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Analysis of MDI High-Degree Mode Frequencies and their Rotational Splittings

  • HELIOSEISMOLOGY, ASTEROSEISMOLOGY, AND MHD CONNECTIONS
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Abstract

We present a detailed analysis of solar acoustic mode frequencies and their rotational splittings for modes with degree up to 900. They were obtained by applying spherical harmonic decomposition to full-disk solar images observed by the Michelson Doppler Imager onboard the Solar and Heliospheric Observatory spacecraft. Global helioseismology analysis of high-degree modes is complicated by the fact that the individual modes cannot be isolated, which has limited so far the use of high-degree data for structure inversion of the near-surface layers (r>0.97R ⊙). In this work, we took great care to recover the actual mode characteristics using a physically motivated model which included a complete leakage matrix. We included in our analysis the following instrumental characteristics: the correct instantaneous image scale, the radial and non-radial image distortions, the effective position angle of the solar rotation axis, and a correction to the Carrington elements. We also present variations of the mode frequencies caused by the solar activity cycle. We have analyzed seven observational periods from 1999 to 2005 and correlated their frequency shift with four different solar indices. The frequency shift scaled by the relative mode inertia is a function of frequency alone and follows a simple power law, where the exponent obtained for the p modes is twice the value obtained for the f modes. The different solar indices present the same result.

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References

  • Basu, S., Antia, H.M.: 1999, Astrophys. J. 525, 517.

    Article  ADS  Google Scholar 

  • Basu, S., Antia, H.M.: 2000, Astrophys. J. 531, 1088.

    Article  ADS  Google Scholar 

  • Basu, S., Antia, H.M.: 2003, In: Sawaya-Lacoste, H. (ed.) Local and Global Helioseismology: The Present and Future SP-517, ESA, Noordwijk, 231.

    Google Scholar 

  • Basu, S., Antia, H.M., Bogart, R.S.: 2004, Astrophys. J. 610, 1157.

    Article  ADS  Google Scholar 

  • Beck, J.G., Giles, P.: 2005, Astrophys. J. 621, L153.

    Article  ADS  Google Scholar 

  • Bevington, P.R., Robinson, D.K.: 1992, In: Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill, New York.

    Google Scholar 

  • Brodsky, M., Vorontsov, S.V.: 1993, Astrophys. J. 409, 455.

    Article  ADS  Google Scholar 

  • Burtseva, O., Kholikov, S., Serebryanskiy, A., Chou, D.-Y.: 2007, Solar Phys. 241, 17.

    Article  ADS  Google Scholar 

  • Chaplin, W.J., Appourchaux, T., Elsworth, Y., Isaak, G.R., New, R.: 2001, Mon. Not. Roy. Astron. Soc. 324, 910.

    Article  ADS  Google Scholar 

  • Chaplin, W.J., Elsworth, Y., Miller, B.A., Verner, G.A., New, R.: 2007, Astrophys. J. 659, 1749.

    Article  ADS  Google Scholar 

  • Christensen-Dalsgaard, J.: 2003, In: Lecture Notes on Stellar Oscillations, Aarhus University Press, Aarhus.

    Google Scholar 

  • Christensen-Dalsgaard, J., Berthomieu, G.: 1991, In: Cox, A.N., Livingston, W.C., Matthews, M. (eds.) Solar Interior and Atmosphere, University of Arizona Press, Tucson, 401.

    Google Scholar 

  • Christensen-Dalsgaard, J., Thompson, M.J., Gough, D.O.: 1989, Mon. Not. Roy. Astron. Soc. 238, 481.

    ADS  Google Scholar 

  • Christensen-Dalsgaard, J., Dappen, W., Ajukov, S.V., Anderson, E.R., Antia, H.M., Basu, S., Baturin, V.A., Berthomieu, G., Chaboyer, B., Chitre, S.M., et al.: 1996, Science 272, 1286.

    Article  ADS  Google Scholar 

  • Corbard, T., Thompson, M.J.: 2002, Solar Phys. 205, 211.

    Article  ADS  Google Scholar 

  • Di Mauro, M.P., Christensen-Dalsgaard, J., Rabello-Soares, M.C., Basu, S.: 2002, Astron. Astrophys. 384, 666.

    Article  ADS  Google Scholar 

  • Duvall, T.L. Jr., Kosovichev, A.G., Murawski, K.: 1998, Astrophys. J. 505, L55.

