### What is the best way to use the chromospheric field information in

```What is the best way to use the
chromospheric field information in
coronal field extrapolation?
Thomas Wiegelmann,
MPI for Solar-System-Research
• Current state of art are nonlinear force-free
extrapolations of measured photospheric field vector.
• Direct measurements of chromospheric fields in
combination with self-consistent MHD-models are
prosperous to understand the ‘magnetic connection’
between photosphere, interface region and corona.
1
NonLinear Force-Free Fields
Equivalent
• Compute initial a potential field
(Requires only Bn on bottom boundary)
• Iterate for NLFFF-field, Boundary conditions:
- Bn and Jn for positive or negative polarity
- Magnetic field vector Bx By Bz on boundary
(Magnetofrictional, Optimization)
2
Magnetofrictional
Optimization
Chodura & Schlueter 1981,
Valori et al. 2005
Wheatland et al. 2000,
Wiegelmann 2004,2007
3
Problems force-free modeling
• Corona is force-free.
• Photosphere contains forces.
• Magnetic connection of interface region
between photosphere, chromosphere and
corona is not well understood.
• Direct measurements of the chromspheric
magnetic field vector would help us.
4
Consistent boundary conditions for force-free fields
(Molodensky 1969, Aly 1989)
Flux-balance
No net force
on boundary
Maxwell Stress
Tensor
No net torque
on boundary
Ventura, 25.08.2010
Coronal magnetic fields
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Magnetic field is measured routinely in the photosphere.
Other boundaries are a priori unknown.
( Gary, 2001)
Non force-free
force-free
Magnetic vector field
measurement in
photosphere
Preprocessing result:
Chromospheric Field
Non force-free
If these relations are
not fulfilled in the bottom
boundary, force-free fields
do not exist for these
boundary conditions.
Possible Solution:
Use these relations
to derive consistent
boundary conditions
for force-free coronal
magnetic field models.
Preprocessing
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Preprocessing of vector magnetograms
(Wiegelmann, Inhester, Sakurai, Sol. Phys. 2006)
• Use photospheric field vector as input.
• Preprocessing removes non-magnetic
forces from the boundary data.
• Boundary is not in the photosphere
(which is NOT force-free).
• The preprocessed boundary data
are chromospheric like.
Preprocessing can be improved by including
chromospheric observations.
(Wiegelmann, Thalmann, Schrijver, DeRosa, Metcalf,
Sol. Phys. 2008)
7
Preprocessed boundary data
No net force
No net torque
Photosphere
Smoothness
8
Chromospheric H-alpha preprocessing
• H-alpha fibrils outline magnetic field lines.
• With image-recognition techniques we get
tangent to the chromospheric magnetic field
vector (Hx, Hy).
• Idea: include a term in the preprocessing to
minimize angle of preprocessed
magnetic field (Bx,By) with (Hx,Hy).
9
Vector
magnetogram
H-Alpha
Image
Optional
Preprocessing tool
Chromospheric
Magnetic Field
Nonlinear Force-free code
Coronal
Magnetic Field
10
We test preprocessing with Aad’s model
Preprocessing
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Result of preprocessing
• For test cases the pre-processed photospheric
field is more chromospheric like.
• Direct measurements of the chromospheric
field would help to check that for real
observations.
• Measured chromospheric fields at one hight
could be used directly for force-free
coronal modeling.
12
Force-free fields
• Preprocessed photospheric vector
magnetograms can be used for
coronal NLFFF-modeling.
• Somewhat unsatisfactory is that we do
not understand the physics of the magnetic
connection from the photosphere through
chromosphere and transition into the
solar corona.
13
Interface Region
• Modeling and measurements in interface
region are challenging because:
-high and low beta plasma exist side
by side.
-plasma flows with super and sub
Alfven and sound speed are present.
• Consequence: We must model
selfconsistently magnetic field and plasma.
=> MHD-model
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Interface Region
• Use chromospheric lines to measure
the field directly.
• As approximation for the magnetic field
magnetic sensitive lines can be inverted
using Miln-Eddington atmosphere.
• We need also density, temperature, Doppler
velocity sensitive lines to derive an
approximation for density, temperature
and plasma flow.
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Interface Region
• Use these approximations of magnetic
field, density, temperature and plasmaflows for a consistent modeling of the
Interface Region (say MHD-model)
• MHD-model combines extrapolations
from photosphere with inversion code.
