Dynamic variations at the base of the solar convection zone

Science

Volumn 287, Issue 5462, 2000, Pages 2456-2460

  Howe, R ^a   Christensen Dalsgaard, J ^b   Hill, F ^a   Komm, R W ^a   Larsen, R M ^c   Schou, J ^c   Thompson, M J ^d   Toomre, J ^e  

^a NATIONAL SOLAR OBSERVATORY   (United States)

^b AARHUS UNIVERSITY   (Denmark)

^c STANFORD UNIVERSITY   (United States)

^d QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

^e University of Colorado   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; ASTRONOMY; MAGNETIC FIELD; OSCILLATION; POWER SPECTRUM; PRIORITY JOURNAL; ROTATION; SUN; THERMODYNAMICS; VELOCITY;

EID: 0034737746     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.287.5462.2456     Document Type: Article

References (48)

1. The 22-year solar cycles of global magnetic activity might be described by an interface mean-field dynamo, operating in the tachocline, whose rotational shear can stretch the poloidal magnetic field generated by cyclonic turbulence in the convection zone into a strong toroidal field at its base [E. N. Parker, Astrophys. J. 408, 707 (1993); N. O. Weiss, in Lectures on Solar and Planetary Dynamos, M. R. E. Proctor and A. D. Gilbert, Eds. (Cambridge Univ. Press, Cambridge, 1994), pp. 59-95; S. M. Tobias, Astron. Astrophys. 322, 1007 (1997); P. Charbonneau and K. B. MacGregor, Astrophys. J. 486, 502 (1997)]. Such a toroidal field should be susceptible to buoyancy instabilities that lead to portions of the field rising through the convection zone and subsequently erupting into the atmosphere as large-scale magnetic loops [P. Caligari, F. Moreno-Insertis, M. Schüssler, Astrophys. J. 441, 886 (1995)].
2. The 22-year solar cycles of global magnetic activity might be described by an interface mean-field dynamo, operating in the tachocline, whose rotational shear can stretch the poloidal magnetic field generated by cyclonic turbulence in the convection zone into a strong toroidal field at its base [E. N. Parker, Astrophys. J. 408, 707 (1993); N. O. Weiss, in Lectures on Solar and Planetary Dynamos, M. R. E. Proctor and A. D. Gilbert, Eds. (Cambridge Univ. Press, Cambridge, 1994), pp. 59-95; S. M. Tobias, Astron. Astrophys. 322, 1007 (1997); P. Charbonneau and K. B. MacGregor, Astrophys. J. 486, 502 (1997)]. Such a toroidal field should be susceptible to buoyancy instabilities that lead to portions of the field rising through the convection zone and subsequently erupting into the atmosphere as large-scale magnetic loops [P. Caligari, F. Moreno-Insertis, M. Schüssler, Astrophys. J. 441, 886 (1995)].
3. The 22-year solar cycles of global magnetic activity might be described by an interface mean-field dynamo, operating in the tachocline, whose rotational shear can stretch the poloidal magnetic field generated by cyclonic turbulence in the convection zone into a strong toroidal field at its base [E. N. Parker, Astrophys. J. 408, 707 (1993); N. O. Weiss, in Lectures on Solar and Planetary Dynamos, M. R. E. Proctor and A. D. Gilbert, Eds. (Cambridge Univ. Press, Cambridge, 1994), pp. 59-95; S. M. Tobias, Astron. Astrophys. 322, 1007 (1997); P. Charbonneau and K. B. MacGregor, Astrophys. J. 486, 502 (1997)]. Such a toroidal field should be susceptible to buoyancy instabilities that lead to portions of the field rising through the convection zone and subsequently erupting into the atmosphere as large-scale magnetic loops [P. Caligari, F. Moreno-Insertis, M. Schüssler, Astrophys. J. 441, 886 (1995)].
