PROS Bambang S Helmet Streamer Full text
PROSIDING SEMINAR NASIONAL SAINS DAN PENDIDIKAN SAINS VII UKSW
HELMET STREAMER ANIMATION
THROUGH MAGNETOHYDRODYNAMICS
COMPUTER SIMULATION OUTPUT:
SPACE EARLY WARNING PRE-CURSOR
Bambang Setiahadi
Indonesian National Institute of Aeronautics and Space (LAPAN)
bambangsetiahadi@rocketmail.com; bsetiapx@gmail.com
assume a computational lower boundary is put
on upper photospheric level. Evolution of
active region is inferred by simulate magnetic
fields penetration into lower boundary as a
result of magnetic activity and energy transfer
from lower SAR. The penetration is convey in
relatively slow speed transfer to simulate slow
energy build-up in SAR.
INTRODUCTION
One of the most exciting phenomena on the
solar surface is the formation of solar coronal
helmet streamer. Many researches addressed to
know physical processes and tried to relate
directly or indirectly with the CHS formation.
Including how the CHS attains equilibrium in
highly dynamical solar corona. Other study is
addressed to the impact in deep interplanetary
space, planetary magnetosphere and planetary
atmosphere.
We hope this work may initiate interest in
developing a research of how a CHS become
unstable to initiate CME. This process probably
might initiate the so-called solar storm and
initiate solar early warning researcher to deal
with. The loop-CME is important to study since
it probably has huge plasma kinetic energy and
magnetic energy. When interact the planetary
boundary layer (PBL) it may change MHD
balance to all basic physical parameter in PBL.
Intuitive approach of the CHS formation relates
the lower solar coronal activity, especially
evolution of solar active region or SAR. The
SAR is assumed as resulted from lower solar
activity in photospheric level. In turn the
photospheric activity is reflection of solar
dynamo general energy transfer. The dynamo
generates magnetic fields and global systematic
plasma flow.
SAR EVOLUTION
All of solar surface activities are reflections of
solar energy generation in inner part solar core.
The energy is transferred to solar surface by
Computation all of the above aspects are of
course difficult and timely tasks. Therefore we
45
PROSIDING SEMINAR NASIONAL SAINS DAN PENDIDIKAN SAINS VII UKSW
observationally because very weak light.
radiative transfer modes until it reaches plasma
opacities and the energy transfers change its
modes to convective energy transfer. Solar
upper layer which predominantly overwhelm
with convective energy transfer is called solar
convective layer. The photospheric layer is the
upper most level of the convective layers.
MHD SIMULATION
The sunspot magnetic fields are very
concentrated in relatively small region such that
it induces the surrounding region. It may
penetrated into chromosphere and into high
solar corona. This situation works in the
chromosphere and corona because these
atmospheres very conductive to plasma and
magnetic fields. It is very different with
planetary cool and dense atmospheres. In cool
atmosphere we have to take into account many
non-ideal and complex processes.
The magnetic fields exposed on the
photospheric level are viewed as result of
general solar magnetohydrodynamo processes
in the over-all convective layer from 20,000 km
down below the photosphere, to upper
photospheric surface (Setiahadi, 2008a, 2008b).
Energy is flown gradually to upper layers in
years time scale. The 11.0 years cycle show us
that the energy releases escape periodically and
hence number of CHS in the solar corona
exhibit roughly the same period.
As magnetic fields on the photosphere gather to
form sunspot the magnetic fields will gradually
induced upper solar level. In solar coronal level
we may to begin observing a look-fuzzy
structure streamer. As the sunspot attains
strongest and stable magnetic fields we may
observed a more highly-structure streamer that
is the CHS. In very initial phase the structure is
impossible to access observationally since it
glow from coronal free electron through
Thompson’s electron scattering processes.
The photosphere is plasma pressure dominated
region such that the magnetic fields evolution
are controlled by plasma motion in convective
layer and photosphere. In some phases the
magnetic fields will occasionally gather in
smaller region and become strong enough to
slowdown random walk of free electrons and
hydrogen atoms.
Temperature will decrease from 6,000 K to
4,000 K. Consequently the surface brightness
will lower and we may be able to see darker
small region. This is what is called the solar
sunspot. SAR in sunspot may develop to more
complex situations as a sunspot group grow
larger and at the same time develop complex
magnetic topology.
