1. 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. Bemporad INAF – Turin Astronomical Observatory INAF – Italian National Astrophysics Institute OATo – Turin Astro- nomical Observatory ASI – Italian Space Agency

2. A. Bemporad – “Multiple small-scale magnetic reconnections inside post-CME Current Sheets” “4th CESP Meeting”, 30 September – 2 October 2009, Bairisch Kölldorf, Austria 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.

3. A. Bemporad – “Multiple small-scale magnetic reconnections inside post-CME Current Sheets” “4th CESP Meeting”, 30 September – 2 October 2009, Bairisch Kölldorf, Austria Magnetic reconnection: the early history 1908: discovery (G.E. Hale) of magnetic fields in sunspots 1910’s – 1940’s: MHD yet to be discovered, Sun described by hydrodynamic 1942 - 1943: born of MHD (H. Alfvén): frozen- field theorem, Alfvén waves neutral point 1947: first electromagnetic theory of flares (R. Giovanelli): sunspot’s field cancels at a neutral point, where electric fields can accelerate particles and drive currents → “…basis of an explanation of solar flares” (Giovanelli, 1947) (Giovanelli, MNRAS, 1947) magnetic reconnection 1950’s: non-0 resistivity allows the topology of magnetic field to change near the neutral point. The therm magnetic 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)

4. A. Bemporad – “Multiple small-scale magnetic reconnections inside post-CME Current Sheets” “4th CESP Meeting”, 30 September – 2 October 2009, Bairisch Kölldorf, Austria 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 v in v out 1) Mass flux conservation: 2) Induction equation in the diffusive limit: 3) Energy conservation: Sweet & Parker model problem (’60): Inferred reconnection rate is too small v A ~ 10 8 cm/s; S~10 13 →  rec ~ 10 7 s vs  flare ~ 10 2 s !

5. A. Bemporad – “Multiple small-scale magnetic reconnections inside post-CME Current Sheets” “4th CESP Meeting”, 30 September – 2 October 2009, Bairisch Kölldorf, Austria 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’ d v in v out 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 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 > E d Non-uniform “anomalous” resistivity  * >>  c needed!

6. A. Bemporad – “Multiple small-scale magnetic reconnections inside post-CME Current Sheets” “4th CESP Meeting”, 30 September – 2 October 2009, Bairisch Kölldorf, Austria Present: big problems in magnetic reconnection theory The anomalous resistivity (  * ~ 10 6 – 10 7  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 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? 2) 2) in order to produce  * the CS thickness must be as small as 1)what’s the physical explanation for this enhanced resistivity? 1) what’s the physical explanation for this enhanced resistivity? The existence of  * poses at least 2 important questions:

7. A. Bemporad – “Multiple small-scale magnetic reconnections inside post-CME Current Sheets” “4th CESP Meeting”, 30 September – 2 October 2009, Bairisch Kölldorf, Austria 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)

8. A. Bemporad – “Multiple small-scale magnetic reconnections inside post-CME Current Sheets” “4th CESP Meeting”, 30 September – 2 October 2009, Bairisch Kölldorf, Austria Turbulent CS models Starting 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 Sheets Stochastic 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?

9. A. Bemporad – “Multiple small-scale magnetic reconnections inside post-CME Current Sheets” “4th CESP Meeting”, 30 September – 2 October 2009, Bairisch Kölldorf, Austria 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~5×10 6 K) FeXVIII 974.8Å coronal emission detected by UVCS has been interpreted as a signature of post-CME CSs; The FeXVIII 974.8Å line (T max ~ 5×10 6 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 of Sight Which event can we select for this study? (Forbes & Priest 1995) (Isobe 2003)

10. A. Bemporad – “Multiple small-scale magnetic reconnections inside post-CME Current Sheets” “4th CESP Meeting”, 30 September – 2 October 2009, Bairisch Kölldorf, Austria 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: T e (CS)T e (COR) Result: T e (CS) ~ 8·10 6 K → 3.5 ·10 6 K in ~ 2.3 days; T e (COR) ~ 1.3 ·10 6 K n e (CS)n e (COR) n e (CS) ~ 7 ·10 7 cm -3 constant (D ~ 10 4 km); n e (COR) ~ 10 7 cm -3 Result: Result: adiabatic compression cannot account for plasma heating → other process UVCS slit (Bemporad et al. 2006) 2002/11/26, 19:30

11. A. Bemporad – “Multiple small-scale magnetic reconnections inside post-CME Current Sheets” “4th CESP Meeting”, 30 September – 2 October 2009, Bairisch Kölldorf, Austria Post-CME turbulent velocity evolution Each line profile is an average over ~ 2.7 hours of observations (peak ~10 3 counts, Δn/n ~ 3-4%) → very good statistic Result: continuous decrease Result: continuous decrease of turbulent speed v turb from ~ 60 km/s to ~ 30 km/s Result: Result: Δ ~ 0.1 Å in ~ 2.3 days 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? (Bemporad 2008) T eff ~10 7 K

12. A. Bemporad – “Multiple small-scale magnetic reconnections inside post-CME Current Sheets” “4th CESP Meeting”, 30 September – 2 October 2009, Bairisch Kölldorf, Austria (from Lin et al. 2005) Going from macro- to  -scales 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 local The idea is to write usual equations for local reconnections v turb  *  -CSs Using v turb to estimate the local anomalous resistivity  * I’ll try to derive informations on the  -CSs. But how can I compute  *? mass conservation (incompressible fluid) balance between inflow and diffusion