• Use new atmosphere model for inversion
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Interface Region
• As a first step for self-consistent
modeling Wiegelmann&Neukirch 2007
developed a magnetohydrostatic model.
• In principle the model can be generalized
to include compressible or uncompressible
plasma flow (work in progress, planned
to be available well before the launch of
Solar-C)
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What happens to plasma in force-free equilibria?
0
0
In strict force-free equilibria the plasma is only
gravitational stratified, but not structured.
Small but finite Lorentz-Forces
necessary to structure coronal
plasma. Self-consistent Plasma
and magnetic field model requires
in lowest order magnetohydrostatics.
18
Solar Magnetic fields Summary
• Currently the magnetic field vector becomes
routinely measured in the photosphere.
• Magnetic field models are used to extrapolate these
measurements upward into the solar atmosphere.
• Problem: High plasma Beta in photosphere,
low Beta in upper chromosphere and corona.
• In principle it would be ideal to derive boundary
conditions for NLFFF-modeling directly from
chromospheric measurements.
• Indirect chromospheric information are useful, too.
19
Problems with small FOV
• Outside Hinode-FOV we measure only
the line-of-sight magnetic field (SOHO/MDI)
• Embedding Hinode data into MDI has been
tried, but cannot be considered as completely
successful. (No horizontal fields from MDI)
• Embedding Solar-C into SDO/HMI is more promising,
because both measure the vector field.
• Any additional chromospheric information is
useful for preprocessing or deriving NLFFF-boundary
conditions directly.
• Large FOV (full active region) would be a
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and NLFFF-modeling.
Current NLFFF-models are based
on photospheric measurements
• Compute the deviation from force-freeness
of measured data by consistency integrals.
• Apply a mathematical procedure
‘preprocessing’ to remove these
forces and to derive suitable boundary
conditions for force-free modeling.
• Preprocessing can incorporate direct chromospheric
observations. Implemented so far for H-Alpha images,
showing the horizontal magnetic field direction,
but not the field strength.
21
NLFFF-modeling
Vector
magnetogram
H-Alpha
Image
New from Solar-C
LOS-Chromospheric field
Preprocessing tool
Chromospheric
Magnetic Field
Compare
Chromospheric vector
magnetogram
Nonlinear Force-free code
Coronal
Magnetic Field
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What will Solar-C provide I
• We already implemented H-Alpha images
in preprocessing for a better estimate of
chromospheric magnetic field.
• Additional constraints, e.g. the measured LOSchromospheric field can be implemented in
the preprocessing.
• Chromospheric Vector-magnetic field
measurements in one height/plane could be
used directly as boundary condition for
NLFFF-fields.
23
What will Solar-C provide II
• Things become more complicated if the
chromospheric measurements are not in one height.
• At least one can compare preprocessed and
measured field, but also iterate for improvement.
• If the chromospheric measurement height is
unknown, a correlation tracking with preprocessed
and/or extrapolated fields can help to define the
height, which not necessarily is the same everywhere
in the chromospheric magnetogram.
• In regions where chromospheric vector is measured
accurately, it can be implemented in the NLFFFmodelling by a Lagrange multiplier, see next slide. 24
Updated NLFFF-Code
force
div B
free parameter
BT
error
matrix
boundary
data
This term has been added originally
for an improved inclusion of
error-estimations of photospheric
field measurements. In principle,
it can also be used to incorporate
measurements higher in the
atmosphere, e.g. in the chromosphere.
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Chromospheric measurements from
different heights
• Question: If chromospheric field measurements
are available without any "geometrical" height
information, are they still useful?
• Yes, they can be used both for improving
the preprocessing and (additional to photospheric
measurements) as additional constraints for NLFFFmodeling. Knowledge of the geometrical height
would certainly be an advantage, but in an
interplay/iteration of modeled and
measured fields the measurement height can be
approximated by correlation tracking.
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Magneto-Hydro-Statics (MHS)
Lorentz
force
pressure
gravity
Aim: Solve MHS-equations and
self-consistently.
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Non force-free modeling
• Solar-C might also help for a better understanding
of the interface between photosphere and
chromosphere.
• This region is not force-free and requires at
least a magneto-hydro-static codes, which has
been well tested, but not applied to data until now.
• Can we use measured photospheric and
chromospheric fields as boundary to model the
region in between? Additional information on
Temperature and density would be helpful.
• Interplay between measurements and modeling is
necessary.
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