Robust method for determination of magnetic field strength in solar photosphere

Heading: 
1Prysiazhnyi, AI, 1Stodilka, MI, 2Shchukina, NG
1Astronomical Observatory of Ivan Franko National University of Lviv, Lviv, Ukraine
2Main Astronomical Observatory of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
Kinemat. fiz. nebesnyh tel (Online) 2018, 34(6):3-21
https://doi.org/10.15407/kfnt2018.06.003
Start Page: Solar Physics
Language: Ukrainian
Abstract: 

We modify the classical method for determining the magnetic field strength from the distance between the peaks of blue and red wings of the Stokes V profile of magnetically sensitive spectral line. To reduce the influence of noise and to measure more accurately the distance between these peaks the observed Stokes V profile was approximated by a modified wavelet-function. The parameters of the best fitted approximation function were determined by multidimensional optimization. Following such an approach, the magnetic field strength can be found analytically using these parameters. We investigate the modified method by means of calculations of the Fe I λ 1564.8 nm Stokes V and I profiles in a three-dimensional snapshot model atmosphere. We used a magneto-convection simutations with small-scale dynamo action performed by Rempel. We find that the method proposed is less sensitive to noise and shape of the observed V-signal of the line. This makes it possible to conclude that our approach of determing of the magnetic field strength from the observed splitting of the Fe I X 1564.8 nm Stokes V profile is more reliable in comparison with the classical one.

Keywords: diagnostic, magnetic fields, photosphere, Sun, Zeeman effect
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.
https://doi.org/10.1051/0004-6361/201015484

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.
https://doi.org/10.1051/0004-6361:20041277

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.
https://doi.org/10.1051/0004-6361:20030576

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.
https://doi.org/10.1051/0004-6361:20030704

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.
https://doi.org/10.1086/308791

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.
https://doi.org/10.1086/323063

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.
https://doi.org/10.1051/0004-6361/201628313

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.
https://doi.org/10.1051/0004-6361:20030548

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.
https://doi.org/10.1051/0004-6361/201730753

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.
https://doi.org/10.1051/0004-6361:20042553

13. Borrero J. M., Solanki S. K. Convective motions and net circular polarization in sunspot penumbrae. Astrophys. J.2010. 709. P. 349—357.
https://doi.org/10.1088/0004-637X/709/1/349

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.
https://doi.org/10.1051/0004-6361:20041001

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.
https://doi.org/10.1051/0004-6361:20052720

16. Carroll T. A., Staude J. The inversion of Stokes profiles with artificial neural networks. Astron. and Astrophys. 2001. 378. P. 316—326.
https://doi.org/10.1051/0004-6361:20011167

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.
https://doi.org/10.1051/0004-6361/200913379

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.
https://doi.org/10.1086/505129

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.
https://doi.org/10.1051/0004-6361/201628407

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.
https://doi.org/10.1086/184041

25. Gondoin Ph., Giampapa M. S., Bookbinder J. A. Stellar magnetic field measurements utilizing infrared spectral lines. Astrophys. J.1985. 297. P. 710—718.
https://doi.org/10.1086/163570

26. Hanle W. Über magnetische Beeinflussung der Polarisation der Resonanzfluoreszenz. Zeitschrift für Physik. 1924. 30. P. 93—105.
https://doi.org/10.1007/BF01331827

27. Harvey J. W. Observations of small-scale photospheric magnetic fields. Highlights of Astronomy. 1977. 4. P. 223—239.
https://doi.org/10.1007/978-94-010-1250-8_47

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.
https://doi.org/10.1086/512098

32. Khomenko E. V., Collados M., Bellot Rubio L. R. Magnetoacoustic waves in sunspots. Astrophys. J. 2003. 588. P. 606—619.
https://doi.org/10.1086/373918

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.
https://doi.org/10.1051/0004-6361:20030604

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.
https://doi.org/10.1017/S1743921304007112

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.
https://doi.org/10.1051/0004-6361:20052958

37. Kopp G., Rabin D. A relation between magnetic field strength and temperature in sunspots. Solar Phys. 1992. 141. P. 253—265.
https://doi.org/10.1007/BF00155178

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.
https://doi.org/10.1051/0004-6361/201219534

40. Kostik R., Khomenko E. V. Properties of oscillatory motions in a facular region. Astron. and Astrophys. 2013. 559. A107. P. 1—10.
https://doi.org/10.1051/0004-6361/201322363

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.
https://doi.org/10.1051/0004-6361/201628489

