Abstract
Measurement of the coronal magnetic field is a crucial ingredient in understanding the nature of solar coronal phenomena at all scales. We employed STEREO/COR1 data obtained during a deep minimum of solar activity in February 2008 (Carrington Rotation CR 2066) to retrieve and analyze the three-dimensional (3D) coronal electron density in the range of heights from 1.5 to 4 R⊙ using a tomography method. With this, we qualitatively deduced structures of the coronal magnetic field. The 3D electron-density analysis is complemented by the 3D STEREO/EUVI emissivity in the 195 Å band obtained by tomography for the same CR. A global 3D MHD model of the solar corona was used to relate the reconstructed 3D density and emissivity to open/closed magnetic-field structures. We show that the density-maximum locations can serve as an indicator of current-sheet position, while the locations of the density-gradient maximum can be a reliable indicator of coronal-hole boundaries. We find that the magnetic-field configuration during CR 2066 has a tendency to become radially open at heliocentric distances greater than 2.5 R⊙. We also find that the potential-field model with a fixed source surface is inconsistent with the boundaries between the regions with open and closed magnetic-field structures. This indicates that the assumption of the potential nature of the coronal global magnetic field is not satisfied even during the deep solar minimum. Results of our 3D density reconstruction will help to constrain solar coronal-field models and test the accuracy of the magnetic-field approximations for coronal modeling.
Coronal Magnetometry
Guest Editors: S. Tomczyk, J. Zhang, and T.S. Bastian
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References
Airapetian, V., Ofman, L., Sittler, E.C., Kramar, M.: 2011, Probing the thermodynamics and kinematics of solar coronal streamers. Astrophys. J. 728, 67. 10.1088/0004-637X/728/1/67. 2011ApJ...728...67A.
Altschuler, M.D., Newkirk, G.: 1969, Magnetic fields and the structure of the solar corona. I: Methods of calculating coronal fields. Solar Phys. 9, 131. 10.1007/BF00145734. 1969SoPh....9..131A.
Billings, D.E.: 1966, A Guide to the Solar Corona, Academic Press, San Diego, 323. 1966gtsc.book.....B.
Blackwell, D.E., Petford, A.D.: 1966a, Observations of the 1963 July 20 solar eclipse. I. Spectroscopic separation of the F K components of the solar corona at large distances from the Sun. Mon. Not. Roy. Astron. Soc. 131, 383. 1966MNRAS.131..383B.
Blackwell, D.E., Petford, A.D.: 1966b, Observations of the 1963 July 20 solar eclipse. II. The electron density in the solar corona in the region 5<R/R<16 obtained from measurements of Fraunhofer line depth and the polarization of the F corona. Mon. Not. Roy. Astron. Soc. 131, 399. 1966MNRAS.131..399B.
Boffin, H.M.J., Steeghs, D., Cuypers, J. (eds.): 2001, Astrotomography, Lecture Notes in Physics 573, Springer, Berlin, 434. 2001LNP...573.....B.
Casini, R., Judge, P.G.: 1999, Spectral lines for polarization measurements of the coronal magnetic field. II. Consistent treatment of the Stokes vector for magnetic-dipole transitions. Astrophys. J. 522, 524. 10.1086/307629. 1999ApJ...522..524C.
Charvin, P.: 1965, Étude de la polarisation des raies interdites de la couronne solaire. Application au cas de la raie verte λ 5303. Ann. Astrophys. 28, 877. 1965AnAp...28..877C.
Cormack, A.M.: 1963, Representation of a function by its line integrals, with some radiological applications. J. Appl. Phys. 34, 2722. 10.1063/1.1729798. 1963JAP....34.2722C.
Cormack, A.M.: 1964, Representation of a function by its line integrals, with some radiological applications. II. J. Appl. Phys. 35, 2908. 10.1063/1.1713127. 1964JAP....35.2908C.
Davila, J.M.: 1994, Solar tomography. Astrophys. J. 423, 871. 10.1086/173864. 1994ApJ...423..871D.
Demoulin, P., Cuperman, S., Semel, M.: 1992, Determination of force-free magnetic fields above the photosphere using three-component boundary conditions. II – Analysis and minimization of scale-related growing modes and of computational induced singularities. Astron. Astrophys. 263, 351. 1992A%26A...263..351D.
