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Poster Communications Year : 2023

Investigation of the effects of Cowling approximation on adiabatic wave propagation in helioseismology

Abstract

Helioseismology investigates the interior structures and the dynamics of the Sun from oscillations observed on its visible surface. Ignoring flow and rotation, time-harmonic adiabatic waves in a selfgravitating Sun in Eulerian-Lagrangian description are described by the Lagrangian displacement ξ and the gravitational potential perturbation δ ϕ which satisfy Galbrun's equation [1] coupled with a Poisson equation. In most works, perturbation to gravitational potential δ ϕ is neglected under Cowling's approximation [3]. However, this approximation is known to shift the eigenvalues of the forward operator for low-order harmonic modes [4]. Here, we study the effects of this approximation on numerical solutions and discuss its implication for the inverse problem. Removing Cowling's approximation allows us to accurately simulate waves for low-degree modes, and help us better characterize the deep interior of the Sun. The investigation is carried out for a Sun with minimum activity, called quiet Sun, whose background coefficients are given by the radially symmetric standard solar model Model S in the interior, with a choice of extension beyond the surface to include the presence of atmosphere cf [5]. Radial symmetry is exploited to decouple the problem on each spherical harmonic mode ℓ to give a system of ordinary differential equations in radial variable. This extends previous work [1] which employed Cowling approximation. The modal system is resolved by using the Hybridizable Discontinuous Galerkin method (HDG). For purpose of validation, the equations are coupled with free-surface boundary condition which is adapted for low-frequency modes and is commonly employed in helioseismology cf. [6]. Since eigenvalues are poles of Green's tensor, the magnitude of the latter as a function of frequency peaks around an eigenvalue. As preliminary results, we compare the location where the Green's tensor peaks to the values of eigenvalues computed by the GYRE code [2], between which we find a good agreement.
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hal-04359755 , version 1 (21-12-2023)

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  • HAL Id : hal-04359755 , version 1

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Hélène Barucq, Lola Chabat, Florian Faucher, Damien Fournier, Ha Pham. Investigation of the effects of Cowling approximation on adiabatic wave propagation in helioseismology. AIP 2023 - 11th Applied Inverse Problems, Sep 2023, Gottingen, Germany. 2023. ⟨hal-04359755⟩
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