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Robust Method for Determination of Magnetic Field Strength in the Solar Photosphere

  • SOLAR PHYSICS
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Abstract

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 a magnetically sensitive spectral line is modified. To reduce the influence of noise and to more accurately measure 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 such an approximation. 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. Magneto-convection snapshot model with small-scale dynamo action performed by Rempel was used. It was found that the method proposed is less sensitive to noise and the shape of the observed V-signal of the line. This makes it possible to conclude that the approach of determining of the magnetic field strength from the observed splitting of the Fe I λ 1564.8 nm Stokes V profile is more reliable in comparison with the classical one.

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REFERENCES

  1. C. Beck, “An uncombed inversion of multiwavelength observations reproducing the net circular polarization in a sunspot’s penumbra,” Astron. Astrophys. 525, 1–17 (2011).

    Article  Google Scholar 

  2. L. R. Bellot Rubio, “The fine structure of the penumbra: From observations to realistic physical models,” in Proc. 3rd Int. Workshop on Solar Polarization, Tenerife, Canary Islands, Spain, Sept. 30 – Oct. 4, 2002, Ed. by J. Trujillo-Bueno and J. Sanchez Almeida (Astron. Soc. Pac., San Francisco, CA, 2003), pp. 301–323, in Ser.: ASP Conference Series, Vol. 307.

  3. L. R. Bellot Rubio, H. Balthasar, and M. Collados, “Two magnetic components in sunspot penumbrae,” Astron. Astrophys. 427, 319–334 (2004).

    Article  ADS  Google Scholar 

  4. L. R. Bellot Rubio, H. Balthasar, M. Collados, and R. Schlichenmaier, “Field-aligned Evershed flows in the photosphere of a sunspot penumbra,” Astron. Astrophys. 403, L47–L50 (2003).

    Article  ADS  Google Scholar 

  5. L. R. Bellot Rubio and M. Collados, “Understanding internetwork magnetic fields as determined from visible and infrared spectral lines,” Astron. Astrophys. 406, 357–362 (2003).

    Article  ADS  Google Scholar 

  6. L. R. Bellot Rubio, M. Collados, B. Ruiz Cobo, and I. Rodriguez Hidalgo, “Oscillations in the photosphere of a sunspot umbra from the inversion of infrared Stokes profiles,” Astrophys. J. 534, 989–996 (2000).

    Article  ADS  Google Scholar 

  7. L. R. Bellot Rubio, I. Rodriguez Hidalgo, M. Collados, et al., “Observation of convective collapse and upward-moving shocks in the quiet Sun,” Astrophys. J. 560, 1010–1019 (2001).

    Article  ADS  Google Scholar 

  8. J. M. Borrero, A. Asensio Ramos, M. Collados, et al., “Deep probing of the photospheric sunspot penumbra: No evidence of field-free gaps,” Astron. Astrophys. 596, 1–14 (2016).

    Article  Google Scholar 

  9. J. M. Borrero, L. R. Bellot Rubio, P. S. Barklem, and J. C. Del Toro Iniesta, “Accurate atomic parameters for near-infrared spectral lines,” Astron. and Astrophys. 404, 749–762 (2003).

    Article  ADS  Google Scholar 

  10. J. M. Borrero, M. Franz, R. Schlichenmaier, et al., “Penumbral thermal structure below the visible surface,” Astron. Astrophys. 601, L8 (2017).

    Article  ADS  Google Scholar 

  11. J. M. Borrero, A. Lagg, S. K. Solanki, et al., “Modeling the fine structure of a sunspot penumbra through the inversion of Stokes profiles,” in Proc. Current Theoretical Models and Future High Resolution Solar Observations: Preparing for ATST, Sunspot, NM, Mar. 11–15, 2002, Ed. by A. A. Pevtsov and H. Uitenbroek. (Astron. Soc. Pac., San Francisco, CA, 2003), pp. 235–242, in Ser.: ASP Conference Series, Vol. 286.

  12. J. M. Borrero, A. Lagg, S. K. Solanki, and M. Collados, “On the fine structure of sunspot penumbrae. II. The nature of the Evershed flow,” Astron. Astrophys. 436, 333–345 (2005).

