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!

• If you have your own idea for research project, you can work on it yourself. We will help the simulation setup.

Possible projects

1. Asymmetric flare loop (1DHD)2. Three-minutes oscillation and spicule (1D HD)3. Upflow in coronal dimming after CME (1D HD)4. Multiple loop modeling of solar/stellar flares (1D HD)5. Wave propagation in stratified atmosphere (2D

HD/MHD)6. Standing sausage mode (coronal wave) (2D MHD)7. Magnetic reconnection (2D MHD)8. (Magneto-)convection (2D HD/MHD)…

1. Asymmetric flare loop

1. Energy input at the loop top (by reconnection)

2. Energy transport to chromosphere– Heat conduction– Non-thermal particles (electrons)

3. Chromospheric evaporation heat conduction,particles

evaporation

energy input

Scenario of flare loop evolution

Isobe et al. 2005

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)

Sakao 1994

Aim of this study:•What about heat conduction? •Can we find observational signature of asymmetric heat conduction?

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?)

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.

3. Upflow in coronal dimming after CME

Imada et al. 2007

Temperature-dependent upflow found in dimming region (Imada et al 2007)

Mass supply from chromosphere (Jin & Chen 2009)?

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?

4. Multiple loop modeling of stellar flares• Motivation: – stellar flares can not be spatially resolved– loop size can be estimated from cooling time

€

∂nkBT

∂t=

∂

∂sκ

∂

∂sT − n2Q T( )

€

nkB

T

τ d

≈κT

L2− n2Q(T)

Energy equation:

conduction radiation

Longer loop length L is results in longer cooling time τd

Application to X-ray observationsPeriodic X-ray flare on class I protostar (Tsuboi et al. 1999)

Estimate of L from τd yields L ≈ 14Rsun > Rstar ≈ a few Rsun

X-ra

y in

tens

itykT

EM

Flare loop connecting the star and its accretion disk?

Isobe et al. 2003

Disk-star flare

Hayashi, Matsumoto & Shibata 1996

• Magnetic loop is twisted by differential rotation

• Expansion and eruption of the loop

• Reconnection => flare

Effect of continuous heating

€

∂nkBT

∂t=

∂

∂sκ

∂

∂sT − n2Q T( ) + H

In reality, weaker energy release continues during decay phase

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.

Shortage in Reale’s model• R97 assumed continuous heating in the same loop.• In reconnection model, continuous heating occurs in different

(=outer) loops.

• Observed light curve is a super position of many successively heated loops. • Will this change the scaling for loop length?

Hori et al. 1997

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?

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

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.

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

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 M∝ A=Vin/VA

Theories of magnetic reconnection 1.

Reconnection becomes Sweet-Parker type if the resistivity is uniform.

Sweet-Parker reconnection

... too slow

Mass conservation:

Balance of advection and diffusion in steady state:

=> Reconnection rate:Parker 1957, Sweet 1958

Petschek reconnection

•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)

Theories of magnetic reconnection 2.

Petschek 1964

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?

Research project 2: High-beta reconnection

Observations indicates fast reconnection occurs also in chromosphere and photosphere• Chromospheric jets• Ellerman bombs• Magnetic cancallation• etc..

Shibata et al. 2007

If Petschek reconnection realized in high-beta plasma?

8. Magneto-convectionMovies from Hinode/SOT

Granules (weak B) Umbral dots (strong B)

Magnetic fields suppress convection.

Example of convection simulation…

Possible projects:1. Deep convection

Stein 2006

•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?

Possible projects

• 2. Magneto-convection with horizontal fields

Application: sunspot penumbra, emerging flux region..

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…