Magnetic Flux Emergence In Granular Convection

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

2. 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 Magnetic Flux Emergence

3. 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) Harvey & Martin 1973 Zwaan 1985, 1987 Hagenaar 2001 De Pontieu 2002, Ishikawa 2007, Centeno-Elliot 2007 Magnetic Flux Emergence

4. 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) Magnetic Flux Emergence

5. 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) • 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). Magnetic Flux Emergence

6. Radiative MHD Equations Continuity equation Momentum equation Induction equation Magnetic Flux Emergence

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

8. 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 Magnetic Flux Emergence

9. 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) Right: Volume rendering of temperature in the numerical model. Magnetic Flux Emergence

10. Small-scale flux emergence • 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) , 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. Magnetic Flux Emergence

11. Small-scale flux emergence Emergent intensity Vector Magnetic Field Greyscale - Bz (-1kG to 1kG) Arrows - Bhor Magnetic Flux Emergence

12. Small-scale flux emergence Field inclination angle Green ~ horizontal Orange/blue = vertical Bz Vertical velocity Red = downflow Violet/Blue = upflow EmergentIntensity • 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. Magnetic Flux Emergence

13. 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 G-band Stokes V (NFI) Magnetic Flux Emergence

14. 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: • Bl(r) = B0exp (-r2/R02) • Bt(r) = (λr/R0) Bl(r) • B0 = 20 kG (plasma β ~ 20 at tube axis) • Twist parameter λ = 0.2 • R0 = 600 km • Flux = 2x1020 Mx • Sinusoidal specific entropy profile -> development into an arched structure. Magnetic Flux Emergence

15. Cross-sectional view Log |B| • 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 vz Specific entropy Magnetic Flux Emergence

16. 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 Magnetic Flux Emergence

17. 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. Magnetic Flux Emergence

18. Magnetic Helicity Injection • Magnetic helicity flux (Berger & Field 1984) Braiding term Emergence term • 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 Magnetic Flux Emergence

19. Injection of Magnetic Helicity 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 Magnetic Flux Emergence

20. Magnetic Helicity Injection Total = Emergence + Braiding • 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. Magnetic Flux Emergence

21. 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. Magnetic Flux Emergence

22. 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? Magnetic Flux Emergence

23. 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!) Magnetic Flux Emergence