Стійкий метод визначення напруженості магнітного поля у фотосфері Сонця
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| 1Присяжний, АІ, 1Стоділка, МІ, 2Щукіна, НГ 1Астрономічна обсерваторія Львівського національного університету імені Івана Франка, Львів, Україна 2Головна астрономічна обсерваторія Національної академії наук України, Київ, Україна |
| Kinemat. fiz. nebesnyh tel (Online) 2018, 34(6):3-21 |
| Start Page: Фізика Сонця |
| Мова: українська |
Анотація: Запропоновано модифікацію класичного методу визначення напруженості магнітного поля за відстанню між положеннями піків синього і червоного крил V-профілю Стокса магніточутливої спектральної лінії. Для зменшення впливу шумів та більш коректного визначення відстані між положеннями піків спостережуваний профіль Стокса V було апроксимовано модифікованою вейвлет-функцією. Оптимальні значення коефіцієнтів апроксимаційної функції було визначено шляхом багатовимірної оптимізації. В рамках даного підходу напруженість магнітного поля можна знайти аналітично за відомими коефіцієнтами апроксимаційної функції. Для тестування методу було використано V-профілі Стокса спектральної лінії нейтрального заліза Fe Iλ 1564.8 нм. Профілі було синтезовано з використанням тривимірної фотосферної моделі магнітоконвекції Ремпеля. Показано результат застосування запропонованого методу до спостережуваних V-профілів Стокса. Даний метод менш чутливий до шумів та форми спостережуваного сигналу, що дозволяє отримувати більш надійні значення напруженості магнітного поля із спостережень у порівнянні з класичним методом визначення напруженості поля за розщепленням профілю Стокса V. |
| Ключові слова: діагностика, ефект Зеємана, магнітні поля, Сонце, фотосфера |
References:
1. Beck C. An uncombed inversion of multiwavelength observations reproducing the net circular polarization in a sunspot’s penumbra. Astron. and Astrophys. 2011. 525. P. 1—17.
2. Bellot Rubio L. R. The fine structure of the penumbra: from observations to realistic physical models. ASP Conf. Ser. 2003. 3o7. P. 301—323. (Proceedings ofthe Conference held 30 September — 4 October, 2002 at Tenerife, Canary Islands, Spain. Edited by Javier Trujillo-Bueno and Jorge Sanchez Almeida.).
3. Bellot Rubio L. R., Balthasar H., Collados M. Two magnetic components in sunspot penumbrae. Astron. and Astrophys. 2004. 427. P. 319—334.
4. Bellot Rubio L. R., Balthasar H., Collados M., Schlichenmaier R. Field-aligned Evershed flows in the photosphere of a sunspot penumbra. Astron. and Astrophys. 2003. 403. P. L47—L50.
5. Bellot Rubio L. R., Collados M. Understanding internetwork magnetic fields as determined from visible and infrared spectral lines. Astron. and Astrophys. 2003. 406. P. 357—362.
6. Bellot Rubio L. R., Collados M., Ruiz Cobo B., Rodriguez Hidalgo I. Oscillations in the photosphere of a sunspot umbra from the invertion of inirated Stokes protiles. Astrophys. J. 2000. 534. P. 989—996.
7. Bellot Rubio L. R., Rodriguez Hidalgo I., Collados M., et al. Observation of convective collapse and upward-moving shocks in the quiet Sun. Astrophys. J. 2001. 560. P. 1010—1019.
8. Borrero J. M., Asensio Ramos A., Collados M., et al. Deep probing of the photospheric sunspot penumbra: no evidence of field-free gaps. Astron. and Astrophys. 2016. 596. P. 1—14.
9. Borrero J. M., Bellot Rubio L. R., Barklem P. S., Del Toro Iniesta J. C. Accurate atomic parameters for near-infrared spectral lines. Astron. and Astrophys. 2003. 404. P. 749—762.
