### Abstract

Time-distance helioseismology has shown that f-mode travel times contain information about horizontal flows in the Sun. The purpose of this study is to provide a simple interpretation of these travel times. We study the interaction of surface gravity waves with horizontal flows in an incompressible, plane-parallel solar atmosphere. We show that for uniform flows less than roughly 250 m s^{-1}, the travel-time shifts are linear in the flow amplitude. For stronger flows, perturbation theory up to third order is needed to model waveforms. The case of small-amplitude spatially varying flows is treated using the first-order Born approximation. We derive two-dimensional Fréchet kernels that give the sensitivity of travel-time shifts to local flows. We show that the effect of flows on travel times depends on wave damping and on the direction from which the observations are made. The main physical effect is the advection of the waves by the flow rather than the advection of wave sources or the effect of flows on wave damping. We compare the two-dimensional sensitivity kernels with simplified three-dimensional kernels that only account for wave advection and assume a vertical line of sight. We find that the three-dimensional f-mode kernels approximately separate in the horizontal and vertical coordinates, with the horizontal variations given by the simplified two-dimensional kernels. This consistency between quite different models gives us confidence in the usefulness of these kernels for interpreting quiet-Sun observations.

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

Pages (from-to) | 1051-1064 |

Number of pages | 14 |

Journal | Astrophysical Journal |

Volume | 671 |

Issue number | 1 |

DOIs | |

State | Published - Dec 10 2007 |

### Fingerprint

### Keywords

- Convection
- Scattering
- Sun: helioseismology
- Sun: oscillations
- Waves

### ASJC Scopus subject areas

- Space and Planetary Science
- Nuclear and High Energy Physics

### Cite this

*Astrophysical Journal*,

*671*(1), 1051-1064. https://doi.org/10.1086/522914

**Time-distance helioseismology : Sensitivity of f-mode travel times to flows.** / Jackiewicz, J.; Gizon, Laurent; Birch, A. C.; Duvall, T. L.

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 671, no. 1, pp. 1051-1064. https://doi.org/10.1086/522914

}

TY - JOUR

T1 - Time-distance helioseismology

T2 - Sensitivity of f-mode travel times to flows

AU - Jackiewicz, J.

AU - Gizon, Laurent

AU - Birch, A. C.

AU - Duvall, T. L.

PY - 2007/12/10

Y1 - 2007/12/10

N2 - Time-distance helioseismology has shown that f-mode travel times contain information about horizontal flows in the Sun. The purpose of this study is to provide a simple interpretation of these travel times. We study the interaction of surface gravity waves with horizontal flows in an incompressible, plane-parallel solar atmosphere. We show that for uniform flows less than roughly 250 m s-1, the travel-time shifts are linear in the flow amplitude. For stronger flows, perturbation theory up to third order is needed to model waveforms. The case of small-amplitude spatially varying flows is treated using the first-order Born approximation. We derive two-dimensional Fréchet kernels that give the sensitivity of travel-time shifts to local flows. We show that the effect of flows on travel times depends on wave damping and on the direction from which the observations are made. The main physical effect is the advection of the waves by the flow rather than the advection of wave sources or the effect of flows on wave damping. We compare the two-dimensional sensitivity kernels with simplified three-dimensional kernels that only account for wave advection and assume a vertical line of sight. We find that the three-dimensional f-mode kernels approximately separate in the horizontal and vertical coordinates, with the horizontal variations given by the simplified two-dimensional kernels. This consistency between quite different models gives us confidence in the usefulness of these kernels for interpreting quiet-Sun observations.

AB - Time-distance helioseismology has shown that f-mode travel times contain information about horizontal flows in the Sun. The purpose of this study is to provide a simple interpretation of these travel times. We study the interaction of surface gravity waves with horizontal flows in an incompressible, plane-parallel solar atmosphere. We show that for uniform flows less than roughly 250 m s-1, the travel-time shifts are linear in the flow amplitude. For stronger flows, perturbation theory up to third order is needed to model waveforms. The case of small-amplitude spatially varying flows is treated using the first-order Born approximation. We derive two-dimensional Fréchet kernels that give the sensitivity of travel-time shifts to local flows. We show that the effect of flows on travel times depends on wave damping and on the direction from which the observations are made. The main physical effect is the advection of the waves by the flow rather than the advection of wave sources or the effect of flows on wave damping. We compare the two-dimensional sensitivity kernels with simplified three-dimensional kernels that only account for wave advection and assume a vertical line of sight. We find that the three-dimensional f-mode kernels approximately separate in the horizontal and vertical coordinates, with the horizontal variations given by the simplified two-dimensional kernels. This consistency between quite different models gives us confidence in the usefulness of these kernels for interpreting quiet-Sun observations.

KW - Convection

KW - Scattering

KW - Sun: helioseismology

KW - Sun: oscillations

KW - Waves

UR - http://www.scopus.com/inward/record.url?scp=40249085645&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=40249085645&partnerID=8YFLogxK

U2 - 10.1086/522914

DO - 10.1086/522914

M3 - Article

AN - SCOPUS:40249085645

VL - 671

SP - 1051

EP - 1064

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 1

ER -