    Article  ADS  Google Scholar 

  13. J. M. Borrero and S. K. Solanki, “Convective motions and net circular polarization in sunspot penumbrae,” Astrophys. J. 709, 349–357 (2010).

    Article  ADS  Google Scholar 

  14. J. M. Borrero, S. K. Solanki, L. R. Bellot Rubio, et al., “On the fine structure of sunspot penumbrae. I. A quantitative comparison of two semiempirical models with implications for the Evershed effect,” Astron. Astrophys. 422, 1093–1104 (2004).

    Article  ADS  Google Scholar 

  15. D. Cabrera Solana, L. R. Bellot Rubio, and J. C. Del Toro Iniesta, “Sensitivity of spectral lines to temperature, velocity, and magnetic field,” Astron. Astrophys. 439, 687–699 (2005).

    Article  ADS  Google Scholar 

  16. T. A. Carroll and J. Staude, “The inversion of Stokes profiles with artificial neural networks,” Astron. Astrophys. 378, 316–326 (2001).

    Article  ADS  Google Scholar 

  17. M. Collados, “Infrared polarimetry,” in Advanced Solar Polarimetry — Theory, Observation, and Instrumentation: The 20th NSO/SAC Summer Workshop, Sunspot, NM, Sept. 11–15, 2000, Ed. by M. Sigwarth (Astron. Soc. Pac., San Francisco, CA, 2001), pp. 255–271, in Ser.: ASP Conference Series, Vol. 236.

  18. S. Danilovic, M. Schüssler, and S. K. Solanki, “Probing quiet Sun magnetism using MURaM simulations and Hinode/SP results: Support for a local dynamo,” Astron. Astrophys. 513, Al (2010).

  19. D. Degenhardt, S. K. Solanki, B. Montesinos, and J. H. Thomas, “Evidence for siphon flows with shocks in solar magnetic flux tubes,” Astron. Astrophys. 279, L29–L32 (1993).

    ADS  Google Scholar 

  20. D. Deming, T. Hewagama, D. E. Jennings, and G. Wiedemann, “Polarimetry in the infrared. Solar Polarimetry,” in Solar Polarimetry, Proc. 11th National Solar Observatory/Sacramento Peak Summer Workshop, Sunspot, NM, Aug. 27–31, 1990, Ed. by L. J. November (Natl. Sol. Obs., Sunspot, NM, 1991), pp. 341–355.

  21. I. Domínguez Cerdeña, J. Sánchez Almeida, and F. Kneer, “Quiet-Sun magnetic fields: Simultaneous inversion of visible and IR spectro-polarimetric observations,” in Proc. Solar Polarization 4, Boulder, CO, Sept. 19–23, 2005, Ed. by R. Casini and B. W. Lites (Astron. Soc. Pac., San Francisco, CA, 2006), pp. 88–91, in Ser.: ASP Conference Series, Vol. 358.

  22. I. Domínguez Cerdeña, J. Sánchez Almeida, and F. Kneer, “Quiet Sun magnetic fields from simultaneous inversions of visible and infrared spectropolarimetric observations,” Astrophys. J. 646, 1421–1435 (2006).

    Article  ADS  Google Scholar 

  23. M. Franz, M. Collados, C. Bethge, et al., “Magnetic fields of opposite polarity in sunspot penumbrae,” Astron. Astrophys. 596, A4 (2016).

    Article  Google Scholar 

  24. L. Golub, M. S. Giampapa, and S. P. Worden, “The magnetic field on the RS Canum Venaticorum star Lambda Andromedae,” Astrophys. J. Lett. 268, L121–L125 (1983).

    Article  ADS  Google Scholar 

  25. Ph. Gondoin, M. S. Giampapa, and J. A. Bookbinder, “Stellar magnetic field measurements utilizing infrared spectral lines,” Astrophys. J. 297, 710–718 (1985).

    Article  ADS  Google Scholar 

  26. W. Hanle, “Über magnetische Beeinflussung der Polarisation der Resonanzfluoreszenz,” ZeitschriftfarPhysik 30, 93–105 (1924).

