advances and frontiers in solar- terrestrial ... · intensive and extensive usages of computer...

Prosiding Semiloka Teknologi Simulasi dan Komputasi serta Aplikasi 2005

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ADVANCES AND FRONTIERS IN SOLAR-TERRESTRIAL MAGNETOHYDRODYNAMICS

COMPUTER SIMULATIONS AND SPACE EARLY WARNINGS AT LAPAN WATUKOSEK 2005

Bambang Setiahadi

Solar Activity Researcher and Space Early Warning Expert at LAPAN-Watukosek, East Java.

Indonesian National Institute of Aeronautics and Space (LAPAN) Watukosek, Gempol P.O. Box 04, Pasuruan 67155, East Java, INDONESIA

e-mail: [email protected]

Abstract Solar activity and solar originated disturbance are investigated because of the effects into solar-terrestrial space and its deep influences to planetary physical systems as well. It is well known that the main agent of the initial activity and disturbance emerged from the slow but energetic magnetohydrodynamo process in the solar convective layers. The energetic generations and energy liberations are then manifested as the dynamics and the disturbances in solar-terrestrial system. To study and analyze the dynamics, it is necessary to implement the nonlinear magnetohydrodynamic physics. The use of MHD physics is unavoidable since in solar-terrestrial space and environment, the plasma and magnetic fields of the disturbances are “frozen-in” and behave nonlinearly even in their simplest mode of interactions. The physics of interactions may well evolve to be heavily anisotropy and inhomogeneous in both space and time during propagation of the disturbances into interplanetary space. Computer simulation is considered as the most comprehensive and objective way to study the highly nonlinear phenomena. Direct and strategic application of this work is to alert the incoming disturbances to planetary physical systems. Intensive and extensive usages of computer simulations become a necessity. In order to be operational, a space alert computer code has to be tested and inspected whether the code is capable to reproduce various well-known phenomena and disturbances in interplanetary space. Some of them are the loop flares, coronal helmet streamer formations, coronal mass ejections, and the planet-proximity phenomena, the magnetospheric bow shocks and the plasmoid formation and ejection on geomagnetic tail. Key words: Solar disturbance, MHD simulations, space early warnings.

1. Introduction

It is not easy to study and to understand the solar-terrestrial physics from only the data collecting from ground-based, aerospace-based, and space-based observations. This is because the data are very limited and disperse in space or in time. Even more that the solar-terrestrial phenomena have a particular feature characterized by high non-isotropy and non-linearity, strong non-homogeneity, and great temporal variations and deviations from the steady state conditions. The difficulty to describe the disturbance is also come from the celestial body is called the Sun, where the origin of the

main disturbances in interplanetary space is initialized. The Sun lies in a very great distance that many detail studies of the physical properties of precursor on the Sun’s surface is extremely difficult to perform.

The dynamics of magnetic fields and plasmas in solar surface of an active region is considered as the main cause of the initially solar activity and disturbance. A magnetic topology on an active region is always subjected to slow but global disturbance by the so-called solar differential rotation (see e.g. Geffen, 1993; Ossendrijver, 1996). The dynamics introduced by the solar differential rotation has opened other


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branch of the plasma physics of the Sun with a basic concept of dynamo action generates by plasma motions in solar convective layers below the solar photospheric layers. This slow dynamo action manifest itself as super-slow disturbance and transfer it through the photospheric motion into magnetic fields above solar active region. The magnetic fields topology will be subjected to a slow magnetic energy build up and react by slowly adjusting its magnetic topology to higher energy content. In some conditions the magnetic topology becomes critical and as the solar differential goes on, any additional energy will eventually turn the magnetic topology to be unstable and explosive, and then liberates energy into interplanetary space. As at initially the magnetic field topology covers a large area from the chromosphere into the high corona (see e.g. Pontin et al., 2003), it is believed that a huge energy will be released into interplanetary space. In the sense of plasma temperature it will raise coronal temperature from 2.0x10 6 K to 20.0x10 6 K, and in the sense of total energy it involves no less than 1.0x10 32 erg of energy. The time scale of energy release from the Solar surface is relatively short, i.e. only in several seconds.

With the high thermal and total energy, solar activities have long been known to have some possibility of influences to human activities such as to long-range navigations and communications. Ground-based, aerospace-based, as well as space-based activities and related technological systems might be disturbed by the solar activity. Study of various effects to space bodies as planetary physical systems and artificial satellite systems seems rely on our understandings of the physics of disturbance creates by some energetic processes in solar surface and the physics of how the disturbance travels and propagates into interplanetary space. Effects of disturbance may be detected on a planet because of some local process in intermediate and low magnetosphere of the planet amplifies the disturbance by focusing and accumulating energy of the disturbance. In near Earth’s magnetic poles such as in Canada or in Arctic the magnetic topology has larger magnetic flux and then automatically accumulates and amplifies the disturbance.

As an example, the most profound effects of such disturbance were really occur and took place in Canada on March 1989. Two days after the Sun exhibited gigantic and energetic phenomenon, the city electricity was disrupted for a while. Magnetic survey was also disrupted by unusual enhancement of local magnetic fields to far away from Canada that is south of Italy. The

near or around pole countries may well be affected by the disturbance because of amplification of disturbance by magnetic fields topology on the magnetic poles. The dipole magnetic fields topology of the Earth is eventually considered as a potential agent to enhance the disturbance. Other profound effects on those days are the disturbance and decreasing on average heights of artificial satellites orbital, as well as data blank sending from satellites.

The development of the high-speed digital computer has had a great influences on the way in which the principles of physics in interplanetary space is applied to solve the problems of the nonlinear interplays between plasmas and magnetic fields escaping from the solar surface, and the subsequence nonlinear interactions to interplanetary bodies. The finite algebra and numerical mathematics suddenly were reexamined, restudied, and then developed very fast with greater enthusiasm by solar-terrestrial scientists. These because the way of thinking of a digital computer is suitably best approached by the finite algebra and numerical mathematic, and moreover it becomes highly possible to the scientists to solve the highly nonlinear and non-steady state physical behaviors in solar-terrestrial phenomena.

However, careful tests have to be done since the computer might amplify and at the same time clip some physical meaningful of the magnetohydrodynamical waves phenomena in interplanetary space and its subsequence interactions with planetary physical systems (Kamide and Baumjohann, 1993). The scientist might seem to enter the world of the arts of scientific programming. From daily and intensive observations on the solar surface by using a solar telescope and very careful treatise on algebraic structure of related mathematics, we might innovate most possible way to construct a computer code able to follow the disturbances from where it initialized from deep in solar convective layers to the surrounding interplanetary space and computes the impacts to planetary physical systems (see e.g. Troshichev et al., 2004).

If we wish to follow the disturbances from where they generated until deep into interplanetary space, the computer code have to be tested for various environments, for super-hot, super-fast, and hazardous environments, as well as for cool, super slow, and calm environments. As an example, the solar differential rotation is a very slow phenomenon but might transfer a huge energy excess into its surrounding. It is believed the energy might be released as various solar-surface phenomena such as flares and coronal


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mass ejections. Flares, especially the two-ribbon flares are considered as manifestation on converting the huge magnetic energy excess to super-hot thermal energy and super-fast particle accelerations. Some of the coronal mass ejections exhibit energy release by cool evolution of coronal helmet streamers into gigantic energy momentum (Setiahadi et al., 1998). Both of them have severe impacts to space-system and technology. 2. Magnetostatic Equilibrium Analysis

The magnetostatic equilibrium analysis is needed to provide initial configurations for computer simulation, as well as to compare the numerical output from the computation. Most direct and popular way to enter the problem is inspecting some related physical conditions before the system turn to dynamically evolve to a high nonlinear state. The equation of force balance of various decisive global forces (equation 3.2) in the solar surface is worth to consider first, because the equation hide some initial nonlinear properties and may be inspected analytically as follows

02 =∇++×⎟⎠⎞

⎜⎝⎛ ×∇+∇−

→→→→

VGBBP ρνρ (2.1)

Which is essentially the second basic MHD differential equation adopted in chapter 3, except we nullify the dynamical and transportive parts of the partial differential equation. This means that all forces exactly balance to each other so that the system will not make any change in space

and time, and consequently 0=→

V . Instead of point wise analysis as will exposed in chapter 5, all the physical parameters involved in the equations are globally treated. If the structure pointed out by equation (2.1) is considered in magnetostatic corona within sufficiently small scale-height then the equation may be written as

0=×⎟⎠⎞

⎜⎝⎛ ×∇+∇−

→→

BBP (2.2)

The omission of gravitational vector acceleration is permitted as the scale height is small enough and the gravitational force acts passively. The situation will be entirely different for near exploding or exploding stars, for example the Cepheids and the nova or supernova.

Analysis of the above equation (2.2) for various solar surface applications is abundant, e.g. paper written by Zwingman (1987). The magnetostatic analysis on the above papers are essentially rely on the Grad-Shafranov equation (Shafranov, 1958). For example, in two-

dimensional expression the equation can be written as follow,

02 =+∇dAdBBA (2.3)

It is obvious that equation (2.3) is nonlinear for the most simplest magneto potential .A. Analytical solutions are known only for particular forms of the function )(AB , namely

)(ABx =constant for potential magnetic field test model.

