Effects of Temperature Gradients on Generation of Solar Acoustic Wave Energy Spectra and Fluxes

Abstract

The general formula for the acoustic wave energy flux derived for sound generation in non-isothermal turbulent fluids by Routh and Musielak (2025, Fluids 10, 156) is applied, for the first time quantitatively, to the superadiabatic layer of the solar convection zone, using thermodynamic profiles from a standard solar model and an eddy-time correlation function calibrated against three-dimensional (3D) solar convection simulations. Three main results are obtained. First, an exact, closure-independent relation is derived for vertically propagating waves, \(F_{m}/F_{q} = 9\,\Omega _{0}^{4}/(\omega ^{2}-\Omega _{0}^{2})^{2}\), where \(F_{m}\) and \(F_{q}\) are the monopole and quadrupole contributions to the acoustic wave energy flux, \(\omega \) is the angular wave frequency, and \(\Omega _{0}\) is the acoustic cutoff frequency of the stratified background medium. This relation is valid for any turbulence spectrum and temporal correlation function; it shows that the temperature-gradient monopole source dominates over the classical Lighthill quadrupole only in a narrow band just above \(\Omega _{0}\). Second, the dipole source term \(F_{d}\) produces a net negative correction to the emitted flux (\(-8\%\) to \(-11\%\)): the temperature gradient partially suppresses, rather than enhances, the emission through this term. Third, the non-isothermal corrections are strongly band-selective: the frequency-integrated total flux changes by only a few percent, but the flux in the chromospherically relevant \(0\,\text{--}\,20\text{ mHz}\) band is enhanced by \(\approx 15\%\) (with the monopole alone contributing \(+26\%\)), precisely the part of the spectrum available for chromospheric heating. The classical quadrupole mechanism remains dominant throughout the source layer, the total fluxes (\(5.5\,\text{--}\,6.6\times 10^{7}\) erg cm⁻² s⁻¹) agree with the classical benchmarks, and the sensitivity of these results to the assumed turbulence closure is quantified, providing a framework for future calculations based on turbulence statistics extracted from numerical convection simulations.