Question: Origin of coronal eruptions?

Transcription

1 Magnetic field extrapolation methods: state-of-the-art applications Motivation: Instabilities in the coronal magnetic field cause eruptions. Thomas Wiegelmann Max-Planck-Institut für Sonnensystemforschung Ventura, Coronal magnetic fields Coronal magnetic Fields: Origin of Space weather Question: Origin of coronal eruptions? Solar magnetic field measured routinely only in photosphere Aim: Extrapolate measured photospheric magnetic field into the corona under model assumptions. Solar magnetic fields: Measurements and Impact We see field lines in coronal EUV-images We measure the magnetic field in photosphere Magnetic fields are measured routinely in the Solar photosphere (SOHO/MDI). Magnetic fields structure the coronal plasma (SOHO/EIT). 5 5 How to derive the coronal magnetic field structure? 1. Use loops visible in EUV as proxy for fieldlines => Stereoscopy to derive 3D structure Profile of an active region seen in SDO Photospheric magnetic field measurements (Feb , 2011). The hot plasma (line-of-sight-component) with SDO/HMI. seen in EUV outlines the magnetic field lines, => which Requires are always in coronal motion. magnetic field model Source: Extrapolate photospheric field vector in the corona 1

2 Force-free magnetic fields Magneto-hydro-static equations Force-Free Fields Equivalent In the coronal low beta plasma we can neglect in lowest order non-magnetic forces like pressure gradients and gravity and derive the (usually nonlinear) force-free field equations: 7 7 Relation between currents and magnetic field. Force-free functions is constant along field lines, but varies between field lines. => nonlinear force-free fields Further simplifications Potential Fields (no currents) Linear force-free fields (currents globally proportional to B-field) 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. 9 Consistent boundary conditions for force-free fields (Molodensky 1969, Aly 1989) Flux-balance, differential flux-balance Maxwell Stress Tensor No net force on boundary No net torque on boundary Magnetic field is measured routinely in the photosphere. Other boundaries are a priori unknown. force-free Magnetic vector field measurement in photosphere ( Gary, 2001) Non force-free 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

3 Vector magnetogram Preprocessing tool Chromospheric Magnetic Field Nonlinear Force-free code Coronal Magnetic Field H-Alpha Image Optional Space missions and extrapolation models SOHO-era (since 1995): Line-of-sight magnetograms from MDI => Potential and linear force-free models Hinode-era (since 2006): active region vector magnetograms => Nonlinear force-free models (but: often FOV very small) SDO-era (since 2010): full disk + AR vector magnetograms => Nonlinear force-free models Solar-C, Solar-Orbiter (2017?): photospheric vector magnetograms and chromospheric magnetograms => Advanced non-force-free modelling 13 SOHO (Solar and Heliospheric Observatory) Potential Field Model EUV-emission Launched in December 1995 Contains 12 scientific instruments. For coronal field extrapolations the most important are: MDI: Photospheric line-of-sight magnetograms EIT: Coronal plasma images. Emitting plasma outlines magnetic field lines. SUMER: Doppler images, plasma flow. Simple potential field models provide already a reasonable estimate regarding the global magnetic field structure. Mainly closed loops in active regions and open field lines in coronal holes. Potential fields and coronal holes Potential field extrapolation EIT 195 Fe XII Formation temperature 1.5 million K EIT 304 He II Formation temperature 60,000-80,000 K 3

4 Net flux Some statistic properties of coronal holes (CH) compared with the quiet Sun (QS) Source: Wiegelmann & Solanki 2004 We investigated 12 CHs identified in He I (NSO/Kitt Peak coronal hole maps prepared by Karen Harvey and Frank Recely) CH QS 7.6 G G 0.4 G G Unbalanced flux 77% +- 14% 9% +- 9% Ave loop length Mm Mm Ave loop height Mm Mm Distribution of loop length f(l) in Coronal holes and quiet Sun Loop length and temperatures Rosner, Tucker and Vaiana (RTV 1978) developed scaling-laws with help of a hydrostatic loop model (no plasma flow, zero gravity, uniform heating and constant cross section) T ~ (pl) 1/3 We use the scaling law to compute the temperature distribution f(t). The emitting volume filled by gas at that temperature corresponds to the emitted radiation. CH ~70% at low and ~10% at high temperatures compared with the quiet Sun. => Strongly reduced radiation in corona, but hardly difference in transition region.. Closed (for Bz>30G) and open (for Bz>100G) magnetic field-lines in a coronal hole and the nearby quiet Sun. The red line corresponds to the FOV of SUMER (Ne VIII). Source: Wiegelmann et al