4. The 22-year solar cycles of global magnetic activity might be described by an interface mean-field dynamo, operating in the tachocline, whose rotational shear can stretch the poloidal magnetic field generated by cyclonic turbulence in the convection zone into a strong toroidal field at its base [E. N. Parker, Astrophys. J. 408, 707 (1993); N. O. Weiss, in Lectures on Solar and Planetary Dynamos, M. R. E. Proctor and A. D. Gilbert, Eds. (Cambridge Univ. Press, Cambridge, 1994), pp. 59-95; S. M. Tobias, Astron. Astrophys. 322, 1007 (1997); P. Charbonneau and K. B. MacGregor, Astrophys. J. 486, 502 (1997)]. Such a toroidal field should be susceptible to buoyancy instabilities that lead to portions of the field rising through the convection zone and subsequently erupting into the atmosphere as large-scale magnetic loops [P. Caligari, F. Moreno-Insertis, M. Schüssler, Astrophys. J. 441, 886 (1995)].
5. The 22-year solar cycles of global magnetic activity might be described by an interface mean-field dynamo, operating in the tachocline, whose rotational shear can stretch the poloidal magnetic field generated by cyclonic turbulence in the convection zone into a strong toroidal field at its base [E. N. Parker, Astrophys. J. 408, 707 (1993); N. O. Weiss, in Lectures on Solar and Planetary Dynamos, M. R. E. Proctor and A. D. Gilbert, Eds. (Cambridge Univ. Press, Cambridge, 1994), pp. 59-95; S. M. Tobias, Astron. Astrophys. 322, 1007 (1997); P. Charbonneau and K. B. MacGregor, Astrophys. J. 486, 502 (1997)]. Such a toroidal field should be susceptible to buoyancy instabilities that lead to portions of the field rising through the convection zone and subsequently erupting into the atmosphere as large-scale magnetic loops [P. Caligari, F. Moreno-Insertis, M. Schüssler, Astrophys. J. 441, 886 (1995)].
6. For general reviews on helioseismology, see work by J. Christensen-Dalsgaard, D. Gough, J. Toomre, Science 229, 923 (1985); D. O. Gough and J. Toomre, Annu. Rev. Astron. Astrophys. 29, 627 (1991); and J. Christensen-Dalsgaard, W. Däppen, W. A. Dziembowski, J. A. Guzik, in Variable Stars as Essential Astrophysical Tools, C. Ibanoǧlu, Ed. (Kluwer, Dordrecht, Netherlands, 2000), pp. 59-167. A mode of oscillation is characterized by the degree l and azimuthal order m of the spherical harmonic, which describes its behavior over the solar surface, and the radial order n, which typically measures the number of nodes in the displacement eigen-function in the radial direction. The modes observed on the sun are typically acoustic modes (pressure or p modes), although in the MDI data, surface gravity modes (f modes) are also observed at high degree.
7. For general reviews on helioseismology, see work by J. Christensen-Dalsgaard, D. Gough, J. Toomre, Science 229, 923 (1985); D. O. Gough and J. Toomre, Annu. Rev. Astron. Astrophys. 29, 627 (1991); and J. Christensen-Dalsgaard, W. Däppen, W. A. Dziembowski, J. A. Guzik, in Variable Stars as Essential Astrophysical Tools, C. Ibanoǧlu, Ed. (Kluwer, Dordrecht, Netherlands, 2000), pp. 59-167. A mode of oscillation is characterized by the degree l and azimuthal order m of the spherical harmonic, which describes its behavior over the solar surface, and the radial order n, which typically measures the number of nodes in the displacement eigen-function in the radial direction. The modes observed on the sun are typically acoustic modes (pressure or p modes), although in the MDI data, surface gravity modes (f modes) are also observed at high degree.
8. For general reviews on helioseismology, see work by J. Christensen-Dalsgaard, D. Gough, J. Toomre, Science 229, 923 (1985); D. O. Gough and J. Toomre, Annu. Rev. Astron. Astrophys. 29, 627 (1991); and J. Christensen-Dalsgaard, W. Däppen, W. A. Dziembowski, J. A. Guzik, in Variable Stars as Essential Astrophysical Tools, C. Ibanoǧlu, Ed. (Kluwer, Dordrecht, Netherlands, 2000), pp. 59-167. A mode of oscillation is characterized by the degree l and azimuthal order m of the spherical harmonic, which describes its behavior over the solar surface, and the radial order n, which typically measures the number of nodes in the displacement eigen-function in the radial direction. The modes observed on the sun are typically acoustic modes (pressure or p modes), although in the MDI data, surface gravity modes (f modes) are also observed at high degree.