To go further with equilibrium analysis, let consider a more general solar surface magnetic topology often inferred from observation as follow

⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

∂∂

=zA

yABB x ,, (2.4)

The magnetic field is assumed to be line tied in the dense solar photosphere plasma. The magnetic field B is a function of y and z, and x is assumed as ignorable coordinate. We see that B decides the plasma pressure profile through A by the equation below,

)/exp()( HzAPP −=

(2.5) The over-all magnetostatic structure can now be

represented by our direct modification of the famous Grad-Shafranov equation as depicted below.

[ ] 0)/exp()(821

022 =−+

∂∂

+∇ HzAPBA

A x π (2.6)

The above equation has almost the story of solar surface observable activities, although it will never shows us the prime cause and the very origin of the solar disturbance. The main disturbance is supposed to be created below the observable surface of the Sun through the differential rotation of the general plasma motion in the Sun. Assumed that at initially the differential rotation is in initial relaxation, that is at the beginning of a new sunspot cycle (see e.g. Durrant, 1988), in this situation the second term of equation (2.6) can be quoted as zero

02 =∇ A , (2.7) The above expression is considered as initial magnetostatic equilibrium before the solar differential rotation forced it to evolve and deviate away from the equilibrium. We interpret the second term of equation (2.6) as a reflection of differential rotation to interfere and to distort or to deviate the solar surface magnetic fields away from the magnetostatic equilibrium.

As the time goes on, the magnetostatic condition will gradually deviate from its initial equilibrium and may generally be exposed as below


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0),(2 =+∇ zAFA λ (2.8) The second term λF(A,z) can be considered as a load-factor due to the solar differential motion to the pre-existing magnetostatic fields, and the field configuration is increasingly distorted as λ varies from zero to larger values. As λ evolves with time the magnetostatic fields will react toward sequences of equilibrium state.

The non-linear behavior of equation (2.8) is the reflection of the non-linear interaction among differential rotation, and the evolution of the solar surface magnetostatic field through its deep-rooted foot points in the photosphere. More generally, multiplicity of solution in Grad-Shafranov equation may be a reflection of the non-linear interaction and the non-uniqueness solution of evolutionary track of magnetic fields and plasma.

To ease toward the understanding of the behavior of the evolution, let consider stability and equilibrium of a membrane as a direct analogy to the distortion process in the magnetic field. The equation of a membrane may express as written below

τ ξ σ∇ + =2 0g (2.9)

Where ( )τ ξ is the tension, σ is the surface density, g is the gravitational acceleration, and ξ is the displacement in the membrane which vanishes on the boundary. We find the following analogy

ξ ↔ A (2.11) τ ↔ 1/ F (2.12) σ λg ↔ (2.13)

From the above equation we see that larger λ corresponds to heavier mass loading in the membrane. The larger F is, the more fragile the membrane is. If we set roughly that ∇ →2 21 / L , where L represents as the size of the magnetic field in space, then from equations (2.9) to (2.13), we simplify as

λF A L= / 2 (2.14) σ ξg L= / 2 (2.15)

Explanation of the Grad-Shafranov equation can now be shown by simple graphical representation with magnetic topology A as a controller variable in an area above active region proportional to L2 . The analogy to the membrane can always be followed directly by considering equations (2.14) and (2.15).

Let F be definite positive quantity over the active region area L2 , and if ∂ ∂F A/ < 0 then the solution exist and unique. This is said that the

magnetic topology to satisfy an over-stable state. Even the solution is unique but it is considered as less relevant to the real solar problems. An over-stable state may not produce various solar surface activities and disturbance. Other objection is, although the solution formally exist and unique as ∂ ∂F A/ < 0 , the solution sequence terminates physically at some λ, beyond which the quantity B p z Hx

208+ −π exp( / ) goes to negative value.

We leave this solution because it is irrelevance to our space warnings and space alerts.

Naturally a magnetic field has to be more stresses or distorts as the differential rotation forces the magnetic field to evolve. It is then very natural to think that the loading factor will grow larger as evolution of magnetic field continue. It is meant if F is definite positive then ∂ ∂F A/ > 0 and ∂ ∂2 2 0F A/ > . There is no solution exist for λ λ> * , but two or more solution exist for λ λ< * . Similar argument also holds if F<0 ,

∂ ∂F A/ > 0 and ∂ ∂2 2 0F A/ < . As the magnetic field is continuously being

distorted to deviate away from its magnetostatic configuration A, then λ will develop in a way similar as a restoring force in membrane analogy. The area in which the restoring force is always trying to push back to initial equilibrium is called stable region. Whilst the other side the restoring force which do not drive to initial equilibrium is called unstable region. We use essentially the basic Grad-Shafranov on our initial configuration for computer simulations to reproduce and stimulate various initial perturbations on the initial solar surface originated disturbance. There are at least three initial perturbation model applied on our simulation for solar originated disturbance, there are the shear perturbation, twist perturbation, and plasma pumping perturbation. Initial basic geometry of A is generally semi-circular two-dimensional magnetic arcade. This type is generally inferred from solar surface observations. Higher into the corona it will take a shape as a helmet streamer geometry. This geometry can be attained automatically by running the computer in stability mode without introducing initial perturbation subroutines (see Figure 6.12). 3. Basic MHD Differential Equations

We implemented basic MHD time dependent partial differential equations and treated the main physical parameters as global MHD parameters as we work with vast interplanetary space. Otherwise, if we taken into


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account all local and short range interactions such as the Coulomb forces, then no available computer technology able to perform such computation. In chapter 4 we will discuss in brief the technique to taken into account microscopic interactions within solar micro-ranular scale and integrate accumulative physics on global computations. To express the dynamics of physics and at the same time to catch any possibilities that the physical system has some degree of static condition in the same computational domain, we consider the primitive ideas of the fundamental Navier-Stokes equations (see e.g. Fefferman, 2000).The most basic idea is the change of plasma density in time is assumed due to a flow if we adopted the notion of continues hydrodynamics. But it also be said as a propagation of mass associated with the plasma density if we adopted the notion of the waves physics. Consequently, waves frequency always enter computational works whatever our approach to task the problems. In space MHD the Alfvenic or the fast mode MHD waves (Alfven, 1942. Cross, 1988) have to be carefully handled, other wise it hindered the physics of interaction from our conclusions. In one-dimensional computation the flow pass through the grid point is difficult to imagine. As in space physics we deal with at least two-dimensional problems, the notion of plasma flow is easier because we may imagine it as a flow through a cell boundary. The basic MHD time dependent partial differential equations in our task are constructed in accordance with the notion of flow or propagation of physical quantity passing through the cell boundary, follow it for a while, and computes some related physics in it. The concept is that the flow following derivative, written down as the left-hand side of the equations depicted below:

0. =∇+∂∂ →

Vt

ρρ (3.1)

→→→→→→

+×⎟⎠⎞

⎜⎝⎛ ×∇+−∇=∇+

∂∂ GBBPVVVt

ρρρ . (3.2)

⎟⎠⎞

⎜⎝⎛∇+⎟

⎠⎞

⎜⎝⎛ ∇=∇+

∂∂ →→→→→→→

BVVBVBBt

... (3.3)

⎟⎠⎞

⎜⎝⎛∇−−=∇+

∂∂ →→

VPVPPt

.)1(. γ 3.4)

The flow following derivatives of the above set of equations in terms of mathematical formalism is said as convective derivatives and the main physical quantities, the density, momentum, magnetic fields, and pressure are said to be convected quantities. They may also derive from the tensor covariant derivative after some

modifications. The left-hand side is similar as the space-time derivative in the general relativistic flow, for example the d’Alembertian derivative. We represent the equation (3.1) to (3.4) in more general and compact form as below

SVQQt

=∇+∂∂ →

. (3.5)

Where Q is the main basic physical quantities to be convected,

⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

=→

→

PB

VQ

ρ

ρ

(3.6)

so that in general Q is the function of the main basic physical quantities, and might be

remembered as ),,,( PBVQQ→→

≡ ρρ . While S is the general representation of the right-hand side of the set of partial differential equations (3.1) to (3.4) and automatically is assigned as

( )⎪⎪⎪⎪

⎩

⎪⎪⎪⎪

⎨

⎧

⎟⎠⎞

⎜⎝⎛∇−−

⎟⎠⎞

⎜⎝⎛∇+⎟

⎠⎞

⎜⎝⎛ ∇

+×⎟⎠⎞

⎜⎝⎛ ×∇+∇−

=

→

→→→→

→→→

VP

BVVB

GBBP

S

.1

..