5 What did we learn from potential field extrapolations in coronal holes? Large net magnetic flux in coronal holes (CH ~80 %, QS ~ 10%) Long hot loops are almost absent in coronal holes Number of small cool loops is only slightly reduced Strongly reduced emission in CH for hot coronal lines (~10% of the emission in QS) Only slightly reduced emission in cooler transition region radiation (~70% of QS) Plasma almost at rest in closed loops Significant outflow (up to 20 km/s) on open fieldlines Potential fields in the quiet Sun Magnetic recycling by Close et al. 2004/05 based on SOHO/MDI-data (pixel size 1400 km) Quiet Sun magnetogram contains mixed polarity magnetic elements, grey area unmagnetized (in MDI) Extrapolated loops connect these elements, magnetic carpet. Coronal recyling time about 1.4h Source: Wiegelmann et al. 2010/13 Sunrise is a balloone born Solar telescope (largest one ever left the ground) which observed the Sun for almost a week in June 2009 and IMax magnetograph provides high resolution measurements of quiet Suns photospheric field. Pixel size 40 km (MDI 1400 km) Quiet Sun s photosphere contains magnetic elements and magneticed inter network structures Most extrapolated loops are assymmetric and connect strong network elements with weak internetwork fields Atmospheric recycling time: 3 min Time series show evidence for magnetic reconnection. Estimated upper limit of energy conversion by reconnection still somewhat too low to be sole source for chromospheric and coronal heating. Region 2 Region 2 Flux and loop heights hardly vary Mainly network-internetwork loops 5

6 Region 3 Region 3 Flux and loop heights vary significantly Connectivity varies, loops connection strong elements dominate first 3 min and 13-17min Linear force-free fields in Active Regions We use a linear force-free model with MDI-data and have the freedom to choose an appropriate value for the force-free parameter α. EIT-image and projections of magnetic field lines for a potential field (α=0). (bad agreement) Linear force-free field with α=+0.01 [Mm -1 ] (bad agreement) Linear force-free field with α=-0.01 [Mm -1 ] (good agreement) 3D-magnetic field lines, linear force-free α=-0.01 [Mm -1 ] We can use the 3D magnetic field model afterwards for the analysis of other data, e.g. the plasma flow with SUMER. Comparison of observed magnetic loops and extrapolations from photospheric measurements down up Nonlinear force-free Models are superior. Measured loops in a newly developed AR (Solanki et al. Nature 2003) Potential field reconstruction SUMER Dopplergram in NeVIII ( 77 nm) and a 2-D-projection of some field lines. Mass flux density inferred from Doppler- Source: Marsch et al., 2004 shift and intensity from SUMER observations. Linear force-free reconstruction Non-linear force-free reconstruction 6

7 Ground based vector magnetographs Application of optimization method to 2 Active Regions (Thalmann et al. A&A, 2008) Synoptic Optical Long-term Investigations of the Sun (SOLIS) Kit Peak, USA, since 2003, AR and Full disk vector magnetograms, line-of-sight chromospheric magnetograms. Solar Flare Telescope, Mitaka/Japan, since 1992, AR magnetograms BBSO Digital Vector magnetograph, California, about Flaring Active Region Magnetic energy builds up and is releases during flare M6.1 Flare Quiet Active Region Solar X-ray flux. Vertical blue lines: vector magnetograms available Comparison of two Active Regions M6.1 Flare Magnetic field extrapolations from Solar Flare telescope Extrapolated from SOLIS vector magnetograph 39 Temporal evolution of free energy in 4 ARs associated with X-class Flares (Jing et al. 2009) Snapshots of the 4 Flares observed in H-Alpha 7

