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Complexity & non-potentiality of the solar corona G. Aulanier ( Observatoire de Meudon, LESIA ) G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Overview of this tutorial 1. Basic physics 1.1 Introduction 1.2 Non-potentiality 1.3 Complexity 2. Learning from 3D MHD simulations 2.1 Current sheets & reconnection in quasi-separatrices 2.2 Breakout model of an observed eruption 3. Magnetic field extrapolations 3.1 Motivation 3.2 Potential & linear force-free fields 3.3 Non-linear force-free fields 4. Toward SDO & other future missions G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Complexity & non-potentiality At the origin of all solar flares & eruptions TRACE, FeXI 171A July 14 1998, 12:05 UT – 14:00 UT Yohkoh SXT, SXR 11:48 UT Among the major goals of all upcoming solar instruments G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Magnetic energy : storage & release Magnetically driven activity Corona : b ~ ETh / EB ~ 2mP / B² < 1 Long-duration energy storage phase a few days (flares) to a few weeks (prominence eruptions) Sudden energy release & triggering of active phenomenon Alfvénic timescales ~ a few minutes G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Overview of this tutorial 1. Basic physics 1.1 Introduction 1.2 Non-potentiality 1.3 Complexity 2. Learning from 3D MHD simulations 2.1 Current sheets & reconnection in quasi-separatrices 2.2 Breakout model of an observed eruption 3. Magnetic field extrapolations 3.1 Motivation 3.2 Potential & linear force-free fields 3.3 Non-linear force-free fields 4. Toward SDO & other future missions G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Pre-eruptive B : force-free fields Conservation of momentum : dt ( r u )= 0 dt u = – (u .s) u + (mr)–1 (sx B) x B + sP + rg tA²/t² = u²/cA² + 1 + b + b L / HP Slow evolution : t ~ days >> tA ~ minutes Photospheric velocities : u ~ 0.1 km/s << cA ~ 1000 km/s « Cold » plasma : b = 0.0001 – 0.1 << 1 Loop sizes : L~ 10 – 100 Mm ~ Hp ~ 50 Mm JxB=0 & sx B = mJ Field-aligned currents : sx B = a B G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Force-free fields : three classes Potential fields : a = 0 sx B = 0 B = sY B defined by a scalar potential Linear force-free fields : a = cst sx (sx B = a B ) s² B + a² B = 0 Helmoltz equation has analytical solutions Non-linear force-free fields : a = varying s(sx B = a B ) ( B s)a = 0 A field line is defined by its a value G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Non potentiality : free magnetic energy Potential field : sx B0 = 0 B0 = sF ; EB0 = III ½ B0² dV Non potential field : ; s B0 = 0 B = B0+ B1 ; s B1 = 0 ; II B1 dS = 0 EB = III ½ B0² dV + III ½ B1² dV + III B0B1 dV = EB0 + EB1 = EB0 + EB1 = = > EB0 EB0 EB0 + + EB1 EB1 + III sF B1 dV + III s(F B1) dV + II F B1 dS Same as Kelvin’s theorem for incompressible fluids Potential field = lower bound of energy G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA How to store energy in the corona Paradigm : The Sun has no experimental-like well-defined confining boundaries But energy stored for Dt >> tAlfvén Wavelengths L of coronal waves with C = CA ~ cst : Energy burst during dt : L ~ CA dt ~ 10 Mm (for CA= 200 km/s & dt = 50 s) Slow & continuous motion of a footpoint : L ~ Lcoronal loop > 10 Mm Corona / photosphere interface (assuming equal B) : 17 9 4 CAcor / CAphot ~ (rphot / rcor)½ ~ (10 cm-3 / 10 cm-3 )½ ~ 10 4 2 2 Lwavelength / HP scale-height > 10 km / 10 km > 10 G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Energy storage : line-tying When an Alfvén waves reaches the photosphere At the wave-front, over 1% only of the whole wavelength Propagation speed m by a factor 104 Velocity amplitude m by a factor 108 This leads to a quasi-complete reflexion back into the corona - This is not only the result of strong r differences, it requires a sharp interface ! - Its is not always valid : e.g. steep waves & shocks, short loops, very short energy bursts Line-tying = extreme assumption = full reflexion G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Origin of Energy : emergence & motions Sub-photospheric emergence Current carrying flux tube from convection zone Flux tubes traveling the whole CZ twist necessary Slow photospheric motions Twisting of 1 or 2 of the polarities Shearing motions // inversion line Energy stored in closed field lines only Evacuation of EB at Alfvénic speeds in open fields G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Overview of this tutorial 1. Basic physics 1.1 Introduction 1.2 Non-potentiality 1.3 Complexity 2. Learning from 3D MHD simulations 2.1 Current sheets & reconnection in quasi-separatrices 2.2 Breakout model of an observed eruption 3. Magnetic field