Mini-research project

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

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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)

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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
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What happens in asymmetric loop?

• Footpoint with stronger magnetic field has
  stronger convergence (because BAconst.)
• 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
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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 Nanjings code?)

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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.

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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
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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 Imadas
  observation?

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

• Magnetic loop is twisted by differential
  rotation
• Expansion and eruption of the loop
• Reconnection gt flare

Hayashi, Matsumoto Shibata 1996
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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.
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Shortage in Reales 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?

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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?

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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 gt1 to lt1.
• gt Mode conversion between fast and slow modes

Study the various magnetic and non-magnetic waves
in stratified atmosphere.
Hasan 2005
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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.

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7. Magnetic reconnection

• Flare sudden conversion of the magnetic energy
  to the thermal and kinetic energy of plasma
• Resistivity ? is tiny in the coronal plasma
• Releasing the magnetic energy of a typical solar
  flare (1030 erg) by simple diffusion takes 107
  years!
• The time scale of flares are comparable to Alfven
  time tA (dynamical time of the system). We need
  a fast energy release mechanism fast
  reconnection.

Rm magnetic Reynolds number
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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 MAVin/VA
  

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

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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?

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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?
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8. Magneto-convection
Movies from Hinode/SOT
Granules (weak B)
Umbral dots (strong B)
Magnetic fields suppress convection.
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Example of convection simulation
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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
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Possible projects

• 2. Magneto-convection with horizontal fields

Application sunspot penumbra, emerging flux
region..
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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