### Abstract

Measurements of oscillation frequencies of the Sun and stars can provide important independent constraints on their internal structure and dynamics. Seismic models of these oscillations are used to connect structure and rotation of the star to its resonant frequencies, which are then compared with observations, the goal being that of minimizing the difference between the two. Even in the case of the Sun, for which structure models are highly tuned, observed frequencies show systematic deviations from modeled frequencies, a phenomenon referred to as the "surface term." The dominant source of this systematic effect is thought to be vigorous near-surface convection, which is not well accounted for in both stellar modeling and mode-oscillation physics. Here we bring to bear the method of homogenization, applicable in the asymptotic limit of large wavelengths (in comparison to the correlation scale of convection), to characterize the effect of small-scale surface convection on resonant-mode frequencies in the Sun. We show that the full oscillation equations, in the presence of temporally stationary three-dimensional (3D) flows, can be reduced to an effective "quiet-Sun" wave equation with altered sound speed, Brünt-Väisäla frequency, and Lamb frequency. We derive the modified equation and relations for the appropriate averaging of 3D flows and thermal quantities to obtain the properties of this effective medium. Using flows obtained from 3D numerical simulations of near-surface convection, we quantify their effect on solar oscillation frequencies and find that they are shifted systematically and substantially. We argue therefore that consistent interpretations of resonant frequencies must include modifications to the wave equation that effectively capture the impact of vigorous hydrodynamic convection.

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

Article number | 246 |

Journal | Astrophysical Journal |

Volume | 806 |

Issue number | 2 |

DOIs | |

State | Published - Jun 20 2015 |

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### Keywords

- convection
- methods: analytical
- Sun: helioseismology
- waves

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Astrophysical Journal*,

*806*(2), [246]. https://doi.org/10.1088/0004-637X/806/2/246

**FREQUENCY SHIFTS OF RESONANT MODES OF THE SUN DUE TO NEAR-SURFACE CONVECTIVE SCATTERING.** / Bhattacharya, J.; Hanasoge, Shravan; Antia, H. M.

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 806, no. 2, 246. https://doi.org/10.1088/0004-637X/806/2/246

}

TY - JOUR

T1 - FREQUENCY SHIFTS OF RESONANT MODES OF THE SUN DUE TO NEAR-SURFACE CONVECTIVE SCATTERING

AU - Bhattacharya, J.

AU - Hanasoge, Shravan

AU - Antia, H. M.

PY - 2015/6/20

Y1 - 2015/6/20

N2 - Measurements of oscillation frequencies of the Sun and stars can provide important independent constraints on their internal structure and dynamics. Seismic models of these oscillations are used to connect structure and rotation of the star to its resonant frequencies, which are then compared with observations, the goal being that of minimizing the difference between the two. Even in the case of the Sun, for which structure models are highly tuned, observed frequencies show systematic deviations from modeled frequencies, a phenomenon referred to as the "surface term." The dominant source of this systematic effect is thought to be vigorous near-surface convection, which is not well accounted for in both stellar modeling and mode-oscillation physics. Here we bring to bear the method of homogenization, applicable in the asymptotic limit of large wavelengths (in comparison to the correlation scale of convection), to characterize the effect of small-scale surface convection on resonant-mode frequencies in the Sun. We show that the full oscillation equations, in the presence of temporally stationary three-dimensional (3D) flows, can be reduced to an effective "quiet-Sun" wave equation with altered sound speed, Brünt-Väisäla frequency, and Lamb frequency. We derive the modified equation and relations for the appropriate averaging of 3D flows and thermal quantities to obtain the properties of this effective medium. Using flows obtained from 3D numerical simulations of near-surface convection, we quantify their effect on solar oscillation frequencies and find that they are shifted systematically and substantially. We argue therefore that consistent interpretations of resonant frequencies must include modifications to the wave equation that effectively capture the impact of vigorous hydrodynamic convection.

AB - Measurements of oscillation frequencies of the Sun and stars can provide important independent constraints on their internal structure and dynamics. Seismic models of these oscillations are used to connect structure and rotation of the star to its resonant frequencies, which are then compared with observations, the goal being that of minimizing the difference between the two. Even in the case of the Sun, for which structure models are highly tuned, observed frequencies show systematic deviations from modeled frequencies, a phenomenon referred to as the "surface term." The dominant source of this systematic effect is thought to be vigorous near-surface convection, which is not well accounted for in both stellar modeling and mode-oscillation physics. Here we bring to bear the method of homogenization, applicable in the asymptotic limit of large wavelengths (in comparison to the correlation scale of convection), to characterize the effect of small-scale surface convection on resonant-mode frequencies in the Sun. We show that the full oscillation equations, in the presence of temporally stationary three-dimensional (3D) flows, can be reduced to an effective "quiet-Sun" wave equation with altered sound speed, Brünt-Väisäla frequency, and Lamb frequency. We derive the modified equation and relations for the appropriate averaging of 3D flows and thermal quantities to obtain the properties of this effective medium. Using flows obtained from 3D numerical simulations of near-surface convection, we quantify their effect on solar oscillation frequencies and find that they are shifted systematically and substantially. We argue therefore that consistent interpretations of resonant frequencies must include modifications to the wave equation that effectively capture the impact of vigorous hydrodynamic convection.

KW - convection

KW - methods: analytical

KW - Sun: helioseismology

KW - waves

UR - http://www.scopus.com/inward/record.url?scp=84934976653&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84934976653&partnerID=8YFLogxK

U2 - 10.1088/0004-637X/806/2/246

DO - 10.1088/0004-637X/806/2/246

M3 - Article

AN - SCOPUS:84934976653

VL - 806

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 2

M1 - 246

ER -