extrapolations 3.1 Motivation 3.2 Potential & linear force-free fields 3.3 Non-linear force-free fields 4. Toward SDO & other future missions G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Non-bipolar fields : complex topologies 2.5-D & 3D models : Quadru-polar fields Null In point B=0 separatrix surfaces 3D : spine field line & fan surface z x Karpen et al. (1998) Aulanier et al. (2000) G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Complexity : current sheet formation Quasi-spontaneous current sheet formation in 2.5-D : Field line equation : Dy = S By dxz/Bxz = By S dxz/Bxz ( Bxzsxz) By = 0 since J x B = 0 & d/dy = 0 On each side of separatrix : Dy equal & dxz /Bxz different Jump in By z y x G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA x Null point : magnetic reconnection Basic principle in a current sheet : dB/dt = hs² B & field line equation reconnection (Aulanier, 2004, La Recherche) mass & energy conservations uin /CA = Lu -½ (Sweet-Parker regime) The Switch-on problem : shearing separatrix spontaneous J sheet no flare, but heating Advect stronger B, increasing h , stronger driving, other physics (Petscheck, Hall…) Or separatrix-less reconnection… G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Overview of this tutorial 1. Basic physics 1.1 Introduction 1.2 Non-potentiality 1.3 Complexity 2. Learning from 3D MHD simulations 2.1 Current sheets & reconnection in quasi-separatrices 2.2 Breakout model of an observed eruption 3. Magnetic field extrapolations 3.1 Motivation 3.2 Potential & linear force-free fields 3.3 Non-linear force-free fields 4. Toward SDO & other future missions G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Generic four flux concentrations model Quasi-separatrices no 3D null point Topology / geometry : Continuous field line mapping Quasi-separatrices Sharp connectivity gradients G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Gradual formation of current layers Log Q a=J/ B J = sx B Aulanier et al. (2005) Current layers & topology : pas de symétrie 2.5D Along the pre-existing Quasi Separatrix Layer (QSL) J sheet thinnest in Hyperbolic Flux Tube (HFT) Quasi-separatrices J (z=0) Thickness decreases with time in HFT G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Formation of current layers : where & how Current sheets : In pre-existing QSL For any boundary motion Thickness of J ~ thickness of QSL Aulanier et al. (2005) G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Slip-running reconnection in 3D Field line dynamics : Coronal reconnection Alfvénic continuous footpoint slippage Origin of apparent fast motion of particle impact along flare ribbons ? G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Overview of this tutorial 1. Basic physics 1.1 Introduction 1.2 Non-potentiality 1.3 Complexity 2. Learning from 3D MHD simulations 2.1 Current sheets & reconnection in quasi-separatrices 2.2 Breakout model of an observed eruption 3. Magnetic field extrapolations 3.1 Motivation 3.2 Potential & linear force-free fields 3.3 Non-linear force-free fields 4. Toward SDO & other future missions G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA A case study : The July 14, 1998 eruption Yohkoh SXT, SXR 11:48 UT TRACE, FeXI 171A 12:05 UT – 14:00 UT G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Realistic model of B & line-tied motions Coronal field : top view B(Kitt Peak) modified to have |Bzmax|=2900 G potential field extrapolation view from earth Local photospheric twisting : 1 polarity in d-spot satisfies dBz/dt = 0 umax = 2% CA (slow) G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA A generalized magnetic breakout ? Aulanier et al. (2000) d-spot coronal configuration : Null point aside of (not above) the sheared field lines at z = 3.9 Mm Sheared fields beneath the fan surface 2.5-D MHD breakout model Projection view of The full 3D MHD domain (Antiochos et al. 1999) G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Dynamics of sheared & complex coronal fields Potential field Projection view (field lines & Bz[z=0] ) 2D cut of currents J G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Dynamics of sheared & complex coronal fields Eruption with continuous photospheric motions & null point reconnection Projection view (field lines & Bz[z=0] ) 2D cut of currents J t = 0000 s , ndump = 00 G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Dynamics of sheared & complex coronal fields Eruption with continuous photospheric motions & null point reconnection Projection view (field lines & Bz[z=0] ) 2D cut of currents J t = 0090 s , ndump = 03 G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Dynamics of sheared & complex coronal fields Eruption with continuous photospheric motions & null point reconnection Projection view (field lines & Bz[z=0] ) 2D cut of currents J t = 0180 s , ndump = 06 G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Dynamics of sheared & complex coronal fields Eruption with continuous photospheric motions & null point reconnection Projection view (field lines & Bz[z=0] ) 2D cut of currents J t = 0270 s , ndump = 09 G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Dynamics of sheared & complex coronal fields Eruption with continuous photospheric motions & null point reconnection Projection view (field lines & Bz[z=0] ) 2D cut of currents J t = 0360 s , ndump = 12 G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Dynamics of sheared & complex coronal fields Eruption with continuous photospheric motions & null point reconnection Projection view (field lines & Bz[z=0] ) 2D cut of currents J t = 0450 s , ndump = 15 G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Dynamics of sheared & complex coronal fields Eruption with continuous photospheric motions & null point reconnection Projection view (field lines & Bz[z=0] ) 2D cut of currents J t = 0540 s , ndump = 18 G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Dynamics of sheared & complex coronal fields Eruption with continuous photospheric motions & null point reconnection Projection view (field lines & Bz[z=0] ) 2D cut of currents J t = 0630 s , ndump = 21 G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Dynamics of sheared & complex coronal fields Eruption with continuous photospheric motions & null point reconnection Projection view (field lines & Bz[z=0] ) 2D cut of currents J t = 0720 s , ndump = 24 G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Dynamics of sheared & complex coronal fields Eruption with continuous photospheric motions & null point reconnection Projection view (field lines & Bz[z=0] ) 2D cut of currents J Null point reconnection t = 0810 s , ndump = 27 G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Dynamics of sheared & complex coronal fields Eruption with continuous photospheric motions & null point reconnection Projection view (field lines & Bz[z=0] ) 2D cut of currents J Null point reconnection t = 0900 s , ndump = 30 G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Dynamics of sheared & complex coronal fields Eruption with continuous photospheric motions & null point reconnection Projection view (field lines & Bz[z=0] ) Flux tube acceleration 2D cut of currents J Null point reconnection t = 0990 s , ndump = 33 G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Dynamics of sheared & complex coronal fields Eruption with continuous photospheric motions & null point reconnection Projection view (field lines & Bz[z=0] ) 2D cut of currents J Flux tube acceleration t = 1080 s , ndump = 36 G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Dynamics of sheared & complex coronal fields Eruption with continuous photospheric motions & null point reconnection Projection view (field lines & Bz[z=0] ) 2D cut of currents J Flux tube acceleration t = 1170 s , ndump = 39 G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Dynamics of sheared & complex coronal fields Eruption with continuous photospheric motions & null point reconnection Projection view (field lines & Bz[z=0] ) 2D cut of currents J Flux tube acceleration t = 1260 s , ndump = 42 G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Dynamics of sheared & complex coronal fields Eruption with continuous photospheric motions & null point reconnection Projection view (field lines & Bz[z=0] ) 2D cut of currents J Flux tube acceleration t = 1350 s , ndump = 45 G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Dynamics of sheared & complex coronal fields Eruption with continuous photospheric motions & null point reconnection Projection view (field lines & Bz[z=0] ) 2D cut of currents J Flux tube acceleration t = 1440 s , ndump = 48 G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA TRACE observations vs. MHD model Eruption with photospheric motions supressed TRACE 171A View from Earth ( field lines & Jz[z=0] ) G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA A generalized magnetic breakout ? Physical & observational ingredients : Photospheric twisting & slow expansion 0 < t < 750 Magnetic energy: EBfree = 9.5 % EBpotential field Null point reconnection & leaning sideward of overlaying fields rooted in the d-spot t = 990 750 < t < 1080 Fast eruption of sheared fields & 2-ribbon flare ( idem if photospheric driving supressed ) 990 < t < 1440 Moving brightenings observed in EUV = dtJz (z=0) during reconnection So far difficulties to calculate full eruption : numerical instabilities in current sheets calculation halts work in progress