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Magnetic Flux Emergence In Granular Convection

Magnetic Flux Emergence In Granular Convection

Mark Cheung, LMSALMark Cheung, LMSAL

SHINE 2007, Whistler Magnetic Flux Emergence

Magnetic flux emergenceMagnetic flux emergence

• Why do we want to model flux emergence through the photosphere?

• Simulation setup and results• Implications for inferences of coronal conditions

• Magnetic helicity measurements

• Azimuthal disambiguation

• Summary

• Why do we want to model flux emergence through the photosphere?

• Simulation setup and results• Implications for inferences of coronal conditions

• Magnetic helicity measurements

• Azimuthal disambiguation

• Summary


Why model magnetic flux emergence through the photosphere?

Why model magnetic flux emergence through the photosphere?

• Importance for understanding the solar dynamo• Flux emerges over a wide range of scales (time, length and flux):

• Statistical studies of emergence events yields potentially important clues about the solar dynamo. (Hagenaar 2001)

• Intrinsically interesting (lots of physics to learn)• Interplay between emerging magnetic flux and the ambient convecting

plasma -> I.e. effects of magnetoconvection• Changes appearance of photosphere (e.g. dark lanes, bright points,

pores, sunspots)

• Importance for understanding the solar dynamo• Flux emerges over a wide range of scales (time, length and flux):

• Statistical studies of emergence events yields potentially important clues about the solar dynamo. (Hagenaar 2001)

• Intrinsically interesting (lots of physics to learn)• Interplay between emerging magnetic flux and the ambient convecting

plasma -> I.e. effects of magnetoconvection• Changes appearance of photosphere (e.g. dark lanes, bright points,

pores, sunspots)

Flux Emergence timescale

Large Active Regions > 5 x 1021 Mx ~ Days

Small Active Regions 1020 to 5x1021 Mx ~ Hours to 1-2 days

Ephemeral active regions 3x1018 to 1020 Mx ~ Tens of minutes to hours (< 1day)

Small-scale flux emergence events

< 3 x 1018 Mx ~ Minutes / granulation timescale

Harvey & Martin 1973

Zwaan 1985, 1987

Hagenaar 2001

De Pontieu 2002, Ishikawa 2007, Centeno-Elliot 2007


Why study magnetic flux emergence through the photosphere?

Why study magnetic flux emergence through the photosphere?

• Practically speaking• Relatively ‘easy’ to measure the (vector) magnetic field in the

photosphere using spectropolarimetry. Detailed observational diagnostics available to constrain the models (less and less wiggle room).

• E.g. Comparison with observed Stokes Profiles

• Consequences for the overlying atmosphere• Issue of 180 deg ambiguity (K.D. Leka)

• Injection of Magnetic Helicity into the corona, subphotospheric origin of twist + currents (Pevtsov, K.D. Leka),

• Extrapolation of photospheric field (M. DeRosa)

• Practically speaking• Relatively ‘easy’ to measure the (vector) magnetic field in the

photosphere using spectropolarimetry. Detailed observational diagnostics available to constrain the models (less and less wiggle room).

• E.g. Comparison with observed Stokes Profiles

• Consequences for the overlying atmosphere• Issue of 180 deg ambiguity (K.D. Leka)

• Injection of Magnetic Helicity into the corona, subphotospheric origin of twist + currents (Pevtsov, K.D. Leka),

• Extrapolation of photospheric field (M. DeRosa)


Simulation of magnetic flux emergence at the photosphere

Simulation of magnetic flux emergence at the photosphere

• Essential physics:• Fully-compressible MHD in 3D

• Energy exchange via radiative transfer in Local Thermodynamic Equilibrium (LTE)

• Effects of ionization state changes in Equation of state (LTE)

• Essential physics:• Fully-compressible MHD in 3D

• Energy exchange via radiative transfer in Local Thermodynamic Equilibrium (LTE)

• Effects of ionization state changes in Equation of state (LTE)

• MPS/University of Chicago Radiative MHD (MURaM) code (Vögler et al 2005), used to study

• Quiet Sun and plage magnetoconvection (Vögler et al, A&A 2005) • Origin of solar faculae (Keller et al., ApJ 2004)• Umbral convection (Schüssler & Vögler, ApJL 2006)• Simulation of solar pores (Cameron & Schüssler, A&A submitted)• Reversed granulation in the photosphere (Cheung, Schüssler & Moreno-Insertis, A&A

2007)• Flux emergence in granular convection (Cheung, Schüssler & Moreno-Insertis, A&A

2007).