Frazin, R.A., Janzen, P.: 2002, Tomography of the solar corona. II. Robust, regularized, positive estimation of the three-dimensional electron density distribution from LASCO-C2 polarized white-light images. Astrophys. J. 570, 408. 10.1086/339572. 2002ApJ...570..408F.
Frazin, R.A., Kamalabadi, F.: 2005, Rotational tomography for 3D reconstruction of the white-light and EUV corona in the post-SOHO era. Solar Phys. 228, 219. 10.1007/s11207-005-2764-0. 2005SoPh..228..219F.
Frazin, R.A., Vásquez, A.M., Kamalabadi, F., Park, H.: 2007, Three-dimensional tomographic analysis of a high-cadence LASCO-C2 polarized brightness sequence. Astrophys. J. Lett. 671, L201. 10.1086/525017. 2007ApJ...671L.201F.
Gary, G.A.: 2001, Plasma beta above a solar active region: rethinking the paradigm. Solar Phys. 203, 71. 10.1023/A:1012722021820. 2001SoPh..203...71G.
Hounsfield, G.N.: 1972, A method of and apparatus for examination of a body by radiation such as X-ray or gamma radiation. Patent. BP 1283915.
House, L.L.: 1977, Coronal emission-line polarization from the statistical equilibrium of magnetic sublevels. I – Fe XIII. Astrophys. J. 214, 632. 10.1086/155289. 1977ApJ...214..632H.
Howard, R.A., Moses, J.D., Vourlidas, A., Newmark, J.S., Socker, D.G., Plunkett, S.P., Korendyke, C.M., Cook, J.W., Hurley, A., Davila, J.M., Thompson, W.T., St. Cyr, O.C., Mentzell, E., Mehalick, K., Lemen, J.R., Wuelser, J.P., Duncan, D.W., Tarbell, T.D., Wolfson, C.J., Moore, A., Harrison, R.A., Waltham, N.R., Lang, J., Davis, C.J., Eyles, C.J., Mapson-Menard, H., Simnett, G.M., Halain, J.P., Defise, J.M., Mazy, E., Rochus, P., Mercier, R., Ravet, M.F., Delmotte, F., Auchère, F., Delaboudinière, J.P., Bothmer, V., Deutsch, W., Wang, D., Rich, N., Cooper, S., Stephens, V., Maahs, G., Baugh, R., McMullin, D., Carter, T.: 2008, Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI). Space Sci. Rev. 136, 67. 10.1007/s11214-008-9341-4. 2008SSRv..136...67H.
Jiao, L., McClymont, A.N., Mikic, Z.: 1997, Reconstruction of the three-dimensional coronal magnetic field. Solar Phys. 174, 311. 10.1023/A:1004927101300. 1997SoPh..174..311J.
Judge, P.G.: 2010, The chromosphere: gateway to the corona? ...Or the purgatory of solar physics? Mem. Soc. Astron. Ital. 81, 543. 2010MmSAI..81..543J.
Kramar, M., Inhester, B., Solanki, S.K.: 2006, Vector tomography for the coronal magnetic field. I. Longitudinal Zeeman effect measurements. Astron. Astrophys. 456, 665. 10.1051/0004-6361:20064865. 2006A%26A...456..665K.
Kramar, M., Jones, S., Davila, J., Inhester, B., Mierla, M.: 2009, On the tomographic reconstruction of the 3D electron density for the solar corona from STEREO COR1 data. Solar Phys. 259, 109. 10.1007/s11207-009-9401-2. 2009SoPh..259..109K.
Kramar, M., Davila, J., Xie, H., Antiochos, S.: 2011, On the influence of CMEs on the global 3-D coronal electron density. Ann. Geophys. 29, 1019. 10.5194/angeo-29-1019-2011. 2011AnGeo..29.1019K.
Kramar, M., Inhester, B., Lin, H., Davila, J.: 2013, Vector tomography for the coronal magnetic field. II. Hanle effect measurements. Astrophys. J. 775, 25. 10.1088/0004-637X/775/1/25. 2013ApJ...775...25K.
Lee, C.O., Luhmann, J.G., Hoeksema, J.T., Sun, X., Arge, C.N., de Pater, I.: 2011, Coronal field opens at lower height during the solar cycles 22 and 23 minimum periods: IMF comparison suggests the source surface should be lowered. Solar Phys. 269, 367. 10.1007/s11207-010-9699-9. 2011SoPh..269..367L.
