Transcript Document
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