Validity of using Elsasser variables to study the interaction of compressible solar wind fluctuations with a coronal mass ejection

Context. Alfvenic fluctuations, as modelled by the non-linear interactions of Alfven waves of various scales, are seen to dominate solar wind turbulence. However, there is also a non-negligible component of non-Alfvenic fluctuations. The Elsasser formalism, which is central to the study of Alfvenic turbulence due to its ability to differentiate between parallel and anti-parallel Alfven waves, cannot strictly separate wavemodes in the presence of compressive magnetoacoustic waves. In this study, we analyse the deviations generated in the Elsasser formalism as density fluctuations are naturally generated through the propagation of a linearly polarised Alfven wave. The study was performed in the context of a coronal mass ejection (CME) propagating through the solar wind, which enables the creation of two solar wind regimes, pristine wind and a shocked CME sheath, where the Elsasser formalism can be evaluated. Aims. We studied the deviations of the Elsasser formalism in separating parallel and anti-parallel components of Alfvenic solar wind perturbations generated by small-amplitude density fluctuations. Subsequently, we evaluated how the deviations cause a misinterpretation of the composition of waves through the parameters of cross helicity and reflection coefficient. Methods. We used an ideal 2.5D magnetohydrodynamic model with an adiabatic equation of state. An Alfven pump wave was injected into the quiet solar wind by perturbing the transverse magnetic field and velocity components. This wave subsequently generates density fluctuations through the ponderomotive force. A CME was injected by inserting a flux-rope modelled as a magnetic island into the quasi-steady solar wind. Results. The presence of density perturbations creates a approximate to 10% deviation in the Elsasser variables and reflection coefficient for the Alfven waves as well as a deviation of approximate to 0.1 in the cross helicity in regions containing both parallel and anti-parallel fluctuations.