Evolution of the 2012 July 12 CME fromthe Sun to the Earth: Data-Constrained
Three-Dimensional MHD Simulations
F. Shen1, C. Shen2, J. Zhang3, P. Hess3, Y. Wang2 and X. Feng1
1State Key Laboratory of Space Weather, NSSC, CAS, China
2School of Earth and Space Sciences, USTC, China
3School of Physics, Astronomy and Computational Sciences, George Mason

University, USA

F. Shen, C. Shen, J. Zhang et al., JGR, 20142015-03-03, AOSWA-3, Fukuoka, Japan

Outline:• Introduction to the 2012 July 12-16 CMEevent• 3D MHD Model and Simulation Method• Kinematic Evolution of the CME• Conclusions

The Time Line of the Event[Hess and Zhang, APJ, 2014]• 07/12 16:48 UT: CME first appear in SOHO/C20 hr• 07/12 18:54 UT: CME at 20 Rs

2 hr 06 min• 07/13 00:49 UT: CME at 50 Rs

8hr 01 min• 07/13 06:49 UT: CME at 80 Rs

14 hr 01 min• 07/14 17:00 UT: Shock arrival at 1 AU

48 hr 12 min• 07/15 06:00 UT: Magnetic Cloud arrival at 1 AU

61 hr 12 min• 07/15 19:00 UT: Peak time of Dst (-127 nT)

74 hr 12 min• 07/17 14:00 UT: Magnetic Cloud end at 1 AU

117 hr 12 min

Coronagraph Observations
16:54 UT

17:24 UTSTEREO-A COR2

SOHO/LASCO C2

STEREO-B COR2

The event was recently studied by several authors using
observational or theoretical method[Mӧstl et al., 2014; Cheng et al., 2014; Dudík et al., 2014; Hess and Zhang, 2014]•Drag model: shock front•Drag model: ejecta front[Hess and Zhang, 2014]

[[Mӧstl et al., 2014, APJ]

3D MHD Model and Simulation Method[Feng et al., 2003; 2005; Shen et al., 2007; 2011; 2012; 2013]

Computational domain for 3D MHD◎ Sun-centered spherical coordinate system (r, θ, φ)◎ r-axis in the ecliptic plane◎ Earth (L1 point) located at r = 215 Rs (213 Rs ),θ = 0°, and φ = 180°
◎ The computational domain: 1 Rs ≤ r ≤ 220 Rs; -89° ≤ θ ≤ 89°
and 0°≤ ϕ ≤ 360°.

 3D time-dependant MHD equations:∂U
1 ∂r 2 F
1 ∂ sin θG
1 ∂H+ 2++=S∂r∂tr sin θr sin θ ∂ϕr∂θ

whereρ ρu r ρu  θ ρvϕ U =B r B  θ  Bϕ p, ρu r
2 ρu rρuuθr ρu r vϕ
F =
0
u B − u B θ r  r θ u r Bϕ − vϕ Br 
pu

 r,

 ρuθρuu
 r θ2ρuθ ρuθ vϕ
G=uBu
B− θ rr θ 0 uθ Bϕ − vϕ Bθ 
pu

 θ,

 ρvϕ ρu r vϕuvρ θ ϕ2v
ρϕ
H =
v B − u B r ϕ ϕ r
 vϕ Bθ − uθ Bϕ 0 pv ϕ022BB 1 ∂ 211BBr∂ sin θBr Bθ∂)+( r ϕ) 
 − r 2 ∂r (r ( p + 2 µ − µ )) + r sin θ ∂θ ( µr sin θ ∂ϕ µ 0000
222
uθ + vϕρGM s2pBr++ρ+−+ frrrrµ 0r2
222BB111rBBBB∂∂∂θϕr θ()−(sin θ ( p +()− θ )) +2 r ∂rµ02µ0 µ0r sin θ ∂θr sin θ ∂ϕ µ 0222vϕ cot θ − u r vθ Bϕ cot θ − Br Bθ Inertialcot θB(p+)+ ρ+−+ fθ centrifugal
µµ2rrr00
S=forces2 1 ∂ r 2B B11∂∂ sin θBϕ Bθ
B 2 Bϕ r ϕ
 2(sin θ ( p +))()+()−−µθθµθϕµµsin2sin∂∂∂rrrr
0000θθcotcot++uvuv
BBB
Brrϕθϕϕθϕ−ρ++ fϕrrµ 00 (B u − B u ) / r
θ rr θθ()
cot()/−+−uBv
Bv
Bv
Br θ ϕ ϕ θϕ rr ϕvolumetric heating function γγ(1)(1)
−−∇•
+−pv
Q




3D MHD Model and Simulation Method[Feng et al., 2003; 2005; Shen et al., 2007; 2011; 2012; 2013]
Modified Lax-Friedrichs MHD COrona-INterplanetary
Coupling Model: COIN TVD-MHD ModelMethod descriptionI) Use different numerical method to deal with corona area and interplanetary area
II) Non-reflecting Boundary Conditions at inner boundaryIII) Parallel Implementation with Fortran MPIIV) The numerical 3D MHD scheme used was a modified total variation
diminishing /Lax-Friedrichs (TVD/LF) type scheme with consideration ofdivergence-free condition
V)

The potential field, extrapolated from the observed line-of-sight magnetic fieldof CR2125 on the photosphere, is used as the initial magnetic field.

