Theoretical perspectives on the study of coronal dynamic phenomena

Adv. Space Rer. Vol. 17. No. 415. pp. (4/5)251-(4/5)259. 1996 Copyright 0 1995 COSPAR Printedin Great Btitain. All rights resewed. 0273-l 177/96 $9.50 + 0.00

0273-l 177(95)00579-X

THEORETICAL PERSPECTIVES ON THE STUDY OF CORONAL DYNAMIC PHENOMENA B. V. Somov

Astronomical Institute, Moscow State University, Universitetskii Prospekt 13, Moscow B-234 119899, Russia

ABSTRACT New data on dynamic theory

phenomena

of cosmic plasma.

in the solar corona

Reconnection

netic energy’ to kinetic and thermal accelerated

particles.

reconnection

new outstanding

questions

of the so-called

energies of the plasma, to hard electromagnetic

These effects occur in the solar atmosphere

and flare-like events, coronal transients ory are reviewed,

create

plays a key role in conversion

and new problems

and mass ejections. are pointed

of electric currents in the corona.

out.

and manifest

for the

‘free mag-

radiation

themselves

and

as flares

Some new results of reconnection

The most important

the-

of them is magnetic

This effect can be significant, for example,

in active

regions with observed large shear but it is not studied well yet. In order to explain the acceleration of protons outside

and heavier

ions up to several GeV in a time of < 0.1 s, the transverse

the reconnecting

current

efficiently can ‘lock’ nonthermal

sheet must be taken into account. ions in the current

direct electric field. Evolutionarity yet either. magnetic

Another expulsion,

well-known magnetic

by the presence of plasma regions with considerably

field

electric

field

by the

current sheets are not investigated

which can play a role in dynamics

different from Parker’s

electric

sheet, thus allowing their acceleration

and stability of reconnecting

phenomenon,

The transverse

of coronal plasma,

buoyancy.

different conductivity

is electro-

This force is induced in the corona.

INTRODUCTION According magnetic

to the present

prominences planetary

observational The process

As a consequence, and theoretical of magnetic

is especially X-ray

and interacts

The corona

of a magnetic

reconnection,

i.e. interaction

dominated

and mass ejections

field-plasma

into inter-

field determines

system

by

bright points, these

are promising

from

fluxes having antiparallel

com-

2/). of magnetic

(see /3/).

with an old (pre-existing)

flux. Evidently,

microflares,

in lower corona,

can

in such very small active regions. is well dominated

place in a large-scale, coronal transient

by magnetic

pre-existing,

magnetic

field-plasma

interaction

field configuration

and mass ejection into the interplanetary

solar wind can be responsible

Finally,

coronal transients

(like X-ray

It is clear that the magnetic

points of view (e.g., /l,

significant

are, in general,

Thi s p recess really determines many phenomena. For bright points are regions where a new magnetic flux emerges from under the pho-

tosphere

be generated

researches

and corona

processes in solar plasma

and flares in the solar atmosphere,

example,

dynamics

the chromosphere

space) have a similar physical nature.

phenomena.

ponents,

concept,

fields. Many steady and non-steady

for a coronal non-steady

medium.

character

/4/.

Coronal

streamers

take

which then may be involved as a Reconnection

driven by the

and plays the key role in a global

of plasma in the corona /5/. flares and flare-like processes

in the solar atmosphere (4/5)25 1

are the well known example

of the

B. V. Somov

(4/5)252

reconnection

process.

To what extent is this true ? To understand

have for a long time been placed on the process of magnetic papers in /6, 7/). Th e current RECONNECTION: Flare

scientists

state of the problem

NEW RESULTS

know that,

before

is summarized

AND NEW

the Yohkoh

the nature

reconnection

mission,

of flares, great hopes

(see the review of early

below.

