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Global-Oscillation Eigenfunction Measurements of Solar Meridional Flow

  • SOLAR DYNAMICS AND MAGNETISM
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Abstract

We describe and apply a new helioseismic method for measuring solar subsurface axisymmetric meridional and zonal flow. The method is based on a theoretical model of the response of global-oscillation eigenfunctions to the flow velocity and uses cross spectra of the time-varying coefficients in the spherical-harmonic expansion of the photospheric Doppler-velocity field. Eigenfunction changes modify the leakage matrix, which describes the sensitivity of the spherical-harmonic coefficients to the global-oscillation modes. The form of the leakage matrix in turn affects the theoretically expected spherical-harmonic cross spectra. Estimates of internal meridional and zonal flow were obtained by fitting the theoretical flow-dependent cross spectra to spherical-harmonic cross spectra computed from approximately 500 days of full-disk Dopplergrams from the Helioseismic and Magnetic Imager (HMI) on the SDO spacecraft. The zonal-flow measurements, parameterized in the form of “a” coefficients, substantially agree with measurements obtained from conventional global-mode-frequency analysis. The meridional-flow estimates, in the form of depth-weighted averages of the flow velocity, are similar to estimates obtained from earlier analyses, for oscillation modes that penetrate the outermost one-third of the convection zone. For more deeply penetrating modes, the inferred flow velocity increases significantly with penetration depth, indicating the need for either a modification of the simple conveyor-belt picture of meridional flow or improvement in the cross-spectral model.

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Acknowledgements

We thank Doug Braun for useful discussions and Ashley Crouch for useful discussions and calculations. HMI data are courtesy of NASA/SDO and the HMI science team. This research was supported by NASA contracts NAS5-03114 and NNH09CF93C to NWRA/CoRA. HMI is supported by NASA contract NAS5-02139 to Stanford University.

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Authors and Affiliations

  1. NorthWest Research Associates, Inc., 3380 Mitchell Lane, Boulder, CO, 80301-5410, USA

    M. Woodard & A. C. Birch

  2. W. W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA, 94305-4085, USA

    J. Schou & T. P. Larson

  3. Max-Planck-Institut für Sonnensystemforschung, 37191, Katlenburg-Lindau, Germany

    A. C. Birch

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  1. M. Woodard
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Correspondence to M. Woodard.

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Solar Dynamics and Magnetism from the Interior to the Atmosphere

Guest Editors: R. Komm, A. Kosovichev, D. Longcope, and N. Mansour

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Woodard, M., Schou, J., Birch, A.C. et al. Global-Oscillation Eigenfunction Measurements of Solar Meridional Flow. Sol Phys 287, 129–147 (2013). https://doi.org/10.1007/s11207-012-0075-9

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