Jörg Büchner, Max-Planck-Institut für Sonnensystemforschung Katlenburg-Lindau, Germany

Transcription

1 RECONNECTION IN THE SOLAR CORONA: NUMERICAL SIMULATION Jörg Büchner, Max-Planck-Institut für Sonnensystemforschung Katlenburg-Lindau, Germany TSSSP group Katlenburg-Lindau: E. Adamson and K.-W. Lee Collaboration: N. Elkina (Munich University ) M. Barta (Ondrejov Observatory, Czech Academy of Sciences) A.Otto (University of Fairbanks, Alaska) J. Santos (INPE, Sao Jose dos Campos)

2 MPS moves 2014 to Göttingen 2014: New MPS building in Göttingen --> (since 1973 MPAe with Ian Axford as director / since 2003 MPS below)

3 Why simulate the solar corona? The 10 6 K hot solar corona and eruptions influence the Space Weather near Earth in the interplanetary space. Basic open questions: what causes the heating of the corona? the acceleration of the solar wind? eruptions (flares and coronal mass ejections)? particle acceleration -> X-ray emission? Where, why, when? Triggering conditions? -> Magnetic reconnection is a key process after thin current sheets are formed in the corona

4 Challenges for simulations 1.) Non-ideal plasma effects & collisionless dissipation occur at very small plasma scales (e.g. ion inertial length current sheets) 2.) But solar phenomena including reconnection are often large scale processes, i.e. the energy has to be transfered from very large (observed sizes) to small (plasma-non-ideality) scales 3.) Specific coronal plasma conditions Strong Poynting fluxes starting from the photosphere, cross the chromosphere and transition region toward the corona A complicated structure of photospheric (source) B-fields A considerable inhomogeneity of the coronal plasma, structured by the solar gravity and magnetic fields Heat conduction, radiative losses, radiation transfer

5 One hour of X-ray and three - wavelengh SDO observations Top pg graph: X-ray flux at geostationary orbit (GOES-15) Main movie: SDO composite observations at 211 Å, 193 Å and 171 Å EUV wavelengths (21.1, 19.3, 17.1 nm) taken on June 7 between 6:10 UT and 7:13 UT (Blast: 6:20 6:41)

6 Processes and their scales Energy Energy transfer, accumulation & Inertial range, self- ideal evolution, similar il over how many decdes? Energy dissipation, e.g. by plasma micro-turbulence Energy Input Scale Energy densi ity Inertial ran nge Dissipation range Wave number Coronal phenomena: Mega-Meters at least 6 decades to the ion inertial length scale: Meters k D

7 Natural coronal length scales MHD induction equation: B tt v B B 0 As soon as we introduce the size of phenomena as a physical length scale -> for typical l in the collisionless corona the magnetic Reynolds numbers become R m ~ ie i.e. B-field /jcannot simply by dissipated! Since v ~ 10 km/s there are two ways to decrease Rm: 1.) Decrease l e.g. the width of thin current sheets 2.) Enlarge the resistivity - e.g. by plasma turbulence due to micro-instabilities

8 Inherent plasma length scales If e & i are considered as fluids->generalized Ohm`s law: c/ pe electron inertia <- spatial -> <- scales -> i electron - ion decoupling, Hall term c/ pi off-diag onal elements of the pressure tensor <- dissipation due to highfrequency microturbulence

9 Physical scales in the corona Current sheets Most of the plasma of the solar atmosphere is ideal (Rm~10 8 ) cm

10 Microscale dissipation physics Ensemble averaging: -> Modified Vlasov equation, after velocity averaging -> momentum exchange in the parallel direction -> correlation of e/m fluctuations and plasma density /current fluctuations -> Correlations due to wave-particle i.a. can rarely be taken from theory (e.g. quasilinear) -> kinetic simulations are needed!

11 Strong β : 1D plasma instabilities electrostatic double layers Inset: electrostatic potential around the double layer. The ion holes merge into the double layer while the electron motion becomes highly turbulent behind the layer [from Büchner & Elkina, 2006].

12 -> effective collision rates

13 Moderate β: transition to 2D /LH β = β = Linearily unstable modes γ > 0 (colors) in kpar vs. k Only for very small β the most unstable waves are B-field aligned, but in the corona often β ~ 0.1-1

14 2D Vlasov & 1D fluid simulation Vlasov solver: Unsplit finite volume conservative central scheme [Elkina and Büchner, 2007; Büchner et al, 2008] Velocity- and real space grid (Debye length resolution):. 128 x 128 x 128 x 128 x 128 Mass ratios Mi/me = 25, 100, 1800 Performance tested, e.g., on a 62.3 TFlop/s and 17 TBytes shared memory Altix 4700 (9728 Montecito dual-core CPUs) Now to be extended to 3D: PIC codes on 5 Pflops and processor computers (IBM)