QUESTIONS

magnetic

reconnection

as a mechanism

energy release in solar flares was a matter

of strong debate and doubts, where both theoreticians

observers

often based on belief rather

seemed to have strong feelings,

or observational argued

that

accumulated

Referring

to observational

of reconnecting

current

as well as provide the required

and explain of XUV

grounds.

the models

other observational

lines

interaction

although

The above, oversimplified,

arguments

an advocate

particle

sheets in the corona?

over the required field-aligned

timescale?

electric

Do we take into

broadening structure

in the future

overlooked

and missing

Reconnection Generally

reconnecting

current

reconnect

in the corona,

to high energies?

or something

essential

is

Independent

prolongated

flares.)

Moreover,

and/or inside it as well as they are generated

of their origin, the electric

with magnetic

the same with currents

currents

field lines (see Chapter

as with magnetic

ways as before a

due to upward motion of an eruptive filament.

gamma-ray

under the photosphere together

and ions) are accelerated

acting

forms,

is the role of magnetic

sheets can be created by many different

for example,

seems to be the case of high-energy are created

What

Currents

flare and during its development,

every forces.

of the

at the required level, in the required

(electrons forces

undestanding

Can energy be stored in metastable

badly?

of Electric

speaking,

How particles

It is my hope, however,

on the way to better

Can it then be dissipated

all the dynamic

the idea

sheets.

If so, how is this process accomplished?

currents?

account

/8/)

acceleration,

the non-thermal

of the large scale magnetic

issues of energy release in coronal dynamic phenomena:

current

(e.g.,

how the flare energy is

were taken as a sign of the ‘flavour’.

they will help us below and mainly

major

the theoreticians

/lo/, claimed that they had never seen any evidence in the data that supports

that the flare energy is stored in such current

that

theoretical

sheet are able to explain such as, for example,

and

than indisputable

energy release power, including

flare parameters

Th e observers,

/9/.

data analysis,

of

distributed

electric

in the corona by

in the solar atmosphere

16 in /2/). The reconnection disrupts

field lines, i.e.

(This

currents

process

them and connects

does

in different

way. Shearing

motions

the vicinity

in the photosphere

of the so-called

this kind is disrupted

and redistributed

the lines where the separatrix

surfaces

release in active regions with observed Physical

consequences

tized plasmas, However,

current

acceleration

Reeimes

Two classical Syrovatskii

are crossing

in of

process

at the separators

This effect can be significant

(the role of anysotropic

channeling

-

for energy

and current Because

closure,

conductivity etc.)

in highly-magne-

are not investigated

of large dimensions,

the current

yet.

system

So, an interruption of electric current can produce a strong for energy release in large-scale coronal dynamic phenomena

of Reconnection are generally

of a non-neutral (with transverse

and similar

IS/.

reconnection

currents

Half of each current

/2/.

cases of reconnection

data

highly-concentrated

large shear.

/7/ and the flow regime by Petschek.

observational

generate

in the solar atmosphere.

by the magnetic

some of them look really unavoidable.

with particle

a regime

surfaces

of this phenomenon

filamentary

in the corona has a huge inductance. electric field. This can be important

Different

can, in principle,

separatrix

(mainly,

distinguished:

