Outgoing modal solutions for Galbrun's equation in helioseismology

We construct modal outgoing Green's kernels for the simplified Galbrun's equation under spherical symmetry, in the context of helioseismology. The coefficients of the equation are C2 functions representing the solar interior model S, complemented with an isothermal atmospheric model. We so...

Full description

Saved in:
Bibliographic Details
Published in:Journal of Differential Equations 2021-06, Vol.286, p.494-530
Main Authors: Barucq, Hélène, Faucher, Florian, Fournier, Damien, Gizon, Laurent, Pham, Ha
Format: Article
Language:English
Subjects:
Analysis of PDEs
Astrophysics
Galbrun's equation
Helioseismology
Indicial analysis
Long-range scattering
Mathematics
Modal outgoing Green's kernel
Physics
Sciences of the Universe
Solar and Stellar Astrophysics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We construct modal outgoing Green's kernels for the simplified Galbrun's equation under spherical symmetry, in the context of helioseismology. The coefficients of the equation are C2 functions representing the solar interior model S, complemented with an isothermal atmospheric model. We solve the equation in vectorial spherical harmonics basis to obtain modal equations for the different components of the unknown wave motions. These equations are then decoupled and written in Schrödinger form, whose coefficients are shown to be C2 apart from at most two regular singular points, and to decay like a Coulomb potential at infinity. These properties allow us to construct an outgoing Green's kernel for each spherical mode. We also compute asymptotic expansions of coefficients up to order r−3 as r tends to infinity, and show numerically that their accuracy is improved by including the contribution from the gravity although this term is of order r−3.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2021.03.031