9. Recent helioseismic results on solar rotation are presented by M. J. Thompson et al., Science 272, 1300 (1996); T. Corbard et al., Astron. Astrophys. 324, 298 (1997); and J. Schou et al. (16). The splitting of global-mode frequencies by rotation provides the means to sample only the latitudinally symmetric component of the variation of angular velocity Ω.
10. Recent helioseismic results on solar rotation are presented by M. J. Thompson et al., Science 272, 1300 (1996); T. Corbard et al., Astron. Astrophys. 324, 298 (1997); and J. Schou et al. (16). The splitting of global-mode frequencies by rotation provides the means to sample only the latitudinally symmetric component of the variation of angular velocity Ω.
11. The radial gradients of angular velocity Ω in the tachocline may arise from anisotropic turbulent mixing of angular momentum in the stably stratified boundary layer at the base of the convection zone. The much stronger transport in the latitudinal direction than in the radial direction serves to circumvent the diffusive spread of latitudinal differential rotation into the deeper interior over long time scales [E. A. Spiegel and J.-P. Zahn, Astron. Astrophys. 265, 106 (1992); J. R. Elliott, Astron. Astrophys. 327, 1222 (1997)]. Other models invoke magnetic fields to enforce solid-body rotation in the radiative interior [D. O. Gough and M. E. McIntyre, Nature 394, 755 (1998)]. Linear instability studies of latitudinal shear combined with toroidal magnetic fields [P. A. Gilman and P. A. Fox, Astrophys. J. 510, 1018 (1999); M. Dikpati and P. A. Gilman, Astrophys. J. 512, 417 (1999)] suggest mechanisms for achieving enhanced horizontal turbulent mixing in the tachocline.
12. The radial gradients of angular velocity Ω in the tachocline may arise from anisotropic turbulent mixing of angular momentum in the stably stratified boundary layer at the base of the convection zone. The much stronger transport in the latitudinal direction than in the radial direction serves to circumvent the diffusive spread of latitudinal differential rotation into the deeper interior over long time scales [E. A. Spiegel and J.-P. Zahn, Astron. Astrophys. 265, 106 (1992); J. R. Elliott, Astron. Astrophys. 327, 1222 (1997)]. Other models invoke magnetic fields to enforce solid-body rotation in the radiative interior [D. O. Gough and M. E. McIntyre, Nature 394, 755 (1998)]. Linear instability studies of latitudinal shear combined with toroidal magnetic fields [P. A. Gilman and P. A. Fox, Astrophys. J. 510, 1018 (1999); M. Dikpati and P. A. Gilman, Astrophys. J. 512, 417 (1999)] suggest mechanisms for achieving enhanced horizontal turbulent mixing in the tachocline.
13. The radial gradients of angular velocity Ω in the tachocline may arise from anisotropic turbulent mixing of angular momentum in the stably stratified boundary layer at the base of the convection zone. The much stronger transport in the latitudinal direction than in the radial direction serves to circumvent the diffusive spread of latitudinal differential rotation into the deeper interior over long time scales [E. A. Spiegel and J.-P. Zahn, Astron. Astrophys. 265, 106 (1992); J. R. Elliott, Astron. Astrophys. 327, 1222 (1997)]. Other models invoke magnetic fields to enforce solid-body rotation in the radiative interior [D. O. Gough and M. E. McIntyre, Nature 394, 755 (1998)]. Linear instability studies of latitudinal shear combined with toroidal magnetic fields [P. A. Gilman and P. A. Fox, Astrophys. J. 510, 1018 (1999); M. Dikpati and P. A. Gilman, Astrophys. J. 512, 417 (1999)] suggest mechanisms for achieving enhanced horizontal turbulent mixing in the tachocline.
