Exploring Magnetosphere-Exosphere Coupling at Mercury:
A Joint MESSENGER-BepiColombo Workshop
Boulder, Colorado, USA
November 2-5, 2010
Hybrid Simulations
Exospheric and Magnetospheric
Responses to Large Solar Wind
Disturbances
Yung-Ching Wanga
S.-H. Laia, W.-H. Ipa, S. Bourouaineb, J. Müllerc, U. Motschmannc
aInstitute
of Astronomy, National Central University, Jhongli, Taiwan (R.O.C.)
bMax-Planck Institute for Solar System Research, Katlenburg-Lindau, Germany
cInstitute for Theoretical Physics, TU Braunschweig, Germany
1
Outline
Introduction
3D Hybrid Model
Mercury Simulations
ICMEs/Low Mach Number Solar Wind Interactions
Helios 1/2 data (1975-1983)
Adaptive Hybrid Simulation
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
2
PART I
3D Hybrid Model
and
Mercury Simulations
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
3
3D Hybrid Model (1)
Full Particle
Hybrid
MHD
ion
e-
Full Particle:
System ~ rg,e
Hybrid Model:
System dimension > rg,e
in the order of ~ rg,i
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
MHD:
System >> rg,i
4
3D Hybrid Model (2)
“Particle-in-Cell” (PIC) method
Gather moments
Move particles
Solve field eqs.
eq. (A)(B)
eq. (C)(D)
Interpolate forces
Basic eqs. in Hybrid Model
r
dx s r
= vs
dt
r
dv s qs r r r
=
E ′ + vs × B
dt ms
(
(A)
)
(B)
€
r r
r
r r ∇×B×B 1
∇ρ κc
E ′ = −ui × B +
− βe0
ρc
2
ρc
(C)
r r

r
r
r
r
∇ × B × B
∂ t B = ∇ × ui × B − ∇
 − η∇ × ∇ × B (D)
ρc


(
)
r
r
r
E ′ = E − η∇ × B
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
Bagdonat, 2004
5
MESSENGER flybys
Input parameters
BIMF = 21 nT a
nsw0 = nsw[H+]0 = 32 cm-3 a
Vrsw0 = ( +430, 0, 0 ) km/s a
M = ( 0, 0, -300 ) nT RM3 a
RM = 2440 km a
"surface = 10-4 S/m b
!
Normalized parameters
t0 = #i0-1 $ 0.5 s
x0 = c/%p,i0 $ 40 km
v0 = VA0 $ 81 km/s
Normalized parameters
E0 = VA0 BIMF $ 1.7 mV/m
P0 = BIMF2/(2µ0) $ 0.18 nPa
T0 = P0/nsw0k $ 397,347 K
IMF direction: !B & !B
Vsw0 BIMF
r
M
!B
z
Vsw0
Polar plane
x!
Vsw0 BIMF
r
M
r
M
!B
y
Equatorial
Equatorial plane
x!
Case (1): !B = 53˚
!B = 27˚
Case (2): !B = 118˚
!B = 37˚
y x
z
plane
!
Polar plane
x
a Milillo
et al., 2005
2000
b Glassmeier,
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
6
IOn Flow & Density (1)
Polar Plane
No exospheric ions
are injected in the
simulation.
Bow shock shape is
controlled by IMF
direction.
Wang et al., 2010
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
7
IOn Flow & Density (2)
Equatorial Plane
No stable drift belt.
Protons would tend
to flow sunward
toward the
magnetosphere.
Wang et al., 2010
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
8
Bow Shock Structure
Wang et al., 2010
Proton temperature shows foreshock ions along the open
field lines (Trávníček et al., 2007)
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
9
• ~ 1,000 km
• May be caused by
- Hot Na+ picked up and
accelerated by the fast solar
wind flow in magnetosheath
(Slavin et al., 2008)
- Ion drift belt (Benna et al.,
2010)
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
Slavin et al., 2008 10
Adaptive Hybrid
A new adaptive hybrid code A.I.K.E.F. (Adaptive Ion
Kinetic Electron Fluid). (Müller et al., 2010)
The code could adapt to the physical structures in
both space and time.
