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

coronal field extrapolation?

• Current state of art are nonlinear force-freeextrapolations of measured photospheric field vector.

• Direct measurements of chromospheric fields in combination with self-consistent MHD-models areprosperous to understand the ‘magnetic connection’between photosphere, interface region and corona.

Thomas Wiegelmann, MPI for Solar-System-Research

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NonLinear Force-Free Fields

• Compute initial a potential field (Requires only Bn on bottom boundary)

• Iterate for NLFFF-field, Boundary conditions:- Bn and Jn for positive or negative polarityon boundary (Grad-Rubin)- Magnetic field vector Bx By Bz on boundary (Magnetofrictional, Optimization)

Equivalent

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MagnetofrictionalChodura & Schlueter 1981,Valori et al. 2005

OptimizationWheatland et al. 2000,Wiegelmann 2004,2007

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Problems force-free modeling

• Corona is force-free.• Photosphere contains forces.• Magnetic connection of interface region

between photosphere, chromosphere andcorona is not well understood.

• Direct measurements of the chromsphericmagnetic field vector would help us.

Coronal magnetic fields 5Ventura, 25.08.2010

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Consistent boundary conditions for force-free fields (Molodensky 1969, Aly 1989)

Flux-balance

Maxwell StressTensor

No net force on boundary

No net torque on boundary

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Magnetic field is measured routinely in the photosphere.Other boundaries are a priori unknown.

If these relations arenot fulfilled in the bottomboundary, force-free fieldsdo not exist for these boundary conditions.

Possible Solution:Use these relationsto derive consistentboundary conditionsfor force-free coronalmagnetic field models.

Preprocessing

( Gary, 2001)

force-free

Non force-free

Non force-free

Magnetic vector fieldmeasurement in photosphere

Preprocessing result:Chromospheric Field

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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)

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No net force

No net torque

Photosphere

Smoothness

Preprocessed boundary data

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Chromospheric H-alpha preprocessing• H-alpha fibrils outline magnetic field lines.• With image-recognition techniques we get

tangent to the chromospheric magnetic fieldvector (Hx, Hy).

• Idea: include a term in the preprocessing tominimize angle of preprocessed magnetic field (Bx,By) with (Hx,Hy).

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CoronalMagnetic Field

Nonlinear Force-free code

Preprocessing tool

Vectormagnetogram

H-AlphaImage

ChromosphericMagnetic Field

Optional

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Prepro-cessing

We test preprocessing with Aad’s model

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Result of preprocessing

• For test cases the pre-processed photospheric field is more chromospheric like.

• Direct measurements of the chromosphericfield would help to check that for realobservations.

• Measured chromospheric fields at one hightcould be used directly for force-free coronal modeling.

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Force-free fields

• Preprocessed photospheric vector magnetograms can be used for coronal NLFFF-modeling.

• Somewhat unsatisfactory is that we donot understand the physics of the magneticconnection from the photosphere throughchromosphere and transition into thesolar corona.

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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 measurethe field directly.

• As approximation for the magnetic field magnetic sensitive lines can be inverted using Miln-Eddington atmosphere.

• We need also density, temperature, Dopplervelocity sensitive lines to derive an approximation for density, temperatureand plasma flow.

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Interface Region

• Use these approximations of magneticfield, density, temperature and plasma-flows for a consistent modeling of theInterface Region (say MHD-model)

• MHD-model combines extrapolationsfrom photosphere with inversion code.

• Use new atmosphere model for inversioninstead of Miln-Eddington atmosphere.

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Interface Region

• As a first step for self-consistentmodeling Wiegelmann&Neukirch 2007developed a magnetohydrostatic model.

• In principle the model can be generalizedto include compressible or uncompressible plasma flow (work in progress, plannedto be available well before the launch ofSolar-C)

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What happens to plasma in force-free equilibria?

0 0

Small but finite Lorentz-Forcesnecessary to structure coronalplasma. Self-consistent Plasmaand magnetic field model requiresin lowest order magnetohydrostatics.

In strict force-free equilibria the plasma is onlygravitational stratified, but not structured.

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Solar Magnetic fields Summary

• Currently the magnetic field vector becomesroutinely 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.

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Problems with small FOV

• Outside Hinode-FOV we measure onlythe line-of-sight magnetic field (SOHO/MDI)

• Embedding Hinode data into MDI has beentried, but cannot be considered as completelysuccessful. (No horizontal fields from MDI)

• Embedding Solar-C into SDO/HMI is more promising, because both measure the vector field.

• Any additional chromospheric information isuseful for preprocessing or deriving NLFFF-boundaryconditions directly.

• Large FOV (full active region) would be agreat advantage for consistent preprocessingand NLFFF-modeling.

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Current NLFFF-models are basedon photospheric measurements

• Compute the deviation from force-freenessof measured data by consistency integrals.

• Apply a mathematical procedure ‘preprocessing’ to remove theseforces and to derive suitable boundaryconditions 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.

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Nonlinear Force-free code

ChromosphericMagnetic Field

CoronalMagnetic Field

Preprocessing tool

Vectormagnetogram

H-AlphaImage

NLFFF-modeling

LOS-Chromos-pheric field

New from Solar-C

Chromos-pheric vectormagnetogramCompare

Height correlation

Measurements

in one height?

ÞUse directly as B.C.

Not in one height?

=>Additional term

in NLFFF-functional.

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What will Solar-C provide I

• We already implemented H-Alpha imagesin preprocessing for a better estimate ofchromospheric magnetic field.

• Additional constraints, e.g. the measured LOS-chromospheric field can be implemented inthe preprocessing.

• Chromospheric Vector-magnetic field measurements in one height/plane could beused directly as boundary condition forNLFFF-fields.

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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 preprocessedand/or extrapolated fields can help to define theheight, which not necessarily is the same everywhere in the chromospheric magnetogram.

• In regions where chromospheric vector is measuredaccurately, it can be implemented in the NLFFF-modelling by a Lagrange multiplier, see next slide.

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Updated NLFFF-Code

force div B

BT

errormatrix

boundarydata

free pa-rameter

This term has been added originallyfor an improved inclusion of error-estimations of photosphericfield measurements. In principle,it can also be used to incorporatemeasurements higher in the atmosphere, e.g. in the chromosphere.

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• Question: If chromospheric field measurements are available without any "geometrical" height information, are they still useful?

• Yes, they can be used both for improvingthe preprocessing and (additional to photospheric measurements) as additional constraints for NLFFF-modeling. Knowledge of the geometrical height would certainly be an advantage, but in an interplay/iteration of modeled andmeasured fields the measurement height can be approximated by correlation tracking.

Chromospheric measurements from different heights

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Magneto-Hydro-Statics (MHS)

Lorentz force

pressure gradient

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 atleast 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 theregion in between? Additional information onTemperature and density would be helpful.

• Interplay between measurements and modeling is necessary.