### Abstract

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.

Original language | English (US) |
---|---|

Article number | A109 |

Journal | Astronomy and Astrophysics |

Volume | 608 |

DOIs | |

State | Published - Dec 1 2017 |

### Fingerprint

### Keywords

- Methods: numerical
- Sun: atmosphere
- Sun: helioseismology

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Astronomy and Astrophysics*,

*608*, [A109]. https://doi.org/10.1051/0004-6361/201731283

**Atmospheric-radiation boundary conditions for high-frequency waves in time-distance helioseismology.** / Fournier, D.; Leguèbe, M.; Hanson, C. S.; Gizon, Laurent; Barucq, H.; Chabassier, J.; Duruflé, M.

Research output: Contribution to journal › Article

*Astronomy and Astrophysics*, vol. 608, A109. https://doi.org/10.1051/0004-6361/201731283

}

TY - JOUR

T1 - Atmospheric-radiation boundary conditions for high-frequency waves in time-distance helioseismology

AU - Fournier, D.

AU - Leguèbe, M.

AU - Hanson, C. S.

AU - Gizon, Laurent

AU - Barucq, H.

AU - Chabassier, J.

AU - Duruflé, M.

PY - 2017/12/1

Y1 - 2017/12/1

N2 - 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.

AB - 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.

KW - Methods: numerical

KW - Sun: atmosphere

KW - Sun: helioseismology

UR - http://www.scopus.com/inward/record.url?scp=85038417168&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85038417168&partnerID=8YFLogxK

U2 - 10.1051/0004-6361/201731283

DO - 10.1051/0004-6361/201731283

M3 - Article

VL - 608

JO - Astronomy and Astrophysics

JF - Astronomy and Astrophysics

SN - 0004-6361

M1 - A109

ER -