Astron. Astrophys. Rev. manuscript No. (will be inserted by the editor) The Magnetic Field in the Solar Atmosphere Thomas Wiegelmann · Julia K. Thalmann · Sami K. Solanki Draft version: October 17, 2014 Abstract This publication provides an overview of magnetic fields in the solar atmo- sphere with the focus lying on the corona. The solar magnetic field couples the solar interior with the visible surface of the Sun and with its atmosphere. It is also respon- sible for all solar activity in its numerous manifestations. Thus, dynamic phenomena such as coronal mass ejections and flares are magnetically driven. In addition, the field also plays a crucial role in heating the solar chromosphere and corona as well as in accelerating the solar wind. Our main emphasis is the magnetic field in the up- per solar atmosphere so that photospheric and chromospheric magnetic structures are mainly discussed where relevant for higher solar layers. Also, the discussion of the solar atmosphere and activity is limited to those topics of direct relevance to the mag- netic field. After giving a brief overview about the solar magnetic field in general and its global structure, we discuss in more detail the magnetic field in active regions, the quiet Sun and coronal holes. Keywords Sun · Photosphere · Chromosphere · Corona · Magnetic Field · Active Region · Quiet Sun · Coronal Holes Thomas Wiegelmann Max-Planck-Institut fur¨ Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077 Gottingen,¨ Germany Tel.: +49-551-384-979-155 Fax: +49-551-384-979-240 E-mail: [email protected] Julia K. Thalmann Institute for Physics/IGAM, University of Graz, Universitatsplatz¨ 5/II, 8010, Graz, Austria Tel.: +43-316-3808599 Fax: +49-316-3809825 E-mail: [email protected] Sami K. Solanki Max-Planck-Institut fur¨ Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077 Gottingen,¨ Germany Tel.: +49-551-384-979-552 Fax: +49-551-384-979-190 E-mail: [email protected] and arXiv:1410.4214v1 [astro-ph.SR] 15 Oct 2014 School of Space Research, Kyung Hee University, Yongin, Gyeonggi 446-701, Republic of Korea 2 Thomas Wiegelmann et al. Contents 1 Introduction . .3 1.1 Photosphere . .4 1.1.1 Magnetic flux emergence . .5 1.1.2 Spatial properties of magnetic features . .6 1.1.3 Origin of internetwork fields . .7 1.1.4 Temporal evolution of the magnetic field . .7 1.1.5 Relative importance of magnetic forces . 10 1.2 Chromosphere . 11 1.2.1 Characteristic chromospheric magnetic structures . 12 1.2.2 Indirect tracing of chromospheric fields . 14 1.2.3 Plasma-β in the chromosphere . 15 1.3 Magnetic coupling from the lower solar atmosphere to the corona . 16 1.3.1 Magnetic canopy . 16 1.4 Corona . 19 1.4.1 Transition region and coronal base . 19 1.4.2 Morphology of coronal magnetic fields . 19 2 Magnetic field modelling . 20 2.1 Direct coronal magnetic field measurements . 21 2.1.1 Chromospheric magnetic field measurements in the infrared . 21 2.1.2 Coronal magnetic field measurements in infrared . 21 2.1.3 Coronal magnetic field measurements at radio wavelengths . 22 2.2 Force-free modelling from photospheric measurements . 23 2.2.1 Potential and linear force-free fields . 23 2.2.2 Nonlinear force-free fields . 24 2.3 MHD models . 26 2.3.1 MHD models of the coronal magnetic field . 26 2.3.2 MHS models . 26 2.3.3 Flux transport models . 27 2.4 Coronal stereoscopy, tomography and seismology . 28 2.4.1 Stereoscopy and magnetic stereoscopy . 28 2.4.2 Tomography and vector tomography . 29 2.4.3 Coronal seismology . 30 3 Global coronal magnetic fields . 31 3.1 Magnetic field topology . 31 3.1.1 Performance of PFSS models . 32 3.1.2 Achievements of global MHD models . 33 3.2 Cross-equatorial fields . 33 3.2.1 Creation of transequatorial loops . 34 3.2.2 Properties of transequatorial loops . 35 3.3 Spatio-temporal aspects of activity . 36 3.3.1 Cyclic changes of the coronal magnetic field . 36 3.3.2 Association to dynamic events . 37 3.4 Magnetic helicity budget . 38 3.4.1 Helicity dissipation and helicity transport . 38 3.4.2 Hemispheric trends . 39 4 Coronal active-region magnetic fields . 40 4.1 Coronal loops . 40 4.2 Local field topology . 43 4.2.1 Magnetic skeleton . 43 4.2.2 Association to current-sheets and magnetic reconnection . 43 4.2.3 Relation to dynamic phenomena . 45 4.3 Temporal evolution of active-region magnetic fields . 47 4.3.1 Dynamic evolution: eruptive phenomena . 47 4.4 Favourable conditions for eruptions . 48 4.4.1 Magnetic flux emergence and complex magnetic field structure . 48 The Magnetic Field in the Solar Atmosphere 3 4.4.2 Magnetic shear and twist . 49 4.5 Magnetic energy budget . 50 4.5.1 Energy build-up and storage . 50 4.5.2 Relation to flare productivity . 51 4.5.3 Energy release . 52 4.5.4 Coronal implosion and photospheric response . 54 4.6 Magnetic helicity budget . 56 4.6.1 Helicity build-up and storage . 56 4.6.2 Relation to flare productivity . 57 4.6.3 Helicity dissipation and transport . 59 5 Quiet-Sun magnetic fields . 60 5.1 3D magnetic field structure in the quiet Sun . 61 5.1.1 Photospheric quiet-Sun loops . 61 5.2 Associated photospheric fields and the response on the upper atmosphere . 62 5.2.1 Doubts about the concept of a magnetic canopy . 62 5.2.2 Network and internetwork magnetic loops . 63 5.2.3 Magnetic carpet . 64 5.2.4 Role of magnetic fields in coronal and chromospheric heating . 65 5.2.5 Force-freeness of quiet-Sun magnetic fields . 67 5.2.6 Magnetic energy and helicity budget . 67 5.3 Small-scale dynamics . 68 5.3.1 Jets . 69 6 Coronal holes . 70 6.1 Properties of coronal holes . 71 6.1.1 Properties of photospheric fields associated with coronal holes . 71 6.1.2 Modelling of coronal-hole magnetic fields . 72 6.2 Polar coronal holes . 73 6.2.1 Magnetic flux in polar coronal holes . 73 6.2.2 Comparison to the quiet-Sun magnetic field . 73 6.2.3 Polar plumes . 75 6.2.4 Polar Jets . 75 6.2.5 Contribution to the solar wind . 77 6.3 Equatorial coronal holes . 77 6.3.1 Formation and evolution . 77 6.3.2 Comparison with quiet-Sun magnetic fields . 78 6.3.3 Contribution to the solar wind . 79 7 Conclusion and Outlook . 80 A Abbreviations . 82 References . 83 1 Introduction In order to understand the physical processes in the solar interior, its atmosphere as well as the interplanetary environment (including “space weather” close to Earth), a.