10. Borrero J. M., Franz M., Schlichenmaier R., et al. Penumbral thermal structure below the visible surface. Astron. and Astrophys. 2017. 601. L8. P. 1—4.
11. Borrero J. M., Lagg A., Solanki S. K., et al. Modeling the fine structure of a sunspot penumbra through the inversion of Stokes profiles. ASP Conf. Ser. 2003. 286. P. 235—242. (Current Theoretical Models and Future High Resolution Solar Observations: Preparing for ATST, held 11-15 March 2002 at NSO, Sunspot, New Mexico, USA. Edited by Alexei A. Pevtsov and Han Uitenbroek. San Francisco: Astronomical Society of the Pacific).
12. Borrero J. M., Lagg A., Solanki S. K., Collados M. On the fine structure of sunspot penumbrae. II. The nature of the Evershed flow. Astron. and Astrophys. 2005. 436. P. 333—345.
13. Borrero J. M., Solanki S. K. Convective motions and net circular polarization in sunspot penumbrae. Astrophys. J.2010. 709. P. 349—357.
14. Borrero J. M., Solanki S. K., Bellot Rubio L. R., et al. On the fine structure of sunspot penumbrae. I. A quantitative comparison of two semiempirical models with implications for the Evershed effect. Astron. and Astrophys. 2004. 422. P. 1093— 1104.
15. Cabrera Solana D., Bellot Rubio L. R., Del Toro Iniesta J. C. Sensitivity of spectral lines to temperature, velocity, and magnetic field. Astron. and Astrophys. 2005. 439. P. 687—699.
16. Carroll T. A., Staude J. The inversion of Stokes profiles with artificial neural networks. Astron. and Astrophys. 2001. 378. P. 316—326.
17. Collados M. Infrared polarimetry. ASP Conf. Ser. 2001. 236. P. 255—271. (Advanced Solar Polarimetry — Theory, Observation, and Instrumentation — 20th NSO/Sac Summer Workshop. Edited by M. Sigwarth. San Francisco: Astronomical Society of the Pacific).
18. Danilovic S., Schüssler M., Solanki S. K. Probing quiet Sun magnetism using MURaM simulations and Hinode/SP results: support for a local dynamo. Astron. and Astrophys. 2010. 513. A1. P. 1—8.
19. Degenhardt D., Solanki S. K., Montesinos B., Thomas J. H. Evidence for siphon flows with shocks in solar magnetic flux tubes. Astron. and Astrophys. 1993. 279. P. L29—L32.
20. Deming D., Hewagama T., Jennings D. E., Wiedemann G. Polarimetry in the infrared. Solar Polarimetry, Proceedings of the 11th Sacramento Peak Summper Workshop. Edited by L. J. November. Sunspot, NM: National Solar Observatory. 1991. P. 341—355.
21. Dominguez Cerdeña I., Sánchez Almeida J., Kneer F. Quiet-Sun magnetic fields: Simultaneous inversion of visible and IR spectro-polarimetric observations. ASP Conf. Ser. 2006. 358. P. 88—91. (Proceedings of the conference held 19-23 September, 2005, in Boulder, Colorado, USA. Edited by R. Casini and B. W. Lites).
22. Dominguez Cerdeña I., Sánchez Almeida J., Kneer F. Quiet Sun magnetic fields from simultaneous inversions of visible and infrared spectropolarimetric observations. Astrophys. J. 2006. 646. P. 1421—1435.
23. Franz M., Collados M., Bethge C., et al. Magnetic fields of opposite polarity in sunspot penumbrae. Astron. and Astrophys. 2016. 596, A4. P. 1—13.
24. Golub L., Giampapa M. S., Worden S. P. The magnetic field on the RS Canum Venaticorum star Lambda Andromedae. Astrophys. J. 1983. 268. P. L121—L125.
25. Gondoin Ph., Giampapa M. S., Bookbinder J. A. Stellar magnetic field measurements utilizing infrared spectral lines. Astrophys. J.1985. 297. P. 710—718.