13. A. Bemporad – “Multiple small-scale magnetic reconnections inside post-CME Current Sheets” “4th CESP Meeting”, 30 September – 2 October 2009, Bairisch Kölldorf, Austria Estimate of  : current-aligned  -instabilities At small scales turbulence may be induced via current – aligned instabilities leading to anomalous resistivity. The main candidates are: 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 T e >> T i, but for strong currents may develop even for T e ~ T i. 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) 2) Lower-Hybrid Drift-instability: 2) Lower-Hybrid Drift-instability: driven by drifts associated with strong pressure gradients. Is efficient even for T e < T i, 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)

14. A. Bemporad – “Multiple small-scale magnetic reconnections inside post-CME Current Sheets” “4th CESP Meeting”, 30 September – 2 October 2009, Bairisch Kölldorf, Austria Given the observed turbulent speed we may estimate: 1) Fraction of turbulent energy density: Kinetic ener- gy increase  k =  (  v 2 /2) Thermal ener- gy increase  t =  (2n e kT e ) 1/2 Work by Lorentz force v·(j×B) Ohmic dissip. j 2 /  B MCS v flow 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 ** Magnetic energy u m = B 2 /2  Reconnection 3) MCS outflow velocity and magnetic field from an energy balance: 4) By assuming v out ~ v flow and v in ~ v turb it is possible to estimate the  CSs sizes d, l d, l

15. A. Bemporad – “Multiple small-scale magnetic reconnections inside post-CME Current Sheets” “4th CESP Meeting”, 30 September – 2 October 2009, Bairisch Kölldorf, Austria Results IA instability:  * ~ 2-3·10 5 m 2 /s ~ 0.3-0.4 Ω m l CS ~ 80 m d CS ~ 12 m LH instability:  * ~ 2-3·10 8 m 2 /s ~ 300-400 Ω m l CS ~ 90 km d CS ~ 14 km v in ~ 40-50 km/s v out ~ 250-350 km/s M A ~ 0.15-0.16 B(MCS) ~ 1 G (Bemporad 2008)

16. A. Bemporad – “Multiple small-scale magnetic reconnections inside post-CME Current Sheets” “4th CESP Meeting”, 30 September – 2 October 2009, Bairisch Kölldorf, Austria Energy balance: required number density of  -CS how many  -CS n  CS But how many  -CS we need? Let’s consider inside the macro-CS a box with volume L 2 D; the power dissipated by  -CSs with number density n  CS is At the same time the power required to heat the coronal plasma entering the macro-CS through 2L 2 is 2l 2d2d By assuming B ~ 1 G and D ~ 10 4 km we get: 10 10  -CS Ion-acoustic instability: 10 10  -CS in a volume of (10 4 ) 3 km 3 10 4  -CS Lower-hybrid drift instability: 10 4  -CS in the same volume D L2L2 L2L2

17. A. Bemporad – “Multiple small-scale magnetic reconnections inside post-CME Current Sheets” “4th CESP Meeting”, 30 September – 2 October 2009, Bairisch Kölldorf, Austria 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 where H > l e is the MCS length and v A is the Alfvén speed. In a volume DL 2 there are n  CS · DL 2 micro-CS, the energy is injected over a surface n  CS · 8l 2 · DL 2, hence over a length where we assumed v  ~ v turb. With values given above for n  CS, l, v turb and v A and by assuming H ~ h UVCS ~ 0.7 R ʘ it turns out that D ~ 1.3 x 10 4 km in very good agreement with previous estimates of MCS thickness from white light data! (Isobe 2003)

18. A. Bemporad – “Multiple small-scale magnetic reconnections inside post-CME Current Sheets” “4th CESP Meeting”, 30 September – 2 October 2009, Bairisch Kölldorf, Austria Macro vs. micro microscopic At microscopic levels: d ~ 10 m – 10 km l ~ 80 m – 90 km (M A ~ 0.15) v in,loc ~ 40 – 50 km/s v out,loc ~ 250 – 350 km/s  loc ~ 10 5 – 10 8 m 2 /s n  CS ~ 10 4 – 10 10  CS/(10 12 km 3 ) macroscopic At macroscopic levels: D ~ 10 4 – 10 5 km L ~ 10 5 – 10 6 km (if M A ~ 0.1) v in,glob ~ 10 – 50 km/s v out,glob ~ 500 – 1000 km/s  glob ~ 10 10 - 5·10 11 m 2 /s ~ 10 4 – 6·10 5 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

19. A. Bemporad – “Multiple small-scale magnetic reconnections inside post-CME Current Sheets” “4th CESP Meeting”, 30 September – 2 October 2009, Bairisch Kölldorf, Austria 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 R o, with peak T ~ 10 7 K. Thermal energy content in X-ray source more than 10 times larger than in the CS …BUT: → could be alternatively the source of hot CS plasma observed by UVCS …BUT: (Saint-Hilaire et al. 2009) 1)How heat transport occurs from 0.2 to 0.7 R o 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…

20. A. Bemporad – “Multiple small-scale magnetic reconnections inside post-CME Current Sheets” “4th CESP Meeting”, 30 September – 2 October 2009, Bairisch Kölldorf, Austria 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 v turb decrease due to progressive dissipation of B in MCS Existence of  -CSs is not demonstrated here, but this is a valid working hypothesis.

21. A. Bemporad – “Multiple small-scale magnetic reconnections inside post-CME Current Sheets” “4th CESP Meeting”, 30 September – 2 October 2009, Bairisch Kölldorf, Austria Thank you!