Reconnection process in

Sun and Heliosphere

A.C. Das

Physical Research Laboratory

Ahmedabad 380 009

IHY school for Asia – Pacific Region, Kodaikanal, Dec.10-22, 2007

• Heliosphere – Magnetosphere of our sun

•Interaction of Solar wind and the interstellar medium

•Heliopause: Balance between interstellar medium and solar wind pressure

•Termination shock: Solar wind becomes subsonic at this point

•Interplanetary medium moving in opposite direction becomes subsonic as it collides with heliopause – Bow shock

•Solar wind, solar flares and coronal mass ejection – sends materials and fields into the heliosphere

•Heliospheric current sheet, ripple in the heliosphere

Solar Flares

Coronal Mass Ejections

And Closed Magnetic loop structure in helispheric current sheet

Generated by a powerful plasma process – Reconnection of magnetic field lines

Giovaneli – importance of neutral point in Solar Flares

Dungey – Developed a radically different model in physics of magnetosphre

Following his concept, we will describe the process of reconnection

Essential to introduce some basic understanding of

plasma flow and magnetic field structure.

In absence of plasma valocity, Ohm’s law

EJ

where the magnetic field is secondary and can be calculated from Ampere’s law c Curl B

= 4 For MHD, velocity v and the magnetic field B are primary and J and E

can be calculated from

.

J

Jc

BCurl4

c

BvJE

Now for large , can be neglected and electric field is then driven by the

velocity and magnetic field. Ratio of the 2nd term to the first term on the right

hand side of (5) defines the magnetic Reynold number given by

/J

vL

L

B

L

vBRm

2/

is extremely large (~1010) in solar atmosphere mR

Basic Reconnection Process

Depends on

(1)Topology of the magnetic field

(2)Motion of plasma near the neutral point

Magnetic field lines are anti-parrellel

One neutral point, with limiting field lines – Separatrix.

Two are going in and two are coming out

Plasma behaviour in absence of pressure E+1/C (VxB) = 0

Field lines moving from both sides

They remain field lines. Electric field.

Current enhances, But no reconnection.

Reconnection-consequence of the break-down of frozen-in-field approximation.

May be caused because of high current density

Finite Resistivity

A different scenario

A pair of inflowing field lines become limiting field lines and then immediately after that they form outflowing field lines.

Permits

Limiting field lines to cut at neutral point and then reconnect to form a different set of field lines.

Possible because of violation of frozen in approximation.

This is reconnection in pictorial form

Diffusion, and Reconnection

In thin region diffusion is substantial

Magnetic Induction becomes.

t

BB2

In one dimension

t

Bx,

2

2

z

Bx

where Bx is the magnetic field along x-direction and z is the vertical direction as shown in Figure 1.2.

Solution

Current along y direction

Magnetic field lines are in opposite direction around z=0

Magnetic flux from above as well as from below get dumped at

the separatrix feeding the current.

Field gradient decreases, diffusion slows down

process becomes unproductive.

Need to introduce u from both sides.

Can maintain large current

Not physical, unless there is an outflow

Finally reconnection takes place with an outflow

Similar to the picture presented earlier by Dungey.

Important Reconnection Models (Steady State) – MHD Theory

Sweet-Parker Model:

-Magnetic field are anti-parrellel

-Plasma is incompressible

-Plasma flow from both sides with u, current sheet length l and width d.

-Conservation of Mass

ul=vd….. (10)

(consequence of . v = 0

Momentum balance – External magnetized

Internal field free

8/2Bpp o

P is the pressure on the central plane where the magnetic field is almost zero.Po-pressure outside, where the magnetic field is B.

Petschek ModelSP model – large l

No large rate of Reconnection because u=(d/l) va

Petschek pointed out

In MHD flow in the outer region,

Possible that two standing MHD wave front can be maintained – fronts are shocks

Diffusion region can be matched to a region of standing waves.

a – the half angle of the exit flow or the angle of slow shock such that it remains stationary in the flow

In Petschek Model,

u, B are uniform

And Electric field also is uniform

Therefore BuuB

B

As a-increases, u has to increase and then B decreases in the diffusion region and becomes less than

This is achieved by rotating the magnetic field vector towards the normal.

mA Rvu ln/)4/(

Vasyliunas obtained upper limit

Spontaneous reconnection or Patchy Reconnection

Tearing mode instability

Growth rate can be estimated shown below:

We have seen that the growth rate depends on the width of the current sheet and conductivity.

Normal component of the magnetic field. Bn

Electron Tearing mode disappears.

However, ion-tearing mode can be present.

But has limitation on magnetic field range.

External Source – LH turbulence

Enhance the growth rate.

Observational Evidence of the magnetic

Reconnection in solar flares

Top left side Right bottom

Cusped shaped loop structure, Hard X-ray telescope in Yohkoh

Helmet streamer etc. Hard X-ray loop top above

Plasmoid ejection soft X-ray bright loop

Schematic view of Impulsive flare.

Region of acceleration of

particles.

Loop-top Hard X-ray

source above

Soft X-ray bright loop

During SXR loop

Discovery of loop top

HXR

-Made it possible

-Unifying two classes of

flare LDE and impulsive

flare

-Unifying model

Numerical Simulation of reconnection between emerging flux and coronal field

Formation of magnetic island that are ejected out of the current sheet.

Localized resistivity seems to be essential .

Tearing mode instability.

More realistic simulations

Both temperature and density evolution leading to reconnection and island information.

Again localized resistivity appears to be very important for fast reconnection.

Problem of Scale Matching

Two important aspects-unanswered.

(1) Local Enhancement of Magnetic Diffusion – a conjecture

(2) Enormous gap of scale sizes – macro and micro features.

• Scale-size ofthe anomalous resistivity

= i10 m

i; Ion Larmor radius

• Scale size of a flare: 104 km !

; Thickness of the current sheet

Interesting turbulent structure in outflow

MHD-simulation of turbulent reconnection

Structures of different scales and intensities are seen.

Solar Maximum Mission (SMM)

Observation of evidence of Reconnection of previously open magnetic

structure.

-Appearing as pinching of helmet streamers followed by release and

acceleration of a large u or v-shapped structure.

-Observed sequence of events consistent with reconnection across the

heliospheric current sheet between previously open field lines and creation

of detached magnetic structure.

-Coronal disconnection events would return previously open flux to sun as

closed field arches.

-Internal magnetic reconnection can also take place within the flux rope. As

the flux rope field lines are sheared, oppositely directed field lines are

generated which press together and reconnect.

Satellite observation of the Heliospheric

current sheet shows

-Internal structure of the sector boundaries is very complex with many

directional discontinuities in mag field.

-Implies heliospheric current sheet is not a single surface – constantly

changing layer with a varying number of current sheets.

-Studied magnetic reconnection caused by resistive tearing mode

instabilities, multiple current sheets – 2D MHD simulation.

-Results: Complex unsteady reconnection

-NL limits, formation of islands or plasmoids.

-Suggest: Occurrence of multi-direction discontinuities in the heliosphere.

-May be associated with the magnetic islands and plasmoids – caused by

Reconnection.

Magnetic Reconnection is the underlying driver of giant explosive releases of magnetic energy in the Sun’s atmosphere that are observed as solar flare or CMEs.

Many compelling observational evidences for reconnection which support reconnection model of solar flares are presented.

Numerical simulation suggests that the localized resistivity is necessary for magnetic reconnection.

There is still an enormous gap between the microscale of anomalous resistivity and the size of solar flares.

MHD turbulence model of reconnection shows interesting features in various cases and may play an interesting role in solving the scale-matching problem.

Summary