    ADS  Google Scholar 

  27. J. W. Harvey, “Observations of small-scale photospheric magnetic fields,” Highlights Astron. 4, 223–239 (1977).

    Article  Google Scholar 

  28. J. W. Harvey and D. Hall, “Magnetic field observations with Fe I λ 15648 Å,” Bull. Am. Astron. Soc. 7, 459 (1975).

    Google Scholar 

  29. E. Khomenko, “Diagnostics of quiet-Sun magnetism,” in Proc. Solar MHD Theory and Observations: A High Spatial Resolution Perspective, Sunspot, NM, July 18–22, 2005, Ed. by J. Leibacher, R. F. Stein, and H. Uitenbroek (Astron. Soc. Pac., San Francisco, CA, 2006), pp. 63–76, in Ser.: ASP Conference Series, Vol. 354.

  30. E. V. Khomenko and M. Collados, “On the determination of magnetic field strength and flux in inter-network,” in Proc. Solar Polarization 4, Boulder, CO, Sept. 19–23, 2005, Ed. by R. Casini and B. W. Lites (Astron. Soc. Pac., San Francisco, CA, 2006), pp. 42–47, in Ser.: ASP Conference Series, Vol. 358.

  31. E. V. Khomenko and M. Collados, “On the Stokes V amplitude ratio as an indicator of the field strength in the solar internetwork,” Astrophys. J. 659, 1726–1735 (2007).

    Article  ADS  Google Scholar 

  32. E. V. Khomenko, M. Collados, and L. R. Bellot Rubio, “Magnetoacoustic waves in sunspots,” Astrophys. J. 588, 606–619 (2003).

    Article  ADS  Google Scholar 

  33. E. V. Khomenko, M. Collados, L. R. Bellot Rubio, et al., “Formation and destruction of a weak magnetic feature in the solar photosphere,” in Proc. Magnetic Fields and Solar Processes: 9th Eur. Meeting on Solar Physics, Florence, Italy, 12–18 September, 1999, Ed. by A. Wilson. (Eur. Space Agency, Noordwijk, 1999), p. 307.

  34. E. V. Khomenko, M. Collados, S. K. Solanki, et al., “Quiet-Sun inter-network magnetic fields observed in the infrared,” Astron. Astrophys. 408, 1115–1135 (2003).

    Article  ADS  Google Scholar 

  35. E. V. Khomenko, S. Shelyag, S. K. Solanki, et al., “Stokes diagnostics of magneto-convection. Profile shapes and asymmetries,” in Multi-Wavelength Investigations of Solar Activity: Proc. 223rd Symp. of the Int. Astronomical Union, St. Petersburg, Russia, June 14–19, 2004 (Cambridge Univ. Press, Cambridge, 2004), pp. 635–636.

  36. E. V. Khomenko, S. Shelyag, S. K. Solanki, and A. Vögler, “Stokes diagnostics of simulations of magnetoconvection of mixed-polarity quiet-Sun regions,” Astron. Astrophys. 442, 1059–1078 (2005).

    Article  ADS  Google Scholar 

  37. G. Kopp and D. Rabin, “A relation between magnetic field strength and temperature in sunspots,” Sol. Phys. 141, 253–265 (1992).

    Article  ADS  Google Scholar 

  38. M. G. Kopp and D. Rabin, “Magnetic field strength and continuum intensity measurements of sunspots at 1.56 microns,” in Cool Stars, Stellar Systems, and the Sun: Proc. 7th Cambridge Workshop, Tucson, AZ, Oct. 9–12, 1991 (Astron. Soc. Pac., San Francisco, 1992), pp. 246–248, in Ser.: ASP Conference Series, Vol. 26.

  39. R. Kostik and E. V. Khomenko, “Properties of convective motions in facular regions,” Astron. Astrophys. 545, A22 (2012).

    Article  ADS  Google Scholar 

  40. R. Kostik and E. V. Khomenko, “Properties of oscillatory motions in a facular region,” Astron. Astrophys. 559, A107 (2013).

    Article  ADS  Google Scholar 

  41. A. Lagg, S. K. Solanki, H.-P. Doerr, et al., “Probing deep photospheric layers of the quiet Sun with high magnetic sensitivity,” Astron. Astrophys. 596, A6 (2016).

