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Mini-research project

Participants are divided into ≈6 teams. Each team includes 2-4 members and is supervised by Yokoyama or Isobe or ChenPF Each team works on a research project together. On Friday we have presentation from each team. If it works well, we continue collaboration and write papers!

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Mini-research project

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  1. Participants are divided into ≈6 teams. • Each team includes 2-4 members and is supervised by • Yokoyama or Isobe or ChenPF • Each team works on a research project together. • On Friday we have presentation from each team. • If it works well, we continue collaboration and write papers! • If you have your own idea for research project, you can work on it yourself. We will help the simulation setup. Mini-research project

  2. Possible projects • Asymmetric flare loop (1DHD) • Three-minutes oscillation and spicule (1D HD) • Upflow in coronal dimming after CME (1D HD) • Multiple loop modeling of solar/stellar flares (1D HD) • Wave propagation in stratified atmosphere (2D HD/MHD) • Standing sausage mode (coronal wave) (2D MHD) • Magnetic reconnection (2D MHD) • (Magneto-)convection (2D HD/MHD) …

  3. 1. Asymmetric flare loop Scenario of flare loop evolution • Energy input at the loop top (by reconnection) • Energy transport to chromosphere • Heat conduction • Non-thermal particles (electrons) • Chromospheric evaporation energy input heat conduction, particles evaporation Isobe et al. 2005

  4. What happens in asymmetric loop? • Footpoint with stronger magnetic field has stronger convergence (because BA=const.) • Stronger convergence = stronger mirroring = less precipitation of particles = weaker HXR (Sakao 1994) • About 1/3 flares shows opposite sense (Goff et al. 2004) • Aim of this study: • What about heat conduction? • Can we find observational signature of asymmetric heat conduction? Sakao 1994

  5. Simulation setup • 1D hydrodynamics • Heat conduction • Radiative cooling • Flare heating • Possible future extensions: • Include non-thermal particles and calculate HXR flux • Calculate radiative transfer in chromosphere and optical emissions (using Nanjing’s code?)

  6. 2. 3-min oscillation in chromosphere • With the standard solar atmospheric model (VAL3C), even 5-minute oscillations are imposed at the bottom of the photosphere, you will get 3-min oscillation in the chromosphere. Although many people believe that the 3-min period comes from the cut-off frequency, it is still a problem with some debates.

  7. 3. Upflow in coronal dimming after CME Temperature-dependent upflow found in dimming region (Imada et al 2007) Mass supply from chromosphere (Jin & Chen 2009)? Imada et al. 2007

  8. Simulation setup • 1D HD w/ or w/o heat conduction • Evacuated open magnetic field (pressure smaller than hydrostatic). • Is there mass supply from chromosphere? • What kind of heating term can produce Imada’s observation?

  9. 4. Multiple loop modeling of stellar flares • Motivation: • stellar flares can not be spatially resolved • loop size can be estimated from cooling time Energy equation: conduction radiation Longer loop length L is results in longer cooling time τd

  10. Application to X-ray observations Periodic X-ray flare on class I protostar (Tsuboi et al. 1999) Estimate of L from τdyields L ≈ 14Rsun > Rstar ≈ a few Rsun X-ray intensity kT Isobe et al. 2003 EM Flare loop connecting the star and its accretion disk?

  11. Disk-star flare • Magnetic loop is twisted by differential rotation • Expansion and eruption of the loop • Reconnection => flare Hayashi, Matsumoto & Shibata 1996

  12. Effect of continuous heating In reality, weaker energy release continues during decay phase + H Neglecting heating term will overestimate the loop length Using 1D HD simulation, Reale et al. (1997) made a scaling law of loop length and slope in n-T diagram.

  13. Shortage in Reale’s model • R97 assumed continuous heating in the same loop. • In reconnection model, continuous heating occurs in different (=outer) loops. Hori et al. 1997 • Observed light curve is a super position of many successively heated loops. • Will this change the scaling for loop length?

