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Solar Physics

, 292:188 | Cite as

The Temperature – Magnetic Field Relation in Observed and Simulated Sunspots

  • Michal SobotkaEmail author
  • Reza Rezaei
Article

Abstract

Observations of the relation between continuum intensity and magnetic field strength in sunspots have been made for nearly five decades. This work presents full-Stokes measurements of the full-split (\(g = 3\)) line Fe i 1564.85 nm with a spatial resolution of \(0.5^{\prime\prime}\) obtained with the GREGOR Infrared Spectrograph in three large sunspots. The continuum intensity is corrected for instrumental scattered light, and the brightness temperature is calculated. Magnetic field strength and inclination are derived directly from the line split and the ratio of Stokes components. The continuum intensity (temperature) relations to the field strength are studied separately in the umbra, light bridges, and penumbra. The results are consistent with previous studies, and it was found that the scatter of values in the relations increases with increasing spatial resolution thanks to resolved fine structures. The observed relations show trends common for the umbra, light bridges, and the inner penumbra, while the outer penumbra has a weaker magnetic field than the inner penumbra at equal continuum intensities. This fact can be interpreted in terms of the interlocking comb magnetic structure of the penumbra. A comparison with data obtained from numerical simulations was made. The simulated data generally have a stronger magnetic field and a weaker continuum intensity than the observations, which may be explained by stray light and limited spatial resolution of the observations, and also by photometric inaccuracies of the simulations.

Keywords

Sunspots Magnetic fields 

Notes

Acknowledgements

This work was supported by the grant 14-04338S of the Czech Science Foundation, the FP-7 Capacities Project No. 312495 SOLARNET, and the institutional support RVO:67985815 of the Czech Academy of Sciences. R.R. acknowledges financial support by the Spanish Ministry of Economy and Competitiveness through the project AYA2014-60476-P. We thank J.M. Borrero for synthetic spectra computed in the frame of the international working group Extracting Information from Spectropolarimetric Observations: Comparison of Inversion Codes at the International Space Science Institute (ISSI) in Bern (Switzerland). We use data provided by M. Rempel at the National Center for Atmospheric Research (NCAR). The National Center for Atmospheric Research is sponsored by the National Science Foundation. The 1.5-meter GREGOR solar telescope was built by a German consortium under the leadership of the Kiepenheuer Institute for Solar Physics in Freiburg with the Leibniz Institute for Astrophysics Potsdam, the Institute of Astrophysics Göttingen, and the Max Planck Institute for Solar System Research in Göttingen as partners, and with contributions by the Instituto de Astrofísica de Canarias and the Astronomical Institute of the Czech Academy of Sciences. We thank the referee for the comments that led to a substantial improvement of the paper.

Conflict of Interest

The authors declare that they have no conflict of interest.