    Article  Google Scholar 

  42. E. Landi Degl’Innocenti, and M. Landolfi, Polarization in Spectral Lines (Kluwer, Dordrecht, 2004).

  43. H. Lin, “On the distribution of the solar magnetic fields,” Astrophys. J. 446, 421 (1995).

    Article  ADS  Google Scholar 

  44. H. Lin and T. Rimmele, “The granular magnetic fields of the quiet Sun,” Astrophys. J. 514, 448–455 (1999).

    Article  ADS  Google Scholar 

  45. U. Litzen and J. Verges, “The Fe I spectrum in the region 1–4 µm,” Phys. Scr. 13, 240–244 (1976).

    Article  ADS  Google Scholar 

  46. W. Livingston, “Sampling V-Stokes on the solar disk with Fe 115648 Å and H Paschen β,” in Solar Polarimetry, Proc. 11th National Solar Observatory/Sacramento Peak Summer Workshop, Sunspot, NM, Aug. 27–31, 1990, Ed. by L. J. November (Natl. Sol. Obs., Sunspot, NM, 1991), pp. 356–360.

  47. W. Livingston, “Sunspot umbrae: Observed correlation between magnetic field and temperature,” Bull. Am. Astron. Soc. 23, 1030 (1991).

    ADS  Google Scholar 

  48. W. Livingston, “Sunspots observed to physically weaken in 2000–2001,” Sol. Phys. 207, 41–45 (2002).

    Article  ADS  Google Scholar 

  49. W. Livingston and F. Watson, “A new solar signal: Average maximum sunspot magnetic fields independent of activity cycle,” Geophys. Res. Lett. 42, 9185–9189 (2015).

    Article  ADS  Google Scholar 

  50. A. Lopez Ariste, S. Tomczyk, and R. Casini, “Hyperfine structure as a diagnostic of solar magnetic fields,” Astrophys. J. 580, 519–527 (2002).

    Article  ADS  Google Scholar 

  51. R. Manso Sainz, E. Landi Degl’Innocenti, and J. Trujillo Bueno, “Concerning the existence of a "turbulent” magnetic field in the quiet Sun,” Astrophys. J. Lett. 614, L89–L91 (2004).

    Article  ADS  Google Scholar 

  52. M. J. Martínez González, A. Pastor Yabar, A. Lagg, et al., “Inference of magnetic fields in the very quiet Sun,” Astron. Astrophys. 596, A5 (2016).

    Article  Google Scholar 

  53. S. K. Mathew, A. Lagg, S. K. Solanki, et al., “Three dimensional structure of a regular sunspot from the inversion of IR Stokes profiles,” Astron. Astrophys. 410, 695–710 (2003).

    Article  ADS  Google Scholar 

  54. S. K. Mathew, S. K. Solanki, A. Lagg, et al., “Thermal-magnetic relation of a sunspot as inferred from the inversion of 1.5 um spectral data,” in SOLMAG 2002: Proc. Magnetic Coupling of the Solar Atmosphere Euroconf. and IAU Colloquium 188, Santorini, Greece, June 11–15, 2002 (Eur. Astron. Soc, Noordwijk, 2002), pp. 501–503.

  55. S. K. Mathew, S. K. Solanki, A. Lagg, et al., “Structure of a simple sunspot from the inversion of IR spectral data,” Astron. Nachr. 324, 388–389 (2003).

    Article  ADS  Google Scholar 

  56. S. K. Mathew, S. K. Solanki, A. Lagg, et al., “Thermal-magnetic relation in a sunspot and a map of its Wilson depression,” Astron. Astrophys. 422, 693–701 (2004).

    Article  ADS  Google Scholar 

  57. M. R. McPherson, H. Lin, and J. R. Kuhn, “Infrared array measurements of sunspot magnetic fields,” Sol. Phys. 139, 255–266 (1992).

    Article  ADS  Google Scholar 

  58. T. Moran, D. Deming, D. E. Jennings, and G. McCabe, “Solar magnetic field studies using the 12 micron emission lines. III. Simultaneous measurements at 12 and 1.6 microns,” Astrophys. J. 533, 1035–1042 (2000).