A complete MHD simulation that computes all
regions participated to lead the formation of a
CHS is extremely difficult and need almost
unlimited time work. Therefore we includes
lower solar energy or magnetic transfers by
assuming lower physical processes as lower
physical boundary layers. The magnetic
penetration from photospheric level is
simulated to enter computational bottom
boundary in relatively slow time scale
comparable with general photospheric time
scale.
The solar coronal atmosphere is assumed in
magnetohydrostatic or MHS equilibrium and
takes temperature, plasma distribution, and
magnetic topology
(Setiahadi, 2009a) as
equally well with standard HSRA coronal
atmosphere model.
Figure 1: Sequence of solar coronal helmet
streamer formation on both side of the sun on
the coronal level observed by SOHO Very
initial image can not be accessed
46
PROSIDING SEMINAR NASIONAL SAINS DAN PENDIDIKAN SAINS VII UKSW
Magnetic penetration from SAR is simulated by
introducing magnetic boundary time-growth for
all magnetic components. The z-component is
set constant to mimic electric current moves
along neutral sunspot region on photospheric
surface parallel to z-component. The equation
is equally well with magnetic growth in general
sunspot formation. The x- and y-component
includes implicitly the sunspot magnetic flux
tube geometry.
At initial the solar corona above sunspot or
SAR is filled with weak and disperse global
solar magnetic fields and exponentially
decreases low density coronal plasma. The
magnetic fields topology lies horizontally
parallel with the computational boundary.
To anticipate big variations on magnetic fields
penetrating speed and plasma flow entering the
computational domain we computed basic
MHD physical parameters in flow-following
concept of magneto-fluid dynamics for solar
coronal environment. These lead to expression
of basic MHD time dependent partial
differential equations as below:
⎛
1 dB ⎞
BY = B0 sin( y / a )⎜⎜1 +
t ⎟⎟
⎝ B0 dt ⎠
⎛
1 dB ⎞
BX = − B0 cos( y / a )⎜⎜1 +
t⎟
B0 dt ⎟⎠
⎝
BZ = Const
t = 0,1,2,...,τ
(
)
D
ρ = 0 + α ∂ 2X + ∂ Y2 + ∂ 2Z ρ
Dt
[
)]
(
)
)]
(
)
)]
(
)
1
2
(B
2
Y
+ BZ2 + [BY ∂Y BX + BZ ∂ Z BX ] − ρ G X + ν ∂ 2X + ∂Y2 + ∂ 2Z ρVX
[
1
2
(B
2
X
+ BZ2 + [BX ∂ X BY + BZ ∂ Z BY ] − ρ GY + ν ∂ 2X + ∂Y2 + ∂ 2Z ρVY
[
1
2
(B
D
ρ VX = −∂ X P +
Dt
D
ρ VY = −∂Y P +
Dt
D
ρ VZ = −∂ Z P +
Dt
2
X
Where τ is penetration time-scale from the
photospheric level through computational
bottom boundary. Careful must be taken to
choose computational time-step not larger than
τ.
+ BY2 + [BY ∂Y BZ + BX ∂ X BZ ] − ρ GZ + ν ∂ 2X + ∂Y2 + ∂ 2Z ρVZ
(
)
D
BX = ∂Y (BY VX ) + ∂ Z (BZ VX ) + η ∂ 2X + ∂Y2 + ∂ 2Z BX
Dt
D
BY = ∂ X (BX VY ) + ∂ Z (BZ VY ) + η (∂ 2X + ∂ Y2 + ∂ 2Z )BY
Dt
D
BZ = ∂ X (BX VZ ) + ∂Y (BY VZ ) + η (∂ 2X + ∂ Y2 + ∂ 2Z )BZ
Dt
(
)
D
P = −(γ − 1) P [∂ X VX + ∂YVY + ∂ ZVZ ] + κ ∂ 2X + ∂Y2 + ∂ 2Z P
Dt
For practical reasons and computational
stability of the code, we express the basic
Figure 2: Animation from MHD computer
simulation of CHS formation. Initial condition
is on left-side. Intermediate evolution is in the
middle, and equilibrium onset on right-most.