8 Temporal Evolution of: -Free Energy (diamonds) -Photospheric Flux (orange) -Nonthermal Flare emission (gray) Free magnetic energy starts to decrease about 15 min before the Flares (green line) NLFFF in flaring active regions We monitored the free magnetic energy in flaring active regions. Magnetic energy builts up before and becomes released during the flare. Energy release starts about 15min prior to the nonthermal flare emission. Magnetic field topology changes during flare to more potential (current free) fields. Energy changes mainly below ~20Mm height. Formation heights, Guo et al, ApJ 2009 Space-born Japanese mission launched 2006 Hinode/SOT (Solar Optical Telescope) provides high resolution (5 times better than SOHO/MDI) vector magnetograms (but relative small FOV) EIS (Extreme-Ultraviolet Imaging Spectrometer) XRT (X-ray Telescope) velocity map, single Gaussian fit double Gaussian fit Correlation of NLFFF model with EIS allows to identify the formation height of lines => Transition region lies higher in strong magnetic areas Changing of magnetic field by Tether cutting reconnection,liu et al. ApJ 2012 single Gaussian fit double Gaussian fit Preflare NLFFF with colour code current density 8

9 Isosurface of electric current density before flare after flare Horizontal field increased after flare Stereoscopy, STEREO mission The 2 STEREO-spacecraft observe the Sun simultaneously. For oberserving (plasma on) magnetic field lines, we use mainly EUV-images from STEREO/SECCHI. SOHO/EIT and SDO/AIA can be used as third eye. Stereoscopy: From EUV-images to 3D structures EUV-images from 2 (or 3) viewpoints 1. Extract curve-like objects How? 2. Associate objects in both images 3D geometry/physics of e.g. coronal loops and polar plumes 3. Geometric Stereoscopy In the original STEREO-proposal a space-born vector magnetograph was planned, but not selected. 4. Estimate reconstruction error in 3D 5. Derive physical quantities

10 Contourplots of filtered images with traced loops Aschwanden et al Aschwanden et al Inhester Stereoscopy vs. force-free field extrapolation Hinode FOV Quantitative comparison was unsatisfactory, why? From Limited DeRosa FOV et al. of 2009: Hinode-vector Blue lines are magnetograms stereoscopic reconstructed loops Error (Aschwanden in stereoscopy-loops et al 2008), Red due lines to small nonlinear separation force-free extrapolated angle between field lines STEREO-spacecraft. from Hinode/SOT with MDI-skirt. 57 Stereoscopy vs. coronal field extrapolation Vector magnetogram data (here: Hinode/SOT) are essential for nonlinear force-free field modeling. Unfortunately Hinode-FOV covered only a small fraction (about 10%) of area spanned by loops reconstructed from STEREO-SECCHI images. Quantitative comparison was unsatisfactory, NLFFF-models not better as potential fields here. In other studies NLFFF-methods have shown to be superior to potential and linear force-free extrapolations. (Comparison with coronal images from one viewpoint, NLFFF-models from ground based data) What to do? Joint suggestions from NLFFF-workshops, DeRosa et al. ApJ, 2009 Successful use of nonlinear force-free models require: 1. large model volumes at high resolution that accommodate most of the connectivity within a region and to its surroundings; 2. accommodation of measurement uncertainties (in particular in the transverse field component) in boundary condition; 3. 'preprocessing of the lower-boundary vector field for a realistic approximation of the high-chromospheric, near force-free field; 4. Force-free models should be compared (or even improved) with coronal observations. Full disk data SDO/HMI + Spherical codes Done 2010 for Optimization and Grad Rubin 59 How to combine EUV-observations and extrapolation methods? Frequently done for linear force-free cases, trial and error (or iteration) for optimal force-free parameter alpha which fits EUV-loops. Nonlinear force-free model + Stereoscopy 3D-loops from stereoscopy Minimize angle between Stereo-loops and B-field. Can this be generalized for loop projections from SDO/AIA? 60 10

