Analysis of Solar Surface Oscillations and Energy Transport with Bispectral Electronic Thermostatistics

Abstract The ubiquitous 5 minute solar p -mode oscillations, excited at the photosphere, play a crucial role in driving various coronal instabilities and mediating upward energy transport. These modes are strongly influenced by nonthermal electron populations. To investigate this, we employ a double-spectral electronic thermostatistical framework—the generalized ( r , q )-distribution—to analyze the oscillation dynamics, growth behavior, and mechanical energy transport properties of longitudinal helioseismic modes at the photosphere. A local linear perturbative analysis, applied to inhomogeneous, viscous, turbulent, and nonthermal solar plasmas, yields a cubic eigenmode equation (dispersion relation) capturing diverse signatures of collective global modes. We examine the influence of nonthermality indices, electron temperature, and ion dynamic viscosity on dispersion and mode stability. Numerical analysis of the coupled dynamics of low-energy (thermal) and high-energy (suprathermal) electrons reveals their significant impact on solar surface oscillations. Notably, the nonthermality spectral indices r and q play mode-accelerating roles, counteracting damping from temperature and viscosity. Our results suggest that the high-frequency (short-period) p -modes can carry energy fluxes exceeding 10 6 W m −2 near the lower photosphere—energizing the chromosphere and quiet corona—thereby potentially influencing the excitation of spicules, microspicules, and coronal loop oscillations. In contrast, the low-frequency (long-period) g -modes have no such active influences on coronal heating. A hybrid power-law decay formalism is developed to model the attenuation of p -mode energy flux with height and is quantitatively fitted to Solar Dynamics Observatory/Helioseismic and Magnetic Imager Doppler velocity observations. Complementary 2D simulations further elucidate the spatiotemporal evolution of vertical energy flux, shaped by the nonthermal electron distribution.