The seismic structure of the sun

Science

Volumn 272, Issue 5266, 1996, Pages 1296-1300

  Gough, D O ^a   Kosovichev, A G ^b   Toomre, J ^c   Anderson, E ^d   Antia, H M ^e   Basu, S ^f   Chaboyer, B ^g   Chitre, S M ^e   Christensen Dalsgaard, J ^f   Dziembowski, W A ^h   Eff Darwich, A ⁱ   Elliott, J R ^a   Giles, P M ^b   Goode, P R ^j   Guzik, J A ^k   Harvey, J W ^d   Hill, F ^d   Leibacher, J W ^d   Monteiro, M J P F G ^l   Richard, O ^m   Sekii, T ^a   Shibahashi, H ⁿ   Takata, M ⁿ   Thompson, M J ^o   Vauclair, S ^m   Vorontsov, S V ^o   more..

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b STANFORD UNIVERSITY   (United States)

^c UNIVERSITY OF COLORADO   (United States)

^d NATIONAL SOLAR OBSERVATORY   (United States)

^e TATA INSTITUTE OF FUNDAMENTAL RESEARCH   (India)

^f AARHUS UNIVERSITY   (Denmark)

^g UNIVERSITY OF TORONTO   (Canada)

^h NICOLAUS COPERNICUS ASTRONOMICAL CENTER   (Poland)

ⁱ INSTITUTO DE ASTROFÍSICA DE CANARIAS   (Spain)

^j NEW JERSEY INSTITUTE OF TECHNOLOGY   (United States)

^k LOS ALAMOS NATIONAL LABORATORY   (United States)

^l UNIVERSITY OF PORTO   (Portugal)

^m OBSERVATOIRE MIDI PYRÉNÉES   (France)

ⁿ UNIVERSITY OF TOKYO   (Japan)

^o QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

more..

Author keywords

[No Author keywords available]

Indexed keywords

CONVECTION ZONE; EQUATION OF STATE; GLOBAL OSCILLATION NETWORK GROUP; OPACITY; SEISMIC STRUCTURE; WAVE MOTION;

SUN;

EID: 0029756839     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.272.5266.1296     Document Type: Article

References (57)