    Article  ADS  Google Scholar 

  • Dziembowski, W.A., Goode, P.R.: 2004, Astrophys. J. 600, 464.

    Article  ADS  Google Scholar 

  • Dziembowski, W.A., Goode, P.R.: 2005, Astrophys. J. 625, 548.

    Article  ADS  Google Scholar 

  • Foukal, P.: 1972, Astrophys. J. 173, 439.

    Article  ADS  Google Scholar 

  • Goldreich, P., Murray, N., Willette, G., Kumar, P.: 1991, Astrophys. J. 370, 752.

    Article  ADS  Google Scholar 

  • Gough, D.O.: 1990, In: Osaki, Y., Shibahashi, H. (eds.) Progress of Seismology of the Sun and Stars, Lecture Notes in Physics 367, Springer, New York, 283.

    Chapter  Google Scholar 

  • Gough, D.O.: 1993, In: Weiss, W.W., Baglin, A. (eds.) Inside the Stars CS-40, Astron. Soc. Pac., San Francisco, 767.

    Google Scholar 

  • Gough, D.O., Kosovichev, A.G., Toomre, J., Anderson, E., Antia, H.M., Basu, S., Chaboyer, B., Chitre, S.M., Christensen-Dalsgaard, J., Dziembowski, W.A., et al.: 1996, Science 272, 1296.

    Article  ADS  Google Scholar 

  • Hill, F.: 1988, Astrophys. J. 333, 996.

    Article  ADS  Google Scholar 

  • Howe, R., Komm, R.W., Hill, F.: 2002, Astrophys. J. 580, 1172.

    Article  ADS  Google Scholar 

  • Howe, R., Christensen-Dalsgaard, J., Hill, F., Komm, R., Schou, J., Thompson, M.J., Toomre, J.: 2007, Adv. Space Res. 40, 7, 915.

    Article  Google Scholar 

  • Jain, R., Roberts, B.: 1996, Astrophys. J. 456, 399.

    Article  ADS  Google Scholar 

  • Jefferies, S.M.: 1998, In: Deubner, F.L., Christensen-Dalsgaard, J., Kurtz, D. (eds.) New Eyes to See Inside the Sun and Stars, IAU Symposium 185, Kyoto, 415.

  • Korzennik, S.G.: 1990, Ph.D. Thesis, Univ. California, Los Angeles.

  • Korzennik, S.G.: 1998, In: Korzennik, S.G., Wilson, A. (eds.) Structure and Dynamics of the Interior of the Sun and Sun-like Stars SP-418, ESA, Noordwijk, 933.

    Google Scholar 

  • Korzennik, S.G., Rabello-Soares, M.C., Schou, J.: 2004, Astrophys. J. 602, 481. (KRS).

    Article  ADS  Google Scholar 

  • Kuhn, J.R., Bush, R.I., Emilio, M., Scherrer, P.H.: 2004, Astrophys. J. 613, 1241.

    Article  ADS  Google Scholar 

  • Larson, T.P., Schou, J.: 2008, In: Gizon, L. (ed.) Helioseismology, Asteroseismology and MHD Connections, J. Phys.: Conf. Ser. in press.

  • Li, L.H., Basu, S., Sofia, S., Robinson, F.J., Demarque, P., Guenther, D.B.: 2003, Astrophys. J. 591, 1267.

    Article  ADS  Google Scholar 

  • Libbrecht, K.G., Woodard, M.F.: 1990, Nature 345, 779.

    Article  ADS  Google Scholar 

  • Murawski, K., Roberts, B.: 1993, Astron. Astrophys. 272, 595.

    ADS  Google Scholar 

  • Nigam, R., Kosovichev, A.G.: 1998, Astrophys. J. 505, L51.

    Article  ADS  Google Scholar 

  • Rabello-Soares, M.C., Korzennik, S.G., Schou, J.: 2001, In: Wilson, A., Pallé, P.L. (eds.) Helio- and Asteroseismology at the Dawn of the Millennium SP-464, ESA, Noordwijk, 129.

    Google Scholar 

  • Rabello-Soares, M.C., Korzennik, S.G., Schou, J.: 2005, AGU Spring Meeting, SP11B-08.

  • Rabello-Soares, M.C., Korzennik, S.G., Schou, J.: 2006, In: Fletcher, K., Thompson, M. (eds.) Beyond the Spherical Sun SP-624, ESA, Noordwijk, 71.1.