Note the helmet geometry is reproduced very
well. The animation is also good for education
to demonstrate CHS formation to student.
physical parameters as ρ , ρV X , ρVY , ρVZ ,
B X , BY , BZ , P , The physical constants to
determine the rate of change in non-ideal
processes and inter-conversion among the
physical parameters are α, ν, η, and κ. The
thermodynamic structure is expressed by usual
standard symbol γ. Other symbols are having
their usual meaning as magnetic fields (B),
plasma density (ρ), pressure (P), velocity (V),
and gravitation (G).
47
PROSIDING SEMINAR NASIONAL SAINS DAN PENDIDIKAN SAINS VII UKSW
REFERENCES
[1]. Setiahadi, B. 2008a, Research on Sunspot
Migration due to Global Solar
Meridional
Plasma Flow, p. 132,
Prosiding Seminar
Nasional
Sistem
&
Teknologi
Informasi
(SNASTI) 2008, Sekolah Tinggi
Manajemen Informatika & Teknik
Komputer Surabaya, Surabaya, 22
Oktober 2008, ISBN: 978-979-89683-310
[2]. Setiahadi, B. 2008b, Existence of Solar
Dynamo
Waves
by
Mean-Fields
Magnetohydrodynamics,
p.
221,
Prosiding
Seminar
Nasional
Matematika, Vol 3 th 2008, Univ
Katolik Parahyangan, Bandung, 6
September 2008, ISSN: 1907-3909
[3]. Setiahadi, B. 2009a, The MHD Equilibrium
Onset of
Solar Coronal Helmet
Streamer:
Warning of
the
Coronal Mass Ejection, p.
116,
Prosiding
Seminar
Nasional
Matematika
&
Pendidikan
Matematika
Tahun
2009,
Universitas Negeri Surabaya (UNESA),
Surabaya, 8 Agustus 2009, ISBN: 978979-028-071-7
[4]. Setiahadi, B. 2009b, Coronal Magnetic
Arcade Dis-Equilibrium as the Cause of
Solar Coronal Mass Ejection, p. 118,
Prosiding
Seminar
Nasional
Matematika, Vol 4 th 2009, Univ
Katolik Parahyangan, Bandung, 5
September 2009, ISSN: 1907-3909
[5]. Setiahadi, B. 2009c, Numerical Scheme for
Non-Linear and Non-LTE MHD Solar
Physics and Astrophysics Developed at
LAPAN Watukosek 2009, p. 189,
Prosiding Seminar Nasional Sains dan
Pendidikan Sains IV, Univ Kristen
Satya Wacana, Salatiga, 13 Juni 2009,
ISBN: 978-979-1098-63-9
[6]. Setiahadi, B. 2009d, Magnetoydrodynamics
Computer Simulation of Solar-Coronal
Disturbance Time Arrival: Space Early
Figure 3: A sketch interpreted from MHD
simulation or animation. The CHS is a
consequence sunspot magnetic system in solar
active region in coronal level, since the corona
is very conductive to the process.
DISCUSSION
From animation it is shown that after magnetic
fields penetrates the computational region then
in several minutes the CHS will attain
dynamical equilibrium. This feature will
maintain its equilibrium no matter we prolong
computational cycle (Setiahadi, 2009c).
The CHS seems to move other
dynamical phase if we introduce essential
perturbation along the CHS bottom boundary
condition and we enter the next phase that is
evolution from CHS to loop-CME (Setiahadi,
2009b). The last phenomenon has severe
impact to interplanetary space and warning of
the impact is important to consider (Setiahadi,
2009d).
Suggestion to next research is careful
investigations on MHD physical processes
from CHS which has strong and predominant
loop magnetic topology at initial before
eruption as the loop-CME. This loop-type CME
has great impact on planetary magnetosphere
and subsequence atmospheric induced electric
fields. The loop structure may be observed
indirectly by solar radiograph at Nobeyama
Solar Radio Observatory.
48
PROSIDING SEMINAR NASIONAL SAINS DAN PENDIDIKAN SAINS VII UKSW
Warning Done at LAPAN Watukosek, p.