and longitudinal

with the SMM results),

events in the solar atmosphere

neutral pinch current

sheet (CS) by

It has been shown (see /8/) that there also exists magnetic

it was suggested

takes place in non-neutral

fields) CS. In context that reconnection high-temperature

with

in flares turbulent

cotow&l Ilymmic

Phenowoa

W5)253

current sheets /8/. The problem of magnetic field evolution in active regions keeps together all the questions mentioned above. It is known that at some conditions (beginning with some critical values) the field cafedated in the the potential approximation may contain an important topological singular line - a sepafator /6, 71. Here, the 3D-reconnection process occurs. Conditions and features of this principal process are, in general, non-trivial and should be investigated in more detail (/ll/; see, however, /12, 13/). 3D-re~o~ection explains such observational signatures of solar Aares as ‘coronal explosions’ and particle acceleration /I$, 15/. Stability of Reconnecting Current Sheets Special field of researches is stability of CS. Somov and Verneta found that the transverse (perpendicular to the CS) magnetic field prevents the growth of the MHD tearing mode /X6/. In the collisionless approximation, this effect was studied in /17, 18/. It was also shown /18/ that the transverse magnetic field stabilizes the high-temperature CS during the main phase of solar flares. This effect is valid both in NfHD as well as in collisionless appro~mation. The rupture of a CS seems to be an essential mechanism for the impulsive phase of solar flares, the nature of which is studied intensively. It was shown /IS/ that plasma ~ompessi~~ty leads to the rise of the tearing instability for a reconnecting CS in the long wave region in which for an incompressible plasma the instability is absent. Longitudinal (parallel to the electric current inside the CS) magnetic field can play the role of a trigger in such a process of destabi~~ation which is of principal importance for the physics of flares and other non-steady phenomena in the solar atmosphere (see Chapter 14 in /2/). Reconnection and Particle Acceleration Longitndin&l magnetic field is also essential for the problem of particle acceleration in the reconnecting CS. Litvinenko and Somov /26/ developed an analitycal technique which allows one to reproduce the previous results (e.g., /21/) concerning the influence of the transverse field on particle motion and acceleration. This new technique also allows us to evaluate the effect of the longitudinal field. The motion of particles in non-neutral current sheets becomes regular rather than chaotic with an increase of the longitudinal magnetic fieId. The latter increases considerably the efficiency of particle acceleratian in CS /2/i Electron energization during the main phase of solar flares can be interpreted as their acceleration in the non-neutral CS. AS for ion acceleration, there is a factor that makes positively charged particles return to the RCS. It is the transverse electric field directed toward the sheet. In an exact self-consistent one-dimensional model of the current sheet due to Harris /22/, this field equals El = 2no9 ) where the magnitude of the electric charge density integrated over the sheet thickness is

On substituting (2) into [1)1 with account of the current velocity pt of electrons in the RCS, we obtain 123/

where the equation @/(8a)

= ?ak T is used, T being the plasma temperature in the RGS,

Physically, the transverse electric field outside the RCS, El, is a consequence of electric charge separation. Both electrons and protons are deflected by the magnetic field when they move out of the sheet. The trajectories of electrons, however, are bent to a greater degree owing to their smaller mass. As for much heavier ions, they stream out of the RCS almost freely, Hence the

(4/5)254 charge

B. V. Somov

separation

arises, leading to the electric field that detains the protons

in the RCS region

/22/e It is not obvious a priori that magnetic

Harris’s solution applies to current

field and finite conductivity

field, at least as a fist

sheets with nonzero

Q. It should be valid, however,,for

approximation.

transverse

small transverse

In fact all we need for calculations

magnetic

is the electric potential

(4)

4=e JEldy, which one can safely take to equal kT,

the usual value owing to spread of a cloud of charged

particles. It is clear that the charge separation of protons perpendicular RCS almost

along its plane.

mechanism

of particle

field will considerably perpendicular

that gives rise to the potential

This property

acceleration. influence

ones (Bl

is a characteristic

feature of the well known Speiser’s

It also seems obvious that even a modest

the motion

of these particles

to this field. Having made this qualitative

the energy gain rate and maximum into account

4 mainly stems from the motion

to the RCS plane. At the same time, some protons are known to leave the

remark,

energy for the protons

both the main components

because

of electromagnetic

transverse

electric

they always move almost

one can proceed

being accelerated

to calculating

in the RCS,

taking

field (Bs and Eo) and the transverse

and El).

According

to the model delineated

perpendicular

above, a positively

charged particle

ejected

from the RCS is

and moves back to the RCS. The reason for this is the electric field El, directed

quickly ‘reflected’

to the sheet, which always exists outside the RCS /22/.