26. Hanle W. Über magnetische Beeinflussung der Polarisation der Resonanzfluoreszenz. Zeitschrift für Physik. 1924. 30. P. 93—105.
27. Harvey J. W. Observations of small-scale photospheric magnetic fields. Highlights of Astronomy. 1977. 4. P. 223—239.
28. Harvey J. W., Hall D. Magnetic field observations with Fe I λ 15648 Å. Bull. Amer. Astron. Soc. 1975. 7. P. 459.
29. Khomenko E. Diagnostics of quiet-Sun magneiism. ASP Conf. Ser. 2006. 354. P. 63—76. (Proceedings of the Conference Held 18-22 July, 2005, at the National Solar Observatory, Sacramento Peak, Sunspot, New Mexico, USA. Edited by J. Leibacher, R. F. Stein, and H. Uitenbroek. San Francisco: Astronomical Society of the Pacific).
30. Khomenko E. V., Collados M. On the determination of magnetic field strength and flux in inter-network. ASP Conf. Ser. 2006. 358. P. 42—47. (Proceedings of the conference held 19-23 September, 2005, in Boulder, Colorado, USA. Eds R. Casini, B. W. Lites).
31. Khomenko E. V., Collados M. On the Stokes V amplitude ratio as an indicator of the field strength in the solar internetwork. Astrophys. J. 2007. 659. P. 1726—1735.
32. Khomenko E. V., Collados M., Bellot Rubio L. R. Magnetoacoustic waves in sunspots. Astrophys. J. 2003. 588. P. 606—619.
33. Khomenko E. V., Collados M., Bellot Rubio L. R., et al. Formation and destruction of a weak magnetic feaiure in the soiar photosphere. Magnetic Fields and Soiar Pro i cesses. The 9th European Meeting on Solar Physics, held 12—18 September, 1999, in Florence, Italy. Edited by A. Wilson. European Space Agency. P. 307.
34. Khomenko E. V., Collados M., Solanki S. K., et al. Quiet-Sun inter-network magnetic fields observed in the infrared. Astron. and Astrophys. 2003. 408. P. 1115—1135.
35. Khomenko E. V., Shelyag S., Solanki S. K., et al. Stokes diagnostics of magneto-convection. Profile shapes and asymmetries. Multi-Wavelength Investigations of Solar Activity, IAU Symposium. Cambridge University Press. 2004. 223. P. 635—636.
36. Khomenko E. V., Shelyag S., Solanki S. K., Vögler A. Stokes diagnostics of simulations of magnetoconvection of mixed-polarity quiet-Sun regions. Astron. and Astrophys. 2005. 442. P. 1059—1078.
37. Kopp G., Rabin D. A relation between magnetic field strength and temperature in sunspots. Solar Phys. 1992. 141. P. 253—265.
38. Kopp M. G., Rabin D. Magnetic field strength and continuum intensity measurements of sunspots at 1.56 microns. ASP Conf. Ser. 1992. 26. P. 246—248. (Cool stars, stellar systems, and the Sun, Proceedings of the 7th Cambridge Workshop).
39. Kostik R., Khomenko E. V. Properties of convective motions in facular regions. Astron. and Astrophys. 2012. 545. A22. P. 1—9.
40. Kostik R., Khomenko E. V. Properties of oscillatory motions in a facular region. Astron. and Astrophys. 2013. 559. A107. P. 1—10.
41. Lagg A., Solanki S. K., Doerr H.-P., et al. Probing deep photospheric layers of the quiet Sun with high magnetic sensitivity. Astron. and Astrophys. 2016. 596. A6. P. 1—13.
42. Landi Degl’Innocenti E., Landolfi M. Polarization in spectral lines. Dordrecht: Kluwer Academic Publishers. 2004. 890 p.