References

  1. Abdussamatov, H.I.: 1971, On the magnetic fields and motions in sunspots at different atmospheric levels. Solar Phys. 16, 384.  DOI. ADS. ADSCrossRefGoogle Scholar
  2. Balthasar, H., Schmidt, W.: 1993, Polarimetry and spectroscopy of a simple sunspot. II: On the height and temperature dependence of the magnetic field. Astron. Astrophys. 279, 243. ADS. ADSGoogle Scholar
  3. Berkefeld, T., Schmidt, D., Soltau, D., von der Lühe, O., Heidecke, F.: 2012, The GREGOR adaptive optics system. Astron. Nachr. 333, 863.  DOI. ADS. ADSCrossRefGoogle Scholar
  4. Borrero, J.M., Ichimoto, K.: 2011, Magnetic structure of sunspots. Living Rev. Solar Phys. 8, 4.  DOI. ADS. ADSCrossRefGoogle Scholar
  5. Borrero, J.M., Lites, B.W., Lagg, A., Rezaei, R., Rempel, M.: 2014, Comparison of inversion codes for polarized line formation in MHD simulations. I. Milne-Eddington codes. Astron. Astrophys. 572, A54.  DOI. ADS. ADSCrossRefGoogle Scholar
  6. Borrero, J.M., Asensio Ramos, A., Collados, M., Schlichenmaier, R., Balthasar, H., Franz, M., Rezaei, R., Kiess, C., Orozco Suárez, D., Pastor, A., Berkefeld, T., von der Lühe, O., Schmidt, D., Schmidt, W., Sigwarth, M., Soltau, D., Volkmer, R., Waldmann, T., Denker, C., Hofmann, A., Staude, J., Strassmeier, K.G., Feller, A., Lagg, A., Solanki, S.K., Sobotka, M., Nicklas, H.: 2016, Deep probing of the photospheric sunspot penumbra: No evidence of field-free gaps. Astron. Astrophys. 596, A2.  DOI. ADS. CrossRefGoogle Scholar
  7. Bruls, J.H., Lites, B.W., Murphy, G.A.: 1991, In: November, L. (ed.) Solar Polarimetry, Proc. 11th Sacramento Peak Workshop, NSO, Sunspot, 444. Google Scholar
  8. Collados, M., López, R., Páez, E., Hernández, E., Reyes, M., Calcines, A., Ballesteros, E., Díaz, J.J., Denker, C., Lagg, A., Schlichenmaier, R., Schmidt, W., Solanki, S.K., Strassmeier, K.G., von der Lühe, O., Volkmer, R.: 2012, GRIS: The GREGOR infrared spectrograph. Astron. Nachr. 333, 872.  DOI. ADS. ADSCrossRefGoogle Scholar
  9. Gurman, J.B., House, L.L.: 1981, Vector magnetic fields in sunspots. I – Weak-line observations. Solar Phys. 71, 5.  DOI. ADS. ADSCrossRefGoogle Scholar
  10. Hofmann, A., Arlt, K., Balthasar, H., Bauer, S.M., Bittner, W., Paschke, J., Popow, E., Rendtel, J., Soltau, D., Waldmann, T.: 2012, The GREGOR polarimetric calibration unit. Astron. Nachr. 333, 854.  DOI. ADS. ADSCrossRefGoogle Scholar
  11. Jaeggli, S.A., Lin, H., Uitenbroek, H.: 2012, On molecular hydrogen formation and the magnetohydrostatic equilibrium of sunspots. Astrophys. J. 745, 133.  DOI. ADS. ADSCrossRefGoogle Scholar
  12. Jurčák, J., Martínez Pillet, V., Sobotka, M.: 2006, The magnetic canopy above light bridges. Astron. Astrophys. 453, 1079.  DOI. ADS. ADSCrossRefGoogle Scholar
  13. Kopp, G., Rabin, D.: 1992, A relation between magnetic field strength and temperature in sunspots. Solar Phys. 141, 253.  DOI. ADS. ADSCrossRefGoogle Scholar
  14. Langhans, K., Scharmer, G.B., Kiselman, D., Löfdahl, M.G., Berger, T.E.: 2005, Inclination of magnetic fields and flows in sunspot penumbrae. Astron. Astrophys. 436, 1087.  DOI. ADS. ADSCrossRefGoogle Scholar
  15. Leonard, T., Choudhary, D.P.: 2008, Intensity and magnetic field distribution of sunspots. Solar Phys. 252, 33.  DOI. ADS. ADSCrossRefGoogle Scholar
  16. Livingston, W.: 2002, Sunspots observed to physically weaken in 2000 – 2001. Solar Phys. 207, 41.  DOI. ADS. ADSCrossRefGoogle Scholar
  17. Maltby, P., Avrett, E.H., Carlsson, M., Kjeldseth-Moe, O., Kurucz, R.L., Loeser, R.: 1986, A new sunspot umbral model and its variation with the solar cycle. Astrophys. J. 306, 284.  DOI. ADS. ADSCrossRefGoogle Scholar
  18. Martínez Pillet, V., Vázquez, M.: 1990, On the continuum intensity-magnetic field relation along the decay phase of sunspots. Astrophys. Space Sci. 170, 75.  DOI. ADS. ADSCrossRefGoogle Scholar
