1. Magnetic Flux Emergence In Granular Convection Mark Cheung, LMSAL

2. SHINE 2007, WhistlerMagnetic Flux Emergence Magnetic 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

3. SHINE 2007, WhistlerMagnetic Flux Emergence 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) FluxEmergence timescale Large Active Regions> 5 x 10 21 Mx~ Days Small Active Regions10 20 to 5x10 21 Mx~ Hours to 1-2 days Ephemeral active regions3x10 18 to 10 20 Mx~ Tens of minutes to hours (< 1day) Small-scale flux emergence events < 3 x 10 18 Mx~ Minutes / granulation timescale Harvey & Martin 1973 Zwaan 1985, 1987 Hagenaar 2001 De Pontieu 2002, Ishikawa 2007, Centeno-Elliot 2007

4. SHINE 2007, WhistlerMagnetic Flux Emergence 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)

5. SHINE 2007, WhistlerMagnetic Flux Emergence 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).

6. SHINE 2007, WhistlerMagnetic Flux Emergence Momentum equation Continuity equation Induction equation Radiative MHD Equations

7. SHINE 2007, WhistlerMagnetic Flux Emergence MURaM Code – MHD equations Energy equation Radiative transfer equation Equation of state T = T(ρ, ε) p = p(ρ, ε)

8. SHINE 2007, WhistlerMagnetic Flux Emergence MURaM 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

9. SHINE 2007, WhistlerMagnetic Flux Emergence Near-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.

10. SHINE 2007, WhistlerMagnetic Flux Emergence Small-scale flux emergence Initial flux tube properties Profiles of longitudinal and transverse components of the magnetic field: B l (r) = B 0 exp (-r 2 /R 0 2 ) B t (r) = ( λ r/R 0 ) B l (r), where λ is the dimensionless twist parameter ( λ /R 0 equivalent to ‘q’ or ‘a’ used by other authors) B 0 = 8500 G Twist parameter λ = 0.25 R 0 = 200 km Flux = 10 19 Mx Sinusoidal specific entropy profile -> development into an arched structure. Initial flux tube properties Profiles of longitudinal and transverse components of the magnetic field: B l (r) = B 0 exp (-r 2 /R 0 2 ) B t (r) = ( λ r/R 0 ) B l (r), where λ is the dimensionless twist parameter ( λ /R 0 equivalent to ‘q’ or ‘a’ used by other authors) B 0 = 8500 G Twist parameter λ = 0.25 R 0 = 200 km Flux = 10 19 Mx Sinusoidal specific entropy profile -> development into an arched structure.

11. SHINE 2007, WhistlerMagnetic Flux Emergence Small-scale flux emergence Vector Magnetic Field Greyscale - B z (-1kG to 1kG) Arrows - B hor Emergent intensity

12. SHINE 2007, WhistlerMagnetic Flux Emergence Small-scale flux emergence BzBzBzBz Emergent Intensity Field inclination angle Green ~ horizontal Orange/blue = vertical Vertical velocity Red = downflow Violet/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.

13. SHINE 2007, WhistlerMagnetic Flux Emergence Hinode 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-bandStokes V (NFI)

14. SHINE 2007, WhistlerMagnetic Flux Emergence Small-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: B l (r) = B 0 exp (-r 2 /R 0 2 ) B t (r) = ( λ r/R 0 ) B l (r) B 0 = 20 kG (plasma β ~ 20 at tube axis) Twist parameter λ = 0.2 R 0 = 600 km Flux = 2x10 20 Mx Sinusoidal specific entropy profile -> development into an arched structure. 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: B l (r) = B 0 exp (-r 2 /R 0 2 ) B t (r) = ( λ r/R 0 ) B l (r) B 0 = 20 kG (plasma β ~ 20 at tube axis) Twist parameter λ = 0.2 R 0 = 600 km Flux = 2x10 20 Mx Sinusoidal specific entropy profile -> development into an arched structure.

15. SHINE 2007, WhistlerMagnetic Flux Emergence Cross-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| vzvz vzvz Specific entropy

16. SHINE 2007, WhistlerMagnetic Flux Emergence Disturbed 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

17. SHINE 2007, WhistlerMagnetic Flux Emergence Disturbed 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.

18. SHINE 2007, WhistlerMagnetic Flux Emergence Magnetic Helicity Injection 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 A p. 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 A p. Calculate helicity flux through two horizontal planes: 3 Mm below base of photosphere Base of photosphere Emergence term Braiding term

19. SHINE 2007, WhistlerMagnetic Flux Emergence Injection 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 through z=-3 Mm plane Yellow curve: Helicity flux through photosphere White curve: Helicity flux through z=-3 Mm plane Yellow curve: Helicity flux through photosphere

20. SHINE 2007, WhistlerMagnetic Flux Emergence Magnetic Helicity Injection Contribution from Braiding term is sensitive to x and y boundary conditions Padded B z magnetograms (zero-valued cells) give different A p, different braiding flux Emergence term is more robust. Contribution from Braiding term is sensitive to x and y boundary conditions Padded B z magnetograms (zero-valued cells) give different A p, different braiding flux Emergence term is more robust. Total = Emergence + Braiding

21. SHINE 2007, WhistlerMagnetic Flux Emergence Azimuthal 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.

22. SHINE 2007, WhistlerMagnetic Flux Emergence The 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?

23. SHINE 2007, WhistlerMagnetic Flux Emergence Summary 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!)