0

γ

ρ

(3.7)

and the usual gas equation of state P=ρT. While S is the general function of the quantities in the right-hand sides of equations (3.1) to (3.4) and defined as the general source function

),,,,,,0( γρ→→→

≡ VGBPSS . The source function S brings a notion of external forces exerted into a MHD system. In terms of the flow following derivative, the basic MHD partial differential equation may be written in the most compact formula

SQDtD

= (3.8)

where →

∇+∂∂

≡ VtDt

D . is the flow following

derivative operator and takes the expression as Lagrangian operator (see e.g. Maron and Howes, 2003). This operator can be used for various Navier-Stokes MHD related phenomena without changing the left-hand side assignment. We need only to change the right-hand side assignment to


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meet all the cases in MHD interactions. In some cases, especially in solar surface phenomena, such as the Helmet Streamer Formation and the Coronal Mass Ejection (or briefly the HSF and the CME), may still be well approved by the set of the ideal MHD equations (3.1) to (3.4) because of the nature of the Sun as ideal MHD terrestrial machine. The equations are our modified ideal Navier-Stokes equations suitably for ideal MHD interaction cases. In the case of Two Ribbon Flare (or briefly the TRF) and in some interplanetary space or in planet-proximity interactions, the ideality might be broken and it might involve some non-ideal processes among the basic physical quantities. The processes are generally represented by the double-derivative (or the 2. ∇=∇∇ ) on the basic physical

quantities ),,,( PBV→→

ρρ (see e.g. Adams and Rogers, 1973. Anderson, et al., 1984). It means that we anticipate diffusive processes among the basic physical quantities. We put them as terms in right-hand side to equations (3.1) to (3.4) and written down as follows

0. 2 +∇=∇+∂∂ →

ραρρ Vt

3.9)

→→→→→→→

+×⎟⎠⎞

⎜⎝⎛ ×∇+∇−∇=∇+

∂∂ GBBPVVVVt

ρρνρρ 2. 3.10)

⎟⎠⎞

⎜⎝⎛∇+⎟

⎠⎞

⎜⎝⎛ ∇+∇=∇+

∂∂ →→→→→→→→

BVVBBVBBt

... 2η 3.11)

⎟⎠⎞

⎜⎝⎛∇−−∇=∇+

∂∂ →→

VPPVPPt

.)1(. 2 γκ 3.12)

The quantities α, ν, η, and κ are the non-ideal coefficients controlling the degree of the non-ideal processes onto MHD system. They may be uniform and small or they will adjust their values automatically as the physical environment is turn to be possible. Therefore, the general expression of the non-ideal MHD system is written as follow

SQVQQt

+∇=∇+∂∂ →

2. ξ (3.13)

Where S is the source function and has the notion similar with equation (3.7). More over ξ≡ξ(α,ν,η,κ) is a general function expressing the general diffusive matrix in our diffusive MHD equations (Setiahadi, 2005c). Components inside the matrix may be assigned as space and time dependent quantities to exhibit the highly non-linear, non-uniform, and non-homogeneous MHD interactions. For example, one of the matrix components may exhibit the magnetic reconnections of magnetic field of lines in the interplanetary and planet-proximity environments.

Usually in ‘normal’ condition when there is no magnetic reconnection process to occur, the

fluid momentum tensor →

Vρ can be used to trace

the direction of magnetic field of lines →

B and vice versa. In magnetic reconnection process, whether it is local or global reconnections, slow or accelerated reconnections (Sonnerup 1970), the magnetic fields tensor and the fluid momentum tensor are unavoidably decoupled at the reconnection points. Making impossible to trace the magnetic field of lines by using the fluid momentum tensor as a tracer. To anticipate if the reconnection process could happen automatically, whenever the physical condition is possible, the magnetic field of lines need additional treatments to redirect the field of lines after decoupling phase due to the magnetic reconnection process. In magnetic reconnection process the magnetic fields may diffuse away and move with different plasma flows. This process is expressed by the magnetic diffusion ‘constant’ η as describe by equation (3.11). The magnetic reconnection process starts to begin in a point somewhere in the computational domain when two opposite magnetic field of lines become too close to each other and η becomes much larger than its natural value that is the magnetic natural diffusion value. Thus by inspecting the growth of opposite magnetic field strength and η in every points at any time during computation, principally we may construct a magnetic reconnection inspector tensor as follow

)()( 200

→

↓

→

↑

→

⊗=ℜ BBBtii ηη , (3.14)

where →

ℜ i is the inspector tensor, 0η becomes

the natural diffusion coefficient, )(tiη becomes the space and time dependent diffusion coefficient and may be expressed as constant increasing function or as accelerated increasing function describing constant or accelerated magnetic reconnection processes. 2

0B describes average magnetic strength of the opposite

magnetic topology and )(→

↓

→

↑⊗ BB describes annihilation tensor for ultimately close and opposite magnetic topology to reconnect each other and move with different plasma flows with different velocity fields. These velocity fields are not simple and they have tensorial properties.

To task the problem further let define a decoupler velocity tensor as

→

DV to the system to represent the decoupling processes when


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magnetic reconnections occur and try to relate globally with the plasma velocity and magnetic velocity evolutions as follow,

ρ

→→→

−= VVV MD , (3.15)

where →

MV is the magnetic velocity tensor and

ρ

→

V is the plasma velocity tensor respectively. To get more insight to the decoupling processes, let we simplify the partial differential equation of the plasma density flow, the momentum flow, and the magnetic flow by dropping the non-ideal terms

→

∇ V2ν in equation (3.10), →

∇ B2η in equation (3.11), and T2∇κ in equation (3.12), and

assumed that 0. =∇→

B everywhere. Consequently, we have the following expressions as the representation of decoupling processes when the magnetic reconnections occur,

0. =∇+∂∂ →

DVt

ρρ, (3.16)

pVVtV

D −∇=∇+∂

∂ →→→

ρρ ρ

ρ. , (3.17)

→→→→→

∇=∇+∂∂

MD VBVBtB ).(. , (3.18)

→→

∇−−=∇+∂∂

ργ VpVptp

D .)1(. (3.19)

Watching that the left-hand side of the above new set of partial differential equations still satisfy the definition of the general Lagrangian operator with only the movement is dictated by the de-coupler velocity tensor

→

DV , so that there is no need to change our numerical procedure. The change is only subjected relative to the source function S on the right-hand side of the equations and any energy conversions happen in this process have been anticipated properly by our expanded notion on S.

These rather special treatments can be performed easily by writing a short special subroutine in our coding. The subroutine is set to active only when the magnetic reconnections work in the computational domain and to perform only at the points where the magnetic reconnections occur. Soon after decoupling-computation is accomplished by our numerical procedure, the magnetic field of lines are redirected again by usual diagonal matrix solver and the results are reintegrated back to the

original set of time-dependent differential equations. 4. Solar Magnetohydrodynamo

The dynamo process in the solar convective layers below the photosphere is the only ultimate energy generation that makes everything changes every second, and the Sun’s surface appears so dynamic. Observationally, the solar magnetohydrodynamo manifest it self as the solar differential rotation and super granular dynamics (Figure 6.2). The only observable phenomena to direct the development of a relevant magnetohydrodynamo theory is strongly depend upon on long-term and tight daily systematic observations on sunspots. We have been observing the sunspot at Watukosek Solar Observatory since 23 October 1987 up to know (Figure 6.6). The energy accumulation by the dynamo process is very slow in time scale of years, therefore it has enough time in super granular cells to deposit huge energy. Relation of the dynamo action with general solar magnetic fields is discovered as the photospheric sunspot activity cycle. The sunspot cycle is clearly demonstrated a long duration cycle of about 11.1 years. It is generally accepted that the long time scale makes the dynamo action has enough time to accumulate gigantic energy. Liberation of the gigantic energy might produce disturbance in interplanetary space.

The most important and decisive case to deal with the solar magnetohydrodynamo is careful inspection and determination of adopted granular scales in solar convective layers and relates them to the physics of interactions within bigger granular structure. The biggest solar granular scale is called the solar super granular cell, where energy of the solar dynamo ultimately accumulated and then released, can be best approached by deterministic physics. As we go into smaller solar granular scales the physics may be more stochastic. Due to the above special physical environments in the solar convective layers, the basic MHD partial differential equations need a little rearrangement. But basic numerical and computational scheme for determining automatically the physical solutions are essentially the same as discuss in chapter 5 and implemented to the basic MHD partial differential equations as adopted in chapter 3.

The big differences may come in two folds. Firstly, it is almost impossible to seek and investigate any magnetostatic stability configurations for the solar dynamo processes to provide it as the computational initial conditions. This is because as we adjusted the dynamo


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equation to be in magnetostatic state, the physics of dynamo generations from the micro granular cells will automatically disappear or rather diminish and make the equation representing the dynamo interaction becomes inconsistent in any way as mentioned by Cowling (1957). The dynamo action is believed as result of resultants of “frozen-in” plasma and magnetic fields interactions in microscopic random motions in solar micro-granular sub-scale and it is impossible to discern from observations by any available technology. Secondly, is the global physical parameter in the basic MHD partial differential equations turn to be averaged in certain granular scale as they come out from resultant of randomly processes from within smaller granular scale.