  14. Strategy of the project • Run 1D simulations with different heating rate and different loop length, corresponding to the different stage in a flare (pseudo-two dimensional approach) • Calculate the temporal evolution of “average” temperature and density of a sum of many loops • Compare the slope in n-T diagram and the loop length. Any difference from R97?

  15. 5. Waves in stratified atmosphere • Stratification introduce variety of complexity in wave modes • acoustic cutoff • internal gravity wave • Near the foot point of a flux tube, • plasma beta change from >1 to <1. • => Mode conversion between fast and slow modes Study the various magnetic and non-magnetic waves in stratified atmosphere. Hasan 2005

  16. 6. Standing sausage mode • Roberts et al. (1983) proposed that the frequency of the standing sausage mode in the flux tube is determined by the radius of the tube. However, Nakariakov et al. (2003) found that the frequency should be determined by the length, rather than the radius.

  17. 7. Magnetic reconnection • Flare = sudden conversion of the magnetic energy to the thermal and kinetic energy of plasma • Resistivity η is tiny in the coronal plasma • Releasing the magnetic energy of a typical solar flare (10^30 erg) by simple diffusion takes 10^7 years! • The time scale of flares are comparable to Alfven time τA (dynamical time of the system). We need a fast energy release mechanism = fast reconnection. Rm: magnetic Reynolds number

  18. What is magnetic reconnection • Diffusion becomes fast when the gradient of magnetic field strength is large: current sheet. • When reconnection of magnetic field lines occurs , the Lorentz force accelerates the plasma (like a slingshot) and expel the plasma from the current sheet, so that current sheet becomes thinner and diffusion becomes faster. • Energy release rate ∝ reconnection rate MA=Vin/VA

  19. Theories of magnetic reconnection 1. Sweet-Parker reconnection Mass conservation: Balance of advection and diffusion in steady state: => Reconnection rate: Parker 1957, Sweet 1958 ... too slow Reconnection becomes Sweet-Parker type if the resistivity is uniform.

  20. Theories of magnetic reconnection 2. Petschek reconnection Petschek 1964 • Diffusion region is localized in a small region. • Plasma heating/acceleration by slow mode MHD shocks. • MHD simulations: if resistivity is localized, Petschek-like reconnection (i.e., with slow shocks) occurs. • Such localized resistivity may be realized by anomalous resistivity (microscopic instabilities)

  21. Research project: Reconnection basics • Either Sweet-Parker nor Petschek reconnection are the exact solution of MHD equation. • Can we reproduce the S-P scaling by simulation? • What happens when we gradually change the spatial profile of resistivity? Transition from SP to Petschek?

  22. Research project 2: High-beta reconnection Shibata et al. 2007 • Observations indicates fast reconnection occurs also in chromosphere and photosphere • Chromospheric jets • Ellerman bombs • Magnetic cancallation • etc.. If Petschek reconnection realized in high-beta plasma?

  23. 8. Magneto-convection Movies from Hinode/SOT Granules (weak B) Umbral dots (strong B) Magnetic fields suppress convection.

  24. Example of convection simulation…

  25. Possible projects: 1. Deep convection • Previous simulations consider only shallow layer near the surface. • In reality, solar convection zone is as deep as 200,000km. • Density changes 5-6 orders of magnitude across CZ. • Do we see multi-scale convection (meso-granulation, super granulation) ? • Effect of magnetic field? Stein 2006

  26. Possible projects • 2. Magneto-convection with horizontal fields Application: sunspot penumbra, emerging flux region..

  27. How to proceed • Think about the problem and determine the numerical setup in your head (1D or 2D, gravity? thermal conduction? initial condition, boundary condition etc..) • Find a similar model (md_*) from already existing models in CANS • e.g., md_flare for asymmetric flare loop • Modify model.f (initial condition), bnd.f (boundary condition) and main.f (data I/O etc) according to your problem • Check the data, think again, change the program and run it again…

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