Lin, H., Casini, R.: 2000, A classical theory of coronal emission line polarization. Astrophys. J. 542, 528. 10.1086/309499. 2000ApJ...542..528L.
Lionello, R., Linker, J.A., Mikić, Z.: 2009, Multispectral emission of the Sun during the first Whole Sun Month: magnetohydrodynamic simulations. Astrophys. J. 690, 902. 10.1088/0004-637X/690/1/902. 2009ApJ...690..902L.
Luhmann, J.G., Li, Y., Arge, C.N., Gazis, P.R., Ulrich, R.: 2002, Solar cycle changes in coronal holes and space weather cycles. J. Geophys. Res. 107, 1154. 10.1029/2001JA007550. 2002JGRA..107.1154L.
Mikić, Z., Linker, J.A., Schnack, D.D., Lionello, R., Tarditi, A.: 1999, Magnetohydrodynamic modeling of the global solar corona. Phys. Plasmas 6, 2217. 10.1063/1.873474. 1999PhPl....6.2217M.
Mikić, Z., Linker, J.A., Lionello, R., Riley, P., Titov, V.: 2007, Predicting the structure of the solar corona for the total solar eclipse of March 29, 2006. In: Demircan, O., Selam, S.O., Albayrak, B. (eds.) Solar and Stellar Physics Through Eclipses CS-370, Astron. Soc. Pac., San Francisco, 299. 2007ASPC..370..299M.
Moran, T.G., Davila, J.M., Morrill, J.S., Wang, D., Howard, R.: 2006, Solar and Heliospheric Observatory/Large Angle Spectrometric Coronagraph Polarimetric calibration. Solar Phys. 237, 211. 10.1007/s11207-006-0147-9. 2006SoPh..237..211M.
Parker, E.N.: 1963, Interplanetary Dynamical Processes, Interscience, New York, 272. 1963QB505.P3........
Quémerais, E., Lamy, P.: 2002, Two-dimensional electron density in the solar corona from inversion of white light images – application to SOHO/LASCO-C2 observations. Astron. Astrophys. 393, 295. 10.1051/0004-6361:20021019. 2002A%26A...393..295Q.
Radon, J.: 1917, Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten. Ber. Verh. Sächs. Akad. Wiss. Leipz., Math.-Phys. Kl. 69, 262.
Riley, P., Linker, J.A., Mikić, Z.: 2001, An empirically-driven global MHD model of the solar corona and inner heliosphere. J. Geophys. Res. 106, 15889. 10.1029/2000JA000121. 2001JGR...10615889R.
Rušin, V., Druckmüller, M., Aniol, P., Minarovjech, M., Saniga, M., Mikić, Z., Linker, J.A., Lionello, R., Riley, P., Titov, V.S.: 2010, Comparing eclipse observations of the 2008 August 1 solar corona with an MHD model prediction. Astron. Astrophys. 513, A45. 10.1051/0004-6361/200912778. 2010A%26A...513A..45R.
Sahal-Brechot, S.: 1977, Calculation of the polarization degree of the infrared lines of Fe XIII of the solar corona. Astrophys. J. 213, 887. 10.1086/155221. 1977ApJ...213..887S.
Sakurai, T.: 1989, Computational modeling of magnetic fields in solar active regions. Space Sci. Rev. 51, 11. 10.1007/BF00226267. 1989SSRv...51...11S.
Schatten, K.H., Wilcox, J.M., Ness, N.F.: 1969, A model of interplanetary and coronal magnetic fields. Solar Phys. 6, 442. 10.1007/BF00146478. 1969SoPh....6..442S.
Schrijver, C.J., DeRosa, M.L.: 2003, Photospheric and heliospheric magnetic fields. Solar Phys. 212, 165. 10.1023/A:1022908504100. 2003SoPh..212..165S.
Tadesse, T., Wiegelmann, T., Gosain, S., MacNeice, P., Pevtsov, A.A.: 2014, First use of synoptic vector magnetograms for global nonlinear, force-free coronal magnetic field models. Astron. Astrophys. 562, A105. 10.1051/0004-6361/201322418. 2014A%26A...562A.105T.