  19. Martínez Pillet, V., Vázquez, M.: 1993, The continuum intensity-magnetic field relation in sunspot umbrae. Astron. Astrophys. 270, 494. ADS. ADSGoogle Scholar
  20. Mathew, S.K., Solanki, S.K., Lagg, A., Collados, M., Borrero, J.M., Berdyugina, S.: 2004, Thermal-magnetic relation in a sunspot and a map of its Wilson depression. Astron. Astrophys. 422, 693.  DOI. ADS. ADSCrossRefGoogle Scholar
  21. Muller, R.: 1973, Étude photométrique des structures fines de la pénombre d’une tache solaire. Solar Phys. 32, 409.  DOI. ADS. ADSCrossRefGoogle Scholar
  22. Penn, M.J., Walton, S., Chapman, G., Ceja, J., Plick, W.: 2003, Temperature dependence of molecular line strengths and Fei 1565 nm Zeeman splitting in a sunspot. Solar Phys. 213, 55.  DOI. ADS. ADSCrossRefGoogle Scholar
  23. Pratt, W.K.: 1978, Digital Image Processing, Wiley, New York. ADS. zbMATHGoogle Scholar
  24. Rempel, M.: 2012, Numerical sunspot models: Robustness of photospheric velocity and magnetic field structure. Astrophys. J. 750, 62.  DOI. ADS. ADSCrossRefGoogle Scholar
  25. Rezaei, R., Beck, C., Schmidt, W.: 2012, Variation in sunspot properties between 1999 and 2011 as observed with the Tenerife infrared polarimeter. Astron. Astrophys. 541, A60.  DOI. ADS. ADSCrossRefGoogle Scholar
  26. Rüedi, I., Solanki, S.K., Livingston, W., Harvey, J.: 1995, Interesting lines in the infrared solar spectrum. III. A polarimetric survey between 1.05 and 2.50 μm. Astron. Astrophys. Suppl. 113, 91. ADS. ADSGoogle Scholar
  27. Ruiz Cobo, B., del Toro Iniesta, J.C.: 1992, Inversion of Stokes profiles. Astrophys. J. 398, 375.  DOI. ADS. ADSCrossRefGoogle Scholar
  28. Schmidt, W., von der Lühe, O., Volkmer, R., Denker, C., Solanki, S.K., Balthasar, H., Bello Gonzalez, N., Berkefeld, T., Collados, M., Fischer, A., Halbgewachs, C., Heidecke, F., Hofmann, A., Kneer, F., Lagg, A., Nicklas, H., Popow, E., Puschmann, K.G., Schmidt, D., Sigwarth, M., Sobotka, M., Soltau, D., Staude, J., Strassmeier, K.G., Waldmann, T.A.: 2012, The 1.5 meter solar telescope GREGOR. Astron. Nachr. 333, 796.  DOI. ADS. ADSCrossRefGoogle Scholar
  29. Socas-Navarro, H., Martínez Pillet, V., Sobotka, M., Vázquez, M.: 2004, The thermal and magnetic structure of umbral dots from the inversion of high-resolution full Stokes observations. Astrophys. J. 614, 448.  DOI. ADS. ADSCrossRefGoogle Scholar
  30. Solanki, S.K., Rüedi, I.K., Livingston, W.: 1992, Infrared lines as probes of solar magnetic features. II – Diagnostic capabilities of Fe I 15648.5 A and 15652.9 A. Astron. Astrophys. 263, 312. ADS. ADSGoogle Scholar
  31. Solanki, S.K., Walther, U., Livingston, W.: 1993, Infrared lines as probes of solar magnetic features. VI. The thermal-magnetic relation and Wilson depression of a simple sunspot. Astron. Astrophys. 277, 639. ADS. ADSGoogle Scholar
  32. Stanchfield, D.C.H. II, Thomas, J.H., Lites, B.W.: 1997, The vector magnetic field, Evershed flow, and intensity in a sunspot. Astrophys. J. 477, 485.  DOI. ADS. ADSCrossRefGoogle Scholar
  33. Thomas, J.H., Weiss, N.O.: 2008, Sunspots and Starspots, Cambridge University Press, Cambridge. ADS. CrossRefGoogle Scholar
  34. Vernazza, J.E., Avrett, E.H., Loeser, R.: 1981, Structure of the solar chromosphere. III – Models of the EUV brightness components of the quiet-Sun. Astrophys. J. Suppl. 45, 635.  DOI. ADS. ADSCrossRefGoogle Scholar
  35. Watson, F.T., Penn, M.J., Livingston, W.: 2014, A multi-instrument analysis of sunspot umbrae. Astrophys. J. 787, 22.  DOI. ADS. ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  1. 1.Astronomical Institute of the Czech Academy of Sciences (v.v.i.)OndřejovCzech Republic
  2. 2.Instituto de Astrofísica de CanariasLa LagunaSpain

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