1. Except in the surface layers of the sun, the characteristic cooling time is much longer than the periods of the seismic waves, so the wave motion is essentially adiabatic. Near the surface, the sun is highly turbulent and is not well understood.
2. 2.
3. D. O. Gough, Sol. Phys. 100, 65 (1985); A. G. Kosovichev, Bull. Crimean Astrophys. Obs. 75, 36 (1986); D. O. Gough and A. G. Kosovichev, in Inside the Sun, Proceedings of International Astronomical Union Colloquium 121, G. Berthomieu and M. Cribier, Eds. (Kluwer, Dordrecht, Netherlands, 1990), pp. 327-340; D. O. Gough and M. J. Thompson, in Solar Interior and Atmosphere, A. N. Cox, W. C. Livingston, M. Matthews, Eds. (Univ. of Arizona Press, Tucson, AZ), pp. 519-561 (1991); W. A. Dziembowski, A. A. Pamjatnykh, R. Sienkiewicz, Mon. Not. R. Astron. Soc. 249, 602 (1991).
4. D. O. Gough, Sol. Phys. 100, 65 (1985); A. G. Kosovichev, Bull. Crimean Astrophys. Obs. 75, 36 (1986); D. O. Gough and A. G. Kosovichev, in Inside the Sun, Proceedings of International Astronomical Union Colloquium 121, G. Berthomieu and M. Cribier, Eds. (Kluwer, Dordrecht, Netherlands, 1990), pp. 327-340; D. O. Gough and M. J. Thompson, in Solar Interior and Atmosphere, A. N. Cox, W. C. Livingston, M. Matthews, Eds. (Univ. of Arizona Press, Tucson, AZ), pp. 519-561 (1991); W. A. Dziembowski, A. A. Pamjatnykh, R. Sienkiewicz, Mon. Not. R. Astron. Soc. 249, 602 (1991).
5. D. O. Gough, Sol. Phys. 100, 65 (1985); A. G. Kosovichev, Bull. Crimean Astrophys. Obs. 75, 36 (1986); D. O. Gough and A. G. Kosovichev, in Inside the Sun, Proceedings of International Astronomical Union Colloquium 121, G. Berthomieu and M. Cribier, Eds. (Kluwer, Dordrecht, Netherlands, 1990), pp. 327-340; D. O. Gough and M. J. Thompson, in Solar Interior and Atmosphere, A. N. Cox, W. C. Livingston, M. Matthews, Eds. (Univ. of Arizona Press, Tucson, AZ), pp. 519-561 (1991); W. A. Dziembowski, A. A. Pamjatnykh, R. Sienkiewicz, Mon. Not. R. Astron. Soc. 249, 602 (1991).
6. D. O. Gough, Sol. Phys. 100, 65 (1985); A. G. Kosovichev, Bull. Crimean Astrophys. Obs. 75, 36 (1986); D. O. Gough and A. G. Kosovichev, in Inside the Sun, Proceedings of International Astronomical Union Colloquium 121, G. Berthomieu and M. Cribier, Eds. (Kluwer, Dordrecht, Netherlands, 1990), pp. 327-340; D. O. Gough and M. J. Thompson, in Solar Interior and Atmosphere, A. N. Cox, W. C. Livingston, M. Matthews, Eds. (Univ. of Arizona Press, Tucson, AZ), pp. 519-561 (1991); W. A. Dziembowski, A. A. Pamjatnykh, R. Sienkiewicz, Mon. Not. R. Astron. Soc. 249, 602 (1991).
7. D. O. Gough, Sol. Phys. 100, 65 (1985); A. G. Kosovichev, Bull. Crimean Astrophys. Obs. 75, 36 (1986); D. O. Gough and A. G. Kosovichev, in Inside the Sun, Proceedings of International Astronomical Union Colloquium 121, G. Berthomieu and M. Cribier, Eds. (Kluwer, Dordrecht, Netherlands, 1990), pp. 327-340; D. O. Gough and M. J. Thompson, in Solar Interior and Atmosphere, A. N. Cox, W. C. Livingston, M. Matthews, Eds. (Univ. of Arizona Press, Tucson, AZ), pp. 519-561 (1991); W. A. Dziembowski, A. A. Pamjatnykh, R. Sienkiewicz, Mon. Not. R. Astron. Soc. 249, 602 (1991).
8. J. Christensen-Dalsgaard et al., Science 272, 1286 (1996).
9. J. Patron, F. Hill, E. J. Rhodes Jr., S. G. Korzennik, A. Cacciani, Astrophys. J. 455, 746 (1995); T. L. Duvall Jr., S. D'Silva, S. M. Jefferies, J. W. Harvey, J. Schou, Nature 379, 235 (1996); A. G. Kosovichev, Asfrophys J. Lett. 461, L55 (1996).
10. J. Patron, F. Hill, E. J. Rhodes Jr., S. G. Korzennik, A. Cacciani, Astrophys. J. 455, 746 (1995); T. L. Duvall Jr., S. D'Silva, S. M. Jefferies, J. W. Harvey, J. Schou, Nature 379, 235 (1996); A. G. Kosovichev, Asfrophys J. Lett. 461, L55 (1996).