157, Prosiding Seminar Nasional
Sistem &
Teknologi
Informasi
(SNASTI) 2009, STIKOM, Surabaya, 2
Desember 2009, ISBN: 978-979-8968303
49
HELMET STREAMER ANIMATION
THROUGH MAGNETOHYDRODYNAMICS
COMPUTER SIMULATION OUTPUT:
SPACE EARLY WARNING PRE-CURSOR
Bambang Setiahadi
Indonesian National Institute of Aeronautics and Space (LAPAN)
bambangsetiahadi@rocketmail.com; bsetiapx@gmail.com
assume a computational lower boundary is put
on upper photospheric level. Evolution of
active region is inferred by simulate magnetic
fields penetration into lower boundary as a
result of magnetic activity and energy transfer
from lower SAR. The penetration is convey in
relatively slow speed transfer to simulate slow
energy build-up in SAR.
INTRODUCTION
One of the most exciting phenomena on the
solar surface is the formation of solar coronal
helmet streamer. Many researches addressed to
know physical processes and tried to relate
directly or indirectly with the CHS formation.
Including how the CHS attains equilibrium in
highly dynamical solar corona. Other study is
addressed to the impact in deep interplanetary
space, planetary magnetosphere and planetary
atmosphere.
We hope this work may initiate interest in
developing a research of how a CHS become
unstable to initiate CME. This process probably
might initiate the so-called solar storm and
initiate solar early warning researcher to deal
with. The loop-CME is important to study since
it probably has huge plasma kinetic energy and
magnetic energy. When interact the planetary
boundary layer (PBL) it may change MHD
balance to all basic physical parameter in PBL.
Intuitive approach of the CHS formation relates
the lower solar coronal activity, especially
evolution of solar active region or SAR. The
SAR is assumed as resulted from lower solar
activity in photospheric level. In turn the
photospheric activity is reflection of solar
dynamo general energy transfer. The dynamo
generates magnetic fields and global systematic
plasma flow.
SAR EVOLUTION
All of solar surface activities are reflections of
solar energy generation in inner part solar core.
The energy is transferred to solar surface by
Computation all of the above aspects are of
course difficult and timely tasks. Therefore we
45
PROSIDING SEMINAR NASIONAL SAINS DAN PENDIDIKAN SAINS VII UKSW
observationally because very weak light.
radiative transfer modes until it reaches plasma
opacities and the energy transfers change its
modes to convective energy transfer. Solar
upper layer which predominantly overwhelm
with convective energy transfer is called solar
convective layer. The photospheric layer is the
upper most level of the convective layers.
MHD SIMULATION
The sunspot magnetic fields are very
concentrated in relatively small region such that
it induces the surrounding region. It may
penetrated into chromosphere and into high
solar corona. This situation works in the
chromosphere and corona because these
atmospheres very conductive to plasma and
magnetic fields. It is very different with
planetary cool and dense atmospheres. In cool
atmosphere we have to take into account many
non-ideal and complex processes.
The magnetic fields exposed on the
photospheric level are viewed as result of
general solar magnetohydrodynamo processes
in the over-all convective layer from 20,000 km
down below the photosphere, to upper
photospheric surface (Setiahadi, 2008a, 2008b).
Energy is flown gradually to upper layers in
years time scale. The 11.0 years cycle show us
that the energy releases escape periodically and
hence number of CHS in the solar corona
exhibit roughly the same period.
As magnetic fields on the photosphere gather to
form sunspot the magnetic fields will gradually
induced upper solar level. In solar coronal level
we may to begin observing a look-fuzzy
structure streamer. As the sunspot attains
strongest and stable magnetic fields we may
observed a more highly-structure streamer that
is the CHS. In very initial phase the structure is
impossible to access observationally since it
glow from coronal free electron through
Thompson’s electron scattering processes.
The photosphere is plasma pressure dominated
region such that the magnetic fields evolution
are controlled by plasma motion in convective
layer and photosphere. In some phases the
magnetic fields will occasionally gather in
smaller region and become strong enough to
slowdown random walk of free electrons and
hydrogen atoms.
Temperature will decrease from 6,000 K to
4,000 K. Consequently the surface brightness
will lower and we may be able to see darker
small region. This is what is called the solar
sunspot. SAR in sunspot may develop to more
complex situations as a sunspot group grow
larger and at the same time develop complex
magnetic topology.