    Article  ADS  Google Scholar 

  59. K. Muglach and S. K. Solanki, “Infrared lines as probes of solar magnetic features. I — A many-line analysis of a network region,” Astron. Astrophys. 263, 301–311 (1992).

    ADS  Google Scholar 

  60. K. Muglach, S. K. Solanki, and W. C. Livingston, “Preliminary properties of pores derived from 1.56 micron lines,” in Solar Surface Magnetism: Proc. NATO Adv. Res. Workshop, Soesterberg, Netherlands, Nov. 1–5, 1993 (Kluwer, Dordrecht, 1994), p. 127, in Ser.: NATO Advanced Science Institutes (ASI) Series C: Mathematical and Physical Sciences, Vol. 433.

  61. D. A. N. Müller, R. Schlichenmaier, O. Steiner, and M. Stix, “Spectral signature of magnetic flux tubes in sunspot penumbrae,” Astron. Astrophys. 393, 305–319 (2002).

    Article  ADS  Google Scholar 

  62. D. Orozco Suarez, L. R. Bellot Rubio, A. Vogler, and J. C. Del Toro Iniesta, “Applicability of Milne-Eddington inversions to high spatial resolution observations of the quiet Sun,” Astron. Astrophys. 518, A2 (2010).

    Article  ADS  Google Scholar 

  63. M. J. Penn, “Infrared solar physics,” Living Rev. Sol. Phys. 11, 2 (2014).

    Article  ADS  Google Scholar 

  64. M. J. Penn, J. A. Ceja, E. Bell, et al., “Infrared spectroscopy from San Fernando observatory: He I 1083 ran, O I 1316 nm, and Fe I 1565 nm,” Sol. Phys. 205, 53–61 (2002).

    Article  ADS  Google Scholar 

  65. M. J. Penn, S. Walton, G. Chapman, et al., “Temperature dependence of molecular line strengths and Fe I 1565 nm Zeeman splitting in a sunspot,” Sol. Phys. 213, 55–67 (2003).

    Article  ADS  Google Scholar 

  66. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge Univ. Press, Cambridge, 1988).

    MATH  Google Scholar 

  67. D. Rabin, “Spatially extended measurements of magnetic field strength in solar plages,” Astrophys. J. 391, 832–844 (1992).

    Article  ADS  Google Scholar 

  68. D. Rabin, “A true-field magnetogram in a solar plage region,” Astrophys. J. Lett. 390, L103–L106 (1992).

    Article  ADS  Google Scholar 

  69. D. Rabin, “Fine-scale magnetic fields in the solar photosphere,” in Cool Stars, Stellar Systems, and the Sun: Proc. 7th Cambridge Workshop, Tucson, AZ, Oct. 9–12, 1991 (Astron. Soc. Pac., San Francisco, 1992), pp. 201–210, in Ser.: ASP Conference Series, Vol. 26.

  70. D. M. Rabin and J. E. Graves, “Measuring sunspot magnetic fields with the infrared line Fe I λ 15649,” Bull. Am. Astron. Soc. 21, 854 (1989).

    Google Scholar 

  71. D. Rabin, D. Jaksha, C. Plymate, et al., “Plage magnetic field strengths from near-infrared spectra,” in Solar Polarimetry, Proc. 11th National Solar Observatory/Sacramento Peak Summer Workshop, Sunspot, NM, Aug. 27–31, 1990, Ed. by L. J. November (Natl. Sol. Obs., Sunspot, NM, 1991), pp. 361–370.

  72. D. E. Rees, C. J. Durrant, and G. A. Murphy, “Stokes profile analysis and vector magnetic fields. II — Formal numerical solutions of the Stokes transfer equations,” Astrophys. J. 339, 1093–1106 (1989).

    Article  ADS  Google Scholar 

  73. M. Rempel, “Numerical simulations of quiet Sun magnetism: On the contribution from a small-scale dynamo,” Astrophys. J. 789, 132 (2014).

    Article  ADS  Google Scholar 

  74. M. Rempel, M. Schüssler, and M. Knölker, “Radiative magnetohydrodynamic simulation of sunspot structure,” Astrophys. J. 691, 640–649 (2009).