G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Overview of this tutorial 1. Basic physics 1.1 Introduction 1.2 Non-potentiality 1.3 Complexity 2. Learning from 3D MHD simulations 2.1 Current sheets & reconnection in quasi-separatrices 2.2 Breakout model of an observed eruption 3. Magnetic field extrapolations 3.1 Motivation 3.2 Potential & linear force-free fields 3.3 Non-linear force-free fields 4. Toward SDO & other future missions G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA To link models & observations (Antiochos et al. 1999) SoHO/EIT 195 filament eruption 2.5-D MHD breakout model Magnetic field extrapolations : Model of Bcoronal using observed Bphot as boundary conditions To better analyze observed events knowing Bcorona initial To test models & provide B for 3D MHD simulations G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Overview of this tutorial 1. Basic physics 1.1 Introduction 1.2 Non-potentiality 1.3 Complexity 2. Learning from 3D MHD simulations 2.1 Current sheets & reconnection in quasi-separatrices 2.2 Breakout model of an observed eruption 3. Magnetic field extrapolations 3.1 Motivation 3.2 Potential & linear force-free fields 3.3 Non-linear force-free fields 4. Toward SDO & other future missions G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Potential & linear force-free field extrapolations Assumption : a = cst (a=0 for potential) s² B + a² B = 0 : Helmoltz equation : analytical solutions Fourier, Bessel functions, spherical harmonics (Nakagawa & Raadu 1972, Alissandrakis 1981, Démoulin et al. 1997, Chiu and Hilton 1977, Semel 1988, Altschuler & Newkirk 1969, Schrijver & DeRosa 2003 …) Advantages & limits : + + + + Fast computation low computer memory & power Based on analytical formulas low dependance on algorithm Do not require full Bphot vector magnetograms rare & noisy Overall topology most topological regimes are stable – – – – Lower bounds on EB & HB poor estimation of free energy & helicity Small-scale shear largest field lines most affected by a a limits cannot treat highly stressed fields a = cst no mixed sheared & potential fields & no return currents G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Setting force-free parameter a = cst Ha (DPSM / Pic du Midi) Yohkoh/SXT Yohkoh/SXT lfff extrapolation a chosen to best match - large SXR loops - transverse Bphot if available small connectivities weakly depend on a G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Confined flare topologies in active regions Arch Filament System Ha (DPSM / Pic du Midi) Flare ribbons : footpoints of QSLs = gradients of connectivites Yohkoh/SXT SXR loops Démoulin et al. (1997), Schmieder et al. (1997) G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Pre-CME topologies in active regions Eruption precursor : shear Alfvén wave along null spine because of reconnection Aulanier et al. (2000) G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Pre-CME topologies between hemispheres Large-scale dimmings : footpoints of TIL’s pushed from below during eruption Delannée et al. (1999) G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Pre-eruptive topologies : potential & lfff sufficient Major results : Topology (skeletons & QSL’s) of overlaying weakly stressed fields Location of associated current sheets reconnection particle impacts confined flare ribbons particle acceleration sites dimmings during CMEs Such extrapolations well addess the issue of global connectivity Some codes already « available » to the community : Potential Field Source Surface (PFSS) on SSWIDL Schrijver & DeRosa (2003) FRench Online MAGnetic Extrapolations (FROMAGE) on the WWW Démoulin et al. (1997), Aulanier et al. (1999) G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Topology of filaments with constant-a extrapolations Aulanier et al. (1999) Aulanier et al. (2000) Full field lines magnetic dips Aulanier & Schmieder (2002) Ha / EUV filament bodies (feet) : magnetic dips within (aside) a flux tube of low twist F<1.5p G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Evolving filaments with constant-a extrapolations 9-hour evolution on Sep 25, 1996 VTT/MSDP 08:43 UT SoHO/MDI 07:40 UT 15:57 UT 15:59 UT 12:14 UT 12:53 UT 17:04 UT 17:35 UT Aulanier et al. (1999) G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Evolving filaments with constant-a extrapolations 9-hour evolution on Sep 25, 1996 VTT/MSDP 08:43 UT 15:57 UT 12:14 UT 17:04 UT Aulanier et al. (1999) Moving parasitic polarities : destruction / formation of dips & evolution of barbs G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Overview of this tutorial 1. Basic physics 1.1 Introduction 1.2 Non-potentiality 1.3 Complexity 2. Learning from 3D MHD simulations 2.1 Current sheets & reconnection