Refinement/removement criterions
L2
L1
L0
(a)
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
(b)
Müller et al., 2010
11
Bx [n
|B| [n
20
100
0
50
50
MESSENGER flybys
0
0
-20
50
-40
18:55
19:00
19:05
19:10
19:15
19:20
19:25
18:55
UTC
0
08:30
08:35
08:40
(c)UTC
08:45
19:00
19:05
08:50
08:55
09:00
C/A
08:30
MP
08:35
Simulation
MESSENGER II
BS
19:25
08:40
(d)UTC
08:45
08:50
08:55
09:00
C/A
MP
BS
100
M
50
Bz [nT]
By [nT]
19:20
(b)
100
flyby 1
19:15
UTC
(a)
Simulation
MESSENGER II
19:10
-50
M
50
0
0
-50
-50
08:30
08:35
08:40
08:45
UTC
08:50
08:55
09:00
(c)
(e)
08:30
08:35
08:40
08:45
UTC
08:50
08:55
09:00
(d)
(f)
Figure 12: Figs. (a) to (d) show the magnetic field and its components for the
MESSENGER I flyby. Fig (e) and (f) show the magnetic field and adaptive mesh of
76
the equatorial cross-section. The three marks on MESSENGER’s trajectory indi-
flyby 2
M
M
cate bow-shock, magnetopause and C/A, respectively. See text for details. Animations are available online at www.tu-braunschweig.de/theophys/people/jmueller.
(e)
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
(f)
Müller et al., 2010
12
Magnetic Strength
flyby 1
200
Simulation
MESSENGER I
C/A
flyby 2
MP
120200
Simulation
Simulation
MESSENGER
II
MESSENGER
I
100
BS
MP MP
BS
BS
100
|B| [nT]
80150
Bx [nT]
|B| [nT]
150
C/A C/A
60
40100
20
0 50
50
-20
0
18:55
19:00
19:05
19:10
UTC
19:15
19:20
-40 0
18:55
08:30
19:25
19:00
08:35
(a)
120
Simulation
MESSENGER I
C/A
19:05
08:40
19:10
08:45
UTC
UTC
19:15
08:50
19:20
08:55
19:25
09:00
(b)
(a)
MP
Simulation
Simulation
MESSENGER
I
MESSENGER
II
BS
100
C/A C/A
Müller
et
MP MP
BS
BS al., 2010
150
100
80
100
T]
]
T]
Nov. 4, 2010
60 MESSENGER-BepiColombo Workshop, Boulder
13
Magnetopause
The MP double structure observed could be
reproduced by adaptive hybrid (A.I.K.E.F.)
simulations without injecting any exospheric
ions.
Details of the plasma flow around Mercury could
by studied by the adaptive hybrid (A.I.K.E.F.)
model.
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
14
PART II
Recent Work on
Low Mach Number
Solar Wind Interactions
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
15
nitialize the calculation, we filled up the simulation box with 20 superparticles
cell. All the particles are randomly generated according to the Maxwellien veistribution with the ion plasma-beta βi0 = 0.5, which is assumed to be equal to
ctron plasma-beta. For each time step, all the particles inside the boundaries’
ept for theLower
+x boundary
replaced
with undisturbed
solar
wind
ions, and the
AlfvénareMach
number
solar wind
near
Mercury’s
orbit.
ic fields are fixed as the IMF for −x boundary. For the other boundaries, The
(Russell et al., 1988)
ic fields are extrapolated from the inner grid nodes with zeroth order approxiFortunately,
the simulation
box is large
enoughlarger
that the
conditions
Na exosphere
reactions
through
ionboundary
sputtering
rate.
not affect the wake structure. Hence, the influence from the moon itself to the
(Killen
et the
al., wake
2001)could be examined.
magnetic fields
inside
Low Mach Solar Wind
ICME events (Liu et al., 2005) → Helios ~ 4 months near Mercury’s orbit
Year
1975
1976
1977
1978
1979
1980
1981
1982
Total
0.3-0.98 AU
1
0
9
21
22
10
10
1
74
0.3-0.5 AU
0
0
2
5
0
0
2
0
9
a Liu et al., 2005
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
Solar Minimum
Increasing phase
<2011>
Solar Maximum
16
<2011>
Solar Min
Solar Min
<2011>
Solar Max
Solar Max
Solar Min
<2011>
Solar Max
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
Solar Min <2011>
Solar Max
17
ICME on 19 June, 1981
0.34 AU
30.24 cm-3
698.4 km/s
107.6 nT
1.6
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
18
a Liu
et al., 2005
Initialization
Table 1: ICME events observed by Helios 1/2
a
MESSENGER flyby cases
ICME cases
BIM F [nT]
21
107.6
nsw0 [cm−3 ]
32
30.24
Vsw0 [km/s]
430
698.4
t0 ( = Ω−1
0.496
0.097
i0 ) [s]
v0 ( = VA0 ) [km/s]
81
427
x0 ( = c/ωp,i0 ) [km]
40.2
41.4
Solar wind ram pressure [nPa]
9.88
24.63
Stand-off distancea [RM ]
∼ 1.6
∼ 1.4
Solar wind flux [cm−2 s−1 ]
1.38 × 109
2.11 × 109
MA0 ( = Vsw0 /VA0 )
5.3
1.6
MF 0 ( = Vsw0 /VF 0 )
3.76
1.16
!
a Siscoe and Christopher, 1975
!