    Article  ADS  Google Scholar 

  75. I. Rüedi, S. K. Solanki, and W. Livingston, “Infrared lines as probes of solar magnetic features. XI. Structure of a sunspot umbra with a light bridge,” Astron. Astrophys. 302, 543–550 (1995).

    ADS  Google Scholar 

  76. I. Rüedi, S. K. Solanki, W. Livingston, and J. O. Stenflo, “Infrared lines as probes of solar magnetic features. Ill — Strong and weak magnetic fields in plages,” Sol. Phys. 263, 323–338 (1992).

    Google Scholar 

  77. I. Rüedi, S. K. Solanki, and D. Rabin, “Infrared lines as probes of solar magnetic features. IV — Discovery of a siphon flow,” Astron. Astrophys. 261, L21–L24 (1992).

    ADS  Google Scholar 

  78. B. Ruiz Cobo and J. C. Del Toro Iniesta, “Inversion of Stokes profiles,” Astrophys. J. 398, 375–385 (1992).

    Article  ADS  Google Scholar 

  79. J. Sánchez Almeida, “Physical properties of the solar magnetic photosphere under the MISMA hypothesis. I. Description of the inversion procedure,” Astrophys. J. 491, 993–1008 (1997).

    Article  ADS  Google Scholar 

  80. J. Sánchez Almeida, “Physical properties of the solar magnetic photosphere under the MISMA hypothesis. III. Sunspot at Disk Center,” Astrophys. J. 622, 1292–1313 (2005).

    Article  ADS  Google Scholar 

  81. J. Sánchez Almeida, I. Domínguez Cerdefia, and F. Kneer, “Simultaneous visible and infrared spectropolarimetry of a solar internetwork region,” Astrophys. J. Lett. 597, LI77–LI80 (2003).

    Article  Google Scholar 

  82. J. Sánchez Almeida and M. J. Martínez González, “The magnetic fields of the quiet Sun,” in Proc. Solar Polarization 6, Maui, Hawaii, May 30 – June 4, 2010, Ed. by J. R. Kuhn, D. M. Harrington, H. Lin, S. V. Berdyugina, J. Trujillo Bueno, S. L. Keil, and T. Rimmele (Astron. Soc. Pac., San Francisco, CA, 2011). ASP Conf. Ser. 437, 451–469.

  83. M. Semel, “Contribution à l’etude des champs magnetiques dans les régions actives solaires,” Ann. Astrophys. 30, 513–551 (1967).

    ADS  Google Scholar 

  84. R. Schlichenmaier and M. Collados, “Spectropolarimetry in a sunspot penumbra. Spatial dependence of Stokes asymmetries in Fe I 1564.8 nm,” Astron. Astrophys. 381, 668–682 (2002).

    Article  ADS  Google Scholar 

  85. R. Schlichenmaier, D. A. N. Müller, O. Steiner, and M. Stix, “Net circular polarization of sunspot penumbrae. Symmetry breaking through anomalous dispersion,” Astron. Astrophys. 381, L77–L80 (2002).

    Article  ADS  Google Scholar 

  86. R. Schlichenmaier, D. Soltau, O. V. D. Lühe, and M. Collados, “Penumbral Stokes-V asymmetries of Fe 11564.8 nm,” in Proc. Advanced Solar Polarimetry — Theory, Observation, and Instrumentation: The 20th NSO/SAC Summer Workshop, Sunspot, NM, Sept. 11–15, 2000, Ed. by M. Sigwarth (Astron. Soc. Pac., San Francisco, CA, 2001), p. 579, in Ser.: ASP Conference Series, Vol. 236.

  87. N. G. Shchukina, A. V. Sukhorukov, and J. Trujillo Bueno, “A Si I atomic model for NLTE spectropolarimetric diagnostics of the 10827 Å line,” Astron. Astrophys. 603, A98 (2017).

    Article  ADS  Google Scholar 

  88. N. G. Shchukina and J. Trujillo Bueno, “Determining the magnetization of the quiet Sun photosphere from the Hanle effect and surface dynamo simulations,” Astrophys. J. Lett. 731, L21–L25 (2011).