43. Lin H. On the distribution of the solar magnetic fields. Astrophys. J. 1995. 446. P. 421.
44. Lin H., Rimmele T. The granular magnetic fields of the quiet Sun. Astrophys. J. 1999. 514. P. 448—455.
45. Litzen U., Verges J. The Fe I spectrum in the region 1 - 4 μm. Physica Scripta, 1976. 13. P. 240—244.
46. Livingston W. Sampling V-Stokes on the solar disk with Fe I 15648 Å and H Paschen β. Solar Polarimetry, Proceedings of the 11th Sacramento Peak Summer Workshop. Edtted by L. J. November. Sunspot, NM: National Sotar Observatory. 1991. P. 356—360.
47. Livingston W. Sunspot umbrae: Observed correlation between magnetic field and temperature. Bull. Amer. Astron. Soc. 1991.23.P. 1030.
48. Livingston W. Sunspots observed to phystcally weaken in 2000-2001. Solar Phys. 2002. 207. P. 41—45.
49. Livingston W., Watson F. A new solar signal: Average maximum sunspot magnetic fields independent of activity cycle. Geophys. Res. Lett. 2015. 42. P. 9185—9189.
50. Lopez Ariste A., Tomczyk S., Casini R. Hyperfine structure as a diagnostic of solar magnetic fields. Astrophys. J. 2002. 580. P. 519—527.
51. Manso Sainz R., Landi Degl’Innocenti E., Trujillo Bueno J. Concerning the existence of a "turbulent" magnetic field in the quiet Sun. Astrophys. J. 2004. 614. P. L89—L91.
52. Martinez González M. J., Pastor Yabar A., Lagg A., et al. Inference of magnetic fields in the very quiet Sun. Astron. and Astrophys. 2016. 596. A5. P. 1—11.
53. Mathew S. K., Lagg A., Solanki S. K., et al. Three dimensional structure of a regular sunspot from the inversion of IR Stokes profiles. Astron. and Astrophys. 2003. 410. P. 695—710.
54. Mathew S. K., Solanki S. K., Lagg A., et al. Thermal-magnetic relation of a sunspot as inferred from the inversion of 1.5 μm spectral data. SOLMAG 2002. Proceedings of the Magnetic Coupling of the Solar Atmosphere Euroconference and IAU Colloquium 188. 11—15 June 2002. P. 501—503.
55. Mathew S. K., Solanki S. K., Lagg A., et al. Structure of a simple sunspot from the inversion of IR spectral data. Astron. Nachr. 2003. 324. P. 388—389.
56. Mathew S. K., Solanki S. K., Lagg A., et al. Thermal-magnetic relation in a sunspot and a map of its Wilson depression. Astron. and Astrophys. 2004. 422. P. 693—701.
57. McPherson M. R., Lin H., Kuhn J. R. Infrared array measurements of sunspot magnetic fields. Solar Phys. 1992. 139. P. 255—266.
58. Moran T., Deming D., Jennings D. E., McCabe G. Solar magnetic field studies using the 12 micron emission lines. III. Simultaneous measurements at 12 and 1.6 microns. Astrophys. J. 2000. 533. P. 1035—1042.
59. Muglach K., Solanki S. K. Infrared lines as probes of solar magnetic features. I - A many-line analytis of a network region. Astron. and Astrophys. 1992. 263. P. 301—311.
60. Muglach K., Solanki S. K., Livingston W. C. Preliminary properties of pores derived from 1.56 micron lines. Solar Surface Magnetism. NATO Advanced Science Institutes (ASI) Series C: Mathematical and Physical Sciences, Proc. NATO Adv. Res. Workshop. 1994. P. 127.
61. Müller D. A. N., Schlichenmaier R., Steiner O., Stix M. Spectral signature of magnetic flux tubes in sunspot penumbrae. Astron. and Astrophys. 2002. 393. P. 305—319.
62. Orozco Suárez D., Bellot Rubio L. R., Vögler A., Del Toro Iniesta J. C. Applicability of Milne-Eddington inversions to high spatial resolution observations of the quiet Sun. Astron. and Astrophys. 2010. 518. A2. P. 1—11.
