Abstract
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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Basu, S., Antia, H.M.: 1997, Seismic measurement of the depth of the solar convection zone. Mon. Not. Roy. Astron. Soc. 287, 189 – 198.
Bjerknes, V.: 1926, Solar hydrodynamics. Astrophys. J. 64, 93 – 121.
Brun, A.S., Toomre, J.: 2002, Turbulent convection under the influence of rotation: Sustaining a strong differential rotation. Astrophys. J. 570, 865 – 885.
Choudhuri, A.R., Schüssler, M., Dikpati, M.: 1995, The solar dynamo with meridional circulation. Astron. Astrophys. 303, L29 – L32.
Christensen-Dalsgaard, J., Berthomieu, G.: 1991, Theory of solar oscillations. In: Cox, A.N., Livingston, W.C., Matthews, M.S. (eds.) Solar Interior and Atmosphere, University of Arizona Press, Tucson, 401 – 478.
Christensen-Dalsgaard, J., Däppen, W., Ajukov, S.V., Anderson, E.R., Antia, H.M., Basu, S., Baturin, V.A., Berthomieu, G., Chaboyer, B., Chitre, S.M., Cox, A.N., Demarque, P., Donatowicz, J., Dziembowski, W.A., Gabriel, M., Gough, D.O., Guenther, D.B., Guzik, J.A., Harvey, J.W., Hill, F., Houdek, G., Iglesias, C.A., Kosovichev, A.G., Leibacher, J.W., Morel, P., Proffitt, C.R., Provost, J., Reiter, J., Rhodes, E.J., Rogers, F.J., Roxburgh, I.W., Thompson, M.J., Ulrich, R.K.: 1996, The current state of solar modeling. Science 272, 1286 – 1292.
Dikpati, M., Charbonneau, P.: 1999, A Babcock-Leighton flux transport dynamo with solar-like differential rotation. Astrophys. J. 518, 508 – 520.
Duvall, T.L. Jr.: 1979, Large-scale solar velocity fields. Solar Phys. 63, 3 – 15.
Edmonds, A.R.: 1974, Angular Momentum in Quantum Mechanics, Princeton University Press, Princeton.
Haber, D.A., Hindman, B.W., Toomre, J., Bogart, R.S., Thompson, M.J., Hill, F.: 2000, Solar shear flows deduced from helioseismic dense-pack samplings of ring diagrams. Solar Phys. 192, 335 – 350.
Haber, D.A., Hindman, B.W., Toomre, J., Bogart, R.S., Larsen, R.M., Hill, F.: 2002, Evolving submerged meridional circulation cells within the upper convection zone revealed by ring-diagram analysis. Astrophys. J. 570, 855 – 864.
Hathaway, D.H.: 1996, Doppler measurements of the Sun’s meridional flow. Astrophys. J. 460, 1027 – 1033.
Hill, F.: 1988, Rings and trumpets – Three-dimensional power spectra of solar oscillations. Astrophys. J. 333, 996 – 1013.
Kippenhahn, R.: 1963, Differential rotation in stars with convective envelopes. Astrophys. J. 137, 664 – 678.
Komm, R.W., Howard, R.F., Harvey, J.W.: 1993, Meridional flow of small photospheric magnetic features. Solar Phys. 147, 207 – 223.
Küker, M., Rüdiger, G.: 2005, Differential rotation on the lower main sequence. Astron. Nachr. 326, 265 – 268.
Küker, M., Stix, M.: 2001, Differential rotation of the present and the pre-main-sequence Sun. Astron. Astrophys. 366, 668 – 675.
Lavely, E.M., Ritzwoller, M.H.: 1992, The effect of global-scale, steady-state convection and elastic-gravitational asphericities on helioseismic oscillations. Roy. Soc. Lond. Phil. Trans. Ser. A 339, 431 – 496.
Miesch, M.S., Brun, A.S., Toomre, J.: 2006, Solar differential rotation influenced by latitudinal entropy variations in the tachocline. Astrophys. J. 641, 618 – 625.
