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Transcript of Tetsuya Magara - 163.180.179.74163.180.179.74/~magara/meetings/APSPM4_magara_final.pdf ...

  • Flux-Emergence Model for the Characterization of

    Solar Active Regions

    Tetsuya Magara(Kyung Hee University)

    Magara (2017)

    APSPM4@Kyoto University, Japan

    Nov. 7 - 10, 2017

    http://web.khu.ac.kr/~magara/index.html
  • Flux emergence produces various types of solar active regions...

  • These active regions are developed from common magnetic structure, i.e. twisted flux tube.

    Convective motions twist a flux tube (magnetoconvection).

    Twisting

    Magnetic buoyancy

    convection zone

  • Similarity between solar active regions and animals...

    Their origins have simple structure.

    Active regions Animals

    https://www.istockphoto.com/jp/%E3%83%99%E3%82%AF%E3%82%BF%E3%83%BC/%E7%94%9F%E7%89%A9%E3%81%AE%E9%80%B2%E5%8C%96%E3%81%AB%E3%82%B9%E3%82%AD%E3%83%BC%E3%83%A0%E3%81%AE%E9%80%B2%E5%8C%96-animalschildren-%E3%81%AE%E6%95%99%E8%82%B2%E7%A7%91%E5%AD%A6%E3%81%BE%E3%81%99-gm486713328-73584975

  • Even though these origins have simple structure, they play fundamental roles in determining characteristics.

    Solar active regions

    Animals

    Here we focus on physical properties of pre-emerged subsurface magnetic field, which determine the characteristics of solar active regions.

    However, it is difficult to obtain these properties via direct observation in electromagnetic waves (the surface of the Sun behaves like an impermeable boundary toward radiative flux).

    Then what shall we do?

  • Forward problem vs. Inverse problem

    Forward problem

    Physical properties of subsurface magnetic field (cause)... input

    Evolution of surface magnetic field (result)... derived

    Inverse problem

    Physical properties of subsurface magnetic field (cause)... derived

    Evolution of surface magnetic field (result)... input

    flux-emergence simulation

  • Surface magnetic fields have been classified on the basis of their morphological features.

    For solving the inverse problem, morphological classification is insufficient as input. Some quantitative relation characterizing individual active regions is necessary.

  • Quantitative relation representing evolutionary characteristics of active regions

    We focus on the following two quantities obtained from observations of surface magnetic field:

    Emerged magnetic flux (emg)... provides scale information

    Injected magnetic helicity (Hinj)... represents magnetic configurations

    emg

    Hinj

    emg

    Hinj

    emg

    Hinj

    emg

    Hinj

    Each active region has its own profile in (emg, Hinj)-space

    => evolutionary path of an active region

  • emg

    Hinj

    emg

    Hinj

    emg

    Hinj

    emg

    Hinj

    Morphology

    Quantitative relation

    By using this relation, we consider the inverse problem.

  • Toward this end, we construct a model of flux emergence...

    Phase I... axis of an emerging flux tube is below surface (h R)

    Phase II... axis of an emerging flux tube is above surface (h R)

    R: radius of a flux tubeL: length of emergence

    h: height of emergence (0 h 2R)w: width of emergence (w = 2 R h h )

  • The model depends on two factors...

    Physical properties of subsurface magnetic field: flux-tube radius, field strength, twist

    R

    B0

    Time-dependent process of flux emergence: emergence length, emergence height

    X

    h = h tL = L t h = fef L

    parametric equation(a pair of time-dependent

    functions)

    : flux-emergence function

    b 0 B r = B0b 0 r + a

    1 + b 0 r2

  • Flux-emergence function... characterized by three parameters

    hmax: maximum of emergence heightLmax: maximum of emergence length

    : parameter controlling how flux emergence proceeds

    h = fef(L) h max sin 2LLmax

    hmax = 2R, Lmax = 15R, = 0.5

    hmax = 1.5R, Lmax = 15R, = 2

    hmax = R, Lmax = 15R, = 1

    full-emergence

    intermediate-emergence

    half-emergence

    When takes a smaller value (red curve), flux-emergence proceeds more actively at an early phase, then it becomes saturated, forming a relatively long late phase.