63. Penn M. J. Infrared solar physics. Liv. Rev. Solar Phys. 2014. 11, article id. 2. P. 1—66.
64. Penn M. J., Ceja J. A., Bell E., et al. Infrared spectroscopy from San Fernando observatory: He I 1083 nm, O I 1316 nm, and Fe I 1565 nm. Solar Phys. 2002. 205. P. 53—61.
65. Penn M. J., Walton S., Chapman G., et al. Temperature dependence of molecular line strengths and Fe I 1565 nm Zeeman splitting in a sunspot. Solar Phys. 2003. 213. P. 55—67.
66. Press W. H., Teukolsky S. A., Vetterling W. T., Flannery B. P. Numerical recipes in C: The art of scientific computing, second edition. Cambridge University Press. 1988. 925 p.
67. Rabin D. Spatially extended measurements of magnetic field strength in solar plages. Astrophys. J. 1992. 391. P. 832—844.
68. Rabin D. A true-field magnetogram in a solar plage region. Astrophys. J. 1992. 390. P. L103—L106.
69. Rabin D. Fine-scale magnetic fields in the solar photosphere. ASP Conf. Ser. 1992. 26. P. 201—210. (Cool stars, stellar systems, and the sun, Proceedings of the 7th Cambridge Workshop).
70. Rabin D. M., Graves J. E. Measuring sunspot magnetic fields with the infrared line Fe I λ 15649. Bull. Amer. Astron. Soc. 1989. 21. P. 854.
71. Rabin D., Jaksha D., Plymate C., et al. Plage magnetic field strengths from near-infrared spectra. Solar Polarimetry, Proc. 11th Sacramento Peak Summer Workshop. Edited by L. J. November. Sunspot, NM: National Solar Observatory. 1991. P. 361—370.
72. Rees D. E., Durrant C. J., Murphy G. A. Stokes profile analysis and vector magnetic fields. II - Formal numerical solutions of the Stokes transfer equations. Astrophys. J. 1989. 339. P. 1093—1106.
73. Rempel M. Numerical simulations of quiet Sun magnetism: On the contribution from a small-scale dynamo. Astrophys. J. 2014. 789. Id. 132. P. 1—22.
74. Rempel M., Schüssler M., Knölker M. Radiative magnetohydrodynamic simulation of sunspot structure. Astrophys. J.2009. 691.P. 640—649.
75. Rüedi I., Solanki S. K., Livingston W. Infrared lines as probes of solar magnetic features. XI. Structure of a sunspot umbra with a light bridge. Astron. and Astrophys. 1995. 302. P. 543—550.
76. Rüedi I., Solanki S. K., Livingston W., Stenflo J. O. Infrared lines as probes of solar magnetic features. III - Strong and weak magnetic fields in plages. Solar Phys. 1992. 263. P. 323—338.
77. Rüedi I., Solanki S. K., Rabin D. Infrared lines as probes of solar magnetic features. IV - Discovery of a siphon flow. Astron. and Astrophys. 1992. 261. P. L21—L24.
78. Ruiz Cobo B., Del Toro Iniesta J. C. Inversion of Stokes profiles. Astrophys. J. 1992. 398. P. 375—385.
79. Sánchez Almeida J. Physical properties of the solar magnetic photosphere under the MISMA hypothesis. I. Description of the inversion procedure. Astrophys. J. 1997. 491. P. 993—1008.
80. Sánchez Almeida J. Physical properties of the solar magnetic photosphere under the MISMA hypothesis. III. Sunspot at Disk Center. Astrophys. J. 2005. 622. P. 1292—1313.
81. Sánchez Almeida J., Dominguez Cerdeña I., Kneer F. Simultaneous visible and infrared spectropolarimetry of a solar internetwork region. Astrophys. J. 2003. 597. P. L177—L180.