11. J. Patron, F. Hill, E. J. Rhodes Jr., S. G. Korzennik, A. Cacciani, Astrophys. J. 455, 746 (1995); T. L. Duvall Jr., S. D'Silva, S. M. Jefferies, J. W. Harvey, J. Schou, Nature 379, 235 (1996); A. G. Kosovichev, Asfrophys J. Lett. 461, L55 (1996).
12. J. B. Keller and S. I. Rubinow, Ann. Phys. 9, 24 (1960); D. O. Gough, in Astrophysical Fluid Dynamics, J. P. Zahn and J. Zinn-Justin, Eds. (North-Holland, Amsterdam, 1993), pp. 399-560. In a sphere, such as the sun, the phases of waves on adjacent planes containing the center of the sphere must also be in appropriate relative phase for resonance to occur.
13. J. B. Keller and S. I. Rubinow, Ann. Phys. 9, 24 (1960); D. O. Gough, in Astrophysical Fluid Dynamics, J. P. Zahn and J. Zinn-Justin, Eds. (North-Holland, Amsterdam, 1993), pp. 399-560. In a sphere, such as the sun, the phases of waves on adjacent planes containing the center of the sphere must also be in appropriate relative phase for resonance to occur.
14. Frequencies also depend on the variation of density but to a lesser extent than they depend on sound speed [see (9)].
15. That time is inversely proportional to the magnitude of the group velocity and is directly proportional to the relative density of ray-path segments.
16. 2 or u = p/ρ rather than c because, being proportional to T/μ, it is more readily comprehended.
17. J. Chrislensen-Dalsgaard, J. Schou, M. J. Thompson, Mon. Not. R. Astron. Soc. 242, 353 (1990).
18. This technique has been carried out with only asymptotic representations of the resonance conditions [for example, see J. Christensen-Dalsgaard et al., Nature 315, 378 (1985)].
19. i divided by the modal inertia, which is the functional form of any surface uncertainty [see (3)].
20. That sets the radius of the base of the adiabatically stratified part of the convection zone at about 0.709R. This value is somewhat less than the value 0.713R obtained previously by J. Christensen-Dalsgaard, D. O. Gough, and M, J. Thompson [Astrophys. J. 378, 413 (1991)], and by A. G. Kosovichev and A. V. Fedorova [Sov. Astron. 35, 507 (1991)]. A study of the transition at the base of the convection zone [see (30)] is consistent with the new result, although a repeat of the analysis with the use of the reference models of Richard et al. (15) yields 0.714R.
21. That sets the radius of the base of the adiabatically stratified part of the convection zone at about 0.709R. This value is somewhat less than the value 0.713R obtained previously by J. Christensen-Dalsgaard, D. O. Gough, and M, J. Thompson [Astrophys. J. 378, 413 (1991)], and by A. G. Kosovichev and A. V. Fedorova [Sov. Astron. 35, 507 (1991)]. A study of the transition at the base of the convection zone [see (30)] is consistent with the new result, although a repeat of the analysis with the use of the reference models of Richard et al. (15) yields 0.714R.
22. S. Basu and H. M. Antia, Mon. Not. R. Astron. Soc. 269, 1137 (1995).
23. O. Richard et al., Astron. Astrophys.. in press.
24. B. Chaboyer, P. Demarque, H. M. Pinsonneault, Astrophys. J. 441, 865 (1995).
25. J. A. Guzik and A. N Cox, ibid 448, 905 (1995).
26. 2 tends to be associated with corresponding relative decreases in ρ and μ.
27. W. A. Dziembowski, A. A. Pamjatnykh, R. Sienkiewicz, Mon. Not. R. Astron. Soc. 249, 602 (1991); W. Däppen et al., in Challenges to Theories of the Structure of Moderate-Mass Stars, D. O. Gough and J. Toomre, Eds. (Lecture Notes-in Physics 388, Springer, Heidelberg, Germany, 1991), pp. 111-120. A. Kosovichev et al., Mon. Not. R. Atron. Soc. 259, 536 (1992); H. M. Antia and S. Basu, Astrophys. J. 426, 801 (1994); A. G. Kosovichev, Adv. Space Res. 15, 95 (1995).