 Distribution of background solar wind inCarrington Rotation (CR)2125Figure 1. The calculated steady-state 3D
shape of the steady current sheet
distribution, from 1 Rs to 220 Rs at 100 hours

Figure 2. The steady-state distribution ofradial-component of magnetic field (top)and velocity (bottom) at 5 Rs CME Model——Magnetized Plasma Blob Model :[Shen et al., JGR, 2011a; 2011b; 2012](1) A high-density, -velocity, -temperature, and magnetized plasma
blob is superposed on the background solar wind model;(2) The density, radial velocity and temperature profile of the initial
perturbation are defined as follows:ρ maxacme − a ( r ,θ ,ϕ )ρθϕπr=−(,,)(1cos())
 CME
acme
2

vmax
acme − a ( r , θ , ϕ )(1 − cos(π))
VCME ( r , θ , ϕ ) =acme
2

Tmax
acme − a ( r, θ , ϕ )θϕπTr=−(,,)(1cos())
 CME
acme
2


(3) The initial magnetic field is defined as:

where1 ∂ψ ( r, θ , ϕ )
(,,)
=−Br
θϕ rCMEr 2 sin θ∂θ Bθ ( r, θ , ϕ ) = 1 ∂ψ ( r, θ , ϕ ) CMEr sin θ∂r

ψ ( r,θ ,ϕ ) = ψ 0 (a ( r,θ ,ϕ ) −2πa ( r, θ , ϕ )aCMEsin())
2πaCME

is the magnetic flux function(4) This initial perturbation will be  ρ = ρ 0 + ρ CME ( r,θ ,ϕ )
v = v + V ( r , θ , ϕ )given by the following relation:

r0CME
 r
T = T0 + TCME ( r , θ , ϕ )B = B + B
rr0rCME ( r , θ , ϕ ) Bθ = Bθ 0 + BθCME ( r, θ , ϕ )Initialization for 2012July12 Event from observational data
[Hess and Zhang, APJ, 2014]◎ The propagation direction of the CME is S09W01 deduced by using
STEREO observations and Graduated Cylindrical Shell (GCS) model;◎ The centre of the initial plasma blob is at latitude θcme=-9o,
and longitude φcme=179o；◎ First STEREO/COR A Appearance date Time: July 12,1654UT, CME arrival time at L1 point: July 14, 1700UT,
Shock transit time: ~48hrs;◎ Initial speed of CME at 5 Rs is ~1494 km/s.

Kinematic Evolution of the CMEComparisons with Coronagraph Observations

Synthetic LASCO/C2/C3, STEREO/COR2A/COR2B movies, showing
white brightness from simulated density result:

C2C3

COR2A

STB

COR2BSOHOSTAComparisons with Time-Elongation Maps (J-maps)

Figure 3. Real J-maps constructed basedon the imaging data from COR2, HI1 andHI2 imagers onboard STA and STB

Figure 4. Synthetic J-maps
corresponding to the position of STA
and STB

Figure 5. Comparison between time-elongation profiles fromthe observations and the synthetic images derived fromsimulation corresponding to the position of STA (top) and STB(bottom).

3D Kinetic Evolution of the CME

Figure 6. 3-D view of the relative density ( ρ − ρ 0 ) / ρ 0 distribution

Supposing the shock locating at the position
with the maximum of the density gradientFigure 7. Evolution of the relative
density along the Sun-Earth line.

Figure 8. Time-height plot and the timespeed plot of the shockFigure 9. A comparisonof the MHD simulationof the magnetic fieldand plasma
parameters using themeasured (Windspacecraft) magnetic
field and solar windparameters at 1 AU.

Conclusions• We have investigated the evolution of the CME in a realistic
ambient solar wind for the July 12-16, 2012 event by using the3D data-constrained COIN-TVD MHD simulation;• From the comparisons with remote sensing observations and Jmaps ,we are able to reproduce successfully the observations
in STA and STB field-of-view, for both the CME morphology andthe CME kinematics;• When the CME evolves to ICME reaching 1 AU, its physicalparameters resemble the observations of the ICME recorded bythe Wind spacecraft: the transit time of the shock isapproximately reproduced; the velocity, the total magnetic
field, the temperature and the density peak value is very close
to the realistic values during the peak period.
• Our next goal is to apply this 3D MHD model to space weather
prediction based on the observational data.