• MPS/University of Chicago Radiative MHD (MURaM) code (Vögler et al 2005), used to study

• Quiet Sun and plage magnetoconvection (Vögler et al, A&A 2005) • Origin of solar faculae (Keller et al., ApJ 2004)• Umbral convection (Schüssler & Vögler, ApJL 2006)• Simulation of solar pores (Cameron & Schüssler, A&A submitted)• Reversed granulation in the photosphere (Cheung, Schüssler & Moreno-Insertis, A&A

2007)• Flux emergence in granular convection (Cheung, Schüssler & Moreno-Insertis, A&A

2007).


Momentum equationMomentum equation

Continuity equationContinuity equation

Induction equationInduction equation

Radiative MHD EquationsRadiative MHD Equations


MURaM Code – MHD equationsMURaM Code – MHD equations

Energy equationEnergy equation

Radiative transfer equation Radiative transfer equation Equation of stateEquation of state

T = T(ρ, ε) p = p(ρ, ε)


MURaM Code - implementationMURaM Code - implementation

• MPS/University of Chicago Radiation MHD• A. Vögler, PhD Thesis; Vögler et al. 2005

• Finite differences scheme• Spatial discretization: 4th-order centered-difference• Time-stepping: explicit, 4th-order Runge-Kutta

• Radiative transfer• Integration along rays - 24 rays through each grid cell for 3D simulations• Grey/non-grey using opacity bins

• Parallelized• Domain decomposition• Message Passing Interface

• MPS/University of Chicago Radiation MHD• A. Vögler, PhD Thesis; Vögler et al. 2005

• Finite differences scheme• Spatial discretization: 4th-order centered-difference• Time-stepping: explicit, 4th-order Runge-Kutta

• Radiative transfer• Integration along rays - 24 rays through each grid cell for 3D simulations• Grey/non-grey using opacity bins

• Parallelized• Domain decomposition• Message Passing Interface


Near-surface convection and photosphereNear-surface convection and photosphere

• Size of simulation domain: 24,000 km by 12,000 km by 2,300 km

• grid-spacing 25 by 25 by 16 km

• Optical depth unity located ~ 1,800 km above bottom boundary

• Open top and bottom boundaries, periodic side boundaries

• Compressibility => asymmetry between

upflows (broad + gentle) and

downflows (narrow + strong)

• Size of simulation domain: 24,000 km by 12,000 km by 2,300 km

• grid-spacing 25 by 25 by 16 km

• Optical depth unity located ~ 1,800 km above bottom boundary

• Open top and bottom boundaries, periodic side boundaries

• Compressibility => asymmetry between

upflows (broad + gentle) and

downflows (narrow + strong)

Right: Volume rendering of temperature in the

numerical model.


Small-scale flux emergenceSmall-scale flux emergence

• Initial flux tube properties• Profiles of longitudinal and transverse components of the magnetic

field:• Bl(r) = B0exp (-r2/R0

2)

• Bt(r) = (λr/R0) Bl(r) , where λ is the dimensionless twist parameter (λ/R0 equivalent to ‘q’ or ‘a’ used by other authors)

• B0 = 8500 G

• Twist parameter λ = 0.25

• R0 = 200 km

• Flux = 1019 Mx

• Sinusoidal specific entropy profile -> development into an arched structure.

• Initial flux tube properties• Profiles of longitudinal and transverse components of the magnetic

field:• Bl(r) = B0exp (-r2/R0

2)

• Bt(r) = (λr/R0) Bl(r) , where λ is the dimensionless twist parameter (λ/R0 equivalent to ‘q’ or ‘a’ used by other authors)

• B0 = 8500 G


• R0 = 200 km

• Flux = 1019 Mx




Vector Magnetic Field

Greyscale - Bz (-1kG to 1kG)

Arrows - BArrows - Bhorhor

Emergent intensity



BBzz

EmergentEmergentIntensityIntensity

Field inclination angleField inclination angle

Green ~ horizontalGreen ~ horizontal

OrangeOrange//blueblue = vertical = vertical

Vertical velocityVertical velocity

Red = downflowRed = downflow

Violet/Blue = upflowViolet/Blue = upflow

Interesting features of small-scale flux emergence event• Expulsion of magnetic flux to downflow network within 5-10 minutes (granulation timescale). See De Pontieu 2002; Fan, Abbett & Fisher 2003; Stein & Nordlund 2006; Cheung et al 2007.

