Download スライド 1 - Nanjing University

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.
2.
3.
4.
5.
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)
6. Standing sausage mode (coronal wave) (2D MHD)
7. Magnetic reconnection (2D MHD)
8. (Magneto-)convection (2D HD/MHD)
…
1. Asymmetric flare loop
Scenario of flare loop evolution
1. Energy input at the loop top (by
reconnection)
2. Energy transport to chromosphere
–
–
energy input
Heat conduction
Non-thermal particles (electrons)
3. Chromospheric evaporation
heat conduction,
particles
evaporation
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)
Aim of this study:
•What about heat conduction?
•Can we find observational
signature of asymmetric heat
conduction?
Sakao 1994
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
Temperature-dependent upflow
found in dimming region (Imada et
al 2007)
Mass supply from chromosphere
(Jin & Chen 2009)?
Imada et al. 2007
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
Energy equation:
nkB T  
  T  n 2QT 
t
s s
conduction
radiation
nkB
T
d

T
L2
 n 2Q(T)
Longer loop length L is results in longer cooling time τd

Application to X-ray observations
Periodic X-ray flare on class I
protostar (Tsuboi et al. 1999)
kT
X-ray intensity
Estimate of L from τd yields
L ≈ 14Rsun > Rstar ≈ a few Rsun
EM
Isobe et al. 2003
Flare loop connecting the star
and its accretion disk?
Disk-star flare
• Magnetic loop is twisted
by differential rotation
• Expansion and eruption
of the loop
• Reconnection => flare
Hayashi, Matsumoto & Shibata 1996
Effect of continuous heating
In reality, weaker energy release continues during decay phase
nkB T  
  T  n 2QT  + H
t
s s
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.
Hori et al. 1997
• Observed light curve is a super position of many
successively heated loops.
• Will this change the scaling for loop length?
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
Rm: magnetic Reynolds number
• 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.
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
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.
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)
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
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?
8. Magneto-convection
Movies from Hinode/SOT
Granules (weak B)
Umbral dots (strong B)
Magnetic fields suppress convection.
Example of convection simulation…
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
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…