The main physical parameters for plasma density, momentum, magnetic fields, pressure, and velocity fields are now represented as average-integration of summations from smaller granular scale up to super granular scale. On the basis of super granular scale the physical parameters are treated as global MHD parameters and simulation is done point-to-point (or grid points) with the adopted scheme as will discuss in chapter 5. The main differential partial time dependent equations of the magnetohydrodynamo process in solar convective layers can be written as follows

ραρρ 2. ∇=∇+∂∂ →

Vt

(4.1)

→→→→→→→

+×⎟⎠

⎞⎜⎝

⎛ ×∇+∇−∇=∇+∂∂ GBBPMVMMt

ρν 2.

(4.2)

⎟⎠

⎞⎜⎝

⎛∇+⎟⎠

⎞⎜⎝

⎛ ∇+∇=∇+∂∂ →→→→→→→→

BVVBBVBBt

... 2η

(4.3)

⎟⎠

⎞⎜⎝

⎛∇−−∇=∇+∂∂ →→

VPPVPPt

.)1(. 2 γκ

(4.4) The general equation to represent the solar magnetohydrodynamo is consequently taken as below

SQVQQt

+∇=∇+∂∂ →

2. ξ (4.5)

The physical interpretation of the symbols are the same as in chapter 3, except the momentum assignment is treated differently and the general equation (4.5) have to be expanded in spherical geometry with a certain depth represents the depth of solar convective layers. The momentum is now treated as the average micro-granular sub-momentum summation and generally it is supposed that it has a property as follow

→→

= VM ρ ≠→

Vρ (4.6)

The above inequality may be set to be equal if we know the process in micro-granular cells is purely stochastic. As we go to larger granular scale it is no guarantee that the condition always be well fulfilled. With available technology we never know what exactly happen in micro granular scale. That is why we make a slight change in the momentum assignment as single symbol as M rather than its component ρ and V.

A general function to take into account various non-ideal processes ξ(α,ν,η,κ) is now also used to represent the general αΩ-magnetohydrodynamo coupling function and to compute various non ideal interactions in solar convective layers. The αΩ means the dynamo generation is come out as a consequence of the geometry of motion in solar spherical shape and the non-rigid solar plasma dynamics. The Sun is not a rigid body, as the Sun rotates there will be differences in solar plasma angular speed in radial direction (the α direction) and in polar-latitudional direction (the Ω direction). In this situation we have added magnetic reconnection amongst small-scale magnetic fields in the micro granular cells. Further reading on small-scale magnetic fields dynamics may be found in text written by Alissandrakis et al. (1991). The magnetic reconnection in micro granular cells is the only plausible and fundamental process within convective layers to have the dynamo action able to convert and subsequently to transfer the energy and accumulate in super granular cells and then release it into interplanetary space. Due to the inclusion of small-scale magnetic reconnections in micro granular scale, the dynamo action becomes energetic αΩ-magnetohydrodynamo. The basic and fundamental ideas of the magnetic reconnection for solar chromospheric and coronal level may be found in the text written by Priest (1981). Meanwhile, the text for small-scale magnetic reconnection in micro-granular scale is rarely found.

In sufficiently some hot and rarefied plasmas, inter-collision among particles may be neglected. If, furthermore, the force is entirely electromagnetic, then we have a rather special relation that is called the Vlasov equation. Because of its relative simplicity, this equation most commonly used in kinetic theory. In solar convective layers where inter-collision among plasma is possible, we have to add collision term and can be approximated as the modified Fokker-Planck equation which anticipated different distribution function of interactions within


40

micro granular cells. We do not calculate the microscopic dynamo generation by one-to-one correspondence into sub-atomic particles and calculate entirely all the short ranges force fields. A huge celestial body like the Sun will face us a never-ending computation on dynamo action in just within the micro granular cells. Instead, we introduce a volume element in a way that the volume represents in some extent particle physical properties and bringing enough some bulges of plasma properties and some elementary magnetic fields. In this case we introduce a kernel quantity to represent elementary dynamo action in micro granular cells.

Onto the kernel we do numerical experiment to have the most plausible kernel size that give observable solar surface phenomena, for example the butterfly diagram of sunspot. The butterfly diagram provides as our control phenomena to check whether our given numerical parameters in the kernel will approach the physical reality on the solar surface. If we give more than 10% of elementary magnetic fields to be in opposite directions with the rest in a kernel, then the magnetic fields will reconnect with other 10% and left behind 80% magnetic fields. We found that the surface of the Sun would be too hot (T>150.000 K) that certainly we do not observe the Sun like that (T<6500 K) and the butterfly diagram will not appear as cyclically phenomena as we observe it. We merely observed “an over active band” on both solar semi-hemispheres (Figure 6.7). By numerical experiments we found that the percentage of the opposite elementary magnetic fields should below 2.4% to produce the cyclic observable features like the butterfly diagram (Figure 6.8).

This kernel is the basic physical quantity solved by our modified Fokker-Planck equation. Physical interactions among main physical parameters are conveyed by the kernel through “distribution function of physical parameter” rather than single physical parameter as in global approach. The results from calculation of the Fokker-Planck equation over the kernels are then averaged to have the over all state in the next bigger granular cells. This process is repeated until integration of the stochastic effects in micro granular cells become resultantly disappear in the next granular scale. In this level then the global deterministic computation is started.

Because of the special processes and computation in micro granular cells have to be done properly before the global MHD simulation started, the magnetohydrodynamo calculation needs much of computational time. Mostly 90% of computation time is only for simulating the

energy generations by solar dynamo action. Result of this computation is extremely important since we will be able to decide in what latitude on the Sun’s surface will the energetic event occur. It is greatly help our space early warnings. 5. Computer Simulations

Directly solve the basic MHD partial differential equation is cumbersome or even it is impossible to get final and definitive solutions. Instead, solar-terrestrial scientists developed global point-to-point solutions both in space and in time. And subsequently, to always check and recheck the numerical stability of solutions by some automatic procedures. In computing world it is easy to be done by any available computer and operating systems. There are two ways to check numerical stability. The first is to develop a procedure to inspect stability of solution in over all computational domains for each computing time step. It is called as global matrix stability inspections. Such algorithm usually developed by a scientist who works with super computer facility in his institution. A good example of the numerical scheme, in which the global matrix stability is intensively applied, is a paper written by Hu and Wu (1984).

A mainframe super computer permits the algorithm without becoming shortage in memory. Since we have no such expensive and extensive computer facility at Watukosek Solar Observatory, we have to developed different algorithm to overcome shortcomings on computing facility. And it comes as the second, but very special algorithm that is the neighborhood point numerical stability inspection. This algorithm need no bulge matrix to work with, but it works on the basis of a component matrix separated to basic one-dimensional matrix. Space dimensionality solved by adding a special scanning algorithm. For three- or four-dimensional computation we may apply our special developed algorithm that is the plane-diagonally-scanning algorithm.

Computational efforts to solve the highly nonlinear problems of interplanetary space is largely devoted and rely on the best handling of the general main physical quantity Q to be convected without getting numerically unstable or even disappear to yield any plausible physical solutions for prolonged computational running. Any quantity, in this case Q, always subjected to floating number round-off errors and the errors may propagate from point-to-point in computational domain and from time-to-time during a running of a computer code. This because the computer syntax can only understand the numerical assignment of any


41

differential equation in finite algebraic form which is only an approximation from exact solution.

One may inspect that the fundamental partial differential MHD equations, displayed in chapter 3, in general consists of single time difference and single to double space difference forms as well, and in our works they are expressed largely by the following difference equations

tQQ

tQ

tQ tt

t ∆−

=∂∂

≡∂∂ +

→∆

1

0lim (5.1)

xQQ

dxdQQ ii

x ∆−

=≡∇ +

→∆

10

lim (5.2)

211

0

2

)(2lim

xQQQ

dxdQ

dxdQ iii

x ∆+−

=⎟⎠⎞

⎜⎝⎛≡∇ −+

→∆ (5.3)

The right most of equations (5.1) to (5.3) are the approximated difference forms that may be understood by the computer. The gradient ( )Q∇ , divergent ( )Q.∇ , and rotation ( )Q×∇ of vector-derivative operations are turn to be similar as they coded into one-dimensional numerical syntax. One may not quote the exact values of ∆t=0 and ∆x=0 since it makes the computer stop running and the operating system will prompt a floating error massage. A computer is not an infinite but a finite machine. We have to add some treatise and assumption onto ∆t and ∆x, and then to investigate a plausible solution of Q in all computational space and time domain.

The first step is to examine Q that would not turn to be negative if at initially Q is not a negative quantity everywhere in computational domain at any time. For example, the plasma density ρ should not negative since it will lose its physical meaning. To ensure the non-negativity of the plasma density upon transporting, that is pushing the density to evolve by approximated difference forms, we write Q into two parts according to formulae

( )[ ]2/12/11

01 / iiiP VVtxxQQ −∆+∆∆= ++ (5.4)

( )[ ]2/12/11

0 / iiiF VVtxxQQ −∆+∆∆= + (5.5) The above two equations are nothing but forward difference of the standard numerical form of the convective part, or the left hand side, of the general MHD equation (3.5) and (3.11). The two equations (5.4) and (5.5) avoid Q to be negative as long as Q positive at initial. The division by a factor of ( )[ ]2/12/1

1 ii VVtx −∆+∆ + is a necessity since we have pushed the basic general MHD equation into a formal co-moving derivative following the flow of plasma dynamics in a propagation-speed included in iV . The physical

fast mode propagation speeds have to be limited to no more than 0.5∆x, avoiding computational instability emerged from disturbance entering the next computational grids in one time step.