Miesch, M.S., Elliott, J.R., Toomre, J., Clune, T.L., Glatzmaier, G.A., Gilman, P.A.: 2000, Three-dimensional spherical simulations of solar convection. I. Differential rotation and pattern evolution achieved with laminar and turbulent states. Astrophys. J. 532, 593 – 615.
Nandy, D., Choudhuri, A.R.: 2002, Explaining the latitudinal distribution of sunspots with deep meridional flow. Science 296, 1671 – 1673.
Parker, E.N.: 1955, Hydromagnetic dynamo models. Astrophys. J. 122, 293 – 314.
Rempel, M.: 2006a, Flux-transport dynamos with Lorentz force feedback on differential rotation and meridional flow: Saturation mechanism and torsional oscillations. Astrophys. J. 647, 662 – 675.
Rempel, M.: 2006b, Transport of toroidal magnetic field by the meridional flow at the base of the solar convection zone. Astrophys. J. 637, 1135 – 1142.
Ritzwoller, M.H., Lavely, E.M.: 1991, A unified approach to the helioseismic forward and inverse problems of differential rotation. Astrophys. J. 369, 557 – 566.
Roberts, P.H., Stix, M.: 1972, α-Effect dynamos, by the Bullard – Gellman formalism. Astron. Astrophys. 18, 453 – 466.
Roth, M., Stix, M.: 1999, Coupling of solar p modes: Quasi-degenerate perturbation theory. Astron. Astrophys. 351, 1133 – 1138.
Roth, M., Howe, R., Komm, R.: 2002, Detectability of large-scale flows in global helioseismic data – A numerical experiment. Astron. Astrophys. 396, 243 – 253.
Rüdiger, G.: 1980, Reynolds stresses and differential rotation. I – On recent calculations of zonal fluxes in slowly rotating stars. Geophys. Astrophys. Fluid Dyn. 16, 239 – 261.
Stix, M.: 2004, The Sun: An Introduction, 2nd edn. Springer, Berlin.
Stix, M., Zhugzhda, Y.D.: 1998, Waves in structured media: Non-radial solar p modes. Astron. Astrophys. 335, 685 – 690.
Tuominen, J., Tuominen, I., Kyröläinen, J.: 1983, Eleven-year cycle in solar rotation and meridional motions as derived from the positions of sunspot groups. Mon. Not. Roy. Astron. Soc. 205, 691 – 704.
Unno, W., Osaki, Y., Ando, H., Saio, H., Shibahashi, H.: 1989, Nonradial Oscillations of Stars, 2nd edn. University of Tokyo Press, Tokyo.
Wöhl, H., Brajša, R.: 2001, Meridional motions of stable recurrent sunspot groups. Solar Phys. 198, 57 – 77.
Woodard, M.F.: 2000, Theoretical signature of solar meridional flow in global seismic data. Solar Phys. 197, 11 – 20.
Zaatri, A., Komm, R., González Hernández, I., Howe, R., Corbard, T.: 2006, North south asymmetry of zonal and meridional flows determined from ring diagram analysis of GONG++ data. Solar Phys. 236, 227 – 244.
Zhao, J., Kosovichev, A.G.: 2004, Torsional oscillation, meridional flows, and vorticity inferred in the upper convection zone of the sun by time-distance helioseismology. Astrophys. J. 603, 776 – 784.
Zhugzhda, Y.D., Stix, M.: 1994, Acoustic waves in structured media and helioseismology. Astron. Astrophys. 291, 310 – 319.
Author information
Authors and Affiliations
Corresponding author
Additional information
Helioseismology, Asteroseismology, and MHD Connections
Guest Editors: Laurent Gizon and Paul Cally.
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Roth, M., Stix, M. Meridional Circulation and Global Solar Oscillations. Sol Phys 251, 77–89 (2008). https://doi.org/10.1007/s11207-008-9232-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11207-008-9232-6