11 SDO: Solar Dynamics Observatory Launched in 2010 Observing all the Sun, (almost) all the time Most important instruments for field extrapolations are: Helioseismic and Magnetic Imager (HMI), Full Disk and Active Region vector magnetograms Atmospheric Imaging Assembly (AIA), coronal and chromospheric EUV imaging from K to 20 million K Coronal magnetic field modeling with SDO: I. Active Region modeling AR 11158, observed 14. Feb HMI-vector data for testing Introduce dimensionless numbers (consistency with force-free model) Correlation (B_Los, Bz)=92% These quantities should be small on the bottom boundary of a NLFFF-simulation Box. If this is not the case =>Preprocessing (Wiegelmann et al. 2006) NLFFF optimization code HMI-Vecmag is almost force-free. For this AR or in general? We do not know. Lagrangian multiplier and mask have to be optimized 11

12 How to choose free parameters? -Perform extrapolations without and with preprocessing -Vary Lagrangian multiplier in suitable range. -Use different mask, e.g. Lorentz-force: Div B: Angle between magnetic field and electric current Evaluate NLFFF in 3D As smaller these quantities as better NLFFF is fulfilled Dependence on Lagrangian multiplier Quantitative comparison with coronal image, AIA-171 I(s) is the intensity along the loop. The aim is to identify bright loops with small gradients along the loop. 12

13 Summary for this dataset Observed AR is force-free consistent and preprocessing not necessary. About 5h needed to compute a 300x300x160 NLFFF-box with optimal parameters. Force-free criteria in 3D excellent fulfilled, comparable with discretization error of potential field. Comparison with AIA shows reasonable agreement, but further Tests necessary. Application to SDO/HMI Experiment-II: Effects of a limited Field-of-View From an ISSI group meeting January 2013 Resolution vs. Field of view Resolution Experiment FOV Experiment Fov1: Black Loops Fov2: White Loops Limited resolution Larger FOV hardly influence influences low lying fields low lying fields. High in the corona, fields But: Result of preprocessing from low and high is slightly different, as global resolution are almost integrals are used (further identical. investigations necessary) Fields high in the corona (and thus long loops) are significantly influenced by nearby ARs. 13

14 Global extrapolations from SDO/HMI Potential Field and Force-Free model Tadesse et al Potential Field at Suns surface Force-Free Field at Suns surface Location of open field lines hardly affected. Main differences for loops closing in ARs. ARs share a fair amount of magnetic flux. Inter-AR-loops hardly carry electric currents. Extrapolations from current instruments 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 I: High plasma Beta in photosphere, low Beta in upper chromosphere and corona. Can we extrapolate from chromospheric measurements? => Future Mission: Solar-C Problem II: Shortage of magnetic field measurements at the Solar poles => Future Mission: Solar Orbiter Solar-C Successor of Japanese Hinode mission, two concepts (A and B), only one will be realized. Plan A.) An out-of-ecliptic mission Plan B.) A high resolution spectroscopic mission For advancement of magnetic field extrapolation methods we concentrate on Plan B here: Aim is to understand the magnetic coupling between: convection zone photosphere chromosphere transition region corona 83 14

15 Chromospheric observations Interface Region between forced photosphere and forcefree chromosphere/corona has a complicated structure. Can we estimate the field in the lowest force-free layer (upper chromosphere) and use as B.C. for extrapolations? 85 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. Any chromospheric information can be useful: Line-of-sight chromospheric magnetograms. H-Alpha fibrils outlining the horizontal field direction in chromosphere (but not field strength) 86 How well does preprocessing approximate the chromospheric field? 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). Source: Jing et al. (2010), ApJ 713, Test: Model Active Region (van Ballegooijen et al. 2007) Test preprocessing with model Model contains the (not force-free) photospheric magnetic field vector and an almost force-free chromosphere and corona. 89 Preprocessing 90 15