    Google Scholar 

  • Rabello-Soares, M.C., Bogart, R.S., Basu, S.: 2008, In: Gizon, L. (ed.) Helioseismology, Asteroseismology and MHD Connections, J. Phys.: Conf. Ser. in press.

  • Rabello-Soares, M.C., Korzennik, S.G., Schou, J.: 2008, Adv. Space Res. 41, 861.

    Article  ADS  Google Scholar 

  • Rabello-Soares, M.C., Basu, S., Christensen-Dalsgaard, J., Di Mauro, M.P.: 2000, Solar Phys. 193, 345.

    Article  ADS  Google Scholar 

  • Rajaguru, S.P., Basu, S., Antia, H.M.: 2001, Astrophys. J. 563, 410.

    Article  ADS  Google Scholar 

  • Reiter, J., Rhodes, E.J. Jr., Kosovichev, A.G., Schou, J., Scherrer, P.H.: 2002, In: Wilson, A. (ed.) From Solar Min to Max: Half a Solar Cycle with SOHO SP-508, ESA, Noordwijk, 91.

    Google Scholar 

  • Reiter, J., Kosovichev, A.G., Rhodes, E.J. Jr., Schou, J.: 2003, In: Sawaya-Lacoste, H. (ed.) Local and Global Helioseismology: The Present and Future SP-517, ESA, Noordwijk, 369.

    Google Scholar 

  • Reiter, J., Rhodes, E.J. Jr., Kosovichev, A.G., Schou, J.: 2004, In: Danesy, D. (ed.) Helio- and Asteroseismology: Towards a Golden Future SP-559, ESA, Noordwijk, 61.

    Google Scholar 

  • Rhodes, E.J. Jr., Reiter, J., Schou, J.: 2002, In: Wilson, A. (ed.) From Solar Min to Max: Half a Solar Cycle with SOHO SP-508, ESA, Noordwijk, 37.

    Google Scholar 

  • Ritzwoller, M.H., Lavely, E.M.: 1991, Astrophys. J. 369, 557.

    Article  ADS  Google Scholar 

  • Salabert, D., Fossat, E., Gelly, B., Kholikov, S., Grec, G., Lazrek, M., Schmider, F.X.: 2004, Astron. Astrophys. 413, 1135.

    Article  ADS  Google Scholar 

  • Schou, J.: 1999, Astrophys. J. 523, L181.

    Article  ADS  Google Scholar 

  • Schou, J., Bogart, R.S.: 1998, Astrophys. J. 504, L131.

    Article  ADS  Google Scholar 

  • Schou, J., Antia, H.M., Basu, S., Bogart, R.S., Bush, R.I., Chitre, S.M., Christensen-Dalsgaard, J., di Mauro, M.P., Dziembowski, W.A., Eff-Darwich, A., et al.: 1998, Astrophys. J. 505, 390.

    Article  ADS  Google Scholar 

  • Snodgrass, H.B.: 1992, In: Harvey, K.L. (ed.) The Solar Cycle CS-27, Astron. Soc. Pac., San Francisco, 250.

    Google Scholar 

  • Toutain, T., Appourchaux, T., Fröhlich, C., Kosovichev, A.G., Nigam, R., Scherrer, P.H.: 1998, Astrophys. J. 506, L147.

    Article  ADS  Google Scholar 

  • Woodard, M.F.: 1989, Astrophys. J. 347, 1176.

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. W.W. Hansen Experimental Physics Laboratory, Stanford University, 455 Via Palou, Stanford, CA, 94305, USA

    M. C. Rabello-Soares & J. Schou

  2. Harvard-Smithsonian Center for Astrophysics, 60 Garden St, Cambridge, MA, 02138, USA

    S. G. Korzennik

Authors
  1. M. C. Rabello-Soares
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  2. S. G. Korzennik
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  3. J. Schou
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Correspondence to M. C. Rabello-Soares.

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Helioseismology, Asteroseismology, and MHD Connections

Guest Editors: Laurent Gizon and Paul Cally

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Rabello-Soares, M.C., Korzennik, S.G. & Schou, J. Analysis of MDI High-Degree Mode Frequencies and their Rotational Splittings. Sol Phys 251, 197–224 (2008). https://doi.org/10.1007/s11207-008-9231-7

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