradas et al (2011) presented a possible explanation for observations of intensity variations that accompany Alfvénic loop oscillations, in terms of linear coupling between Alfvénic and slow magnetoacoustic waves at the loop footpoints. They had modelled this in a uniform plasma using linear wave theory
We have extended the modelling of this coupling by the use of fully non-linear MHD simulations and the inclusion of the effect of transverse structuring which is a common feature for Alfvénic loop oscillations
Summary
In the last few decades, with the development of high spatial resolution telescopes in the extreme ultraviolet and x-ray regime, we have been able to resolve a variety of magnetohydrodynamic (MHD) waves in structures in the solar corona (De Moortel & Nakariakov 2012; Liu & Ofman 2014; Roberts 2019). Verwichte: Acoustic response to transverse oscillations in a solar coronal loop where B, ρ and p are the perturbed magnetic field, density and plasma pressure, and with ⊥ and directions perpendicular and parallel to the loop respectively These quantities may be eliminated in favour of the displacement. The profile f (x) tends to zero in the limit of |x| going to infinity and is symmetric around x = 0 (provided the equilibrium is symmetric) It is well-known that besides the linear footpoint coupling (Terradas et al 2011), a transverse wave can excite longitudinal dynamics through the non-linear ponderomotive force (e.g., Hollweg 1971; Verwichte et al 1999; Terradas & Ofman 2004).
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