14. The radial gradients of angular velocity Ω in the tachocline may arise from anisotropic turbulent mixing of angular momentum in the stably stratified boundary layer at the base of the convection zone. The much stronger transport in the latitudinal direction than in the radial direction serves to circumvent the diffusive spread of latitudinal differential rotation into the deeper interior over long time scales [E. A. Spiegel and J.-P. Zahn, Astron. Astrophys. 265, 106 (1992); J. R. Elliott, Astron. Astrophys. 327, 1222 (1997)]. Other models invoke magnetic fields to enforce solid-body rotation in the radiative interior [D. O. Gough and M. E. McIntyre, Nature 394, 755 (1998)]. Linear instability studies of latitudinal shear combined with toroidal magnetic fields [P. A. Gilman and P. A. Fox, Astrophys. J. 510, 1018 (1999); M. Dikpati and P. A. Gilman, Astrophys. J. 512, 417 (1999)] suggest mechanisms for achieving enhanced horizontal turbulent mixing in the tachocline.
15. The radial gradients of angular velocity Ω in the tachocline may arise from anisotropic turbulent mixing of angular momentum in the stably stratified boundary layer at the base of the convection zone. The much stronger transport in the latitudinal direction than in the radial direction serves to circumvent the diffusive spread of latitudinal differential rotation into the deeper interior over long time scales [E. A. Spiegel and J.-P. Zahn, Astron. Astrophys. 265, 106 (1992); J. R. Elliott, Astron. Astrophys. 327, 1222 (1997)]. Other models invoke magnetic fields to enforce solid-body rotation in the radiative interior [D. O. Gough and M. E. McIntyre, Nature 394, 755 (1998)]. Linear instability studies of latitudinal shear combined with toroidal magnetic fields [P. A. Gilman and P. A. Fox, Astrophys. J. 510, 1018 (1999); M. Dikpati and P. A. Gilman, Astrophys. J. 512, 417 (1999)] suggest mechanisms for achieving enhanced horizontal turbulent mixing in the tachocline.
16. The nearly adiabatic stratification of the convection zone has been determined to extend to a depth of 0.287R below the surface, using helioseismic data, with an uncertainty of 0.003R or better [J. Christensen-Dalsgaard, D. O. Gough, M. J. Thompson, Astrophys. J. 378, 413 (1991); S. Basu and H. M. Antia, Mon. Not. R. Astron. Soc. 287, 189 (1997)]. The base of this zone at radius 0.713R may be contrasted to helioseismic estimates that place the midpoint of the tachocline at radius 0.692R, with a thickness estimated to be of the order of 0.02R to 0.09R [A. G. Kosovichev, Astrophys. J. 469, L61 (1996); T. Corbard, G. Berthomieu, J. Provost, P. Morel, Astron. Astrophys. 330, 1149 (1998); P. Charbonneau et al., Astrophys. J. 527, 445 (1999); (17)]. Thus, the tachocline is largely embedded in a region of very stable stratification.
17. The nearly adiabatic stratification of the convection zone has been determined to extend to a depth of 0.287R below the surface, using helioseismic data, with an uncertainty of 0.003R or better [J. Christensen-Dalsgaard, D. O. Gough, M. J. Thompson, Astrophys. J. 378, 413 (1991); S. Basu and H. M. Antia, Mon. Not. R. Astron. Soc. 287, 189 (1997)]. The base of this zone at radius 0.713R may be contrasted to helioseismic estimates that place the midpoint of the tachocline at radius 0.692R, with a thickness estimated to be of the order of 0.02R to 0.09R [A. G. Kosovichev, Astrophys. J. 469, L61 (1996); T. Corbard, G. Berthomieu, J. Provost, P. Morel, Astron. Astrophys. 330, 1149 (1998); P. Charbonneau et al., Astrophys. J. 527, 445 (1999); (17)]. Thus, the tachocline is largely embedded in a region of very stable stratification.
18. The nearly adiabatic stratification of the convection zone has been determined to extend to a depth of 0.287R below the surface, using helioseismic data, with an uncertainty of 0.003R or better [J. Christensen-Dalsgaard, D. O. Gough, M. J. Thompson, Astrophys. J. 378, 413 (1991); S. Basu and H. M. Antia, Mon. Not. R. Astron. Soc. 287, 189 (1997)]. The base of this zone at radius 0.713R may be contrasted to helioseismic estimates that place the midpoint of the tachocline at radius 0.692R, with a thickness estimated to be of the order of 0.02R to 0.09R [A. G. Kosovichev, Astrophys. J. 469, L61 (1996); T. Corbard, G. Berthomieu, J. Provost, P. Morel, Astron. Astrophys. 330, 1149 (1998); P. Charbonneau et al., Astrophys. J. 527, 445 (1999); (17)]. Thus, the tachocline is largely embedded in a region of very stable stratification.