γ(βi0 + βe0 )
≈)
VA0
(6)
γ(βi0 V
+S0βe0
2
VS0 ≈
VA0
(6)
2
Table 2: Initialization
"
√
2 +V2 =
VF 0 ≈ √VS0
2VA0 , if γ = 2, βi0 = βe0 = 0.5
(7)
A0
2 +V2 =
2VA0 , if γ = 2, βi0 = βe0 = 0.5
(7)
S0
A0
(βi0 might be much smaller in reality)
lts
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
3
19
Adaptive Meshes
Magnetic Field Lines
L0: Δx ~ 1/4 RM
(r < 5 RM)
L1: Δx ~ 1/8 RM
M
(r < 3.5 RM)
L2: Δx ~ 1/16 RM
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
20
Northward IMF: BIMF = (0,0,+107) nT
|B|
n H+
Magnetic Field Lines
Alfvén wing perturbation (Sarantos and Slavin, 2009)
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
21
Alfvén
Wing
Perturbations
D SLAVIN: ALFVÉN WINGS AT MERCURY
L04107
ric Pedersen
estimated a
= 0.1– 0.3 S
minant ion
ER indicate
vier than 23
s) is approx2008]. The
upper limits
ICME
hly conducctance vary
4
S m#1 are
]. The field
ce layers up
urring at the
nuities), the
9 km; for a
Sarantos and Slavin, 2009
Figure
4.
Schematic
of
the
proposed
interaction
of a CME
ver
2 hrs,
the
Nov.
4, 2010
MESSENGER-BepiColombo Workshop, Boulder
22
Northward IMF: BIMF = (0,0,+107) nT
|B|
n H+
Magnetic Field Lines
Bow shock ? ➙Fast-mode wave
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
23
Fast-mode Wave
(a) at (Y, Z) = (0, 5) RM
Normalized Units
2
|B| / |BIMF|
nH+ / nsw0
1.5
1
0.5
0
(b) at (Y, Z) = (0, 0) RM
Normalized Units
2
|B| / |BIMF|
nH+ / nsw0
|B| (1 flyby case)
|B| (2 flyby case)
1.5
1
0.5
0
-12
-10
-8
-6
-4
-2
0
2
X [radius of Mercury]
4
6
8
10
12
Fast-mode wave ➙Amplitude ~ 20% of the solar wind value
Wavelength ~ 14 RM (-6 ~ 8 RM)
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
24
Southward IMF: BIMF = (0,0,-107) nT
|B|
n H+
Magnetic Field Lines
Fast-mode wave and Alfvén wing perturbation
Reconnection sites locate near the equatorial surface of Mercury.
➡ Direct impact of solar wind ions is possible
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
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PART II.2
Low Mach Number
Solar Wind Interactions
Exospheric Responses
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
26
3
Ion Precipitation Rate
Results
Total precipitation rate [× 1025 s−1 ]
Day-side precipitation rate [× 1025 s−1 ]
Day-side precipitation percentage
Total precipitation rate [× 1025 s−1 ]
Day-side precipitation rate [× 1025 s−1 ]
Day-side precipitation percentage
2 [× 1026 s−1 ]
Fsw0 × πRM
Solar wind precipitation rate
Gird size near surface [c/ωp,i0 ]
MESSENGER 1 flyby
1.58
0.94
59.3%
MESSENGER 2 flyby
1.51
1.38
91.8%
MESSENGER flyby cases
2.57
(6 ± 0.15)%
1.5
ICME (northward IMF)
6.91
5.69
82.3%
ICME (southward IMF)
18.86
16.08
85.3%
ICME cases
3.95
(17.49 ∼ 47.75)%
3.89
Table 3: Surface precipitation rate
➡ICME seems to induce more ion precipitation on the
surface.
4
Summary
➡However, the errors arose from the grid size differences
• Acknowledgments
should be notified.
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
27
Ion Precipitation Map
MESSENGER flyby cases
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
ICME cases
28
Na ExospherE Model
Monte-Carlo method is used to trace 10,000 Na
atoms with the influence of solar radiation
pressure.
Thermal accommodation rate (β) and
photoionization rate (Rloss ~ 1.08 × 10-4 s-1 at
0.386 AU) are taken into consideration.
Ion precipitation distributions are treated as the
ion sputtering source distributions.
