1 What is the best way to use the chromospheric field information in coronal field extrapolation? 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. Thomas Wiegelmann, MPI for Solar-System-Research

2 NonLinear Force-Free Fields Compute initial a potential field (Requires only B n on bottom boundary) Iterate for NLFFF-field, Boundary conditions: - B n and J n for positive or negative polarity on boundary (Grad-Rubin) - Magnetic field vector B x B y B z on boundary (Magnetofrictional, Optimization) Equivalent

3 Magnetofrictional Chodura & Schlueter 1981, Valori et al Optimization Wheatland et al. 2000, Wiegelmann 2004,2007

4 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.

Ventura, Coronal magnetic fields5 5 Consistent boundary conditions for force-free fields (Molodensky 1969, Aly 1989) Flux-balance Maxwell Stress Tensor No net force on boundary No net torque on boundary

6 6 Magnetic field is measured routinely in the photosphere. Other boundaries are a priori unknown. 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 ( Gary, 2001) force-free Non force-free Magnetic vector field measurement in photosphere Preprocessing result: Chromospheric Field

7 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)

8 No net forceNo net torquePhotosphereSmoothnessPreprocessed boundary data

9 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).

10 Coronal Magnetic Field Nonlinear Force-free code Preprocessing tool Vector magnetogram H-Alpha Image Chromospheric Magnetic Field Optional

11 Prepro- cessing We test preprocessing with Aad’s model

12 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.

13 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.

14 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

15 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.

16 Interface Region Use these approximations of magnetic field, density, temperature and plasma- flows 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 instead of Miln-Eddington atmosphere.

17 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)

18 What happens to plasma in force-free equilibria? 00 Small but finite Lorentz-Forces necessary to structure coronal plasma. Self-consistent Plasma and magnetic field model requires in lowest order magnetohydrostatics. In strict force-free equilibria the plasma is only gravitational stratified, but not structured.

19 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.

20 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 great advantage for consistent preprocessing and NLFFF-modeling.

21 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.

22 Nonlinear Force-free code Chromospheric Magnetic Field Coronal Magnetic Field Preprocessing tool Vector magnetogram H-Alpha Image NLFFF-modeling LOS-Chromos- pheric field New from Solar-C Chromos- pheric vector magnetogram Compare Height correlation Measurements in one height?  Use directly as B.C. Not in one height? =>Additional term in NLFFF-functional.

23 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 LOS- chromospheric 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.

24 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 NLFFF- modelling by a Lagrange multiplier, see next slide.

25 Updated NLFFF-Code forcediv B B T error matrix boundary data free pa- rameter 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.

26 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 NLFFF- modeling. 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. Chromospheric measurements from different heights

27 Magneto-Hydro-Statics (MHS) Lorentz force pressure gradient gravity Aim: Solve MHS-equations and self-consistently.

28 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.