82. Sánchez Almeida J., Martinez González M. J. The magnetic fields of the quiet Sun. ASP Conf. Ser. 2011. 437. P. 451—469. (Solar Polarization 6. Proceedings of a conference held in Maui, Hawaii, USA on May 30 to June 4, 2010. Eds J. R. Kuhn et al. San Francisco: Astronomical Society of the Pacific).
83. Semel M. Contribution à l’etude des champs magnétiques dans les régions actives solaires. Annales d’Astrophysique. 1967. 30. P. 513—551.
84. Schlichenmaier R., Collados M. Spectropolarimetry in a sunspot penumbra. Spatial dependence of Stokes asymmetries in Fe I 1564.8 nm. Astron. and Astrophys. 2002. 381. P. 668—682.
85. Schlichenmaier R., Müller D. A. N., Steiner O., Stix M. Net circular polarization of sunspot penumbrae. Symmetry breaking through anomalous dispersion. Astron. and Astrophys. 2002. 381. P. L77—L80.
86. Schlichenmaier R., Soltau D., Lühe O. V. D., Collados M. Penumbral Stokes-V asymmetries of Fe I 1564.8 nm. Advanced Solar Polarimetry — Theory, Observation, and Instrumentation — 20thNSO/Sac Summer Workshop, ASP Conf. Proc. 2001. 236. P. 579.
87. Shchukina N. G., Sukhorukov A. V., Trujillo Bueno J. A Si I atomic model for NLTE spectropolarimetric diagnostics of the 10827 Å line. Astron. and Astrophys. 2017. 603. A98. P. 1—16.
88. Shchukina N. G., Trujillo Bueno J. Determintng the magnetization of the quiet Sun photosphere from the Hanle effect and surface dynamo simutations. Astrophys. J. Lett. 2011. 731. P. L21—L25.
89. Shchukina N. G., Trujillo Bueno J. Spectropolarimetric diagnostics of unresolved magnetic fields in the quiet sotar photosphere. Sotar and Astrophystcal Dynamos and Magnetic Activity, Proc. Inter. Astron. Union, IAU Symp. 2013. 294. P. 107—118.
90. Shelyag S., Schüssler M., Solanki S.K., Vögler A. Stokes diagnostics of simulated solar magneto-convection. Astron. and Astrophys. 2007. 469. P. 731—747.
91. Sigwarth M. Properties and origin of asymmetric and unusual Stokes V profiles observed in solar magnetic fields. Astrophys. J. 2001. 563. P. 1031—1044.
92. Socas-Navarro H. Strategies for spectral profile inversion using artificial neural networks. Astrophys. J. 2005. 621. P. 545—553.
93. Socas-Navarro H., Trujillo Bueno J., Ruiz Cobo B. Non-LTE inversion of Stokes profiles induced by the Zeeman effect. Astrophys. J. 2000. 530. P. 977—993.
94. Solanki S. K. Smallscale solar magnetic fields - an overview. Space Sci. Revs. 1993. 63. P. 1—188.
95. Solanki S. K. Sunspots: An overview. Astron. Astrophys. Rev. 2003. 11. P. 153—286.
96. Solanki S. K., Biemont E., Muerset U. Interesting lines in the infrared solar spectrum between 1.49 and 1.8 microns. Astron. and Astrophys. Suppl. Ser. 1990. 83. P. 307—315.
97. Solanki S. K., Finsterle W., Rüedi I. The influence of sunspot canopies on magnetic inclination measurements in solar plages. Solar Phys. 1996. 164. P. 253—264.
98. Solanki S. K., Montavon C., Livingston W. Evershed effect in sunspots and their canopies. The magnetic and velocity fields of solar active regions. Astronomical Society of the Pacific Conference Series; Proc. Inter. Astron. Union (IAU) Colloquium no. 141. 1993. 46. P. 52.