15 High beta-> LH waves take over 2D time-evolution of the electric wave-field Ex(x,y): First ionacoustic field-aligned modes are excited. After t _pe ~ 300 oblique LH modes take over [Büchner et al. 2008]. But needed:3d PIC codes (see fig for older results)-> but with many yparticles since high res. Vlasov codes are too expensive [see poster K.W.Lee]

16 Micro-turbulent dissipation Effective resistivity - for RMHD parametrized by an effective collision frequency : In the (lower) chromosphere:... by the binary particle collision rate [Spitzer-Härm Braginski Theory ] In the solar transistion ti region and corona: by an effective rate due to plasma turbulence as obtained by Vlasov code simulations for coronal conditions (Te~Ti Ti et c.): [Büchner & Elkina 2006/2007] forhigher beta plasma -> 1D: IA double layers for lower beta plasma > 2D: LH turbulence Note: the threshold is a large current carrier dift drift velocity j/ne > v_te -> thinsheets! LH

17 2.) Inertial range investigations: 2D AMR-MHD MHD simulation 2.5 D high-resolution adaptice-mesh refinement MHD, tearing mode instability lets islands grow (see [Bárta, Büchner et al. ApJ, 2011, paper 1]

18 Secondary current sheets and cascading reconnection Coalescence also contributes to the direct cascade! (High-resolution MHD AMR [Bárta, Büchner, Karlicky and Kotrc, ApJ, 2011, paper 1]

19 Cascading reconnection schematics Cascading ( fractal ) reconnection due to subsequent tearing-mode and coalescence instabilities creates structures at smaller and smaller scales in a self-similar manner -> energy is transfered to smaller scales

20 Energy cascade to small scales

21 3.) Large scales: RMHD (the index 0 indicates chromosph. neutrals coupled to the plasma) + closing energy equation

22 Energy equation ) For a conservative energy equation in the ideal MHD limit

23 LINMOD3D - code Non-diffusive discretization scheme: Leapfrog, 2 nd order accuracy For 2 nd order derivatives (e.g. in the induction eq.): Dufort-Frankel method Initial time step (required by the staggered grid) Lax-Wendroff method Optimized Fortran77 OpenMP parallelization SGI-ALTIX: Numatools bind threads to processors 3D grid, non-equidistant in z (radial direction) e.g. x*y*z = 46.5 * 46.5 * 31 Mm grid points (260*260*170) Highest resolution along z => 150km

24 Initial force-balanced plasma-pressure pressure equilibrium Plasma density y[ [height] temperature and pressure in the solar gravitation -Initial height- stratified equilibrium - added B-field, extrapolated from observed LOS - Energy input: Plasma motion in the photosphere - Rescaling of current densities to the plasma scales, not resolved by MHD ( sub-grid )

25 +extrapolated B + plasma motion The solar magnetic is complex. It evolves due to the photospheric plasma motion away from the lowest energy state. This causes currents including non-force-free ones - and, finally, reconnection.

26 Localization of the dissipation by current instability Current density Current carrier velocity V ccv = j / (e n) V ccv = j / (e n), the current carrier velocity, is enhanced mainly near the transition region, where the plasma density drops (Shown is V ccv > V crit)

27 Resulting 3D reconnection Finite-B 3D reconnection due to 3D reconnection is characterized by plasma motion through a QSL strong Epar (E-fields parallel to B)

28 Heating case X-ray Bright Point Japanese Hinode s/c observation: Four X-ray images obtained by the XRT telescope between 23:00 UT and 24:00 UT on December 12, 2006

29 Energy input by various types of photospheric h plasma motion 23:02 23:07 23:12 23:17 23:22 23:07UT 23:12UT 23:17UT 23:22UT 23:27UT 23:27 23:32UT

30 Heating and bulging out of the transition region The figure shows the resulting above the Bright Point region new transition region with an asimuthal structure on top of the usually assumed radial inhomogeneity only! For details: see Poster of Eric Adamson et al.

31 The 3D structure of the corona Confirmed by simulation: scheme of the 3D solar atmosphere - photosphere - chromosphere- transition region as envisioned by [Schrijver et al., 2001]

32 To be confirmed by data Now: SDO data, but 2017, hopefully a closer look into the solar polar regions by SOLAR ORBITER

33 Summary Kinetic, medium scale non-ideal MHD and large scale RHMD simulations are all together needed to advance the understanding of the multi-scale solar reconnection 1.) For the time beeing small scale dissipative processes can be described only for small systems, s, the next step are 3D PIC-code simulations over 3 decades using macroparticles on 10 4 x10 4 x10 3 grids at 5-10 Petaflops 2.) For their inter-scale coupling to large scales: large fluid systems in which kinetically derived transport properties quantify the dissipation 3.) AMR-MHD simulations for the intermediate scales have to be extended to 3D over a range of up to 10 6 to get the limits of the self-similar behaviour right, e.g. of cascading reconnection towards the dissipation scale.