42. Landi Degl’Innocenti E., Landolfi M. Polarization in spectral lines. Dordrecht: Kluwer Academic Publishers. 2004. 890 p.
https://doi.org/10.1007/1-4020-2415-0

43. Lin H. On the distribution of the solar magnetic fields. Astrophys. J. 1995. 446. P. 421.
https://doi.org/10.1086/175800

44. Lin H., Rimmele T. The granular magnetic fields of the quiet Sun. Astrophys. J. 1999. 514. P. 448—455.
https://doi.org/10.1086/306925

45. Litzen U., Verges J. The Fe I spectrum in the region 1 - 4 μm. Physica Scripta, 1976. 13. P. 240—244.
https://doi.org/10.1088/0031-8949/13/4/008

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.
https://doi.org/10.1023/A:1015555000456

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.
https://doi.org/10.1002/2015GL065413

50. Lopez Ariste A., Tomczyk S., Casini R. Hyperfine structure as a diagnostic of solar magnetic fields. Astrophys. J. 2002. 580. P. 519—527.
https://doi.org/10.1086/343111

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.
https://doi.org/10.1086/425176

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.
https://doi.org/10.1051/0004-6361/201628449

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.
https://doi.org/10.1051/0004-6361:20031282

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.
https://doi.org/10.1002/asna.200310139

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.
https://doi.org/10.1051/0004-6361:20040136

57. McPherson M. R., Lin H., Kuhn J. R. Infrared array measurements of sunspot magnetic fields. Solar Phys. 1992. 139. P. 255—266.
https://doi.org/10.1007/BF00159152

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.
https://doi.org/10.1086/308711

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.
https://doi.org/10.1007/978-94-011-1188-1_10

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.
https://doi.org/10.1051/0004-6361:20020990

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.
https://doi.org/10.1051/0004-6361/200913421

63. Penn M. J. Infrared solar physics. Liv. Rev. Solar Phys. 2014. 11, article id. 2. P. 1—66.
https://doi.org/10.12942/lrsp-2014-2

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.
https://doi.org/10.1023/A:1013811705854

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.
https://doi.org/10.1023/A:1023271511373

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.
https://doi.org/10.1086/171392

68. Rabin D. A true-field magnetogram in a solar plage region. Astrophys. J. 1992. 390. P. L103—L106.
https://doi.org/10.1086/186382

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.
https://doi.org/10.1086/167364

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.
https://doi.org/10.1088/0004-637X/789/2/132

74. Rempel M., Schüssler M., Knölker M. Radiative magnetohydrodynamic simulation of sunspot structure. Astrophys. J.2009. 691.P. 640—649.
https://doi.org/10.1088/0004-637X/691/1/640

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.
https://doi.org/10.1086/171862

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.
https://doi.org/10.1086/304999

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.
https://doi.org/10.1086/427930

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.
https://doi.org/10.1086/379969

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.
https://doi.org/10.1051/0004-6361:20011459

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.
https://doi.org/10.1051/0004-6361:20011706

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.
https://doi.org/10.1051/0004-6361/201630236

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.
https://doi.org/10.1088/2041-8205/731/1/L21

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.
https://doi.org/10.1017/S1743921313002330

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.
https://doi.org/10.1051/0004-6361:20066819

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.
https://doi.org/10.1086/323963

92. Socas-Navarro H. Strategies for spectral profile inversion using artificial neural networks. Astrophys. J. 2005. 621. P. 545—553.
https://doi.org/10.1086/427431

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.
https://doi.org/10.1086/308414

94. Solanki S. K. Smallscale solar magnetic fields - an overview. Space Sci. Revs. 1993. 63. P. 1—188.
https://doi.org/10.1007/BF00749277

95. Solanki S. K. Sunspots: An overview. Astron. Astrophys. Rev. 2003. 11. P. 153—286.
https://doi.org/10.1007/s00159-003-0018-4

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.
https://doi.org/10.1007/978-94-009-0231-2_20

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.
https://doi.org/10.1017/S0252921100028761

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.
https://doi.org/10.1017/S025292110002978X

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.
https://doi.org/10.1007/BF00152728

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.
https://doi.org/10.1086/164938

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.
https://doi.org/10.1007/s11214-016-0306-8

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.
https://doi.org/10.1086/520838

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.
https://doi.org/10.1038/nature02669

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.
https://doi.org/10.1051/0004-6361:20041507

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.
https://doi.org/10.1086/140355