“Multiple small-scale magnetic reconnections inside post-CME

A. Bemporad – “Multiple small-scale magnetic reconnections inside post-CME Current Sheets”

“4th CESP Meeting”, 30 September – 2 October 2009, Bairisch Kölldorf, Austria

“Multiple small-scale magnetic reconnections inside post-CME Current Sheets: a possible solution to inconsistencies

between theory and observations”

A. BemporadINAF – Turin Astronomical Observatory

INAF – Italian NationalAstrophysics Institute

OATo – Turin Astro-nomical Observatory

ASI – ItalianSpace Agency



Outline

• Short history of magnetic reconnection; present open problems in magnetic reconnection theory;

• A proposed theoretical solution: plasma turbulence;

• UVCS observations: plasma turbulence in a post-CME Current Sheet;

• Data interpretation: turbulence due to reconnection at -scopic scales;

• Discussion & conclusions.



Magnetic reconnection: the early history

1908: discovery (G.E. Hale) of magnetic fields in sunspots1910’s – 1940’s: MHD yet to be discovered, Sun described by hydrodynamic1942 - 1943: born of MHD (H. Alfvén): frozen-field theorem, Alfvén waves

1947: first electromagnetic theory of flares (R. Giovanelli): sunspot’s field cancels at a neutral pointneutral point, where electric fields can accelerate particles and drive currents → “…basis of an explanation of solar flares” (Giovanelli, 1947)

(Giovanelli, MNRAS, 1947)

1950’s: non-0 resistivity allows the topology of magnetic field to change near the neutral point. The therm magnetic reconnectionmagnetic reconnection is coined by J. Dungey: the neutral point is site of a “discharge” whose effect “is to ‘reconnect’ the line forces” (Dungey, 1958)

(Dungey, 1959)



Sweet & Parker model (1956-1957)First 2D reconnection model proposed by P. Sweet (1956) and published later by E. Parker (1957). The model assumes a diffusion region L >> d, then

(Sweet, Proc. IAU Symp. n°6, 1958)

L

d

vin vin

vout

vout

1) Mass flux conservation:

dLvvdvLv inoutoutin

dv

d

B

d

Bv

Bt

B

inin

2

2 )1(

Aoutin

out vB

vB

v

22

1 22

2) Induction equation in the diffusive limit:

3) Energy conservation:

Lv

SS

v

L

vv AAAin ;

Sweet & Parker model problem (’60):Inferred reconnection rate is too smallvA ~ 108 cm/s; S~1013 → rec ~ 107 s vs flare ~ 102 s !



Petschek model (1963)Proposed by H. Petschek (1963, published in 1964) try to solve the problem by changing the reconnection geometry: the diffusion region is compact (L ~ d)

L’dvin vin

vout

vout

• Equations for the diffusion region identical, but L is replaced by L’ << L

• Plasma is accelerated through 2 slow mode shocks (SMSs)

• Petschek found a limit on L’ by imposing the SMSs stability

;'

' L

L

S

v

L

vv AAin

S

v

S

vv

S

vvS

S

LL AA

MAXinA

in lnln

ln' 2

Petschek model problems (’80):1) Not self consistent: steady state not reached with uniform classical Spitzer resistivity c → larger in the DR is needed!2) Spitzer c applies only for sub-Dreicer E fields → not the case for flares where involved E > Ed

Non-uniform “anomalous” resistivity * >> c needed!



Present: big problems in magnetic reconnection theory

The anomalous resistivity (* ~ 106 – 107 c):• is needed in simulations in order to achieve a steady-state fast Petschek reconnection;• has been observed in laboratory plasma experiments;• is not even sufficient to explain the huge gap between values of

mGB

Tvr i

gi

TiL 101

)(10 2

mDL CSflare

87 1010

122/392

0

10110 smTen

m

eie

ec

msmvd inCSCS 65121211 10101010

and values inferred for the stationarity of post-CME CSs

while tipically the size of flares and the observed thickness of post-CME CSs are

so, how can we fill this huge scale gap?so, how can we fill this huge scale gap?

2)2) in order to produce * the CS thickness must be as small as 1)1) what’s the physical explanation for this enhanced resistivity?what’s the physical explanation for this enhanced resistivity?

The existence of The existence of * poses at least 2 important questions:* poses at least 2 important questions:

1276* 1010 sm



The starting idea: CS fragmentation

Paradigm shift of CS structure: theory and simulations demonstrate that the classical Sweet-Parker CS (left) becomes unstable via tearing, leading to a fragmented topology with many small-scale magnetic islands → plasma turbulence (right)

(Aschwanden 2002)

CME models predict the formation via magnetic reconnection of an elongated post-CME vertical Current Sheet

(Forbes & Priest 1995)



Turbulent CS modelsStarting from this idea, many turbulent reconnection models have been proposed (plasma turbulence → anomalous resistivity)

Plasmoid-induced reconnections form a fractal CS via successive tearing and coalescence instabilities; the many magnetic islands connect macro- and micro-scopic scales (Tajima & Shibata 1997, Shibata & Tanuma 2001)

Fractal Current SheetsFractal Current Sheets Stochastic magnetic fieldsStochastic magnetic fields

Fluctuating magnetic fields lead to micro-Sweet&Parker type reconnection events; a distinction is made between local and global reconnection events (resistivity, rec. rate, etc…; Lazarian & Vishniac 1999, Kim &Diamond 2001)

Is it possible to observe turbulence in post-CME CSs?Is it possible to observe turbulence in post-CME CSs?