    Article  ADS  Google Scholar 

  89. N. G. Shchukina and J. Trujillo Bueno, “Spectropolarimetric diagnostics of unresolved magnetic fields in the quiet solar photosphere,” in Proc. Solar and Astrophysical Dynamos and Magnetic Activity, 294 Symp. of the Int. Astronomical Union, Beijing, China, Aug. 27–31, 2012 (Cambridge Univ. Press, Cambridge, 2013), pp. 107–118.

  90. S. Shelyag, M. Schüssler, S. K. Solanki, and A. Vögler, “Stokes diagnostics of simulated solar magneto-convection,” Astron. Astrophys. 469, 731–747 (2007).

    Article  ADS  Google Scholar 

  91. M. Sigwarth, “Properties and origin of asymmetric and unusual Stokes V profiles observed in solar magnetic fields,” Astrophys. J. 563, 1031–1044 (2001).

    Article  ADS  Google Scholar 

  92. H. Socas-Navarro, “Strategies for spectral profile inversion using artificial neural networks,” Astrophys. J. 621, 545–553 (2005).

    Article  ADS  Google Scholar 

  93. H. Socas-Navarro, J. Trujillo Bueno, and B. Ruiz Cobo, “Non-LTE inversion of Stokes profiles induced by the Zeeman effect,” Astrophys. J. 530, 977–993 (2000).

    Article  ADS  Google Scholar 

  94. S. K. Solanki, “Smallscale solar magnetic fields — An overview,” Space Sci. Rev. 63, 1–188 (1993).

    Article  ADS  Google Scholar 

  95. S. K. Solanki, “Sunspots: An overview,” Astron. Astrophys. Rev. 11, 153–286 (2003).

    Article  ADS  Google Scholar 

  96. S. K. Solanki, E. Biemont, and U. Muerset, “Interesting lines in the infrared solar spectrum between 1.49 and 1.8 microns,” Astron. Astrophys., Suppl. Ser. 83, 307–315 (1990).

    ADS  Google Scholar 

  97. S. K. Solanki, W. Finsterle, and I. Rüedi, “The influence of sunspot canopies on magnetic inclination measurements in solar plages,” Sol. Phys. 164, 253–264 (1996).

    Article  ADS  Google Scholar 

  98. S. K. Solanki, C. Montavon, and W. Livingston, “Evershed effect in sunspots and their canopies. The magnetic and velocity fields of solar active regions,” in The Magnetic and Velocity Fields of Solar Active Regions (Proc. Int. Astron. Union Colloquium 141, Beijing, China, Sept. 6–12, 1992) (Astron. Soc. Pac., San Francisco, CA, 1993), p. 52, in Ser.: ASP Conference Series, Vol. 46.

  99. S. K. Solanki, I. Rüedi, and W. Livingston, “Infrared lines as probes of solar magnetic features. II — Diagnostic capabilities of Fe I 15648.5 Å and 15652.9 Å,” Astron. Astrophys. 263, 312–322 (1992).

    ADS  Google Scholar 

  100. S. K. Solanki, I. Rüedi, and W. Livingston, “Infrared lines as probes of solar magnetic features. V — The magnetic structure of a simple sunspot and its canopy,” Astron. Astrophys. 263, 339–350 (1992).

    ADS  Google Scholar 

  101. S. K. Solanki, I. Rüedi, and D. Rabin, “Siphon flow across the magnetic neutral-line of an active region. The magnetic and velocity fields of solar active regions,” in Proc. The Magnetic and Velocity Fields of Solar Active Regions, Int. Astron. Union Colloquium 141, Beijing, China, Sept. 6–12, 1992 (Astron. Soc. Pac., San Francisco, CA, 1993), p. 534, in Ser.: ASP Conference Series, Vol. 46.

  102. S. K. Solanki, U. Walther, and W. Livingston, “Infrared lines as probes of solar magnetic features. VI. The thermal-magnetic relation and Wilson depression of a simple sun-spot,” Astron. Astrophys. 277, 639 (1993).

    ADS  Google Scholar 

  103. S. K. Solanki, I. Zayer, and J. O. Stenflo, “The internal magnetic field structure of solar magnetic elements,” in High Spatial Resolution Solar Observations: Proc. 10th Sacramento Peak Summer Workshop, Sunspot, New Mexico, Aug.22–26, 1988, Ed. by O. von der Lühe (Natl. Sol. Obs, Sunspot, NM, 1989), p. 409.

