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
N1 - Funding Information:
Acknowledgements. We thank Jesper Schou, Aaron Birch, and Damien Fournier for scientific discussions, Earl Bellinger and Warrick Ball for help with installing and running GYRE, and Richard Townsend for answering questions on eigenfunction computations via the GYRE forum. We thank the anonymous referee for a number of useful suggestions that improved the manuscript. We used the tomso python package written by Warrick Ball for reading ADIPLS eigenfunctions and solar models. This work was supported in part by the Max Planck Society through a grant on PLATO Science. The computational resources were provided by the German Data Center for SDO through a grant from the German Aerospace Center (DLR). We acknowledge partial support from the European Research Council Synergy Grant WHOLE SUN #810218. HH acknowledges the support of the Erasmus Mundus Joint Masters Programme, AstroMundus. Parts of this work were submitted as a MSc. thesis by HH.
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 -