28. W. A. Dziembowski, A. A. Pamjatnykh, R. Sienkiewicz, Mon. Not. R. Astron. Soc. 249, 602 (1991); W. Däppen et al., in Challenges to Theories of the Structure of Moderate-Mass Stars, D. O. Gough and J. Toomre, Eds. (Lecture Notes-in Physics 388, Springer, Heidelberg, Germany, 1991), pp. 111-120. A. Kosovichev et al., Mon. Not. R. Atron. Soc. 259, 536 (1992); H. M. Antia and S. Basu, Astrophys. J. 426, 801 (1994); A. G. Kosovichev, Adv. Space Res. 15, 95 (1995).
29. W. A. Dziembowski, A. A. Pamjatnykh, R. Sienkiewicz, Mon. Not. R. Astron. Soc. 249, 602 (1991); W. Däppen et al., in Challenges to Theories of the Structure of Moderate-Mass Stars, D. O. Gough and J. Toomre, Eds. (Lecture Notes-in Physics 388, Springer, Heidelberg, Germany, 1991), pp. 111-120. A. Kosovichev et al., Mon. Not. R. Atron. Soc. 259, 536 (1992); H. M. Antia and S. Basu, Astrophys. J. 426, 801 (1994); A. G. Kosovichev, Adv. Space Res. 15, 95 (1995).
30. W. A. Dziembowski, A. A. Pamjatnykh, R. Sienkiewicz, Mon. Not. R. Astron. Soc. 249, 602 (1991); W. Däppen et al., in Challenges to Theories of the Structure of Moderate-Mass Stars, D. O. Gough and J. Toomre, Eds. (Lecture Notes-in Physics 388, Springer, Heidelberg, Germany, 1991), pp. 111-120. A. Kosovichev et al., Mon. Not. R. Atron. Soc. 259, 536 (1992); H. M. Antia and S. Basu, Astrophys. J. 426, 801 (1994); A. G. Kosovichev, Adv. Space Res. 15, 95 (1995).
31. W. A. Dziembowski, A. A. Pamjatnykh, R. Sienkiewicz, Mon. Not. R. Astron. Soc. 249, 602 (1991); W. Däppen et al., in Challenges to Theories of the Structure of Moderate-Mass Stars, D. O. Gough and J. Toomre, Eds. (Lecture Notes-in Physics 388, Springer, Heidelberg, Germany, 1991), pp. 111-120. A. Kosovichev et al., Mon. Not. R. Atron. Soc. 259, 536 (1992); H. M. Antia and S. Basu, Astrophys. J. 426, 801 (1994); A. G. Kosovichev, Adv. Space Res. 15, 95 (1995).
32. M. J. Thompson et al., Science 272, 1300 (1996).
33. The wave is also advected by azimuthal flow, but the axisymmetric component of that flow is rotation, which is addressed in (20).
34. E. G. Zweibel and D. O Gough, in Procedings of the Fourth SOHO Workshop: Helioseismology, J. T. Hoeksema et al., Eds. [European Space Agency (ESA) Special Publication (SP)-379, Noordwijk, Netherlands, 1995], Although one cannot distiguish between possible sources of asphericity by analyzing frequencies alone, the different anisotropies of the wave-speed perturbations from different sources renders it possible in principle to distinguish them by their eigenfunctions. That might be possible in the future with the use of techniques such as time-distance seismology.
35. The averaging kernels in this case are quadratic in the horizontal structure of the eigenfunctions. They are therefore even functions of latitude and are sensitive only to the north-south symmetric component of the asphericity. It requires some knowledge of the form of the eigenfunctions to determine the asymmetric component.
36. D, O Gough and M. J. Thompson, in Advances in Helio- and Asteroseismology, J. Christensen-Dalsgaard and S. Frandsen, Eds. (Reidel, Dordrecht, Netherlands, 1988), pp. 175-180; J. R. Kuhn, Astmphys. J. Lett. 331, L131 (1988); P. R. Goode and J. R. Kuhn. Astrophys. J. 356, 310 (1990); K. G. Libbrecht and M. F. Woodard, ibid. 402, L77 (1993).
37. D, O Gough and M. J. Thompson, in Advances in Helio- and Asteroseismology, J. Christensen-Dalsgaard and S. Frandsen, Eds. (Reidel, Dordrecht, Netherlands, 1988), pp. 175-180; J. R. Kuhn, Astmphys. J. Lett. 331, L131 (1988); P. R. Goode and J. R. Kuhn. Astrophys. J. 356, 310 (1990); K. G. Libbrecht and M. F. Woodard, ibid. 402, L77 (1993).