99. Solanki S. K., Rüedi I., Livingston W. Infrared lines as probes of solar magnetic features. II - Diagnostic capabilities of Fe I 15648.5 Å and 15652.9 Å. Astron. and Astrophys. 1992. 263. P. 312—322.
100. Solanki S. K., Rüedi I., Livingston W. Infrared lines as probes of solar magnetic features. V - The magnetic structure of a simple sunspot and its canopy. Astron. and Astrophys. 1992. 263. P. 339—350.
101. Solanki S. K., Rüedi I., Rabin D. Siphon flow across the magnetic neutral-line of an active region. The magnetic and velocity fields of solar active regions. Astronomical Society of the Pacific Conference Series; Proc. Inter. Astron. Union (IAU) Colloquium no. 141. 1993. 46. P. 534.
102. Solanki S. K., Walther U., Livingston W. Infrared lines as probes of solar magnetic features. VI. The thermal-magnetic relation and Wilson depression of a simple sunspot. Astron. and Astrophys. 1993. 277. P. 639.
103. Solanki S. K., Zayer I., Stenflo J. O. The internal magnetic field structure of sol ar magnetic elements. Proceedings of the 10th Sacramento Peak Summer Workshop, Sunspot, New Mexico, August 22—26, 1988. Edited by Oskar von der Luhe. Sunspot, MN: National Solar Observatory. 1989. P. 409.
104. Solanki S. K., Zufferey D., Lin H., et al. Infrared lines as probes of solar magnetic features. XII. Magnetic flux tubes: evidence of convective collapse? Astron. and Astrophys. 1996. 310. P. L33—L36.
105. Stenflo J. O. Magnetic-field structure of the photospheric network. Solar Phys. 1973. 32. P. 41—63.
106. Stenflo J. O., Solanki S. K., Harvey J. W. Diagnostics of solar magnetic fluxtubes with the infrared line Fe I X 15648.54 Å. Astron. and Astrophys. 1987. 173. P. 167— 179.
107. Sun W.-H., Giampapa M. S., Worden S. P. Magnetic field measurements on the sun and implications for stellar magnetic field observations. Astrophys. J. 1987. 312. P. 930—942.
108. Trujillo Bueno J., Asensio Ramos A., Shchukina N. G. The Hanle effect in atomic and molecular lines: A new look at the Sun’s hidden magnetism. ASP Conf. Ser. 2006. 358. P. 269. (Solar Polarization 4, Proceedings ofthe conference held 19-23 September, 2005, in Boulder, Colorado, USA. Edited by R. Casini and B. W. Lites).
109. Trujillo Bueno J., Landi Degl’Innocenti E., Belluzzi L. The physics and diagnostic potential of ultraviolet spectropolarimetry. Space Sci. Revs. 2017.210. P. 182—226.
110. Trujillo Bueno J., Shchukina N. G. The scattering polarization of the Sr I λ 4607 line at the diffraction limit resolution of a 1 m telescope. Astrophys. J. 2007. 664. P. L135—L138.
111. Trujillo Bueno J., Shchukina N. G., Asensio Ramos A. A substantial amount of hidden magnetic energy in the quiet Sun. Nature. 2004. 430. P. 326—329.
112. Vögler A., Shelyag S., Schüssler M., et al. Simulations of magneto-convection in the solar photosphere. Equations, methods, and results of the MURaM code. Astron. and Astrophys. 2005. 429. P. 335—351.
113. Zayer I., Solanki S. K., Stenflo J. O. The internal magnetic field distribution and the diameters of solar magnetic elements. Astron. and Astrophys. 1989. 211. P. 463—475.
114. Zayer I., Solanki S. K., Stenflo J. O., Keller C. U. Dependence of the properties of solar magnetic flux tubes on filling factor. II - Results of an inversion approach. Astron. and Astrophys. 1990. 239. P. 356—366.
115. Zeeman P. On the influence of magnetism on the nature of the light emitted by a substance. Astrophys. J. 1897. 5. P. 332—347.