The effect of plasma expansion on the dispersion properties of MHD waves

TL;DR

This paper theoretically investigates how radial solar wind expansion affects the dispersion properties of linear MHD waves, revealing a decrease in wave frequencies with distance and the influence of polytropic index models on wave behavior.

Contribution

It introduces an analytical approach within the Expanding Box Model to characterize the impact of solar wind expansion on MHD wave dispersion relations, including effects of different polytropic index models.

Findings

Wave frequencies decrease with increasing heliocentric distance.

Fast magnetosonic mode is significantly affected by the polytropic index.

Expansion can accelerate the fast magnetosonic mode in the outer heliosphere.

Abstract

In this work, we employ the set of ideal expanding magnetohydrodynamic (MHD) equations within the Expanding Box Model (EBM) framework to theoretically characterize the effects of radial solar wind expansion on its characteristic linear MHD waves. Through the analytical derivation of dispersion relations by a first-order expansion of the MHD-EBM equations, we explore the changes in wave propagation across a range of heliocentric distances on the linear magnetohydrodynamic modes: the Alfv\'en mode and the fast and slow magnetosonic modes, as obtained from the ideal MHD-EBM equations. Our findings reveal a spatial dependence in the derived dispersion relations that aligns with both the literature and the traditional ideal MHD case in the non-expanding limit, thereby helping to bridge the gap between theory and observation in solar wind dynamics. We observe a general decrease in wave frequencies as the plasma expands farther from the Sun. This decrease is reflected in the dispersion relations through the radial decrease of both the Alfv\'en and sound speeds, which decrease proportionally to $1/R$ and $1/R^{\gamma - 1}$, respectively, where $\gamma$ is the plasma polytropic index. The fast magnetosonic mode frequency and phase speed are significantly affected by the polytropic index value. We consider three models for the polytropic index evolution in the expanding solar wind: a constant (quasi-adiabatic) case, a radially decreasing profile in the outer heliosphere, and a model incorporating thermodynamic heating effects. Notably, we find that in the case of a decreasing polytropic index, the fast magnetosonic mode experiences an acceleration in the distant heliosphere, highlighting the significant influence of expansion on solar wind dynamics.