Other numerical process that would make Q be negative during computation is the numerical flux, coded by f entering and leaving numerical cell boundaries during a computation. It has similar notion with odd-even grids instability as pointed out by some people who specially work in numerical algebra. After computations in the micro-granular and granular cells satisfy resultantly to diminish their stochastic properties, the following algorithm is used cyclically as global MHD computation scheme: Computation of initial numerical diffusive fluxes:

( )titii QQf −= −++

11

0 221 η (5.6)

( )11

0 221

−+− −= t

itii QQf η (5.7)

Advanced the quantity Q on the even grids using the leapfrog algorithm:

( )( )titi

ti

ti

ti

ti VQVQxtQQ −∆∆−= ++

−+

++ 22

11

11 / (5.8)

Advanced the quantity Q on the odd grids: ( )( )1

111

11

11

2 / +−

+−

++

++

+ −∆∆−= ti

ti

ti

ti

ti

ti VQVQxtQQ (5.9)

Compute and define the anti-diffusive numerical fluxes:

( )211

1 221

++++ −= t

itii QQf η (5.10)

( )11

21 221

+−

+− −= t

itii QQf η (5.11)

Apply the numerical diffusion:

0011

1

1

_

21

23 ++

++

+

+ −+= iiti

t

i ffQQ (5.12)

0022_

21

21 −+

++

−+= iiti

t

i ffQQ (5.13)

Take first difference of the numerical diffused transported Q:

2_1

1

_

21

++

++ −=∆t

i

t

ii QQ (5.14)

1

1

_2_

21

+

−

+

− −=∆t

i

t

ii QQ (5.15)

Limits and corrects the fluxes by searching the unphysical negative fluxes:

( )1

21+= ifsignS (5.16)

( )[ ]21

21

21

21 .,,.min,0max. 1

++−+ ∆∆= iiiC

i SfSSf (5.17)

Apply the numerical anti diffusion by means of using the corrected fluxes Cf :

Ci

Ci

t

iti ffQQ

21

21

2_2

−+

++ +−= (5.18)


42

Ci

Ci

t

iti ffQQ

23

23

1

1

_11 −+

+

+++ +−= (5.19)

Because of the nature of the corrected flux, this numerical scheme is called the flux corrected transport algorithm (see e.g. Boris et al., 1975, Rompteaux et al.1992). 6. Simulation Results

If we decided to develop the space early warning physics due to solar energetic energy liberations into surrounding then we have to know the main origin of the disturbance physics. The key to the problem is the understanding of the dynamo action of convective layer below the photosphere. The physics below the photosphere is extremely difficult to infer directly from observation or it is impossible to reach directly only from observation. The physics may be inferred by combination of theory and confirmation from the only observational data, that is the butterfly diagram. We do numerical simulation by putting the fraction of opposite elementary magnetic fields inside our micro granular kernel model and run the computer code for several months. We plot the results and compare it with the observational butterfly diagram. At last we decided that the opposite fraction of magnetic fields should be around 2.2% to 2.4% in order to exhibit the cyclically phenomena of the butterfly diagram.

The dynamo action will not produce observable features if we approach it by a fully pre-deterministic physics. If we approach it by fully stochastic physics then we face a never-ending computation since the Sun is a vast physical body. It is also impossible if we try to compute stochastic physics deep into smallest scale in convective layer. A way out is assumed that dynamo action is a mix-physics that we have to make it operational under some circumstances. We have to be realistic that the physics we develop have to be conclusive and use it as our operational tool. The stochastic physics assumption is related by our observational and instrumental limitations.

The solar surface phenomena that unresolved by our technological system at Watukosek Solar Observatory is assumed in the domain of stochastic physics. By our daily experience under some relatively good seeing condition the smallest region which is still be discerned is 400x400 km 2 surface area with an assumed average depth of 500 km and is taken as our micro granular sub scale outer boundary where the stochastic physics smear out to gradually transform to pre-deterministic physic. The adopted micro granular scale is fiducially

chosen and rather lose of physical reasoning. Consequently the result may not properly match with the observational data. The result is depicted in figure (6.8) as our theoretical butterfly diagram. Even though it is clearly exhibit the cyclic phenomena and high latitude sunspot appearance at the beginning of a new cycle.

In our dynamo theory the elementary magnetic fields in micro granular cells accumulate to integrate in bigger and bigger granular scales. The last and the largest granular scale is the super granular cell. The elementary magnetic fields which are treated by stochastic physic in smaller granular scale is gradually manifest their selves as the solar general magnetic fields as they integrate into bigger granular scale and gradually the pre-deterministic solar differential rotation will take place to decide their evolution. This will have general effects to the general magnetic fields in super granular to transfer its toroidal component to poloidal component (see Figure 6.3).

The toroidal component is continuously subjected to differential rotation and with local buoyancy force the flux tube will be popped up to be observable as sunspot group on photosphere. The spherical geometry of the Sun makes the toroidal component near poles are wounded firstly to multiple the buoyancy force around. It is marked as the beginning of the new sunspot cycle. As the time goes on the wounded area will gradually moves to solar equator from both hemispheres. The motion is weakly and systematically non-linear from around ±30 0 to ±2 0 heliographic. Small circles in the graphics in figure (6.7) and figure (6.8) are not the place where the sunspot appears on the solar surface but rather the most probable regions where the sunspots will emerge after integrating and calculating their last related super granular cells. The computations need much time, from several weeks to several months. The probable latitude of magnetic storm to flash may be decided observationally from the systematic motion of probable emerging sunspot groups or automatically from our dynamo model.

The emerging magnetic fields will appear as darker regions on photosphere. It is essentially loop flux tube geometry with the foot points rooted in dense photosphere. The sunspot magnetic loop is a very stable magnetic topology since it roots in the dense photosphere. Even though at the same its evolution is greatly controlled by the photospheric motion through the systematic solar differential rotation. Evolution of sunspot magnetic loop is at least subjected to photospheric slow motion perturbation, that are


43

the shear perturbations, the twist perturbations, and the plasma pumping perturbations (Figure 6.9). The magnetic fields have a capability to cool down the photospheric brightness temperature from 6000K to 4000K and it is meant that the sunspot magnetic field strength is no less than 1000G. Darker and extensive sunspot means stronger and potentially deposit large magnetic energy.

We give an example by using MHD simulation of growing unstable of sunspot magnetic loop by plasma pumping instability (Figure 6.10) (Setiahadi, 2001). The magnetic flux tube geometry of sunspot has also a capability to direct plasma flow from both foot points. As the time proceeds, more plasma will be trapped and plasma density increases by a weakly non-linier factor. More time proceeds the plasma density is going denser and denser. The friction among plasma particles will grow exponentially and rise temperature in much shorter time scale. As the loop temperature increasing in much number, it may be observed by other wave lengths. For example, it may be observed at soft X-ray as discussed by Anwar and Akioka (1998). The loop will flaring at a temperature of no less than 20x10 6 K. and after eruption the remnant of the foot point is still be observed in Balmer wavelength (λ=6562.8 A) as observed at Watukosek Solar Observatory (see Figure 6.11). It is meant that the flaring energy is largely accumulated in the loop top of the magnetic flux tube. The loop top’s non-linear dynamics during flaring may easily be seen by plotting the time sequence of the loop top height (Figure 6.10). At the first 5 minutes of eruption it is obvious there is a wave propagates back and forth very fast along the flux tube with a speed approximately 1000km/sec and it is characteristically the Alfven wave mode.

Emergence of sunspot magnetic flux tube into upper photospheric level will also penetrate up to chromospheric or the Balmer layer of the Sun’s atmosphere. This is why we able to observe the flux tube in Balmer line by our Hα telescope at Watukosek Solar Observatory. As the flux tube of sunspot with strong magnetic fields of 1000G emerge to photosphere and penetrate the chromosphere, there is also much weaker magnetic fields of 10G develop surrounding a sunspot magnetic flux tube. This type of weaker magnetic fields may slowly penetrate into high corona and channeling weak flows of electron plasma with ambient coronal speed of 140km/sec deep into planetary space. Generally it takes a shape as a helmet with electron plasma streaming gradually from its

cusp top (Setiahadi, 2005b). It is said that a helmet streamer (HST) is then formed in high corona with many consequences. The HST generally lies above a sunspot, especially large sunspot group, because of the strong sunspot magnetic fields induce the surrounding electron plasma in solar atmosphere. Therefore, the dynamics of sunspot magnetic flux tube gives physical influences on the HST structure and vice versa. The HST may also erupts and sweeps up much electron into interplanetary space. Even though the HST has much weaker average magnetic field of strength (10G), since it covers large volume in corona, any instability on its evolution will presumably has energetic consequences.