    Examples of h = fef L :

  • Emerged magnetic flux (emg): Apparent emerged flux (emgA )... signed flux crossing a horizontal

    plane (surface):

    Net emerged flux (emgN )... unsigned flux crossing a vertical plane:

    Injected magnetic helicity (Hinj):

    We then calculate emerged magnetic flux & injected magnetic helicity...

    emgA (Phase I) = B0 L

    b 0ln 1 + b 0

    2 R2

    1 + b 02 (R h)

    2

    emgA (Phase II) = B0 L

    b 0ln 1 + b 0

    2 R2

    1 + b 02 (R h)

    21 2

    b 0 L

    Hinj (Phase I) =B0

    2 L4 b 0

    3 ( 2 h) ln 1 + b 02 R2

    2

    ln 1 + b 02 (R h)

    2

    sin2

    2

    d h

    h

    Hinj (Phase II) =B0

    2 L4 b 0

    3 ( + 2 h) ln 1 + b 02 R2

    2

    + ln 1 + b 02 (R h)

    2

    sin2

    2

    d h

    h

    h = arcsin 1 h / R

    used for calculating injected magnetic helicity

    directly observed

  • A set of six parameters determines the evolutionary path of an active region...

    Physical properties of a subsurface magnetic field: R, B0, b 0Time-dependent process of flux emergence: hmax, Lmax,

    emgA and Hinj are

    expressed as functions of h and L.

    emgA (Phase I) = B0 L

    b 0ln 1 + b 0

    2 R2

    1 + b 02 (R h)

    2

    emgA (Phase II) = B0 L

    b 0ln 1 + b 0

    2 R2

    1 + b 02 (R h)

    21 2

    b 0 L

    Hinj (Phase I) =B0

    2 L4 b 0

    3 ( 2 h) ln 1 + b 02 R2

    2

    ln 1 + b 02 (R h)

    2

    sin2

    2

    d h

    h

    Hinj (Phase II) =B0

    2 L4 b 0

    3 ( + 2 h) ln 1 + b 02 R2

    2

    + ln 1 + b 02 (R h)

    2

    sin2

    2

    d h

    h

    h = arcsin 1 h / R

    }}

    h = fef L

    emgA = emg

    A LHinj = Hinj L

    parametric equation

    Hinj = f emgA

  • hmax = 2R, Lmax = 15R, = 0.5

    hmax = 1.5R, Lmax = 15R, = 2

    hmax = R, Lmax = 15R, = 1

    full-emergence

    intermediate-emergence

    half-emergence

    Examples of evolutionary paths...

    0 = B0b 0

    2 ln 1 + b 02 R2

    H0 =b 02 0

    2 Lmax

    ... total net flux

    ... maximum helicity

    Evolutionary path:

    Flux-emergence function:

    b 0 = 1 / R

    h = fef L

    Hinj = f emgA

  • Inversion process...

    Hinj = f emgA

    six parameters

    emgA

    Hinj

    Model:

    Observation:

    For estimating injected magnetic helicity from observed data, there are several methods (Chae 2001; Kusano et al. 2002; Dmoulin & Berger 2003; Magara & Tsuneta 2008).

    curve fitting => determine the six parametersR, B0, b 0 hmax, Lmax,

  • We use a flux-emergence simulation to check how well the inversion works.

    42.5 3.54

    202.16

    ~ 36 (final state) 1 (left-handed twist)

    17.42

    L

    b0

    B0

    R

    inversionsimulation

    End state

    First state

    A possible explanation of this discrepancy is that after they emerge, magnetic field lines tend to be twisted strongly around the footpoints of an axis field line, which may enhance the inversion value compared to the value of uniform twist assumed initially in the simulation.

    L ~ 36

  • Discussion & future workToward the understanding of solar magnetism, physical properties of subsurface magnetic field giving rise to sunspots are important (Choudhuri et al. 2007), not just the number of sunspots appearing at the solar surface.

    R, B0, b 0 hmax, Lmax,

    R, B0, b 0 hmax, Lmax,

    R, B0, b 0 hmax, Lmax,

  • This work was financially supported by Core Research Program (NRF-2017R1A2B4002383, PI: T. Magara) through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology, as well as by BK21 plus program through the NRF.