Angular Dependence of Magnetosonic and Alfvén Wave Speeds in a Stratified Solar Atmosphere

This study quantitatively examines the angular dependence of the squared phase speed ratios () for fast and slow magnetosonic waves in a highly gravitationally stratified solar atmosphere. The methodology employed the fundamental MHD governing equations (continuity, momentum, and energy), where the complex, non-linear system was simplified through normalization and subsequent linearization to derive the characteristic dispersion relation, which was then solved numerically using Python. Results for the Fast Magnetosonic Wave (FMSW) show near-unity ratios () at parallel propagation in the lower, denser layers (photosphere/chromosphere), but a dramatic, multi-order suppression of the ratio in the upper atmosphere. This suppression is a direct result of the increasing Alfvén speed () due to decreasing mass density, confirming that FMSW phase speed becomes negligible relative to the background magnetic dynamics in the corona. The most significant finding concerns the Slow Magnetosonic Wave (SMSW), which exhibited large-magnitude negative values for across wide oblique angles in the photosphere and chromosphere (e.g., as low as  at ). The negative confirms that SMSW is predominantly evanescent or strongly damped in the lower atmosphere, suggesting that gravitational stratification effectively prevents this mode from efficiently transporting acoustic energy into the corona. These findings reinforce the crucial role of Alfvén waves as the dominant energy carriers in the upper solar atmosphere and offer new, highly anisotropic diagnostic ratios for solar magneto-seismology, critical for modeling energy flux and improving geomagnetic storm forecasting.