19. The nearly adiabatic stratification of the convection zone has been determined to extend to a depth of 0.287R below the surface, using helioseismic data, with an uncertainty of 0.003R or better [J. Christensen-Dalsgaard, D. O. Gough, M. J. Thompson, Astrophys. J. 378, 413 (1991); S. Basu and H. M. Antia, Mon. Not. R. Astron. Soc. 287, 189 (1997)]. The base of this zone at radius 0.713R may be contrasted to helioseismic estimates that place the midpoint of the tachocline at radius 0.692R, with a thickness estimated to be of the order of 0.02R to 0.09R [A. G. Kosovichev, Astrophys. J. 469, L61 (1996); T. Corbard, G. Berthomieu, J. Provost, P. Morel, Astron. Astrophys. 330, 1149 (1998); P. Charbonneau et al., Astrophys. J. 527, 445 (1999); (17)]. Thus, the tachocline is largely embedded in a region of very stable stratification.
20. The nearly adiabatic stratification of the convection zone has been determined to extend to a depth of 0.287R below the surface, using helioseismic data, with an uncertainty of 0.003R or better [J. Christensen-Dalsgaard, D. O. Gough, M. J. Thompson, Astrophys. J. 378, 413 (1991); S. Basu and H. M. Antia, Mon. Not. R. Astron. Soc. 287, 189 (1997)]. The base of this zone at radius 0.713R may be contrasted to helioseismic estimates that place the midpoint of the tachocline at radius 0.692R, with a thickness estimated to be of the order of 0.02R to 0.09R [A. G. Kosovichev, Astrophys. J. 469, L61 (1996); T. Corbard, G. Berthomieu, J. Provost, P. Morel, Astron. Astrophys. 330, 1149 (1998); P. Charbonneau et al., Astrophys. J. 527, 445 (1999); (17)]. Thus, the tachocline is largely embedded in a region of very stable stratification.
21. The GONG project is described by J. W. Harvey et al. [Science 272, 1284 (1996)], and the Solar Oscillation Investigation (SOI), which utilizes the MDI instrument, is described by P. H. Scherrer et al., Sol. Phys. 162, 129 (1995).
22. The GONG project is described by J. W. Harvey et al. [Science 272, 1284 (1996)], and the Solar Oscillation Investigation (SOI), which utilizes the MDI instrument, is described by P. H. Scherrer et al., Sol. Phys. 162, 129 (1995).
23. 35, for ∼1800 multiplets with l ≤ 300. The GONG and MDI data analyses continue to be extended as new observational data become available.
24. In the OLA inversion, linear combinations of the observations are formed such as to correspond to localized averages, in radius and latitude, of the angular velocity, while controlling the error in the inference [F. P. Pijpers and M. J. Thompson, Astron. Astrophys. 262, L33 (1992); see also (16)]. In the RLS technique, a parameterized representation of Ω is fitted to the observations in a least squares sense, including in the minimization of an integral of the square of the second derivative of Ω; this term suppresses the tendency for rapid variations in the solution and also, implicitly, limits the error (18). The methods are controlled by trade-off parameters that provide a balance between resolution and errors. In both cases, the inference can be represented as an average of the true solution, weighted by an averaging kernel whose extent provides a measure of the resolution. In addition to the error, it is also important to take into account the error correlation between the inferences at different locations in the sun [R. Howe and M. J. Thompson, Mon. Not. R. Astron. Soc. 281, 1385 (1996); D. O. Gough, T. Sekii, P. Stark, Astrophys. J. 459, 779 (1996)].
