A unified approach to the helioseismic forward and inverse problems of differential rotation

Ritzwoller, M. H.; Lavely, Eugene M.

doi:10.1086/169785

Cited by 137 publications

(115 citation statements)

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“…Where the basis functions are polynomials that are related to Clebsch-Gordan coefficients (Ritzwoller & Laveley 1991). The offset term in the expansion, ν…”

Section: Appendix A: Comparison With Resolved Observationsmentioning

confidence: 99%

Solar p-mode frequencies at $\mathsf{\ell=2}$: What do analyses of unresolved observations actually measure?

Chaplin

Appourchaux

Elsworth

et al. 2004

A&A

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Abstract.We have studied in detail the extraction of estimates of = 2 p-mode frequencies from unresolved observations of the visible disc of the Sun. Examples of data of this type include ground-based observations made by the Birmingham SolarOscillations Network (BiSON), and space-borne observations made by the GOLF and VIRGO/SPM instruments on board the ESA/NASA SOHO satellite. The fitting of the modes is complicated in practice by the asymmetric arrangement in frequency of the three components (m = −2, 0 and 2) that are prominent in such data. In order to investigate the effect of this we used a series of 10-yr artificial datasets into which varying degrees of asymmetry were introduced. The sets were designed to mimic the characteristics of the BiSON and GOLF data, and were analyzed both with and without the BiSON window function from the period 1992 through 2001. Since reliable estimates of the asymmetry have only recently been extracted from unresolved observations (Chaplin et al. 2003a) it has for a long time been standard practice to fit the = 2 modes to a model that assumes a symmetrically arranged multiplet. We have tested the impact of this on the accuracy of the extracted frequencies. Furthermore, we demonstrate that asymmetric models can be successfully applied, provided the data are of sufficient length and quality. We also discuss the implications of our simulations for analyses of real solar data.

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“…Where the basis functions are polynomials that are related to Clebsch-Gordan coefficients (Ritzwoller & Laveley 1991). The offset term in the expansion, ν…”

Section: Appendix A: Comparison With Resolved Observationsmentioning

confidence: 99%

Solar p-mode frequencies at $\mathsf{\ell=2}$: What do analyses of unresolved observations actually measure?

Chaplin

Appourchaux

Elsworth

et al. 2004

A&A

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“…The basis functions are orthogonal polynomials, which are related to Clebsch-Gordon coefficients C lm s0lm (Ritzwoller & Lavely 1991) by…”

Section: Inversion For Angular Velocitymentioning

confidence: 99%

Detectability of large-scale flows in global helioseismic data – A numerical experiment

Roth

Howe

Komm

2002

A&A

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Abstract. Convective motions affect the solar p-modes by shifting their frequencies. In comparison to the frequency splitting caused by the differential rotation, this is only a small additional effect. As the spatial resolution of the inversions for the differential rotation becomes better, it is important to know how these additional frequency shifts modify the splitting coefficients and how these two effects might be disentangled. Therefore we carry out a numerical experiment. We use quasi-degenerate perturbation theory to create frequencies of p-modes that are affected by differential rotation and by large-scale flows. The simulated frequency sets are analyzed and inverted for differential rotation. We use changes in the (l, ν) coverage, the multiplets, and the inversion results as diagnostics to draw conclusions about the detectability of large-scale flows in global helioseismic data. The result is a detectability limit of the order of 10 m s −1 for large-scale flows in the convection zone. A sectoral poloidal flow with greater amplitude will lead to a noticeable distortion of the rotation rate, while a zonal poloidal flow with greater amplitude will lead to distorted even-a coefficients and disrupted multiplets.

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“…These studies were successfully used to solve the forward problem for the influence of differential rotation on the p modes. The results lead to an improved inversion method for determining the radial dependence of the differential rotation (Ritzwoller and Lavely, 1991). Following Lavely and Ritzwoller (1992), Roth and Stix (1999) studied the influence of large-scale sectoral poloidal flow components that could be related to giant convection cells.…”

Section: Introductionmentioning

confidence: 99%

Meridional Circulation and Global Solar Oscillations

Roth

Stix

2008

Sol Phys

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We investigate the influence of large-scale meridional circulation on solar p modes by quasi-degenerate perturbation theory, as proposed by Lavely and Ritzwoller (Roy. Soc. Lond. Phil. Trans. Ser. A 339, 431, 1992). As an input flow we use various models of stationary meridional circulation obeying the continuity equation. This flow perturbs the eigenmodes of an equilibrium model of the Sun. We derive the signatures of the meridional circulation in the frequency multiplets of solar p modes. In most cases the meridional circulation leads to negative average frequency shifts of the multiplets. Further possibly observable effects are briefly discussed.

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A unified approach to the helioseismic forward and inverse problems of differential rotation

Cited by 137 publications

References 0 publications

Solar p-mode frequencies at $\mathsf{\ell=2}$: What do analyses of unresolved observations actually measure?

Solar p-mode frequencies at $\mathsf{\ell=2}$: What do analyses of unresolved observations actually measure?

Detectability of large-scale flows in global helioseismic data – A numerical experiment

Meridional Circulation and Global Solar Oscillations

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