38. D, O Gough and M. J. Thompson, in Advances in Helio- and Asteroseismology, J. Christensen-Dalsgaard and S. Frandsen, Eds. (Reidel, Dordrecht, Netherlands, 1988), pp. 175-180; J. R. Kuhn, Astmphys. J. Lett. 331, L131 (1988); P. R. Goode and J. R. Kuhn. Astrophys. J. 356, 310 (1990); K. G. Libbrecht and M. F. Woodard, ibid. 402, L77 (1993).
39. D, O Gough and M. J. Thompson, in Advances in Helio- and Asteroseismology, J. Christensen-Dalsgaard and S. Frandsen, Eds. (Reidel, Dordrecht, Netherlands, 1988), pp. 175-180; J. R. Kuhn, Astmphys. J. Lett. 331, L131 (1988); P. R. Goode and J. R. Kuhn. Astrophys. J. 356, 310 (1990); K. G. Libbrecht and M. F. Woodard, ibid. 402, L77 (1993).
40. E, A. Spiegel and N. O. Weiss, Nature 287, 616 (1980); C. A. Morrow, P. A. Gilman, E. E. DeLuca, in Seismology of the Sun and Sun-Like Stars, V. Domingo and E. J. Rolfe, Eds (ESA SP-286, Noordwijk, Netherlands, 1988), vol. 2, pp. 73-76; S. Moreno-Insertis, in Sunspots: Theory and Observation, J. H. Thomas and N. O. Weiss, Eds. (Kluwer, Dordrecht, Netherlands, 1994).
41. E, A. Spiegel and N. O. Weiss, Nature 287, 616 (1980); C. A. Morrow, P. A. Gilman, E. E. DeLuca, in Seismology of the Sun and Sun-Like Stars, V. Domingo and E. J. Rolfe, Eds (ESA SP-286, Noordwijk, Netherlands, 1988), vol. 2, pp. 73-76; S. Moreno-Insertis, in Sunspots: Theory and Observation, J. H. Thomas and N. O. Weiss, Eds. (Kluwer, Dordrecht, Netherlands, 1994).
42. E, A. Spiegel and N. O. Weiss, Nature 287, 616 (1980); C. A. Morrow, P. A. Gilman, E. E. DeLuca, in Seismology of the Sun and Sun-Like Stars, V. Domingo and E. J. Rolfe, Eds (ESA SP-286, Noordwijk, Netherlands, 1988), vol. 2, pp. 73-76; S. Moreno-Insertis, in Sunspots: Theory and Observation, J. H. Thomas and N. O. Weiss, Eds. (Kluwer, Dordrecht, Netherlands, 1994).
43. D, O. Gough and T. Sekii, Astron. Soc. Pac. Conf. Ser. 42, 177 (1993); M. J. P. F. G. Monteiro, J. Christensen-Dalsgaard, M. J. Thompson, ibid., p. 253; A. G Kosovichev, in Advances in Solar Physics, Proceedings of the Seventh European Meeting on Solar Physics, G. Belvedere, M. Rodono, G. M. Simnett, Eds. (Lecture Notes in Physics 432, Springer-Verlag, Germany, 1994), pp. 47-52; S. Basu and H. M. Antia, Mon. Not. R. Astron. Soc. 269, 1137 (1995).
44. D, O. Gough and T. Sekii, Astron. Soc. Pac. Conf. Ser. 42, 177 (1993); M. J. P. F. G. Monteiro, J. Christensen-Dalsgaard, M. J. Thompson, ibid., p. 253; A. G Kosovichev, in Advances in Solar Physics, Proceedings of the Seventh European Meeting on Solar Physics, G. Belvedere, M. Rodono, G. M. Simnett, Eds. (Lecture Notes in Physics 432, Springer-Verlag, Germany, 1994), pp. 47-52; S. Basu and H. M. Antia, Mon. Not. R. Astron. Soc. 269, 1137 (1995).
45. D, O. Gough and T. Sekii, Astron. Soc. Pac. Conf. Ser. 42, 177 (1993); M. J. P. F. G. Monteiro, J. Christensen-Dalsgaard, M. J. Thompson, ibid., p. 253; A. G Kosovichev, in Advances in Solar Physics, Proceedings of the Seventh European Meeting on Solar Physics, G. Belvedere, M. Rodono, G. M. Simnett, Eds. (Lecture Notes in Physics 432, Springer-Verlag, Germany, 1994), pp. 47-52; S. Basu and H. M. Antia, Mon. Not. R. Astron. Soc. 269, 1137 (1995).
46. D, O. Gough and T. Sekii, Astron. Soc. Pac. Conf. Ser. 42, 177 (1993); M. J. P. F. G. Monteiro, J. Christensen-Dalsgaard, M. J. Thompson, ibid., p. 253; A. G Kosovichev, in Advances in Solar Physics, Proceedings of the Seventh European Meeting on Solar Physics, G. Belvedere, M. Rodono, G. M. Simnett, Eds. (Lecture Notes in Physics 432, Springer-Verlag, Germany, 1994), pp. 47-52; S. Basu and H. M. Antia, Mon. Not. R. Astron. Soc. 269, 1137 (1995).