25. In the OLA inversion, linear combinations of the observations are formed such as to correspond to localized averages, in radius and latitude, of the angular velocity, while controlling the error in the inference [F. P. Pijpers and M. J. Thompson, Astron. Astrophys. 262, L33 (1992); see also (16)]. In the RLS technique, a parameterized representation of Ω is fitted to the observations in a least squares sense, including in the minimization of an integral of the square of the second derivative of Ω; this term suppresses the tendency for rapid variations in the solution and also, implicitly, limits the error (18). The methods are controlled by trade-off parameters that provide a balance between resolution and errors. In both cases, the inference can be represented as an average of the true solution, weighted by an averaging kernel whose extent provides a measure of the resolution. In addition to the error, it is also important to take into account the error correlation between the inferences at different locations in the sun [R. Howe and M. J. Thompson, Mon. Not. R. Astron. Soc. 281, 1385 (1996); D. O. Gough, T. Sekii, P. Stark, Astrophys. J. 459, 779 (1996)].
26. In the OLA inversion, linear combinations of the observations are formed such as to correspond to localized averages, in radius and latitude, of the angular velocity, while controlling the error in the inference [F. P. Pijpers and M. J. Thompson, Astron. Astrophys. 262, L33 (1992); see also (16)]. In the RLS technique, a parameterized representation of Ω is fitted to the observations in a least squares sense, including in the minimization of an integral of the square of the second derivative of Ω; this term suppresses the tendency for rapid variations in the solution and also, implicitly, limits the error (18). The methods are controlled by trade-off parameters that provide a balance between resolution and errors. In both cases, the inference can be represented as an average of the true solution, weighted by an averaging kernel whose extent provides a measure of the resolution. In addition to the error, it is also important to take into account the error correlation between the inferences at different locations in the sun [R. Howe and M. J. Thompson, Mon. Not. R. Astron. Soc. 281, 1385 (1996); D. O. Gough, T. Sekii, P. Stark, Astrophys. J. 459, 779 (1996)].
27. The agreement between OLA and RLS inversion methods can be assessed by examining the difference between OLA and RLS rotation residuals δΩ at a given location. As can be seen in Fig. 2, these are within 1σ in all but a few cases, and the root mean square of the difference to error ratio for each of the cases illustrated is less than unity.
28. 2 for all combinations at this location is mostly due to the increase in amplitude later in the period, which is not well reproduced by a single sine wave.
29. Global simulations of turbulent compressible convection in full spherical shells to study the resulting differential rotation have been discussed by J. R. Elliott et al., in Structure and Dynamics of the Interior of the Sun and Sun-Like Stars, S. Korzennik and A. Wilson, Eds. (ESA SP-418, European Space Agency, Noordwijk, Netherlands, 1998), pp. 765-770; J. R. Elliott, M. S. Miesch, J. Toomre, Astrophys. J. 533, 548 (2000); and M. S. Miesch et al., Astrophys. J., 532, 593 (2000).
30. Global simulations of turbulent compressible convection in full spherical shells to study the resulting differential rotation have been discussed by J. R. Elliott et al., in Structure and Dynamics of the Interior of the Sun and Sun-Like Stars, S. Korzennik and A. Wilson, Eds. (ESA SP-418, European Space Agency, Noordwijk, Netherlands, 1998), pp. 765-770; J. R. Elliott, M. S. Miesch, J. Toomre, Astrophys. J. 533, 548 (2000); and M. S. Miesch et al., Astrophys. J., 532, 593 (2000).
31. Global simulations of turbulent compressible convection in full spherical shells to study the resulting differential rotation have been discussed by J. R. Elliott et al., in Structure and Dynamics of the Interior of the Sun and Sun-Like Stars, S. Korzennik and A. Wilson, Eds. (ESA SP-418, European Space Agency, Noordwijk, Netherlands, 1998), pp. 765-770; J. R. Elliott, M. S. Miesch, J. Toomre, Astrophys. J. 533, 548 (2000); and M. S. Miesch et al., Astrophys. J., 532, 593 (2000).