  104. S. K. Solanki, D. Zufferey, H. Lin, et al., “Infrared lines as probes of solar magnetic features. XII. Magnetic flux tubes: Evidence of convective collapse?,” Astron. Astrophys. 310, L33–L36 (1996).

    ADS  Google Scholar 

  105. J. O. Stenflo, “Magnetic-field structure of the photospheric network,” Sol. Phys. 32, 41–63 (1973).

    Article  ADS  Google Scholar 

  106. J. O. Stenflo, S. K. Solanki, and J. W. Harvey, “Diagnostics of solar magnetic fluxtubes with the infrared line Fe I λ 15648.54 Å,” Astron. Astrophys. 173, 167–179 (1987).

    ADS  Google Scholar 

  107. W.-H. Sun, M. S. Giampapa, and S. P. Worden, “Magnetic field measurements on the sun and implications for stellar magnetic field observations,” Astrophys. J. 312, 930–942 (1987).

    Article  ADS  Google Scholar 

  108. J. Trujillo Bueno, A. Asensio Ramos, and N. G. Shchukina, “The Hanle effect in atomic and molecular lines: A new look at the Sun’s hidden magnetism,” in Proc. Solar Polarization 4, Boulder, CO, Sept. 19–23, 2005, Ed. by R. Casini and B. W. Lites (Astron. Soc. Pac., San Francisco, CA, 2006), p. 269, in Ser.: ASP Conference Series, Vol. 358.

  109. J. Trujillo Bueno, E. Landi Degl’Innocenti, and L. Belluzzi, “The physics and diagnostic potential of ultraviolet spectropolarimetry,” Space Sci. Rev. 210, 182–226 (2017).

    Article  ADS  Google Scholar 

  110. J. Trujillo Bueno and N. G. Shchukina, “The scattering polarization of the Sr I lambda 4607 line at the diffraction limit resolution of a 1 m telescope,” Astrophys. J. Lett. 664, L135–L138 (2007).

    Article  ADS  Google Scholar 

  111. J. Trujillo Bueno, N. G. Shchukina, and A. Asensio Ramos, “A substantial amount of hidden magnetic energy in the quiet Sun,” Nature 430, 326–329 (2004).

    Article  ADS  Google Scholar 

  112. A. Vögler, S. Shelyag, M. Schussler, et al., “Simulations of magneto-convection in the solar photosphere. Equations, methods, and results of the MURaM code,” Astron. Astrophys. 429, 335–351 (2005).

    Article  ADS  Google Scholar 

  113. I. Zayer, S. K. Solanki, and J. O. Stenflo, “The internal magnetic field distribution and the diameters of solar magnetic elements,” Astron. Astrophys. 211, 463–475 (1989).

    ADS  Google Scholar 

  114. I. Zayer, S. K. Solanki, J. O. Stenflo, and C. U. Keller, “Dependence of the properties of solar magnetic flux tubes on filling factor. II — Results of an inversion approach,” Astron. Astrophys. 239, 356–366 (1990).

    ADS  Google Scholar 

  115. P. Zeeman, “On the influence of magnetism on the nature of the light emitted by a substance,” Astrophys. J. 5, 332–347 (1897).

    Article  ADS  MATH  Google Scholar 

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Authors and Affiliations

  1. Astronomical Observatory, Ivan Franko National University of Lviv, 79005, Lviv, Ukraine

    A. I. Prysiazhnyi & M. I. Stodilka

  2. Main Astronomical Observatory, National Academy of Sciences of Ukraine, 03143, Kyiv, Ukraine

    N. G. Shchukina

Authors
  1. A. I. Prysiazhnyi
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  2. M. I. Stodilka
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  3. N. G. Shchukina
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Correspondence to A. I. Prysiazhnyi, M. I. Stodilka or N. G. Shchukina.

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Translated by E. Seifina

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Prysiazhnyi, A.I., Stodilka, M.I. & Shchukina, N.G. Robust Method for Determination of Magnetic Field Strength in the Solar Photosphere. Kinemat. Phys. Celest. Bodies 34, 277–289 (2018). https://doi.org/10.3103/S0884591318060041

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