47. D. O. Gough, in Solar-Terrestrial Relationships and the Earth Environment in the Last Millenia, G. Castagnoli-Cini, Ed. (Italiana Fisica, Bologna, Italy, 1988), pp. 90-132 ; E. Knobloch and W. J. Merryfield, Astrophys. J. 401, 196 (1992).
48. D. O. Gough, in Solar-Terrestrial Relationships and the Earth Environment in the Last Millenia, G. Castagnoli-Cini, Ed. (Italiana Fisica, Bologna, Italy, 1988), pp. 90-132 ; E. Knobloch and W. J. Merryfield, Astrophys. J. 401, 196 (1992).
49. J.-P.Zahn, Astron. Astrophys. 265, 115 (1992).
50. E. A. Spiegel and J.-P. Zahn, ibid., p. 106.
51. We have investigated the structure of the transition between the convection zone and the radiative interior by first considering how mode frequency varies with the phase difference between the surface of the sun and the base of the convection zone, after having filtered out surface effects, and then comparing it with theoretical models (32). The signature of the transition oscillates with phase, in step with the eigenfunctions, with an amplitude that is smaller than that of the reference model, confirming that, if spherical, the transition is smoother than that of the model. The apparent smoothness might have come about because what has been observed is actually the spherical average of an aspherical structure. Adiabatic convective overshooting is likely to increase the amplitude; therefore, if such overshooting occurs in the sun, the physical discrepancy is actually greater than It appears at first sight. There is some indication that the amplitude of the oscillatory signal varies with the ratio m/( of azimuthal order to degree. This suggests that the structure of the lower boundary layer of the convection zone might vary with latitude. Although at present this is no more than a hint, it points to an exciting direction of research with further longterm seismic data.
52. J. N. Bahcall and H. A. Bethe, Phys. Rev. D47, 1298 (1993)
53. M. J. P. F. G. Monteiro and M. J. Thompson, Astron. Astrophys. 283, 247 (1994), J. Christensen-Dalsgaard, M. J. P. F. G. Monteiro, M. J. Thompson, Mon. Not. R Astron. Soc. 276, 283 (1995); I. W. Roxburgh and S. V. Vorontsov, ibid. 268, 880 (1994); S. Basu, H. M. Antia, D. Narasimha, ibid. 267, 207 (1994).
54. M. J. P. F. G. Monteiro and M. J. Thompson, Astron. Astrophys. 283, 247 (1994), J. Christensen-Dalsgaard, M. J. P. F. G. Monteiro, M. J. Thompson, Mon. Not. R Astron. Soc. 276, 283 (1995); I. W. Roxburgh and S. V. Vorontsov, ibid. 268, 880 (1994); S. Basu, H. M. Antia, D. Narasimha, ibid. 267, 207 (1994).
55. M. J. P. F. G. Monteiro and M. J. Thompson, Astron. Astrophys. 283, 247 (1994), J. Christensen-Dalsgaard, M. J. P. F. G. Monteiro, M. J. Thompson, Mon. Not. R Astron. Soc. 276, 283 (1995); I. W. Roxburgh and S. V. Vorontsov, ibid. 268, 880 (1994); S. Basu, H. M. Antia, D. Narasimha, ibid. 267, 207 (1994).
56. M. J. P. F. G. Monteiro and M. J. Thompson, Astron. Astrophys. 283, 247 (1994), J. Christensen-Dalsgaard, M. J. P. F. G. Monteiro, M. J. Thompson, Mon. Not. R Astron. Soc. 276, 283 (1995); I. W. Roxburgh and S. V. Vorontsov, ibid. 268, 880 (1994); S. Basu, H. M. Antia, D. Narasimha, ibid. 267, 207 (1994).
57. GONG is managed by the National Solar Observatory, a division of the National Optical Astronomy Observatories, operated by AURA under a cooperative agreement with NSF. We acknowledge financial support from the U.K. Particle Physics and Astronomy Research Council, NSF, NASA, and Danmarks Gruncfforskningsfond.