in quasi-separatrices 2.2 Breakout model of an observed eruption 3. Magnetic field extrapolations 3.1 Motivation 3.2 Potential & linear force-free fields 3.3 Non-linear force-free fields 4. Toward SDO & other future missions G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Performing non-linear force-free extrapolations Properties : a = varying (as observed in vector magnetograms & in MHD models) sx B = a B & ( B s)a = 0 must be computed numerically in general Great care with mathematical ill-posed methods ! i.e. redundant BC’s at boundary(ies) discontinuities in domain Simple vertical integration doomed to failure no side/upper BC’s existing k modes growing as ~exp(k.z) Common feature in most algorithms : Stress imposed at 1 photospheric footpoint or on the whole photospheric plane or on all faces via increments of abdry or Bbdry or ubdry Relax toward force-free state by imposing some transport method (e.g. physical or numerical) & conditions (e.g. Emin or |JxB|min) G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Results : sheared loops & sigmoids PHOT Bz PHOT Bz Pre-post eruption EB & HB ; non-homogeneous shear & return currents PHOT az PHOT az Yohkoh/SXT Jiao, McClymont & Mikic (1997) Yohkoh/SXT Bleybel et al. (2002) G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Results : flux ropes & filaments Régnier & Amari (2004) Filament bodies : magnetic dips within a flux tube of medium twist F ~ or > 2p courtsesy van Ballegooijen van Ballegooijen (2004) G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Some results, but difficulties at every level Numerical : PDE’s for locally strong gradients diBj Growth (& instability) of non-physical spatial oscillations Physical : for regions of strong a values Multiple solutions can exist for 1 same boundary condition MHD-unstable solutions can exist Many non force-free regions where b>1 & in (quasi-) separatrices Observational : spectro-polarimetry & magnetography o Inversion of Stokes profiles I,Q,U,V & solving 180 ambiguity B Weak Q,U noise in Bxy & weak I errors in B Limited field of view artificial flux imbalance sunspots G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Finding the best method(s) Valori (2005), Schrijver et al. (2006), Inhester & Wiegelmann (2006), Amari et al. (2006) Some input models : Low & Lou (1990) (sa)/a < (sBz)/Bz & a weak & no return currents analytical solution 3D MHD [Török&Kliem03] or 3D nlfff [Titov&Démoulin01] or Bz & a symmetries 2D arbitrary [Inhester&Wiegelmann06] no analytical solution for most models Photospheric bipolar Best methods : Optmization method better for analytical models Grad-Rubin (& magneto-frictional) better on symmetric twisted flux tubes Grad-Rubin a priori best (well posed, no redundant BC’s), but J x B m not imposed convergence not ensured losses of convergence found for strong a (with BC’s on 6 faces imposed) G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA More realistic & demanding input models from MHD simulation of the July 14, 1998 pre-eruptive B a = Jz/Bz (z=0) BBzz(z=0) (z=0) & field lines (sa)/a > (sB )/B z z a phot phot strong & varies faster than Bz narrow non force-free layers with strong a at the fan/spine footpoints a>0 & a<0 in one polarity return currents a ~ 0 on all 5 coronal faces «open» field lines are potential G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Overview of this tutorial 1. Basic physics 1.1 Introduction 1.2 Non-potentiality 1.3 Complexity 2. Learning from 3D MHD simulations 2.1 Current sheets & reconnection in quasi-separatrices 2.2 Breakout model of an observed eruption 3. Magnetic field extrapolations 3.1 Motivation 3.2 Potential & linear force-free fields 3.3 Non-linear force-free fields 4. Toward SDO & other future missions G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA Toward SDO & other future missions Forward modeling : 3D MHD Non-linear fff extrapolations Take BzPhotObs from LOS magnetogram Calculate potential field BPOT Take BPhotObs from vector magnetogram Calculate potential field BPOT Prescribe uxyphot or Ephot and tend toward Bcorona ~ EUV loops and/or BPhotMHD ~ BPhotObs Prescribe Stress on bounary(ies) and tend toward Bcorona ~ EUV loops Super-computer resources Super-computer resources (high resol. needed) Then analyze observations & pursue MHD simulation to model coronal dynamics Then analyze observations & analyze stability with MHD simulations Beyond potential and linear force-free fields analyses of observations : MHD & nlfff algorithms to be validated & tested against observations Observing full coronal field lines (multi-l : SDO/AIA) Measuring photospheric full vector B (SDO/HMI & inversion techniques) G. Aulanier – AIA HMI Team Meeting – Feb 13-17, 2006 – Monterey, CA, USA