Magnetic Flux Emergence In Granular Convection Mark Cheung, LMSAL

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!)

Documents

Magnetic Flux Emergence In Granular Convection Mark Cheung, LMSAL