### Abstract

Context. Solar gravity modes (g modes) are buoyancy waves that are trapped in the solar radiative zone and have been very difficult to detect at the surface. Solar g modes would complement solar pressure modes (p modes) in probing the central regions of the Sun, for example the rotation rate of the core. Aims. A detection of g modes using changes in the large frequency separation of p modes has recently been reported. However, it is unclear how p and g modes interact. The aim of this study is to evaluate to what extent g modes can perturb the frequencies of p modes. Methods. We computed the first-order perturbation to global p-mode frequencies due to a flow field and perturbations to solar structure (e.g. density and sound speed) caused by a g mode. We focused on long-period g modes and assumed that the g-mode perturbations are constant in time. The surface amplitude of g modes is assumed to be 1 mm s^{-1}, which is close to the observational limit set by Doppler observations. Results. Gravity modes do perturb p-mode frequencies to first order if the harmonic degree of the g mode is even and if its azimuthal order is zero. The effect is extremely small. For dipole and quadrupole p modes, all frequency shifts are smaller than 0.1 nHz, or 2 × 10^{-8} in relative numbers. This is because the relative perturbation to solar structure quantities caused by a g mode of realistic amplitude is of the order of 10^{-6}-10^{-5}. Additionally, we find that structural changes dominate over advection. Surprisingly, the interaction of g and p modes takes place to a large part near the surface, where p modes spend most of their propagation times and g modes generate the largest relative changes to solar structure. This is due to the steep density stratification, which compensates the evanescent behaviour of g modes in the convection zone. Conclusions. It appears to be impossible to detect g modes solely through their signature in p-mode frequency shifts. Whether g modes leave a detectable signature in p-mode travel times under a given observational setup remains an open question.

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

Article number | A26 |

Journal | Astronomy and Astrophysics |

Volume | 629 |

DOIs | |

State | Published - Sep 1 2019 |

### Fingerprint

### Keywords

- Sun: helioseismology
- Sun: interior
- Sun: oscillations
- Waves

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Astronomy and Astrophysics*,

*629*, [A26]. https://doi.org/10.1051/0004-6361/201935434

**Signature of solar g modes in first-order p -mode frequency shifts.** / Böning, Vincent G.A.; Hu, Huanchen; Gizon, Laurent.

Research output: Contribution to journal › Article

*Astronomy and Astrophysics*, vol. 629, A26. https://doi.org/10.1051/0004-6361/201935434

}

TY - JOUR

T1 - Signature of solar g modes in first-order p -mode frequency shifts

AU - Böning, Vincent G.A.

AU - Hu, Huanchen

AU - Gizon, Laurent

PY - 2019/9/1

Y1 - 2019/9/1

N2 - Context. Solar gravity modes (g modes) are buoyancy waves that are trapped in the solar radiative zone and have been very difficult to detect at the surface. Solar g modes would complement solar pressure modes (p modes) in probing the central regions of the Sun, for example the rotation rate of the core. Aims. A detection of g modes using changes in the large frequency separation of p modes has recently been reported. However, it is unclear how p and g modes interact. The aim of this study is to evaluate to what extent g modes can perturb the frequencies of p modes. Methods. We computed the first-order perturbation to global p-mode frequencies due to a flow field and perturbations to solar structure (e.g. density and sound speed) caused by a g mode. We focused on long-period g modes and assumed that the g-mode perturbations are constant in time. The surface amplitude of g modes is assumed to be 1 mm s-1, which is close to the observational limit set by Doppler observations. Results. Gravity modes do perturb p-mode frequencies to first order if the harmonic degree of the g mode is even and if its azimuthal order is zero. The effect is extremely small. For dipole and quadrupole p modes, all frequency shifts are smaller than 0.1 nHz, or 2 × 10-8 in relative numbers. This is because the relative perturbation to solar structure quantities caused by a g mode of realistic amplitude is of the order of 10-6-10-5. Additionally, we find that structural changes dominate over advection. Surprisingly, the interaction of g and p modes takes place to a large part near the surface, where p modes spend most of their propagation times and g modes generate the largest relative changes to solar structure. This is due to the steep density stratification, which compensates the evanescent behaviour of g modes in the convection zone. Conclusions. It appears to be impossible to detect g modes solely through their signature in p-mode frequency shifts. Whether g modes leave a detectable signature in p-mode travel times under a given observational setup remains an open question.

AB - Context. Solar gravity modes (g modes) are buoyancy waves that are trapped in the solar radiative zone and have been very difficult to detect at the surface. Solar g modes would complement solar pressure modes (p modes) in probing the central regions of the Sun, for example the rotation rate of the core. Aims. A detection of g modes using changes in the large frequency separation of p modes has recently been reported. However, it is unclear how p and g modes interact. The aim of this study is to evaluate to what extent g modes can perturb the frequencies of p modes. Methods. We computed the first-order perturbation to global p-mode frequencies due to a flow field and perturbations to solar structure (e.g. density and sound speed) caused by a g mode. We focused on long-period g modes and assumed that the g-mode perturbations are constant in time. The surface amplitude of g modes is assumed to be 1 mm s-1, which is close to the observational limit set by Doppler observations. Results. Gravity modes do perturb p-mode frequencies to first order if the harmonic degree of the g mode is even and if its azimuthal order is zero. The effect is extremely small. For dipole and quadrupole p modes, all frequency shifts are smaller than 0.1 nHz, or 2 × 10-8 in relative numbers. This is because the relative perturbation to solar structure quantities caused by a g mode of realistic amplitude is of the order of 10-6-10-5. Additionally, we find that structural changes dominate over advection. Surprisingly, the interaction of g and p modes takes place to a large part near the surface, where p modes spend most of their propagation times and g modes generate the largest relative changes to solar structure. This is due to the steep density stratification, which compensates the evanescent behaviour of g modes in the convection zone. Conclusions. It appears to be impossible to detect g modes solely through their signature in p-mode frequency shifts. Whether g modes leave a detectable signature in p-mode travel times under a given observational setup remains an open question.

KW - Sun: helioseismology

KW - Sun: interior

KW - Sun: oscillations

KW - Waves

UR - http://www.scopus.com/inward/record.url?scp=85072120640&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85072120640&partnerID=8YFLogxK

U2 - 10.1051/0004-6361/201935434

DO - 10.1051/0004-6361/201935434

M3 - Article

AN - SCOPUS:85072120640

VL - 629

JO - Astronomy and Astrophysics

JF - Astronomy and Astrophysics

SN - 0004-6361

M1 - A26

ER -