Thompson, W.T., Reginald, N.L.: 2008, The radiometric and pointing calibration of SECCHI COR1 on STEREO. Solar Phys. 250, 443. 10.1007/s11207-008-9228-2. 2008SoPh..250..443T.
Tikhonov, A.N.: 1963, Solution of incorrectly formulated problems and the regularization method. Sov. Math. Dokl. 4, 1035.
Tomczyk, S., McIntosh, S.W.: 2009, Time–distance seismology of the solar corona with CoMP. Astrophys. J. 697, 1384. 10.1088/0004-637X/697/2/1384. 2009ApJ...697.1384T.
Tomczyk, S., McIntosh, S.W., Keil, S.L., Judge, P.G., Schad, T., Seeley, D.H., Edmondson, J.: 2007, Alfvén waves in the solar corona. Science 317. 10.1126/science.1143304. 2007Sci...317.1192T.
Tóth, G., van der Holst, B., Sokolov, I.V., De Zeeuw, D.L., Gombosi, T.I., Fang, F., Manchester, W.B., Meng, X., Najib, D., Powell, K.G., Stout, Q.F., Glocer, A., Ma, Y.-J., Opher, M.: 2012, Adaptive numerical algorithms in space weather modeling. J. Comput. Phys. 231, 870. 10.1016/j.jcp.2011.02.006. 2012JCoPh.231..870T.
van de Hulst, H.C.: 1950, The electron density of the solar corona. Bull. Astron. Inst. Neth. 11, 135. 1950BAN....11..135V.
van der Holst, B., Sokolov, I.V., Meng, X., Jin, M., Manchester, W.B. IV, Tóth, G., Gombosi, T.I.: 2014, Alfvén Wave Solar Model (AWSoM): coronal heating. Astrophys. J. 782, 81. 10.1088/0004-637X/782/2/81. 2014ApJ...782...81V.
Wang, Y.-M., Sheeley, N.R. Jr.: 1992, On potential field models of the solar corona. Astrophys. J. 392, 310. 10.1086/171430. 1992ApJ...392..310W.
Wiegelmann, T.: 2008, Nonlinear force-free modeling of the solar coronal magnetic field. J. Geophys. Res. 113, 3. 10.1029/2007JA012432. 2008JGRA..113.3S02W.
Wiegelmann, T., Lagg, A., Solanki, S.K., Inhester, B., Woch, J.: 2005, Comparing magnetic field extrapolations with measurements of magnetic loops. Astron. Astrophys. 433, 701. 10.1051/0004-6361:20042421. 2005A%26A...433..701W.
Wilson, D.C.: 1976, The three dimensional solar corona. A coronal streamer, PhD thesis, National Center for Atmospheric Research, Boulder, CO. 1976PhDT.......102W.
Wuelser, J.-P., Lemen, J.R., Tarbell, T.D., Wolfson, C.J., Cannon, J.C., Carpenter, B.A., Duncan, D.W., Gradwohl, G.S., Meyer, S.B., Moore, A.S., Navarro, R.L., Pearson, J.D., Rossi, G.R., Springer, L.A., Howard, R.A., Moses, J.D., Newmark, J.S., Delaboudiniere, J.-P., Artzner, G.E., Auchere, F., Bougnet, M., Bouyries, P., Bridou, F., Clotaire, J.-Y., Colas, G., Delmotte, F., Jerome, A., Lamare, M., Mercier, R., Mullot, M., Ravet, M.-F., Song, X., Bothmer, V., Deutsch, W.: 2004, EUVI: the STEREO-SECCHI extreme ultraviolet imager. In: Fineschi, S., Gummin, M.A. (eds.) Telescopes and Instrumentation for Solar Astrophysics, Proc. SPIE 5171, 111. 10.1117/12.506877. 2004SPIE.5171..111W.
Zidowitz, S.: 1999, Coronal structure of the Whole Sun Month: a tomographic reconstruction. J. Geophys. Res. 104, 9727. 10.1029/1998JA900099. 1999JGR...104.9727Z.
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Kramar, M., Airapetian, V., Mikić, Z., Davila, J. (2014). 3D Coronal Density Reconstruction and Retrieving the Magnetic Field Structure during Solar Minimum. In: Tomczyk, S., Zhang, J., Bastian, T. (eds) Coronal Magnetometry. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2038-9_13
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