It is of paramount

that the protons are ejected from the RCS almost along the magnetic field lines /21/.

importance

The transverse

electric field efficiently ‘locks’ the particles in the RCS because they always move almost in the RCS plane.

On getting

into the sheet again, the particles

are further accelerated

and the cycle repeats

itself. In order to find the properties on the particle

motion

and momentum is pl

x tip

equation

of the acceleration

mechanism,

p. According

to /21/,

<< p for such a proton.

of motion for the particle

the component Here (1

=

(5) a 11ows us to estimate

of momentum

perpendicular to the sheet component of the

Bl / Bo . The perpendicular

outside the RCS is

tpL(t)= -e Equation

we need to dwell at some length

outside the RCS. Consider a proton leaving the RCS plane with energy &

El.

the time spent by the proton between two successive interactions

with the RCS, 6t out = 3J.L~::.

2kP

eE_L

The largest energy attainable

(6)

eEl

by a particle is determined

by the condition

that the potential

(4) is

just enough to prevent the proton from leaving the RCS. In other words, the field El must cancel the perpendicular

momentum.

The energy conservation

&mnx=

gives:

4&,-P:c2+~,

where

pf c2 = [f (t&t!&,- m2 c4). Eliminating

pl

between (7) and (8), we get the sought-after

maximum

(8) energy

(9)

Coronal Dyoamic Phenomena

(4/5)255

where 4 z k I‘. Formula (9) shows that protons can actually be accelerated to GeV energies in the high-temperature RCS /8/; for instance E,,,,, z 2.4GeV provided T = lo8 K. This simple result demonstrates the possibility of efficient proton acceleration by dint of the direct electric field in the RCS. Litvinenko and Somov /23/ suggest that the extended acceleration of protons (and perhaps heavier ions) to relativistic energies during the late phase of large solar flares occurs in reconnecting current sheets, where the magnetic field lines are driven together and forced to reconnect. Such RCSs naturally form below erupting loop prominences. The time of RCS formation corresponds to the delay of the second phase of acceleration after the first, impulsive phase. An interesting feature of the mechanism considered is that neither the maximum energy nor the acceleration rate depend upon the particle mass. Hence the me~a~sm may play a role in the preferential acceleration of heavy ions during solar flares. To conclude, though MHD shocks are usually thought to be responsible for the relativistic generation of protons during the late phase of extended (gradual) gala-ray/proton flares, another mechanism-the direct electric field acceleration in RCSs-is necessary for explanation of the proton acceleration to the highest energies observed, at least in flares with strong variability of gammaemission. Of course, the same sudden mass motions that lead to formation of RCSs also give rise to strong shock waves, so the two mechanisms of acceleration can easily coexist in a single flare. Evolutionarity

of Reconnecting

Current Sheets

Remaining in the MHD appoximation, it seems to be possible to consider the question about the so-called e~l~&ut~o~a~ty /24, 25/ of a CS as a discontinuity with respect to linear magnetosonic waves. In general, if a steady-state discontinuity (for example, a fast or slow shock wave) exists in a real plasma, it must be stable with respect to decay into other discontinuities and with respect to a time-varying flow. Let us assume that a discontinuity is initially subjected to an infinitesimal perturbation. Linear waves propagating away from the discontinuity surface then arise. If the amplitudes of these waves can be determined unaml)iguously from the linearized boundary con~tions, the problem of the time evolution of an initial perturbation has a unique solution, and the discontinuity is by definition evolutionary. With respect to evolutionary discontinuities, the usual problem of stability can be formulated. If, on the other hand, the linear problem of the time evolution does not have a unique solution, then it is not legitimate to make the assumption that the initial pert~bation is small. By contrast to the usual instability, a perturbation instantaneously becomes large in the non-evolutionary discontinuity. This leads to a decay of the non-evolutionary discontinuity into evolutionary discontinuities (see Chapter 9 in 12,‘). Mathematical criterion of evolutionarity was introduced in MHD by Akhiezer et al. /24/. They considered discontinuous solutious of the 1D MHD equations: shock waves, tangential, Alfven and contact discontinuities; and they assumed that the d&continuities are subjected to an infinitesimal pert~bation at the initial instant of time, In this case the surface of the ~scontin~ty displaces, and outgoing (reflected and refracted) waves occur. Amplitudes of these waves are related by the linearized boundary conditions on the discontinuity surface, deduced in a general form by Syrovatskii 1251. They represent conservation laws of mass, momentum and energy as well as the normal component of magnetic field and the tangential component of electric field. After elimination of the value of the discontinuity displacement, these conditions are reduced to a set of equations for the amplitudes of the perturbations:

