Volume 608, December 2017
|Number of page(s)||9|
|Published online||13 December 2017|
Atmospheric-radiation boundary conditions for high-frequency waves in time-distance helioseismology
1 Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany
2 Institut für Astrophysik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
3 Center for Space Science, NYUAD Institute, New York University Abu Dhabi, PO Box 129188, Abu Dhabi, UAE
4 Magique-3D, Inria Bordeaux Sud-Ouest, Université de Pau et des Pays de l’Adour, 64013 Pau, France
5 Magique-3D, Inria Bordeaux Sud-Ouest, Université de Bordeaux, 33400 Talence, France
Received: 31 May 2017
Accepted: 6 September 2017
The temporal covariance between seismic waves measured at two locations on the solar surface is the fundamental observable in time-distance helioseismology. Above the acoustic cut-off frequency (~5.3 mHz), waves are not trapped in the solar interior and the covariance function can be used to probe the upper atmosphere. We wish to implement appropriate radiative boundary conditions for computing the propagation of high-frequency waves in the solar atmosphere. We consider recently developed and published radiative boundary conditions for atmospheres in which sound-speed is constant and density decreases exponentially with radius. We compute the cross-covariance function using a finite element method in spherical geometry and in the frequency domain. The ratio between first- and second-skip amplitudes in the time-distance diagram is used as a diagnostic to compare boundary conditions and to compare with observations. We find that a boundary condition applied 500 km above the photosphere and derived under the approximation of small angles of incidence accurately reproduces the “infinite atmosphere” solution for high-frequency waves. When the radiative boundary condition is applied 2 Mm above the photosphere, we find that the choice of atmospheric model affects the time-distance diagram. In particular, the time-distance diagram exhibits double-ridge structure when using a Vernazza Avrett Loeser atmospheric model.
Key words: Sun: helioseismology / Sun: atmosphere / methods: numerical
© ESO, 2017
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