• Post-CME CSs turbulence can be induced by macroscopic processes (tearing instability, plasmoid formation/ejection), but also by microscopic processes (current aligned instabilities);

• If the CS plasma is really turbulent, non-thermal line broadening is expected from spectroscopic observations;

• In the last few years, very high temperature (T~5×106 K) FeXVIII 974.8Å coronal emission detected by UVCS has been interpreted as a signature of post-CME CSs;

• The FeXVIII 974.8Å line (Tmax~ 5×106 K) is suitable to study turbulences in CSs (good statistic), but a study on post-CME CSs was missing so far.

Turbulence in CSs: observational feasibility

Line ofLine ofSightSight

Which event can we select for this study?Which event can we select for this study?

(Forbes & Priest 1995)

(Isobe 2003)



Post-CME CS temperature evolution

26/11/2002 CME is a good candidate event also for the study of line profiles because:• we have ~2.3 days of continuous observ. (→ as many counts we want)• the CS was on the plane of the sky (→ negligible outflow LOS comp.)

• Result: TResult: Tee(CS)(CS) ~ 8·106K → 3.5 ·106K in ~ 2.3 days ; TTee(COR)(COR) ~ 1.3 ·106 K

nnee(CS)(CS) ~ 7 ·107 cm-3 constant (D ~ 104 km) ; nnee(COR)(COR) ~ 107 cm-3 • Result:Result: adiabatic compression cannot account for plasma heating → other process

UVCS slit

(Bemporad et al. 2006)

2002/11/26, 19:30



Post-CME turbulent velocity evolution

• Each line profile is an average over ~ 2.7 hours of observations (peak ~103 counts, Δn/n ~ 3-4%)

→ very good statistic

• Result: continuous decreaseResult: continuous decrease of turbulent speed vturb from ~ 60 km/s to ~ 30 km/s

• Result:Result: Δ ~ 0.1 Å in ~ 2.3 days

How can we explain the observed:How can we explain the observed:1) Post-CME high T emission?2) Post-CME plasma turbulence?3) Time evolution (i.e. decay) of both?

Fe

Beeffturb m

kTTv2

(Bemporad 2008)

Teff~107 K



(from Lin et al. 2005)

Going from macro- to -scales

dv

dvlv

inloc

outin

*

In the following I’ll test the feasibility of this scenario: observed high T plasma heated by reconnection occurring locally at -scales in the macroscopic CS

The idea is to write usual equations for locallocal reconnections

Using vvturbturb to estimate the local anomalous resistivity ** I’ll try to derive informations on the -CSs-CSs.But how can I compute *?

mass conservation (incompressible fluid)

balance between inflow and diffusion



Estimate of : current-aligned -instabilities At small scales turbulence may be induced via current – aligned instabilities

leading to anomalous resistivity. The main candidates are:

turbe

pee

ISe

eIA w

en

m

en

m2

0*2

0

*

1) Ion-Acoustic instability:1) Ion-Acoustic instability: excited by resonant interaction of drifting electrons or ions with the electric field oscillations of ion-sound waves. Usually efficient only for Te >> Ti, but for strong currents may develop even for Te ~ Ti .

Recent simulations concluded that IA-instability could be important in reconnecting CS (Wu et al. 2005, Buechner & Elkina 2006, Karlicky & Barta 2008).

(Birn & Priest 1972)

turbLHD

pe

e

e

LHDe

eLHD w

en

m

en

m

2

20

*20

*

22 /1 epe

piLHD

2) Lower-Hybrid Drift-instability:2) Lower-Hybrid Drift-instability: driven by drifts associated with strong pressure gradients. Is efficient even for Te < Ti, but was thought to be localized at the edge of the current layer and uneffective at the central region. More recent simulations predict that longer-wavelength LHD modes can penetrate in the central region (see e.g. Silin & Buechner 2003, Daughton et al. 2004, Ricci et al. 2005)



Given the observed turbulent speed we may estimate:

1) Fraction of turbulent energy density: eBeturbpeturb Tknvmnw 221 2

turbe

pee

ISe

eIA w

en

m

en

m2

0*2

0

*

turb

LHD

pe

e

e

LHDe

eLHD w

en

m

en

m

2

20

*20

*

22 /1 epe

piLHD

Kinetic ener-gy increasek = (v2/2)

Thermal ener-gy increase

t = (2nekTe)

1/2

1/2

Work byLorentz force

v·(j×B)

Ohmic dissip. j2/ BMCS

vflow

Estimate of MCS and CS parameters

Ion-acoustic instability: Lower-hybrid drift instability:

2) If the observed turbulence is due to plasma micro-instabilities, anomalous resistivity * can be computed in the hypothesis of