Here 6pi are the amplitudes of outgoing (reflected and refracted) waves, 6~1 are the amplitudes of incoming (incident) waves, index “j” enumerates the boundary conditions, the but coefficients Mij and Mlj are certain matrix functions of unperturbed quantities. If 6~; cannot be determined unambiguously by 6pl, then the problem on further time evolution

B. V. Somov

@IS)256

of the infinitesimal non-evolutionary.

perturbations

does not have a unique solution,

and the discontinuity

Since a physical problem must always have a unique solution,

to make an assumption Such a discontinuity

that the perturbation

cannot

of a non-evolutionary

exist in a real medium,

because

is called

it is not legitimate

discontinuity

the infinitesimal

is infinitesimal.

perturbation

leads

to an instant finite change of the initial flow. This change is the splitting of the discontinuity into other (evolutionary) discontinuities. Note that the perturbation of a non-evolutionary discontinuity is not small already the ordinary remains Thus,

in the initial

instability.

instant

of time, as distinct

Being growing exponentially,

which leads to

of an unstable

discontinuity

small during small enough period of time. the investigation

the unperturbed discontinuity unknown

Equation

parameters

solutions,

of Equation

MHD properties

of independent

(1.1)

equations

of outgoing

of outgoing

(towards the discontinuity

when the number than

of

the number amount

of

and, thus, the number

surface.

In a general

case

entropy wave, AlfvCn wave, and slow and fast waves.

However,

if the flow velocity

is larger than the normal projection

is directed

of the group velocity for

down by the flow towards the discontinuity

and it cannot

one.

On a basis of such analysis Akhiezer

et al. /24/ and Syrovatskii

across shock waves can be either larger than AlfvCn velocity than it (slow magnetosonic for other

or away fromit)

across the discontinuity

among the outgoing

a given wave, then this wave is carried be an outgoing

This happens

In the first case there is an in&rite

allowed by MHD equations:

ones, present

on

For a non-evolutionary

(10) does not have solutions.

on the flow velocity

towards the surface and its magnitude

M and, consequently,

surface.

waves) is either larger or smaller

conditions.

the system

of wave propagation

magnetosonic

on quantities

does not have a unique solution.

- boundary

waves depends

the waves of all types,

(10) gives restrictions

on both sides of the discontinuity

(amplitudes

and in the second,

The direction

(the

so-called

evolutionarity There

from a perturbation

the perturbation

shocks).

requirement

is another

For these shocks Equation

transalfvenic

shocks)

it does not.

/25/ have shown that

(fast magnetosonic

(10) has a unique

Some interesting

flow

shocks)

velocity

or smaller

solution,

consequences

but

of the

for the MHD shocks are reviewed in /2/.

condition,

does not have a solution.

besides

mentioned

If the number

above,

of outgoing

under which the system

of equations

waves is equal to the number

(10)

of independent

equations, but det (n/l;j ) = 0, th en the solution exists formally, however it turns to infinity. This means that resonant reflection and refraction take place, because the amplitudes of the outgoing waves become the outgoing

infinitely

Consequently, An expected restrictions

current

to the amplitude

be described

by linear

to the magnetic

rate in CS /26/, for example, sheet

of the incident

equations,

with reversed

currents

reconnection

problem

Evidently,

is a possible

a change of the regime of magnetic

these effects

are interesting

13 in /2/) but especially

generally

speaking,

in the physics

not only for ‘general

for laboratory

origin

case small.