In many occurrences eruption of HSTs propels 100x10 6 kg of electron mass into interplanetary space with speeds of several hundred kilometers per second to thousands of kilometer per second. Generally the HST will turn to appear as giant arc and it is called as CME loop (Setiahadi, 2005a). When a HST eruption is accompanied by sunspot magnetic flux tube eruption, situated below it, then we will observed a high speed CME with speeds of more than 1000 km/sec and always accompanied with high-energy particles from flaring sunspot. But the HST may also erupts without any relation with sunspot. It is generally come from spotless HST. After a big eruption of a sunspot the remnant of sunspot magnetic fields may still shape the magnetic field to form a HST. Eruption from this HST type is believed come from the shearing perturbation on HST foot points to push the HST into critical stability condition and then erupts as a CME with lower speeds. Our example of MHD simulation on the HST formation is a type of spotless HST formation, that is the HST formation above a remnant of sunspot active region (Figure 6.12). The MHD simulation shows that a HST of this type attains its MHD equilibrium high into corona within 17 to 20 minutes on its formation. CME simulation in this sample is come from previous HST in MHD equilibrium to be pushed to unstable condition by assigning shearing perturbation on HST foot points. A giant loop of CME resulted from this simulation with escaping speeds of about 490 km/sec. The CME of this type is called cool CME moves with almost converting magnetic energy of the initial HST into giant kinetic energy.

Thousands of observations on CMEs reveal large range of speeds after escaping from the Sun and it may ranges from 200 km/sec to 1500 km/sec with total mass of electron plasma from 10x10 6 kg to 100x10 6 kg. The movement


44

and the dynamics of CME in interplanetary space is therefore may be slightly different from one case to other case. A general model for propagation of CME in interplanetary space is the magnetically semi directed beam may be applied with great satisfactory. Geometry of propagation of CME depends roughly on the initial speed. Speeds around 200 km/sec would propagate as magnetically turbulence clouds. Speeds around 600 km/sec would propagate as magnetically tongue clouds. And speeds around or higher than 1000 km/sec would propagate as magnetically detached clouds or high-speed giant plasmoid.

Severe impact on planetary system will occur when sunspot position where the disturbance originated almost face-on the planet and the energy propagates almost in ecliptic plane. The disturbance of the clouds will eventually arrive to nearby planet in several days depend on the initial speed and average distance to the planet. A distance Sun to Earth of 150x10 6 km needs about 48 hours to reach the planetary boundary layer (or briefly the PBL). The moving magnetically clouds from the Sun sometimes subjected to different terminology as solar wind. In our case the solar wind arrives to the Earth’s proximity and PBL in a speed 300 km/hour with magnetic field strength 5nT and duration of the total solar wind momentum to 12 minutes. In this occasion, our automatic numerical experiments with two-dimensional MHD are performed for two extreme of seasons. The first is spring or autumn when the Sun at spring or autumn solstice. In these seasons the Earth equatorial plane makes 0.0 0 relative to the ecliptic plane. The second is summer or winter when the Sun at summer or winter solstice. Or when the Earth equatorial plane makes ±23.5 0 relative to the ecliptic plane.

We consider a computational space of 100,000 x 100,000 km 2 to represent the space around the Earth where the magnetosphere is present. The disturbance, described as the energetic solar coronal mass ejection or CME, is assumed to merge from a far enough-source, that is the Sun which situated about 150x10 6 km from the Earth. The magnetic component of the solar originated disturbance in the interplanetary space is also usually called as interplanetary magnetic fields or IMF. Far from the source, the IMF will eventually have planar magnetic topology and the plasma flow will approximately have laminar flow geometry. The assumption works properly only if the ratio of the computational domain to the space volume separated between the Sun and the Earth is very

small, so that the disturbance is locally linear and in this case the ratio lies within 6.6x10 4− . The magnetosphere, which is assumed at initially in steady state, is nonlinear and it is proved theoretically and from spacecraft measurements.

After reaching Earth’s day-side PBL the magnetized electron plasma begins to interact with the magnetosphere making the magnetosphere to react dynamically by changing its initial magnetic topology from simple dipole topology to complex asymmetric magnetic topology. The day-side topology form an unseen shielding-arc and term as magnetopause. The disturbance is reflected back and met the subsequent flow to form standing MHD shock waves region far above the Earth. Between these two regions, the magnetopause and the standing shock region, there is a region dominated by MHD turbulence processes. The prominent result of this simulation is the discovery of dynamical magnetically protection mechanism against strong magnetic fields and electron plasma by MHD turbulence processes. The disturbance from the Sun conveyed by MHD waves mode and deflected away from the Earth. Unfortunately, this region lies in a distance where the communication satellites are placed in geo-synchronous orbit (36,000km to 40,000km). This region is noisy at almost microwave length used for communications. Other discovery is the bow-shock more intensive when the Earth in spring or autumn compare with the bow-shock in summer or winter. It is because in spring or autumn, fraction of reflective MHD waves larger than deflective MHD waves due to the zero angle of equator to the ecliptic. In summer or winter, more fraction of deflective MHD occur due to a tilt of ±23.5 0 of equator to the ecliptic. We compare the results of MHD simulation on a planet has no magnetic fields as Venus as well (Figure 6.18). Venus will be surrounded by hazardous magnetic fields and electron plasma 4 minutes after the disturbance interact with the Venus’s PBL. The Planet’ surface will be burn by a combination of high degree of ionization, high temperature, and destructive strong magnetic fields as shown in figure (6.19).

Other important discovery by this simulation is that planets which have magnetosphere, such as Mars or Earth, will form plasmoid and subsequently expels the plasmoid to planetary proximity space in night side of the planets’ magnetosphere (Figure 6.20). The process is computed in different computational domain of 30,000 x 200,000 km 2 to catch non-linear reactions behind the night side of the planet’s magnetosphere. During the process the


45

disturbance push the magnetic fields in the night side to be more close together. Nearby opposite magnetic fields will eventually reconnected and form a plasmoid. This reconnection is termed as

cool magnetic reconnection because of relatively planetary low temperature environment compare to the Sun.

Figure 6.1: The super granular cells are distorted and move relative to each other due to the solar differential rotation in convective layer. The magnetic fields are distorted and stressed. Inset is a super granular cell consist of granular cells and a granular cell consist of sub-granular cells. A sub granular cell consist of micro granular cells.

Figure 6.2: Example of granular cell photographed during finest seeing condition (BBSO) The pattern of granulas are clearly exhibit as plasma-fluid heated from below. Intensive and extensive discussions found in the text written by Chandrasekhar (1961).


46

Figure 6.3: Schematic diagram of poloidal magnetic topology transferring to toroidal magnetic topology due to the differential rotation. The toroidal magnetic fields continuously distorted and may be unstable.

Figure 6.4: Schematic diagram of unstable evolution of toroidal magnetic flux tube entering the boundary of the upper convective layer and become observable as sunspot or solar-surface active region. The buoyancy force is the local force to pop up the already unstable magnetic flux tube (Kaufmann III,1978)


47

Figure 6.5: Spherical geometry of the Sun and differential motion would make the magnetic fields wounded initially near pole regions in high heliographic latitudes. This simple descriptive of global magnetic fields evolution by Babcock explain why the sunspots appear in high latitude at the beginning of activity cycle (Kaufmann III, 1978).

Figure 6.6: The Butterfly diagram observed at Watukosek Solar Observatory LAPAN resulted from daily observations, started from 23 October 1987 up to know. The cyclic phenomena of sunspot emerging regions are clearly seen. The period is around 11.1 year (Setiahadi, 2005d).


48

Figure 6.7: The energetic αΩ-magnetohydrodynamo computer simulation result for more than 10.0% fraction of opposite elementary magnetic fields inside the micro-granular cell.

Figure 6.8: The result for below 2.4% fraction of opposite elementary magnetic fields inside the micro-granular cell. It is clearly be seen that theoretical simulation gives the cyclically 11.1 year butterfly diagram.


49

Figure 6.9: More detail picture of disturbance on a flux tube by shearing perturbation, twist perturbation, and plasma pumping perturbation.

Figure 6.10: Simulation of Loop Flare due to the plasma pumping perturbation. Watch the non-linear time development of the loop-top height. In a flare, large fraction of magnetic energy in the sunspot escapes into interplanetary space and it influences deep into planetary physical system.

Figure 6.11: Observational evidence of loop flare by plasma pumping perturbation patrolled at Watukosek Solar Observatory. Just after eruption, the foot-points remnant is still visible at Balmer line (λ=6562.8 A).


50

Figure 6.12: As an active region develop on the photosphere, the weak magnetic fields surrounding the active region will also evolve and penetrate into high corona and forms a helmet streamer. In about 17 to 20 minutes the helmet streamer (HST) subsequently attains its dynamical MHD equilibrium.

Figure 6.13: A coronal mass ejection (CME) may result by disturbing the HST foot points’ with shearing motion. We use a 2.5 dimensional MHD simulation to make a HST unstable and subsequently erupt as CME. The event is a fast moving giant loop observed by a high altitude coronagraph.


51

Figure 6.14: Observational evidence of HST turn to be CME as observed by NASA. The helmet shape is clearly transformed to giant arc of CME. There is a complexity since the CME accompanied by a prominence eruption from the chromospheric layer.