• Transient darkenings at emergence site, aligned with upflows threaded by predominantly horizontal field.

• Appearance of bright grains at ends of transient darkenings. Bright grains appear where vertical flux concentrations reside in the intergranular lanes.

Interesting features of small-scale flux emergence event• Expulsion of magnetic flux to downflow network within 5-10 minutes (granulation timescale). See De Pontieu 2002; Fan, Abbett & Fisher 2003; Stein & Nordlund 2006; Cheung et al 2007.

• Transient darkenings at emergence site, aligned with upflows threaded by predominantly horizontal field.

• Appearance of bright grains at ends of transient darkenings. Bright grains appear where vertical flux concentrations reside in the intergranular lanes.


Hinode SOT ObservationHinode SOT Observation

• Sequence of small-scale flux emergence events• Transient darkenings / bright grains at the flanks• Mixed polarity in emerging flux region• Cancellation when opposite polarities meet

• Emerged flux organizes itself • Bright points coalescence -> formation of pores

• Sequence of small-scale flux emergence events• Transient darkenings / bright grains at the flanks• Mixed polarity in emerging flux region• Cancellation when opposite polarities meet

• Emerged flux organizes itself • Bright points coalescence -> formation of pores

G-band Stokes V (NFI)


Small-AR-scale flux emergenceSmall-AR-scale flux emergence

• Simulation domain• 32 Mm x 24 Mm in horizontal directions (horizontal grid spacing 50km)

• 5.8 Mm in vertical direction (of which 300 km is the photosphere)• ~ 11 pressure scale heights

• Initial flux tube properties• Profiles of longitudinal and transverse components of the magnetic field:

• Bl(r) = B0exp (-r2/R02)

• Bt(r) = (λr/R0) Bl(r)

• B0 = 20 kG (plasma β ~ 20 at tube axis)


• R0 = 600 km

• Flux = 2x1020 Mx


• Simulation domain• 32 Mm x 24 Mm in horizontal directions (horizontal grid spacing 50km)

• 5.8 Mm in vertical direction (of which 300 km is the photosphere)• ~ 11 pressure scale heights

• Initial flux tube properties• Profiles of longitudinal and transverse components of the magnetic field:

• Bl(r) = B0exp (-r2/R02)

• Bt(r) = (λr/R0) Bl(r)

• B0 = 20 kG (plasma β ~ 20 at tube axis)


• R0 = 600 km

• Flux = 2x1020 Mx



Cross-sectional viewCross-sectional view

• Flux tube rises over many pressure scale heights• Strong horizontal expansion so that it almost looks like a sheet beneath

the photosphere

• Field has strengths ~ few hundred gauss just beneath surface

• Flux tube rises over many pressure scale heights• Strong horizontal expansion so that it almost looks like a sheet beneath

the photosphere

• Field has strengths ~ few hundred gauss just beneath surface

Log |B|Log |B|

vzvz

Specific entropySpecific entropy


Disturbed granulation patternDisturbed granulation pattern

• Initial ‘flash’ due to acoustic wave resulting from impulsive buoyant acceleration of tube at t=0.

• Elongated ‘granules’ and transient darkenings at emergence site -> easy to tell where flux is emerging without aid of magnetogram

• Initial ‘flash’ due to acoustic wave resulting from impulsive buoyant acceleration of tube at t=0.

• Elongated ‘granules’ and transient darkenings at emergence site -> easy to tell where flux is emerging without aid of magnetogram


Disturbed granulation patternDisturbed granulation pattern

• Undulated emerging field lines/mixed polarity field within EFR(Pariat et al 2004) naturally modelled as a consequence of interaction of flux tube with convective flow.

• Expulsion of flux from convective cells leads to encounters between opposite polarities and cancellation.

• Undulated emerging field lines/mixed polarity field within EFR(Pariat et al 2004) naturally modelled as a consequence of interaction of flux tube with convective flow.

• Expulsion of flux from convective cells leads to encounters between opposite polarities and cancellation.


Magnetic Helicity InjectionMagnetic Helicity Injection

• Magnetic helicity flux (Berger & Field 1984)• Magnetic helicity flux (Berger & Field 1984)

• Longcope & Welsch (2000) • Simple model to highlight how emergence of twisted field injects helicity into the corona.

• Magara & Longcope (2003) - 3D MHD simulations• Looked at contributions from emergence and shear terms-> Emergence term dominates at the beginning of emergence event, then subsides. Cumulative contribution from braiding term exceeds the emergence term.