32. Helioseismic inferences regarding the nature of banded zonal flows in the upper regions of the solar convection zone, and their equatorward migration, are presented by J. Schou et al., in Proceedings of IAU Symposium 185. New Eyes to See Inside the Sun and Stars. F.-L. Deubner, J. Christensen-Dalsgaard, D. W. Kurtz, Eds. (Kluwer, Dordrecht, Netherlands, 1998), pp. 199-212; J. Schou, Astrophys. J. 523, L181 (1999); R. Howe, R. W. Komm, F. Hill, Sol. Phys., in press; R. Howe et al., Astrophys J., in press; and J. Toomre et al., Sol. Phys., in press. Similar flows on the solar surface had previously been detected through direct Doppler observations [R. Howard and B. J. LaBonte, Astrophys. J. 239, L33 (1980)]. For extensive results of surface observations of these flows, see work by R. K. Ulrich, in Structure and Dynamics of the Interior of the Sun and Sun-Like Stars, S. Korzennik and A. Wilson, Eds. (ESA SP-418, European Space Agency, Noordwijk, Netherlands, 1998), pp. 851-855.
33. Helioseismic inferences regarding the nature of banded zonal flows in the upper regions of the solar convection zone, and their equatorward migration, are presented by J. Schou et al., in Proceedings of IAU Symposium 185. New Eyes to See Inside the Sun and Stars. F.-L. Deubner, J. Christensen-Dalsgaard, D. W. Kurtz, Eds. (Kluwer, Dordrecht, Netherlands, 1998), pp. 199-212; J. Schou, Astrophys. J. 523, L181 (1999); R. Howe, R. W. Komm, F. Hill, Sol. Phys., in press; R. Howe et al., Astrophys J., in press; and J. Toomre et al., Sol. Phys., in press. Similar flows on the solar surface had previously been detected through direct Doppler observations [R. Howard and B. J. LaBonte, Astrophys. J. 239, L33 (1980)]. For extensive results of surface observations of these flows, see work by R. K. Ulrich, in Structure and Dynamics of the Interior of the Sun and Sun-Like Stars, S. Korzennik and A. Wilson, Eds. (ESA SP-418, European Space Agency, Noordwijk, Netherlands, 1998), pp. 851-855.
34. Helioseismic inferences regarding the nature of banded zonal flows in the upper regions of the solar convection zone, and their equatorward migration, are presented by J. Schou et al., in Proceedings of IAU Symposium 185. New Eyes to See Inside the Sun and Stars. F.-L. Deubner, J. Christensen-Dalsgaard, D. W. Kurtz, Eds. (Kluwer, Dordrecht, Netherlands, 1998), pp. 199-212; J. Schou, Astrophys. J. 523, L181 (1999); R. Howe, R. W. Komm, F. Hill, Sol. Phys., in press; R. Howe et al., Astrophys J., in press; and J. Toomre et al., Sol. Phys., in press. Similar flows on the solar surface had previously been detected through direct Doppler observations [R. Howard and B. J. LaBonte, Astrophys. J. 239, L33 (1980)]. For extensive results of surface observations of these flows, see work by R. K. Ulrich, in Structure and Dynamics of the Interior of the Sun and Sun-Like Stars, S. Korzennik and A. Wilson, Eds. (ESA SP-418, European Space Agency, Noordwijk, Netherlands, 1998), pp. 851-855.
35. Helioseismic inferences regarding the nature of banded zonal flows in the upper regions of the solar convection zone, and their equatorward migration, are presented by J. Schou et al., in Proceedings of IAU Symposium 185. New Eyes to See Inside the Sun and Stars. F.-L. Deubner, J. Christensen-Dalsgaard, D. W. Kurtz, Eds. (Kluwer, Dordrecht, Netherlands, 1998), pp. 199-212; J. Schou, Astrophys. J. 523, L181 (1999); R. Howe, R. W. Komm, F. Hill, Sol. Phys., in press; R. Howe et al., Astrophys J., in press; and J. Toomre et al., Sol. Phys., in press. Similar flows on the solar surface had previously been detected through direct Doppler observations [R. Howard and B. J. LaBonte, Astrophys. J. 239, L33 (1980)]. For extensive results of surface observations of these flows, see work by R. K. Ulrich, in Structure and Dynamics of the Interior of the Sun and Sun-Like Stars, S. Korzennik and A. Wilson, Eds. (ESA SP-418, European Space Agency, Noordwijk, Netherlands, 1998), pp. 851-855.