Figure 6.15: Magnetospheric bow-shock during spring or autumn solstice showing the intensive bow shock due to the largely reflective MHD waves from the solar storm.

Figure 6.16: Magnetospheric bow-shock develops by magnetic system of the Earth for winter or summer solstice. The bow shock structure is not as intensive as at spring or autumn because of the fraction of deflective MHD waves is larger than reflective MHD waves.


52

Figure 6.17: Plasmoid formation and ejection in magnetotail. It is an example of planet-proximity event due to solar energetic event. The magnetic field of lines in the night-side about 900 km above the Earth are pushed to get close to each other. Opposite magnetic fields topology will automatically trigger a cool magnetic reconnection, resulting a plasmoid formation and ejection.

Figure 6.18: Venus can not develop magnetic protection against the magnetic storm with deadly electron plasma giant flow from the Sun. In 12 minutes duration of solar magnetic storm, at 4 minutes after the storm interacts with the Venus planetary boundary layers, the electron plasma burn the over all planet. Biological systems will never survive under this condition.


53

7. Space Warning Efforts Efforts for warning of the solar origin

disturbance need research of the primary cause of the disturbance. Unfortunately, the origin of disturbance creates below the observable surface of the Sun. Sunspots are the only controlling parameter that can be used to verify our dynamical model of how the energy generation become possible to produce active regions and then to release huge energy. The convective layer below the photosphere is believed to generate the dynamo action to accumulate magnetic energy and with the surrounding plasma to be very dynamic and non-linear in nature. Slow energy accumulation by super slow energetic αΩ-magnetohydrodynamo makes an emerging magnetic fields to create observable active region and then develop to have enough time to deposit huge energy. This dynamo has been used to estimate the latitude of where the active region to develop sunspot group and possible area where the magnetic storm to flash and initiate with appropriate accuracy of boundary conditions.

Energetic liberation of particles and magnetic fields from solar active region propagate as interplanetary-disturbance. Some disturbances are magnetic-plasmoids dominated rather than energetic particles. In other occurrences the disturbances contain more energetic particles rather than magnetic-plasmoids. In some occurrences the disturbances consists both energetic particles and magnetic-plasmoids. This is in accordance with the observational reality that an eruption of a CME might happen with or without TRF. In all the cases, the energetic particles always arrive within several minutes after we observed an optical precursor on the solar surface. While the magnetic-plasmoid arrive several days later.

Early warning observatory have to summarize a warning report before the arrival of the disturbance is detected by some instruments. Since the fastest disturbance propagates as fast

as the speed of light, it is important to observe optical signature as a precursor of an evolution on the solar surface leading to the energetic liberation of energy and the start of the interplanetary disturbance, far before the impact reaches the Earth’s atmosphere. International coordinated observations of space based or ground based solar observatory with optical telescopes are therefore extremely important.

Continuous patrolling the dark filament at Balmer line, especially the dark filament which out-lining the neutral region, is important because we frequently observe that the dark filament seems to change its shape by some moderate energy flow from below the sub-photospheric level above the active region. The dark filament changes it shape and length within the order of several minutes. Within seconds, a CME is launched and after two or three minutes later followed by a TRF. In some cases, when a TRF is not initiated, we still be able to notice a dark filament trailing below the CME arc as observed in August 1980 by NASA. The material of the dark filament is pulled away from the solar surface because of the negative pressure left behind by the CME. The two dimensional MHD simulation of this phenomena has been simulated by Setiahadi et al. (1998).

Full disk solar surface patrol at integrated light is also worth to consider. Since sunspots in active region frequently exhibit a relatively quick changes in many features. The first is the change in sunspot number which exposing evidence of the changes of the strength of magnetic fields due to a flux emergence or a fly away of magnetic system into interplanetary space. The magnetic flux emergence will increase the sunspot numbers in a relatively long time scale, since it more relates to the slow magnetic energy build-up above active regions. While the magnetic fly-away will decrease the sunspot numbers in much shorter time scale, since it relates to some fast phenomena such as CME or TRF. The decreasing of the sunspot numbers is

Figure 6.19: The burning Venus. All the planet is being surrounded by electron plasma. The size of the giant cloud has been normalized to fit with the planet size.


54

therefore considered as an important optical precursor to give an alert for the incoming of an interplanetary magnetic storm. The second is the relative positional changes of spots in a sunspot group (or the sunspot proper motion). This type of motion reflects a rough measure of twist within a sunspot group. It is obvious from intensive sunspot observation that after some degrees of rotation a type of flare will occur. Usually it relates to the liberation of the helical magnetic energy excess (Shibata and Uchida, 1986). The angles of rotation at when the flares to occur is uncertain. It is then considered that sunspot proper motions patrol provide only as a weak optical precursor.

On the relations to those precursors, we are trying to modify a Lyot-filter telescope and to construct an entirely new design of an integrated light telescope at Watukosek Solar Observatory (see Figure 7.1). On the focal plane of the telescope we utilize relatively high-resolution CCD cameras. We are trying to make, under our own shortcomings and constrains, and then to implement our artificial intelligence software to search in fully automatic mode for the precursors and subsequently to warn the observer for the

incoming interplanetary disturbance. A dedicated observer is still needed to make a last decision of whether some precursors will give a real impact on the Earth or not. A human touch is still important since we have to anticipate that some degree of uncertainties will always be involved due to complexity and highly non-linear properties of the solar surface phenomena and some incoherent understandings in the non-linear solar magnetic fields stability analysis.

An example to observe and subsequently to catch the precursor was the event on October 2003 (see Figure 7.2, 7.3, and 7.4). We caught the October storm by tight daily observational procedure and tried to decide initial conditions and relevant boundary conditions. It is not easy since the big sunspot from where a storm to flash had developed very complex magnetic topology at about flashing. We calculated total magnetic energy and the fraction of magnetic energy that probably had fly away and escaping into interplanetary space. Estimation by MHD simulation revealed that the disturbance arrived 42 to 48 hours after traveling in interplanetary space between the Sun and the Earth.

Figure 7.1: The telescope, at Watukosek Solar Observatory in East Java province, is being modified to match with new added scientific values, i.e. solar activity patrol and space early warning in LAPAN.


55

Figure 7.2: The gigantic magnetic storm of October 2003 came out from a big sunspot in southern solar hemisphere displayed extensive aurora near Earth’s magnetic poles. The fast moving arc flashed out from an initially giant helmet streamer and move out fast as CME (NASA).

Figure 7.3: Polar view of two dimensional polar computational grid system to put numerical solutions onto the grids for dynamical disturbance from the gigantic solar storm event on October 2003. The energy flash has come out from -10 0 to -20 0 heliographic latitude. These range of heliographic latitudes had been determined by energetic αΩ-magnetohydrodynamo computer simulation.

Figure 7.4: Interplanetary space disturbance on October 2003 for numerical output at 15 hours, 22 hours, and 28 hours. The disturbance arrives to Earth proximity after traveling 42 hours from the Sun. The average distance Sun to Earth is 150x10 6 km. Disturbance profile is projected into the ecliptic plane.


56

8. Discussions We have been trying to implement the

knowledge of this theoretical research. The result is used to generate realistic boundary and initial conditions to task the space weather alerts for our MHD numerical simulation to simulate completely all the non-linear effects in the solar energetic phenomena and their interplanetary disturbances (see e.g. Setiahadi and Sakurai, 1997, Setiahadi, 1997, 2001). The usage of this method will depend strongly on state-of-the-art of our understandings on initial conditions and boundary conditions for various solar coronal magnetic structures. Initial physical condition is important in order to use it prior to run our MHD computer simulations (Setiahadi, 1997). Observational data analysis before, during, and after sunspot groups and HSTs attain their equilibrium structure in the corona exposed subtle differences on their physical parameters. That is why we have some problems to distinguish initial physical condition to convert it into physical parameters as an input for initial condition in our space alert MHD computer code. Combined with their non-linear interactions (see e.g. Setiahadi et al., 1998), multi-track evolution, and incoherent stability analysis, it is still difficult to use the MHD numerical method on space alert activities. Some fast and energetic disturbances, e.g. the TRF type phenomena, always arrive before we accomplish our warning report. This type of disturbances always propagate as fast as light rays in vacuum and along with the high energy particles and radiations arrive within 8 minutes to 16 minutes after we observe an optical precursor of an explosion on the Sun.

The physical effects of these interplanetary disturbances on the Earth are noticeable. Several years ago in March 1989 and again in January 1997 there were historical TRF and CME which ejected a great deal of plasmoid that reached the Earth’s high atmospheric layers after several of days. It caused a high degree of ionization rate in ionosphere and compressed the Earth’s magnetic field as well, and produced an extensive MHD bow-shock on Earth’s magnetosphere.

