1. Magnetic configurations responsible for the coronal heating and the solar wind Hwanhee Lee 1, Tetsuya Magara 1 1 School of Space research, Kyung Hee University The 7 th Hinode Science Meeting in Takayama, Japan 13 Nov. 2013

2. Key points of our study compared to previous studies We try to derive more detailed magnetic configurations Half-circle shaped loop Cross sectional area is constant Potential-field approximation photosphere B Coronal heating model Solar wind model : simple magnetic configurations are assumed Magnetic configurations Previous works

3. Introduction Two aspects of magnetic configurations Global configuration : whole active region Local configuration : individual coronal loop Distributions of the following two parameters (1) Force-Free parameter : α (2) Flux-tube expansion rate : f ex Expansion profile of a coronal loop expanding outward - Distribution of f ex along a loop

4. Definitions of the parameters To investigate these magnetic configurations, we focus on two key parameters Force-Free parameter Flux-tube expansion rate Twist of magnetic field Expansion of magnetic field (A : cross sectional area)

5. Model Description Flux-emergence MHD simulation (Lee & Magara, submitted) Basic equations: ideal MHD equations Initial state Magara (2013); An & Magara (2013), where r is the radial distance from the axis and b is field-line twist parameter Strongly twistedWeakly twisted Initial states of b=1(left) and b=0.2(right) Magnetic field : Gold-Hoyle profile

6. Overview of evolution Strongly twisted caseWeakly twisted case Initial state Late state

7. 1.Global magnetic configuration Distributions of α and f ex in a whole active region

8. Strongly twisted case In the α -distribution, inner loops form double J- shaped structure in the corona where strong electric current flows, while less current flows along outer loops In the f ex distribution, large flux expansion rate is found at the footpoints of outer loops

9. Weakly twisted case In the α -distribution, strong electric current flows along short and low loops (inner part) In the f ex distribution, long outer loops have large flux expansion rate at their footpoints

10. Comparison to potential field (extrapolated from photospheric field)

11. Distribution of flux expansion rate Strongly twisted caseWeakly twisted case emerging field In the potential fields, not only outer but also inner loops have large expansion rate at their footpoints However in the emerging fields, outer loops tend to have large expansion rate at their footpoints potential field emerging field

12. 2. Local magnetic configuration Expansion profile of a coronal loop

13. Expansion types of coronal loops Sun B B Parabolic type Exponential type Definition of flux expansion rate A0A0 A0A0 : cross-section of flux tube A(s)

14. Example: Weakly twisted case, emerging field Expansion profile of a coronal loop Exponential type Range IRange IVRange IIIRange II s : the length of field line (unit: 2H ph ) Z b : the height of field line element ZbZb s Parabolic type

15. Range I ( f ex ~ const. ) is short and Range II is prominent in the emerging fields, while Range I is wide and Range II is short in the potential fields Expansion profiles of various coronal loops Strongly twisted case: emerging field Weakly twisted case: emerging field Strongly twisted case: potential field Weakly twisted case: potential field Outer loops are selected for each case

16. Conclusion In the strongly twisted case, Regarding the global magnetic configurations, inner part : - strong electric current flows in the corona - double-J shaped structure (observed as a sigmoid) outer part : large f ex but small α at footpoints loops expand outward inner part : - strong electric current flows near the surface - seaserpent structure (low loops) (not observed as a sigmoid) outer part : similar to the strongly twisted case In the weakly twisted case,

17. Conclusion Regarding the local magnetic configurations, The expansion of a magnetic field is characterized by the exponential type near the photosphere (Range I) and parabolic type in the corona (Range III) The Range II becomes prominent when the field is strongly confined by surrounding plasma (high plasma beta) Transition from Range II to Range III… magnetic field can determine its configuration by itself without being affected by surrounding gas pressure (high plasma beta → low plasma beta) These detailed magnetic configurations probably contribute to developing realistic models for the coronal heating and solar wind generation.