36. Helioseismic inferences regarding the nature of banded zonal flows in the upper regions of the solar convection zone, and their equatorward migration, are presented by J. Schou et al., in Proceedings of IAU Symposium 185. New Eyes to See Inside the Sun and Stars. F.-L. Deubner, J. Christensen-Dalsgaard, D. W. Kurtz, Eds. (Kluwer, Dordrecht, Netherlands, 1998), pp. 199-212; J. Schou, Astrophys. J. 523, L181 (1999); R. Howe, R. W. Komm, F. Hill, Sol. Phys., in press; R. Howe et al., Astrophys J., in press; and J. Toomre et al., Sol. Phys., in press. Similar flows on the solar surface had previously been detected through direct Doppler observations [R. Howard and B. J. LaBonte, Astrophys. J. 239, L33 (1980)]. For extensive results of surface observations of these flows, see work by R. K. Ulrich, in Structure and Dynamics of the Interior of the Sun and Sun-Like Stars, S. Korzennik and A. Wilson, Eds. (ESA SP-418, European Space Agency, Noordwijk, Netherlands, 1998), pp. 851-855.
37. Helioseismic inferences regarding the nature of banded zonal flows in the upper regions of the solar convection zone, and their equatorward migration, are presented by J. Schou et al., in Proceedings of IAU Symposium 185. New Eyes to See Inside the Sun and Stars. F.-L. Deubner, J. Christensen-Dalsgaard, D. W. Kurtz, Eds. (Kluwer, Dordrecht, Netherlands, 1998), pp. 199-212; J. Schou, Astrophys. J. 523, L181 (1999); R. Howe, R. W. Komm, F. Hill, Sol. Phys., in press; R. Howe et al., Astrophys J., in press; and J. Toomre et al., Sol. Phys., in press. Similar flows on the solar surface had previously been detected through direct Doppler observations [R. Howard and B. J. LaBonte, Astrophys. J. 239, L33 (1980)]. For extensive results of surface observations of these flows, see work by R. K. Ulrich, in Structure and Dynamics of the Interior of the Sun and Sun-Like Stars, S. Korzennik and A. Wilson, Eds. (ESA SP-418, European Space Agency, Noordwijk, Netherlands, 1998), pp. 851-855.
38. Helioseismic inferences regarding the nature of banded zonal flows in the upper regions of the solar convection zone, and their equatorward migration, are presented by J. Schou et al., in Proceedings of IAU Symposium 185. New Eyes to See Inside the Sun and Stars. F.-L. Deubner, J. Christensen-Dalsgaard, D. W. Kurtz, Eds. (Kluwer, Dordrecht, Netherlands, 1998), pp. 199-212; J. Schou, Astrophys. J. 523, L181 (1999); R. Howe, R. W. Komm, F. Hill, Sol. Phys., in press; R. Howe et al., Astrophys J., in press; and J. Toomre et al., Sol. Phys., in press. Similar flows on the solar surface had previously been detected through direct Doppler observations [R. Howard and B. J. LaBonte, Astrophys. J. 239, L33 (1980)]. For extensive results of surface observations of these flows, see work by R. K. Ulrich, in Structure and Dynamics of the Interior of the Sun and Sun-Like Stars, S. Korzennik and A. Wilson, Eds. (ESA SP-418, European Space Agency, Noordwijk, Netherlands, 1998), pp. 851-855.
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48. This work uses data obtained by the GONG project, managed by the National Solar Observatory, a division of the National Optical Astronomy Observatories, which is operated by the Association of Universities for Research in Astronomy (AURA), under a cooperative agreement with NSF. The data were acquired by instruments operated by the Big Bear Solar Observatory, High Altitude Observatory, Learmonth Solar Observatory, Udaipur Solar Observatory, Instituto de Astrofísico de Canarias, and Cerro Tololo Interamerican Observatory. The SOI involving MDI is supported by NASA grant NAG 5-3077 to Stanford University. SOHO is a mission of international cooperation between ESA and NASA. R.W.K. and, in part, R.H. were supported by NASA contract S-92698-F. J.C.-D. was supported in part by the Danish National Research Foundation through the establishment of the Theoretical Astrophysics Center. M.J.T. was supported in part by the UK Particle Physics and Astronomy Research Council. J.T. was supported in part by NASA through grants NAG 5-7996 and NAG 5-8133 and by NSF through grant ATM-9731676. We thank D. O. Gough for helpful comments on the manuscript.