A complete MHD simulation that computes all
regions participated to lead the formation of a
CHS is extremely difficult and need almost
unlimited time work. Therefore we includes
lower solar energy or magnetic transfers by
assuming lower physical processes as lower
physical boundary layers. The magnetic
penetration from photospheric level is
simulated to enter computational bottom
boundary in relatively slow time scale
comparable with general photospheric time
scale.
The solar coronal atmosphere is assumed in
magnetohydrostatic or MHS equilibrium and
takes temperature, plasma distribution, and
magnetic topology
(Setiahadi, 2009a) as
equally well with standard HSRA coronal
atmosphere model.
Figure 1: Sequence of solar coronal helmet
streamer formation on both side of the sun on
the coronal level observed by SOHO Very
initial image can not be accessed
46
PROSIDING SEMINAR NASIONAL SAINS DAN PENDIDIKAN SAINS VII UKSW
Magnetic penetration from SAR is simulated by
introducing magnetic boundary time-growth for
all magnetic components. The z-component is
set constant to mimic electric current moves
along neutral sunspot region on photospheric
surface parallel to z-component. The equation
is equally well with magnetic growth in general
sunspot formation. The x- and y-component
includes implicitly the sunspot magnetic flux
tube geometry.
At initial the solar corona above sunspot or
SAR is filled with weak and disperse global
solar magnetic fields and exponentially
decreases low density coronal plasma. The
magnetic fields topology lies horizontally
parallel with the computational boundary.
To anticipate big variations on magnetic fields
penetrating speed and plasma flow entering the
computational domain we computed basic
MHD physical parameters in flow-following
concept of magneto-fluid dynamics for solar
coronal environment. These lead to expression
of basic MHD time dependent partial
differential equations as below:
⎛
1 dB ⎞
BY = B0 sin( y / a )⎜⎜1 +
t ⎟⎟
⎝ B0 dt ⎠
⎛
1 dB ⎞
BX = − B0 cos( y / a )⎜⎜1 +
t⎟
B0 dt ⎟⎠
⎝
BZ = Const
t = 0,1,2,...,τ
(
)
D
ρ = 0 + α ∂ 2X + ∂ Y2 + ∂ 2Z ρ
Dt
[
)]
(
)
)]
(
)
)]
(
)
1
2
(B
2
Y
+ BZ2 + [BY ∂Y BX + BZ ∂ Z BX ] − ρ G X + ν ∂ 2X + ∂Y2 + ∂ 2Z ρVX
[
1
2
(B
2
X
+ BZ2 + [BX ∂ X BY + BZ ∂ Z BY ] − ρ GY + ν ∂ 2X + ∂Y2 + ∂ 2Z ρVY
[
1
2
(B
D
ρ VX = −∂ X P +
Dt
D
ρ VY = −∂Y P +
Dt
D
ρ VZ = −∂ Z P +
Dt
2
X
Where τ is penetration time-scale from the
photospheric level through computational
bottom boundary. Careful must be taken to
choose computational time-step not larger than
τ.
+ BY2 + [BY ∂Y BZ + BX ∂ X BZ ] − ρ GZ + ν ∂ 2X + ∂Y2 + ∂ 2Z ρVZ
(
)
D
BX = ∂Y (BY VX ) + ∂ Z (BZ VX ) + η ∂ 2X + ∂Y2 + ∂ 2Z BX
Dt
D
BY = ∂ X (BX VY ) + ∂ Z (BZ VY ) + η (∂ 2X + ∂ Y2 + ∂ 2Z )BY
Dt
D
BZ = ∂ X (BX VZ ) + ∂Y (BY VZ ) + η (∂ 2X + ∂ Y2 + ∂ 2Z )BZ
Dt
(
)
D
P = −(γ − 1) P [∂ X VX + ∂YVY + ∂ ZVZ ] + κ ∂ 2X + ∂Y2 + ∂ 2Z P
Dt
For practical reasons and computational
stability of the code, we express the basic
Figure 2: Animation from MHD computer
simulation of CHS formation. Initial condition
is on left-side. Intermediate evolution is in the
middle, and equilibrium onset on right-most.