and non-steady

processes

Non-evolutionarity of the current

experiments

sheet

/27, 28/.

reconnection. theory’

of magnetic

and solar flare applications.

still far from a final solution,

of steady

In this are not

can place some new

in solar active regions.

into a system of MHD slow shock waves observed in the numerical means

one.

since they

is non-evolutionary.

result of such an approach on reconnection

Such a splitting

Chapter

with respect

cannot

the discontinuity

of a reconnecting splitting

large

perturbations

reconnection

(see

Such investigations

are,

but they can provide more deep understanding related

to magnetic

reconnection

in the solar

atmosphere. Reconnection

in the photosphere

The idea that mechanism

magnetic

of prominence

reconnection formation

in the cold dense plasma

of the solar atmosphere

was put forward several years ago by many authors.

can be a The model

of prominence formation by dint of the reconnection process in the photosphere was shown to predict realistic magnetic field topologies near filaments. However, to my knowledge, no investigation has

been performed as to the value of the upward Aux

ofmatter

into the corona.

As was proven in /29/, the flux of cold plasma can be high enough to explain the filament formation in a reasonable time. This seems to be a strong argument in favour the well known Pneuman-van 3~eg~ijen-Martens model. It is shown that current sheets can be formed in the temperature minimum region in the response to the mainly horizont~ plasma flows in the photosphere. Here the reconnection efficiency is determined by the low classical (Coulomb) conductivity rather than by the turbulent conductivity, as opposed to the coronal case discussed above. As a final speculation, high-speed Rows which are predicted by the model 1291 in regions of relatively strong magnetic fields might be identified with spicules. ~L~~TROMAGNETI~

CUNDU~Tl~TY-DEPENDENT

FORCE

Another phenomenon, which can play an important part in dynamics of coronal plasma, is the force induced by the presence of plasma regions with considerably different electric conductivity (see Sec. 10.4 and Chapter 11 in /2/j. The electric field and current density are not uniform in the presence of a ‘body” with conductivity q which is not equal to that of surrounding plasma ao. In this case, the appearing Lorentz force is generally not potential. Hence it cannot be balanced by potential forces like gravity or gas pressure. This is the reason why vortex flows in the plasma mnst be generated by the Lorentz force, This electromagnetic force can contribute significantly as a part of expulsion force in prominences but it is different from well-known Parker’s ‘magnetic buoyancy’ and results in excitation of fast vortex Aows (e.g., 136, 31/) near thin threads which form the prominences. This hypothesis is confirmed by estimates of the vortex flow velocities near the threads, which form the prominences, and the matt,er density in these threads. Space observations with high resolution in EUV and soft X-ray ranges are necessary to study the dynamic effect of the electromagnetic conductivity-dependent force in the solar atmosphere. Prom a theoretical point of view the main ~ffic~ty appears when we try to solve the problem analytically since the magnetic Reynolds number is large but the usual Reynolds number is rather small (see Sec. 11.4 in /2/).

CONCLUSION Magnetic reco~lnectioll, s~o~taueo~s and/or driven by different forces, plays an important role in flares and other coronal dynamic phenomena. This idea is well confirmed by observations with the Soft X-ray Telescope (SXT) and the Hard X-ray Telescope (HXT) aboard Yohkoh (e.g., /32, 33f). However, quantitative interpretation of the reconnection process observed in the solar corona is still one of the most important perspectives on the future study of coronal dynamic phenomena with fast Sows of high-te~~~I~~ratureplasmas and with particle acceleration to high energies. REFERENCES 1. M. Dryer and E. Tandberg-H~ssen Dordrecht, 1980.

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