These gigantic events also drove induction of electric currents through the national electricity network in Canada. The safety mechanism was then triggered unintentionally and caused a power shut down in the whole city of Quebec and the villages around. A great aurora were produced which was seen to far south Italy. Short-wave radio communication and television around the globe were disrupted and jammed because of the gigantic disturbance to the ionosphere. Radio compass readings for long-

range navigation were distorted by 10 degrees posing a threat to intercontinental flight and boat navigation. Some satellites orbiting around the Earth were slowed down, their altitudes, by average, falling down by 0.8 km. Also a Norwegian oil company abandoned surveying because of the effects on the delicate magnetometer sensors used by off shore oil company to explore the crude oil anticline trap.

The events happen again in October 2003, March 2004, and September 2005. All of the events always proceed by appearance of large sunspot groups. With our simulation system and technology we still do not know from northern or southern of the solar hemisphere the storm will be produced. But we have decided using the energetic αΩ-magnetohydrodynamo a rather precision heliographic position that the last events should largely flash from northern or southern solar hemisphere with most probable area around ±10 to ±20 degrees heliographic.

It is still needed much research for shaping the future with an autonomously solar activity and space early warning science, theory and technological system. This is due to still left some incoherent problems of knowledge of the non-linear study of MHD interactions from solar convective layer to interplanetary space and technological limitations. Acknowledgements The author would like to express deep appreciations to the colleagues for some cooperative works: Profs Jorga Ibrahim, The How Liong, Eijiro Hiei, Takashi Sakurai, Hideaki Miyazaki, Hirakozu Yoshimura, Maki Akioka, Dr(s). Zadrach L. Dupe, Hakim L. Malasan, Bachtiar Anwar Zaenuri, John Maspupu, La Ode M. Musyafar K., Nanang Widodo, Stefanus Sudarji, Ahmad Sodikin, Nuraeni, and Marlan. Dr(s). Dony Kushardono, Milton Damanik, Dr(s) Agus Aribowo, Sutan Takdir Ali Munawar. Dr(s) Abdurrachman, Nizam Akhmad, Margono, Neflia, Rasdewita, and Santi Sulistiani. References Alissandrakis, C.E., Dara, H.C., Koutchmy, S.

(1991), Study of Small Scale Magnetic Flux and the Corresponding Velocity Pattern, Astronomy and Astrophysics, 249, p. 533

Alfven, H. (1942), Nature, 105, p. 405. Anderson, D.A., Tennehill, J.C., Pletcher, R.H.

(1984), Computational Fluid Mechanics and Heat Transfer, McGraw-Hill Book Co.

Anwar, B., Akioka, M. (1998), Activity in NOAA AR7172, in Astrophysics and Space Science Library, 229, p. 309.


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Adams, J.A., Rogers, D.F. (1973), Computer Aided Heat Transfer Analysis, McGraw-Hill Kogakusha, Ltd. Boris, J.P., Book, D.L., Hain, K. (1975), Flux-

Corrected Transport II: Generaliza-tion of the Method, Journal of Computational Physics, 18, p. 248.

Chandrasekhar, S. (1961), Hydrodynamics and Hydromagnetic Stability, Dover Publ. Co., New York.

Cowling, T.G. (1957), Magnetohydrodynamics, Interscience Publ. Inc., New York, p. 79. Cross, R. (1988), An Introduction to Alfven Waves, Adam HilgerPubl. Co. Durrant, C.J. (1988), The Atmosphere of the Sun, Adam HilgerPubl. Co. Geffen, J.H.G.M. (1993), Magnetic energy

Balance and Period Stability of the Solar Dynamo, (Thesis), University of Utrecht.

Fefferman, C.L. (2000), Existence and Smoothness of the Navier-Stokes Equation, Princeton University, Department of Mathematics, p. 1.

Hu, Y.Q., Wu, S.T. (1984), A Full-Implicit-Continuous-Eulerian (FICE) Scheme for Multidimensional Transient Magnetohydrodynamics (MHD) Flows, Journal of Computational Physics, 55. p. 33.

Kamide, Y., Baumjohann, W. (1993), Magnetosphere-Ionosphere Coupling, Springer-Verlag, Berlin. Kaufmann III, W.J. (1978), Exploration of the Solar System, Macmillan Publ. Co., New York. Maron, J.L., Howes, G.G. (2003), Gradient

Particle Magnetohydrodynamics: A Lagrangian Particle for Astrophysical Magnetohydrodynamics, Ap. J., 595, p. 564.

Pontin, D.I., Priest, E.R., Longcope, D.W. (2003), A Frame Work for Understanding the Topology of Complex Coronal Structure, Solar Physics, 212, p. 349.

Priest, E.R. (1981), Solar Magnetohydrodynamics, D. Reidel Publ. Co. Ossendrijver, A.J.H. (1996), Fluctuations and

Energy Balance in Solar and Stellar Dynamos, (Thesis), University of Utrecht.

Rompteaux, A., Estivalezes, J.L., Perrin, C. (1992), Mesh Adaptation with A Fully Multidimensional FCT-Algorithm for General Curvilinear Coordinates, Comp. Fluid Dyn., 2, p. 809.

Setiahadi, B. (1990), The Initiation of Solar Coronal Mass Ejection: MHD Simulation of Dis-Equilibrium in Magnetic Arcade, (Thesis), The University of Tokyo, Japan.

Setiahadi, B., Anwar, B., Sakurai, T. (1995), Two Dimensional MHD Simulation of CME Generated Interplanetary Shock Waves, ISEA, Bali, Indonesia, D10.

Setiahadi, B., Sakurai, T. (1997), Simulation by Vectorized Computation for Giant Electron Plasma Cloud Ejection, ICME, Bandung, Indonesia, p. 203.

Setiahadi, B. (1997) A Test for An Interplanetary Hydromagnetic Numerical Simulation, Report on the Work Done in CRL, Tokyo, Japan.

Setiahadi, B., Anwar, B., Akioka, M., Sakurai, T. (1998), Non-Linear Evolution of Erupting Coronal Magnetic Fields, in Observational Plasma Astrophysics, T. Watanabe et al. (eds.), Kluwer Academic Publ., p. 353.

Setiahadi, B. (2001), Results of Solar-Terrestrial MHD Simulations Tests 1985-2001, Prosidings Seminar Sehari 65 Tahun Prof. Jorga Ibrahim, p. 249.

Setiahadi, B. (2004a), Comparative Study of the MHD Interactions of Solar Storm on Venus and Earth, Proceeding Seminar MIPA IV, ITB, Bandung, p. 135.

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Setiahadi, B. (2005c), Non-Ideal MHD Simulation on Interactions Between Solar Magnetic Storm and the Physical System of Venus, Seminar Matematika, Universitas Gajah Mada, in press.

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(2004), Influence of the Solar Wind Variations on Atmospheric Parameters in the Southern Polar Region, Advances in Space Research, p. 1.

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Appendix 1: The general MHD matrix equation It is inferred from equations (3.9) to (3.12)

that our general partial differential time-dependent MHD equations may be represented by a single general MHD matrix in algebraic-abstract form as follow:

Briefly we quoted as GMHDM. While operator on the left-hand side of the above expression,

defined as ⎟⎠⎞

⎜⎝⎛ ∇−∇+∂∂ →

2. ξVt

, is our quoted

general radiative and diffusive Lagrangian operator (GRDLO). This is the most powerful MHD equation to meet all cases of necessary processes in interplanetary space, from the Solar surface to planet-proximity space. If the general diffusive matrix ξ is zero than the MHD system turn to be ideal MHD suitable to represent ideal MHD processes in interplanetary space (see chapter 3).

The matrix in the left-hand side, lies between GRDLO and equal-signed of the above equation, is called physical-parameter matrix (PPM). Components inside PPM naturally can be concluded from observations. Some of them in some cases might be derived almost directly from observation by read-out the data from instrumentation. But in some other cases need further data processing to solve with the PPM.

The right-hand side of the above equation is external-force matrix (EFM) represents external forces exerted into a MHD system. Compare with the previous matrix (the PPM), this matrix is impossible to infer from observations. EFM is more abstract quantity, but the physical-

story has to be extracted and concluded from it. Numerical simulation relates the real physical world in PPM with abstract physical world in EFM by objective and self-consistent way.

The GMHDM always relevant to any extended applications for planet-proximity physics, interplanetary physics, and solar-terrestrial physics. For planet-proximity physics it always be relevant and can be applied to solve the problems in lower atmospheric physics, higher atmospheric physics, ionosphere, exosphere, and magnetosphere. It is also capable to handle super-slow physics to super-fast physics. All of the above cases reflect in PPM as different relative strength among the physical components.

Even though, we limit the GMHDM to work well below 10% of the speed of propagation of light rays in vacuum space ( c=300,000km/sec). This speed is the upper limit of the fastest CME ever observed in the Solar corona, i.e. a little less than 3000km/sec. Above the limit it is necessary to include general relativity effects into the GMHDM. However, it is possible in any way to modify the GMHDM.

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

∇−−

∇+∇

+∇++∇−=

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

⎟⎠⎞

⎜⎝⎛ ∇−∇+∂∂

→

→→→→

→→→

→

→→

).()1(000

0).().(00

00).()(00000

000000

000

000

.2

21

2

VP

BVVB

GBBBP

PB

VV

t

γ

ρρ

ρ

ξ

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