16 NLFFF-modeling Vector magnetogram Preprocessing tool Chromospheric Magnetic Field Nonlinear Force-free code Coronal Magnetic Field H-Alpha Image Compare New from Solar-C LOS-Chromospheric field Chromospheric vector magnetogram 91 Updated NLFFF-Code force div B free parameter B T 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. 92 Interface Region between forced photosphere and force-free corona 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 93 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. 94 Solar Orbiter Launch 2017? Investigation SO-Instruments Measurements Solar Wind Analyzer (SWA) Solar wind ion and electron bulk properties, ion composition (1eV- 5 kev electrons; kev/q ions) Energetic Particle Detector (EPD) Magnetometer (MAG) Composition, timing, and distribution functions of suprathermal and energetic particles (8 kev/n 200 MeV/n ions; kev electrons) DC vector magnetic fields (0 64 Hz) Sun from Earth From Solar Orbiter High resolution observations, distance to Sun only about 1/5 of Earth (Earth orbiting spacecraft) Observations from a high latitude to investigate the Sun s polar regions. Remote sensing and in-situ instruments. 95 Radio & Plasma Waves (RPW) Polarimetric and Helioseismic Imager (PHI) EUV Imager (EUI) Spectral Imaging of the Coronal Environment (SPICE) X-ray Spectrometer Telescope (STIX) Coronagraph (METIS/COR) Heliospheric Imager (SolOHI) AC electric and magnetic fields (~DC 20 MHz) Vector magnetic field and line-of-sight velocity in the photosphere Full-disk EUV and high-resolution EUV and Lyman-α imaging of the solar atmosphere EUV spectroscopy of the solar disk and corona Solar thermal and non-thermal X-ray emission (4 150 kev) Visible, UV and EUV imaging of the solar corona White-light imaging of the extended corona 16

17 2. What are the properties of the magnetic field at high solar latitudes? SO: What are the properties of the magnetic field at high solar latitudes? Solar Orbiter will measure the magnetic field vector at the poles and image the coronal and heliospheric structure in EUV. Extrapolation techniques will provide the magnetic field in the corona above the pole. Comparison of solar granulation at the poles as viewed from the highest latitude achieved by Solar Orbiter during the nominal mission (27º) where the fine scale structure can be resolved with much higher fidelity than is obtained in the ecliptic plane twice a year (7º). The latter is the perspective used by the Hinode satellite to offer the first vector magnetic field imaging of the solar pole. Simulated EUI view of the ultraviolet corona (left) and magnetic field (right) from Solar Orbiter s vantage point at 35 heliolatitude orbit, illustrating the full coverage of the polar coronal hole. (Schrijver and Title, 2001) What are the source regions of the solar wind and heliospheric magnetic field? What mechanisms heat and accelerate the solar wind? Tu et al., Science 2005 Solar Orbiter will establish the links between Modelled magnetic field of the transition region and the observed solar wind streams (in situ + spectroscopic corona in a polar coronal hole. Only the black open field signatures) and their sources back on the Sun.The Sun s lines extend far from the surface. (Marsch 2006) magnetic atmosphere will be extrapolated from photospheric field measurements in polar coronal holes. Solar Convective Orbiter cells will combine can bring high together resolution oppositely observations directed of photospheric magnetic field motion lines, and which magnetic undergo fields interchange with solar wind measurements. reconnection. Reconnection Process important causes generating heating, particle acceleration slow solar wind? and wave (Fisk generation, and Zurbuchen which 2006) will be revealed. What are the source regions of the solar wind and heliospheric magnetic field? The EUV imager and the EUV spectrometer will provide plasma diagnostics of dynamic small scale structures involved in this process. Magnetic atmosphere can be reconstructed from photospheric field measurements with PHI. Solar Orbiter will map structures measured Polar in the plots inner of heliosphere the solar wind to speed features from observed Ulysses. Left: in the solar corona minimum through for cycle a unique 22, combination Right: of remote-sensing solar maximum and for in-situ cycle 23 measurements. (McComas,2008). 17