• Following Chae (2001), use Fourier transforms to calculate Ap.• Calculate helicity flux through two horizontal planes:

• 3 Mm below base of photosphere• Base of photosphere

• Longcope & Welsch (2000) • Simple model to highlight how emergence of twisted field injects helicity into the corona.

• Magara & Longcope (2003) - 3D MHD simulations• Looked at contributions from emergence and shear terms-> Emergence term dominates at the beginning of emergence event, then subsides. Cumulative contribution from braiding term exceeds the emergence term.

• Following Chae (2001), use Fourier transforms to calculate Ap.• Calculate helicity flux through two horizontal planes:

• 3 Mm below base of photosphere• Base of photosphere

Emergence term Braiding term


Injection of Magnetic HelicityInjection of Magnetic Helicity

Red/blue contours: Magnetogram at z=-3 Mm

Greyscale: Photospheric magnetogram

Red/blue contours: Magnetogram at z=-3 Mm

Greyscale: Photospheric magnetogram

White curve: Helicity flux White curve: Helicity flux through z=-3 Mm planethrough z=-3 Mm plane

Yellow curve: Helicity flux Yellow curve: Helicity flux through photospherethrough photosphere

White curve: Helicity flux White curve: Helicity flux through z=-3 Mm planethrough z=-3 Mm plane

Yellow curve: Helicity flux Yellow curve: Helicity flux through photospherethrough photosphere


Magnetic Helicity InjectionMagnetic Helicity Injection

• Contribution from Braiding term is sensitive to x and y boundary conditions• Padded Bz magnetograms (zero-valued cells) give different Ap, different braiding flux

• Emergence term is more robust.

• Contribution from Braiding term is sensitive to x and y boundary conditions• Padded Bz magnetograms (zero-valued cells) give different Ap, different braiding flux

• Emergence term is more robust.

Total = Emergence + Braiding


Azimuthal DisambiguationAzimuthal Disambiguation

• Azimuthal disambiguation important for• Non-potential field extrapolation (LFF, NLFF, Magnetostatic etc.)• Helicity flux injection through photosphere

• Numerous algorithms and codes available • Review by Metcalf et al. 2006; M. Georgoulis (this meeting)

• Simulations such as those presented here are useful as test cases to benchmark and improve reliability.

• Azimuthal disambiguation important for• Non-potential field extrapolation (LFF, NLFF, Magnetostatic etc.)• Helicity flux injection through photosphere

• Numerous algorithms and codes available • Review by Metcalf et al. 2006; M. Georgoulis (this meeting)

• Simulations such as those presented here are useful as test cases to benchmark and improve reliability.


The measure of MagThe measure of Mag

• Do telescope and instrument characteristics introduce bias into measurements of quantities of interest? E.g.• Unsigned flux • Vertical current• Quality of disambiguation• Quality of horizontal surface flows obtained by correlation tracking etc.

• How well do Stokes inversion codes do? What biases do they introduce?

• Do telescope and instrument characteristics introduce bias into measurements of quantities of interest? E.g.• Unsigned flux • Vertical current• Quality of disambiguation• Quality of horizontal surface flows obtained by correlation tracking etc.

• How well do Stokes inversion codes do? What biases do they introduce?


SummarySummary

• Granular convection influences properties of emerging flux• Undulation (sea-serpent-like field lines)• Flux expulsion to intergranular lanes

• Depending on properties of emerging tube, the granulation pattern can be modified.

• These simulations important for benchmarking algorithms and codes used for• Azimuthal disambiguation• Helicity flux measurements• Stokes polarimetry

• Synthetic profiles from simulation (e.g. Leka & Steiner 2001)• Compare inversion results with orignal data in simulation cubes

(Sergey Shelyag, Lotfi Yelles-Chaouche)

• Lots of work to do (but that’s a good thing!)

• Granular convection influences properties of emerging flux• Undulation (sea-serpent-like field lines)• Flux expulsion to intergranular lanes

• Depending on properties of emerging tube, the granulation pattern can be modified.

• These simulations important for benchmarking algorithms and codes used for• Azimuthal disambiguation• Helicity flux measurements• Stokes polarimetry

• Synthetic profiles from simulation (e.g. Leka & Steiner 2001)• Compare inversion results with orignal data in simulation cubes

(Sergey Shelyag, Lotfi Yelles-Chaouche)

• Lots of work to do (but that’s a good thing!)

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