Fast Magnetoacoustic Wave Behavior with Gravitationally Stratified, Magnetically Inhomogeneous Media

TL;DR

This study addresses how fast magnetoacoustic waves propagate near a magnetic null point in a gravitationally stratified, magnetically inhomogeneous medium. It combines high-resolution Lare2D MHD simulations with a semi-analytical WKB ray-tracing approach to solve the linear, low-$\beta$ MHD equations around a 2D X-point, incorporating a stratified density $\rho_0(y)=e^{-C(y+2)}$ and a stratification parameter $C$ that sets the Alfvén-speed gradient. The key finding is that gravitational stratification breaks vertical symmetry in the equilibrium Alfvén speed, producing strong refraction, caustics, and wavefront cusps that depend on which boundary is driven (lower, upper, or left). The results demonstrate that stratification-induced $v_A$ gradients and saddle points govern whether fast waves wrap around the null, form cusps via caustics, or become trapped, with WKB solutions in excellent agreement with the full numerical simulations. These insights enhance understanding of wave–null interactions in the solar corona and offer a framework for interpreting observations, while indicating directions for future work including nonlinear effects and fully 3D topologies.

Abstract

The nature of MHD waves within inhomogeneous media is fundamental to understanding and interpreting wave behavior in the solar atmosphere. We investigate fast magnetoacoustic wave behavior within gravitationally stratified, magnetically inhomogeneous media, by studying a magnetic environment containing a simple 2D X-type magnetic null point. The addition of gravitational stratification fundamentally changes the nature of the system, including breaking the symmetry. There are two main governing effects: the stratified density profile acts in combination with the inhomogeneous magnetic field, creating a large gradient in the Alfven speed and hence a system replete with refraction. The system is investigated using both numerical simulations and a semianalytical WKB solution (via Charpit's method and a fourth-order Runge-Kutta solver) and we find strong agreement between both. The results show a fundamental difference between the stratification-free and stratified cases, including the formation of caustic surfaces and cusps, and we contextualize these results in the theoretical understanding of fast magnetoacoustic waves.

Figures (12)

• Figure 1: The equilibrium magnetic field, with arrows indicating the direction of the magnetic field along the separatrices.
• Figure 2: Contours of the Alfvén speed for a range of $C$ values, with a logarithmic color scale. Separatrices of the equilibrium magnetic field are overplotted in white. The magnetic null point is located at $\left[0,0\right]$.
• Figure 3: 3D surfaces of $\text{log}\left(\text{v}_A\right)$, with a), b), c), and d) corresponding to the profiles in §\ref{['subsec:stratfree']}, §\ref{['subsec:c1']} (driving lower boundary, $C=1$), §\ref{['sec:upper']} (driving upper boundary, $C=1$) and §\ref{['sec:left']} (driving left boundary, $C=1$) respectively. Table \ref{['tab:Drivers']} details the domain boundaries. In each simulation, the magnetic null point is located at $\left[0,0 \right]$.
• Figure 4: Contours of $\text{v}_\perp$ at six different times, with WKB solutions for the front and trailing edge of the wave overplotted as black lines, and separatrices of the equilibrium magnetic field are overplotted as straight black lines. In this case, the lower boundary is driven and there is no gravitational stratification.
• Figure 5: Contours of $\text{v}_\perp$ at six different times, with WKB solutions for the front, middle, and trailing edges of the wave overplotted as black lines, and separatrices of the equilibrium magnetic field are overplotted as straight black lines. In this case, the lower boundary is driven and there is gravitational stratification.