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

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

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

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)

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

Overview of evolutionStrongly twisted case Weakly twisted case

Initial state

Late state

1. Global magnetic configura-tionDistributions of α and fex in a whole active region

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

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

Comparison to potential field(extrapolated from photospheric field)

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

2. Local magnetic configurationExpansion profile of a coronal loop

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)

• 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

• 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

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,

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.