*

Magneticenergy

um = B2/2Reconnection

3) MCS outflow velocity and magnetic field from an energy balance:

4) By assuming vout ~ vflow and vin ~ vturb it ispossible to estimate the CSs sizes d, l

dv

dvlv

inloc

outin

* d, l



Results

IA instability:* ~ 2-3·105 m2/s ~ 0.3-0.4 Ω mlCS ~ 80 mdCS ~ 12 m

LH instability:* ~ 2-3·108 m2/s ~ 300-400 Ω mlCS ~ 90 kmdCS ~ 14 km

vin ~ 40-50 km/svout ~ 250-350 km/s

MA ~ 0.15-0.16

B(MCS) ~ 1 G(Bemporad 2008)



Energy balance: required number density of -CS

DLnlvB

P CSinMCS

CS22

0

2

82

221

LVf

P intMCS

DlBfv

V

DlBfn

MCS

t

in

in

MCS

tCS 22

0

22

0

22

But how many how many -CS-CS we need? Let’s consider inside the macro-CS a box with volume L2D; the power dissipated by -CSs with number density nnCSCS is

At the same time the power required to heat the coronal plasma entering the macro-CS through 2L2 is

2l

2d

MCSCS PP

By assuming B ~ 1 G and D ~ 104 km we get:

• Ion-acoustic instability: 10101010 -CS-CS in a volume of (104)3 km3

• Lower-hybrid drift instability: 101044 -CS-CS in the same volume

D

L2L2



Macro-CS broadened by turbulent reconnections

Lazarian & Vishniac (1999): if in a turbulent CS m is injected on a scale length l with velocity v, the MCS thickness D is

22/1)( AvvlHD where H > le is the MCS length and vA is the Alfvén speed.

In a volume DL2 there are nCS · DL2 micro-CS, the energy is injected over a surface nCS · 8l 2 · DL2, hence over a length

3/8

3/123/4 2222

A

turbCSCS v

vlnHDDnHlSl

where we assumed v ~ vturb. With values given above for nCS , l, vturb and vA and by assuming H ~ hUVCS ~ 0.7 Rʘ it turns out that

D ~ 1.3 x 104 km

in very good agreement with previous estimates of MCS thickness from white light data!(Isobe 2003)



Macro vs. micro

At microscopicmicroscopic levels:

• d ~ 10 m – 10 km• l ~ 80 m – 90 km (MA ~ 0.15)• vin,loc ~ 40 – 50 km/s• vout,loc ~ 250 – 350 km/s• loc ~ 105 – 108 m2/s• nCS ~ 104 – 1010 CS/(1012 km3)

At macroscopicmacroscopic levels:

• D ~ 104 – 105 km• L ~ 105 – 106 km (if MA ~ 0.1)• vin,glob ~ 10 – 50 km/s• vout,glob ~ 500 – 1000 km/s• glob ~ 1010 - 5·1011 m2/s ~ 104 – 6·105 Ω m

??????

Is it possible to reconcile local micro-CS and global macro-CS reconnections?

We need to introduce an ad hoc very large resistivity (that need to be explained!) to reproduce observations

Is it possible to explain observations, once it is assumed

that in macro-CS reconnection events at micro-levels are occurring



Post-CME hard X-ray emission

UVCS slit

• More recent results: during and after the same event RHESSI observed for 12 h a hard X-ray source, moving from 0.1 to 0.3 Ro, with peak T ~ 107 K.• Thermal energy content in X-ray source more than 10 times larger than in the CS → could be alternatively the source of hot CS plasma observed by UVCS ……BUT:BUT:

(Saint-Hilaire et al. 2009)

1) How heat transport occurs from 0.2 to 0.7 Ro through the turbulent CS medium?2) X-ray source starts ~ 4 h before the CME start time → not post-CME reconnection!3) Decays 8 h after the CME → cannot explain 2.3 days of high T UVCS emission…



Summary

• The alternative interpretation that energy is produced at the base of the CS and then ejected up to UVCS altitude is possible, but this interpretation leaves many other questions unsolved.

• Magnetic reconnection theory is at the base of interpretations of solar flares and CMEs; nevertheless this process is not yet fully understood.

• Theoretical problems: 1) needed anomalos resistivity * >> c and 2) huge scale gap between expected and observed CS sizes. Turbulent CS models try to solve these problems connecting small and large scales.

• But, is turbulence really present in post-CME CSs? Answer: yes, as inferred from FeXVIII profiles observed by UVCS after CMEs → turbulence evolution in post-CME CS.

• Turbulent velocity → turbulent energy density → anomalous resistivity in the macro-CS due to IA or LHD instabilities.

• Assumption: small scale reconnections occurs in the macro-CS → sizes, reconnection rates and number density of -CS → energy balance, macro-CS stationarity (pressure balance) and much broader observed thickness explained!

• In this scenario: observed T and vturb decrease due to progressive dissipation of B in MCS

• Existence of -CSs is not demonstrated here, but this is a valid working hypothesis.



Thank you!

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“Multiple small-scale magnetic reconnections inside post-CME