Stability and wave dynamics in polytropic Eddington-inspired Born-Infeld gravitating solar plasmas

Abstract

We investigate the influence of nonlinear gravity corrections, arising from the Eddington-inspired Born-Infeld (EiBI) theory on wave dynamics, stability, and energy transport processes in polytropic, viscous, and turbulent solar plasmas. Analytical and numerical analyses of the Jeans-normalized quadratic dispersion relation demonstrate that both the EiBI gravity parameter $(χ)$ and the relative polytropic sound speed $(β)$ independently regulate oscillation frequencies, growth rates, phase velocities, perturbation energy partitioning, and outward acoustic energy flux. Positive $χ$ systematically elevates oscillation frequencies, phase velocities, and outward energy flux level by $\sim$10% relative to the Newtonian predictions, while larger $β$ enhances them by up to 55%, thereby promoting wave propagation and efficient acoustic transport. Conversely, negative $χ$ strengthens gravitational binding and increases damping rates by $\sim$40%, particularly for the \textit{g}-modes. Energy partitioning analyses reveal that the EiBI corrections fundamentally restructure the kinetic-electrostatic-gravitational energy balance. While the Newtonian gravity contributes negligibly ($<$4%), nonzero $χ$ channels up to one-third of oscillation energy into gravitational modes. The modal surface flux calculations further confirm that only the \textit{p}-modes drive outward energy transport (amplification for $χ>0$, suppression for $χ<0$). A direct comparative analysis with four years of SDO/HMI Doppler velocity observations demonstrate a robust theoretical agreement for $χ=3\times10^7$ m$^5$kg$^{-1}$s$^{-2}$, providing the first empirical constraint on the solar EiBI gravity through helioseismology. The findings offer a rigorous framework for advancing our understanding about solar plasma stability, helioseismic signatures, and ambient atmospheric energy transport processes.

Figures (16)

• Figure 1: Profile of the EiBI gravity--modified solar self-gravitational potential $(\psi)$ as a function of re-scaled distance $(r/R_\odot)$ and EiBI gravity parameter $(\chi)$.
• Figure 2: Two roots of the Jeans-normalized composite frequency $(\Omega)$ as a function of the Jeans-normalized wavenumber $(K)$. The EiBI gravity parameter is fixed at $\chi=3\times10^7$ m$^5$ kg$^{-1}$ s$^{-2}$, and the relative polytropic sound speed is set to $\beta=\Gamma$.
• Figure 3: Variation of the discriminant $(D)$ as a function of Jeans-normalized angular wavenumber $(K)$ for different values of the EiBI gravity parameter $(\chi)$ and the relative polytropic sound speed $(\beta)$. Here, $\chi$ is expressed in SI units.
• Figure 4: Profiles of the Jeans-normalized oscillation frequency $(\Omega_r)$ and the growth rate $(\Omega_i)$ as functions of the Jeans-normalized angular wavenumber $(K)$ and radial distance $(\xi)$. The EiBI gravity parameter is fixed at $\chi=3\times10^7$ m$^5$ kg$^{-1}$ s$^{-2}$, and the relative polytropic sound speed is set to $\beta=\Gamma$.
• Figure 5: Profiles of the Jeans-normalized oscillation frequency $(\Omega_r)$ and the growth rate $(\Omega_i)$ as functions of the Jeans-normalized angular wavenumber $(K)$ for different representative values of the EiBI gravity parameter $(\chi)$ in SI units. The relative polytropic sound speed is fixed at $\beta=\Gamma$.