Magnetic configurations responsible for the coronal heating and the solar wind
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Magnetic configurations responsible for
the coronal heating and the solar windHwanhee Lee1, Tetsuya Magara1
1School of Space research, Kyung Hee University
The 7th Hinode Science Meeting in Takayama, Japan 13 Nov. 2013
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Key points of our study comparedto previous studies
We try to derive more detailed magnetic configu-rations
• Half-circle shaped loop• Cross sectional area is constant• Potential-field approximation
photosphere
BCoronal heating model Solar wind model
: simple magnetic configurations are assumed
• Magnetic configurations
• Previous works
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Introduction• Two aspects of magnetic configurations
• Global configuration : whole active region
• Local configuration : individual coronal loop
• Distributions of the following two parame-ters (1) Force-Free parameter : α (2) Flux-tube expansion rate : fex
• Expansion profile of a coronal loop expanding outward
- Distribution of fex along a loop
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Definitions of the parame-ters
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)
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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 twisted Weakly twisted
Initial states of b=1(left) and b=0.2(right)
• Magnetic field : Gold-Hoyle profile
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Overview of evolutionStrongly twisted case Weakly twisted case
Initial state
Late state
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1. Global magnetic configura-tionDistributions of α and fex in a whole active region
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Strongly twisted case
In the α -distribution, inner loops form double J-shaped structure in the coronawhere strong electric cur-rent flows, while less current flowsalong outer loops
In the fex distribution,large flux expansion rate isfound at the footpoints of outer loops
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Weakly twisted case
In the α -distribution, strong electric current flows along short and low loops(inner part)
In the fex distribution,long outer loops have largeflux expansion rateat their footpoints
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Comparison to potential field(extrapolated from photospheric field)
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Distribution of flux expansion rateStrongly twisted
caseWeakly twisted
case
emerging field
In the potential fields, not only outer but also inner loops have largeexpansion rate at their footpoints
However in theemerging fields,outer loops tend to havelarge expansion rateat their footpoints
potential field
potential field
emerging field
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2. Local magnetic configurationExpansion profile of a coronal loop
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Expansion types of coronal loops
Sun
B
Sun
BParabolic type
Exponential type
Definition of flux expansion rate
A0
A0
: cross-section of flux tubeA(s)
A(s)
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• Example: Weakly twisted case, emerging field
Expansion profile of a coronal loop
Exponential type
Range I Range IVRange IIIRange IIs : the length of field line (unit: 2Hph)Zb : the height of field line ele-ment
Zbs
Parabolic type
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• Range I (fex~ 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
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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 fex 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,
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ConclusionRegarding the local magnetic configurations,
• The expansion of a magnetic field is character-ized by the exponential type near the photosphere (Range I)and parabolic type in the corona (Range III)
• The Range II becomes prominentwhen the field is strongly confined by surrounding plasma (high plasma beta)
• Transition from Range II to Range III…magnetic field can determine its configurationby itself without being affected bysurrounding 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.