Note the helmet geometry is reproduced very
well. The animation is also good for education
to demonstrate CHS formation to student.
physical parameters as ρ , ρV X , ρVY , ρVZ ,
B X , BY , BZ , P , The physical constants to
determine the rate of change in non-ideal
processes and inter-conversion among the
physical parameters are α, ν, η, and κ. The
thermodynamic structure is expressed by usual
standard symbol γ. Other symbols are having
their usual meaning as magnetic fields (B),
plasma density (ρ), pressure (P), velocity (V),
and gravitation (G).
47
PROSIDING SEMINAR NASIONAL SAINS DAN PENDIDIKAN SAINS VII UKSW
REFERENCES
[1]. Setiahadi, B. 2008a, Research on Sunspot
Migration due to Global Solar
Meridional
Plasma Flow, p. 132,
Prosiding Seminar
Nasional
Sistem
&
Teknologi
Informasi
(SNASTI) 2008, Sekolah Tinggi
Manajemen Informatika & Teknik
Komputer Surabaya, Surabaya, 22
Oktober 2008, ISBN: 978-979-89683-310
[2]. Setiahadi, B. 2008b, Existence of Solar
Dynamo
Waves
by
Mean-Fields
Magnetohydrodynamics,
p.
221,
Prosiding
Seminar
Nasional
Matematika, Vol 3 th 2008, Univ
Katolik Parahyangan, Bandung, 6
September 2008, ISSN: 1907-3909
[3]. Setiahadi, B. 2009a, The MHD Equilibrium
Onset of
Solar Coronal Helmet
Streamer:
Warning of
the
Coronal Mass Ejection, p.
116,
Prosiding
Seminar
Nasional
Matematika
&
Pendidikan
Matematika
Tahun
2009,
Universitas Negeri Surabaya (UNESA),
Surabaya, 8 Agustus 2009, ISBN: 978979-028-071-7
[4]. Setiahadi, B. 2009b, Coronal Magnetic
Arcade Dis-Equilibrium as the Cause of
Solar Coronal Mass Ejection, p. 118,
Prosiding
Seminar
Nasional
Matematika, Vol 4 th 2009, Univ
Katolik Parahyangan, Bandung, 5
September 2009, ISSN: 1907-3909
[5]. Setiahadi, B. 2009c, Numerical Scheme for
Non-Linear and Non-LTE MHD Solar
Physics and Astrophysics Developed at
LAPAN Watukosek 2009, p. 189,
Prosiding Seminar Nasional Sains dan
Pendidikan Sains IV, Univ Kristen
Satya Wacana, Salatiga, 13 Juni 2009,
ISBN: 978-979-1098-63-9
[6]. Setiahadi, B. 2009d, Magnetoydrodynamics
Computer Simulation of Solar-Coronal
Disturbance Time Arrival: Space Early
Figure 3: A sketch interpreted from MHD
simulation or animation. The CHS is a
consequence sunspot magnetic system in solar
active region in coronal level, since the corona
is very conductive to the process.
DISCUSSION
From animation it is shown that after magnetic
fields penetrates the computational region then
in several minutes the CHS will attain
dynamical equilibrium. This feature will
maintain its equilibrium no matter we prolong
computational cycle (Setiahadi, 2009c).
The CHS seems to move other
dynamical phase if we introduce essential
perturbation along the CHS bottom boundary
condition and we enter the next phase that is
evolution from CHS to loop-CME (Setiahadi,
2009b). The last phenomenon has severe
impact to interplanetary space and warning of
the impact is important to consider (Setiahadi,
2009d).
Suggestion to next research is careful
investigations on MHD physical processes
from CHS which has strong and predominant
loop magnetic topology at initial before
eruption as the loop-CME. This loop-type CME
has great impact on planetary magnetosphere
and subsequence atmospheric induced electric
fields. The loop structure may be observed
indirectly by solar radiograph at Nobeyama
Solar Radio Observatory.
48
PROSIDING SEMINAR NASIONAL SAINS DAN PENDIDIKAN SAINS VII UKSW
Warning Done at LAPAN Watukosek, p.
157, Prosiding Seminar Nasional
Sistem &
Teknologi
Informasi
(SNASTI) 2009, STIKOM, Surabaya, 2
Desember 2009, ISBN: 978-979-8968303
49