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
29
Ion Sputtering
Steady-State Na exosphere
θTAA = 290 deg
Q = QIS
β = 0.1
(a) MESSENGER 1 flyby
Assume QIS = 3.2 × 1024 s-1
Q = QIS
(b) MESSENGER 2 flyby
Q = 4.5 × QIS
Q = 12.5 × QIS
(c) ICME (Northward IMF)
(d) ICME (Southward IMF)
100
1.5
80
0.5
Z [RM]
Disk
1
60
0
40
-0.5
-1
20
-1.5
-2
D2 Brightness [kR]
2
0
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Y [RM]
Y [RM]
Y [RM]
Y [RM]
200
2
150
Z [RM]
Tail
1
0
100
-1
50
-2
-3
D1+D2 Brightness [kR]
3
0
1
2
3
4
5
X [RM]
6
7 1
2
3
4
5
X [RM]
6
7 1
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
2
3
4
5
X [RM]
6
7 1
2
3
4
5
X [RM]
6
7
30
Photon Stimulated Desorption (PSD)
Mura et al., 2009
2H + Na2SiO3 →2Na + SiO2 + H2O (Potter, 1995)
H reacts with the Na bearing rock and liberate Na
atoms from their chemical bounds in crystal.
Atomic Na can be easily released into the exosphere by
thermal desorption or photon stimulated desorption
(PSD).
➡ Day-side precipitation for PSD
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
31
PSD From Proton Liberation
Steady-State Na exosphere
θTAA = 290 deg
Q = 0.6 × QPSD
β = 0.1
(a) MESSENGER 1 flyby
Assume QPSD = 3 × 1024 s-1
Q = 0.92 × QPSD
Q = 4.5 × 0.82 × QPSD
Q = 12.5 × 0.85 × QPSD
(c) ICME (Northward IMF)
(d) ICME (Southward IMF)
(b) MESSENGER 2 flyby
100
1.5
80
0.5
Z [RM]
Disk
1
60
0
40
-0.5
-1
20
-1.5
-2
D2 Brightness [kR]
2
0
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Y [RM]
Y [RM]
Y [RM]
Y [RM]
200
2
150
Z [RM]
Tail
1
0
100
-1
50
-2
-3
D1+D2 Brightness [kR]
3
0
1
2
3
4
5
X [RM]
6
7 1
2
3
4
5
X [RM]
6
7 1
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
2
3
4
5
X [RM]
6
7 1
2
3
4
5
X [RM]
6
7
32
Summary
In the phase of increasing solar activities, more low Mach
solar wind interactions are expected. (MESSENGER in
orbit)
Fast-mode wave and Alfvén wing perturbations could be
observed with MA ~ 1.6
Direct impact of solar wind ions at subsolar region is
possible with ICME interactions while IMF is southward.
Ion precipitation rates should be verified with finer grid
simulations in the future.
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
33
Future Work
Distributions of pick up Na+ and other exospheric
ions could be studied with 3D hybrid model or
the resultant electromagnetic fields from hybrid
simulation.
Time-dependent model is needed to investigate
the dynamical magnetosphere-exosphere
coupling in the future.
Comments and suggestions are most welcome.
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
34
Thank you
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
35
Surface conductivity
P. Janhunen and E. Kallio: Current closure on Mercury
1835
Janhunen and Kallio, 2004
Perturbation magnetic
field B1 in the equatorial
plane.
B1 field penetrates only
the poorly conducting
parts of the planet.
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
36
Foreshock
L05104
Trávníček et al., 2007
plasma temperature
Some suprathermal
protons are reflected
back upstream in the
quasi-perpendicular
portion of the shock
wave and move further
upstream forming a
proton foreshock.
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
TRÁVNÍÈEK ET AL.: STRUCTURE OF M
[
we
(Fi
pre
(rip
tha
MA
ref
oc
[
am
Fig
tio
of
ma
set
Ma
bo
no
low
[
co
Co
37
BIMF = (0,0,-107) nT
(a) at (Y, Z) = (0, 5) RM
Normalized Units
2
|B| / |BIMF|
nH+ / nsw0
1.5
1
0.5
0
(b) at (Y, Z) = (0, 0) RM
Normalized Units
2
|B| / |BIMF|
nH+ / nsw0
|B| (1 flyby case)
|B| (2 flyby case)
1.5
1
0.5
0
-12
-10
-8
-6
-4
-2
0
2
X [radius of Mercury]
4
6
8
10
12
Fast wave ➙identical with northward case
Nov. 4, 2010 MESSENGER-BepiColombo Workshop, Boulder
38