Solar simulation research focused on space weather

Tetsuya Magara(Kyung Hee University)

1March 2 @AOSWA 3rd conference, Fukuoka

The Sun is full of dynamic phenomena

Observed by YohkohVarious solar dynamic phenomena

Prominence eruption

Coronal mass ejection

Emergence ofa subsurface
magnetic
field

Solar flareCharacteristics of the environment where these dynamic phenomena occur

Transition region• sharp change of temperature• expansion of an emerging magnetic field

Corona• low density & pressure, high temperature (low  region)• expansion & eruption of an emerging magnetic field

Chromosphere• sharp change of density & pressure (  1 region)• radiation is effective• expansion of an emerging magnetic field
Subsurface region (convective zone)• high density, high pressure (high  region)• convective motion is active• emergence of a twisted magnetic field

Photosphere• high density, high pressure (high  region)• radiation becomes effective• expansion of an emerging magnetic fieldTargets of solar simulation research
Target IV: Observational data assimilation
CoronaTransition region
Chromosphere

Target III: Global phenomena

Photosphere

Subsurface region (convective zone)

Target I: Flux emergence

Target II: Coronal loops

Flux emergence
To reproduce the emergence of a subsurface magnetic field into the corona
Domain: convective zone ~ corona (highly stratified), local Cartesian
Essential ingredients: gas pressure, magnetic field, gravitational field, compressible,viscosity, thermal conduction, radiative coolingTransition region

Simulation features: fully compressive, ideal or diffusive MHD

Chromosphere
Photosphere∂ρ+ ∂ ρ uk = 0∂t ∂xkρ ∂ u + u• ∇ u∂tCorona= j × B – ∂ P δ i k – π i k + ρ g0
∂xkg0 ≡ – GM o⋅Ro⋅∂ ρ + ∂ ρ uk∂t
∂xk2
∂u k ∂ F kj= –P–+ Ψ + σ – Lr
∂x k
∂x k

Subsurface region (convective zone)∂B = ∇ × v × B − η ∇ × B
diff∂tFormation of a sigmoid (precursor of a solar flare)

Inverse-S sigmoidal structure obtained from a simulation(emerging flux tube of left-handed twist)

Inverse-S sigmoidal structure
obtained from an observation(Yohkoh)Coronal mass ejection (filament eruption)
Magara (2013)

Magara (2004)
An & Magara (2013)

Solar simulation research
focused on space weather

Observational data assimilation
To reproduce the evolution of a real active region using observational data
Domain: corona (high temperature, weakly stratified), zero- MHD
Essential ingredients: magnetic field, resistivity, (artificial) viscosity
Simulation features: zero-, no stratification, diffusive MHD
Transition region∂ρ+ ∂ ρ uk = 0∂t ∂xk

Chromosphere2ρ ∂ u + u• ∇ u = j × B + µ ∇ u∂tPhotosphereCorona

Subsurface region (convective zone)∂B = ∇ × v × B − η ∇ × B
diff∂tGlobal phenomena
To reproduce the global structure of a solar wind and interplanetary magnetic fieldDomain: corona ~ interplanetary space (including terrestrial space), 3D global region
Essential ingredients: gas pressure, magnetic field, gravitational field, compressible
Simulation features: fully compressive, ideal or diffusive MHD

Interplanetary magnetic fieldsolar windInterplanetary space
CoronaSOLAR WIND MODEL (MODIFIED FROM
NAKAMIZO ET AL., 2009) : BASIC EQUATIONS

B1 r, t ≡ B r, t – B0 r

γ= 53Key factor in a modeling of global phenomena => grid system

SOLAR WIND MODEL : GRID SYSTEM

Unstructured grid system (triangle grid) Avoid the singularity at the north and south poles and therefore relax tight
Courant –Friedrichs-Lewy (CFL) conditions around the poles, both of which would
arise in the spherical coordinate system (Tanaka, 1994)

BOUNDARY & INITIAL CONDITIONS
Calculation domain

50Rs ~ 300Rs

Inner boundary condition (50Rs)

MHD-IPS tomography data during 1 Solar rotation (Hayashi et al., 2003) :velocity (v), density (n(v)), pressure (p(v)), magnetic field (based on PFSS)

Outer boundary condition (300Rs)

Same as Nakamizo et al., 2009

Initial condition

Density, pressure : decreases with 1/r^2
Vr : 400 km/s (other components are 0)
Magnetic field : Extrapolated from PFSS

Calculation domain

Sun

300Rs

MHD-IPS inner boundary data

50Rs
Outer boundary

RESULT : Background solar wind
(CR2142, solar maximum)

Earth orbit

CME MODEL• Simple spheromak type CME model• Gibson and Fan (2008) discuss that this type of CME
may be produced by magnetic reconnection• Basic equation
(1)
(2)
(3)

(Kataoka et al., 2009)Injection of an ICMEan ICME is injected gradually through the inner boundary
Inner boundary

Outerboundary

50RsEarthCME

300Rs

This is done by introducing a time-dependent inner boundary condition

How to inject a spheromak through I.B.
50Rs Inner boundary• rc= r0+v*t  known (if v isassumed)
rrB
Sunrc
Q(rB,t)• Q(r) : A certain physical variable
as a function r
 Known(predetermined by someassumptions)• From the condition |rB| = 50Rs
and |r| = CME radius, we canobtain r(rB) at each time step
• At each time step, Q(rB(t)) isdeterminedrB : Vector from the Sun to the crossing boundary (purple colored)
rc : Vector from the Sun to the CME centerr : Vector from the CME center to the end point of rB vector (r = rB – rc)

RESULTKEY PARAMETERS
Parameters for a spheromak type ICME model• Magnetic field strength :• Orientation of a spheromak :• Twistness :• Density :• Pressure :• (radial) Velocity :• Propagation direction :• Initial position :• CME radius :• Injection speed (function of v(t)) :• Magnetic field strength : Typical amount of magnetic flux 2.55 x 10^21 Mx(Kataoka et al. 2009, Shiota et al. 2010), magnetic field observation at a photosphericfootpoint of an ICME etc.
• Orientation of a spheromak : Magnetic Field observation• Twistness : Vector magnetogram + NLFF modeling, etc.
• Density : 2 x background solar wind density, etc.
• Pressure : 4 x background solar wind pressure, etc.
• (radial) Velocity : From average transit time from the Sun to the Earth, etc.
• Propagation direction : CME cone model (LASCO C3), etc.
• Initial position : By assuming radial propagation direction, etc.
• CME radius : CME cone model, free parameter, etc.
• Injection speed (function of v(t)) : By assuming from averaged transit time fromthe Sun to the Earth, etc.

SUMMARY & DISCUSSION• We developed 3-D MHD code to reproduce the structure of asolar wind, the propagation of an ICME.
• By using IPS data to derive the background steady solar wind,
we can perform a more realistic data-driven simulation.
• We can investigate an ICME event by introducing a timedependent boundary condition into a TVD scheme with anunstructured grid system.
• However, since there are many ambiguities and uncertainties indetermining initial parameters of an ICME model, much more
efforts are needed to derive realistic ICME properties.