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“Multiple small-scale magnetic reconnections inside post-CME

“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. ASI – Italian Space Agency. OATo – Turin Astro- nomical Observatory.

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“Multiple small-scale magnetic reconnections inside post-CME

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

  2. 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 m-scopic scales; • Discussion & conclusions.

  3. 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) 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) 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

  4. Sweet & Parker model problem (’60): Inferred reconnection rate is too small vA~ 108 cm/s; S~1013 → trec~ 107 s vstflare ~ 102 s ! 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 1) Mass flux conservation: vout d 2) Induction equation in the diffusive limit: L vin vin (Sweet, Proc. IAU Symp. n°6, 1958) 3) Energy conservation: vout

  5. Petschek model problems (’80): 1)Not self consistent: steady state not reached with uniform classical Spitzer resistivity hc→ larger h in the DR is needed! 2) Spitzer hc applies only for sub-Dreicer E fields → not the case for flares where involved E > Ed Non-uniform “anomalous” resistivity h* >> hc needed! 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) • 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 vout d vin vin L’ vout

  6. The existence of h* poses at least 2 important questions: 1)what’s the physical explanation for this enhanced resistivity? 2) in order to produce h* the CS thickness must be as small as while tipically the size of flares and the observed thickness of post-CME CSs are so, how can we fill this huge scale gap? Present: big problems in magnetic reconnection theory • The anomalous resistivity (h* ~ 106 – 107hc): • 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

  7. The starting idea: CS fragmentation (Forbes & Priest 1995) CME models predict the formation via magnetic reconnection of an elongated post-CME vertical Current Sheet (Aschwanden 2002) 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)

  8. Fractal Current Sheets Stochastic magnetic fields 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) 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) Turbulent CS models Starting from this idea, many turbulent reconnection models have been proposed (plasma turbulence → anomalous resistivity) Is it possible to observe turbulence in post-CME CSs?

  9. Turbulence in CSs: observational feasibility • Post-CME CSs turbulence can be induced by macroscopic processes (tearing instability, plasmoid formation/ejection), but also bymicroscopicprocesses (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 l974.8Å coronal emission detected by UVCS has been interpreted as a signature of post-CME CSs; • The FeXVIII l974.8Å 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. (Forbes & Priest 1995) Line of Sight Which event can we select for this study? (Isobe 2003)

  10. Post-CME CS temperature evolution UVCS slit 2002/11/26, 19:30 (Bemporad et al. 2006) • Result: Te(CS)~ 8·106K → 3.5 ·106K in ~ 2.3 days ; Te(COR) ~ 1.3 ·106 K • ne(CS) ~ 7 ·107 cm-3 constant (D ~ 104 km) ; ne(COR) ~ 107 cm-3 • Result: adiabatic compression cannot account for plasma heating → other process • 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.)

  11. How can we explain the observed: • Post-CME high T emission? • Post-CME plasma turbulence? • Time evolution (i.e. decay) of both? 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 Teff~107 K (Bemporad 2008) • Result:Δl ~ 0.1 Å in ~ 2.3 days • Result: continuous decrease of turbulent speed vturbfrom~ 60 km/s to ~ 30 km/s

  12. The idea is to write usual equations for local reconnections Using vturb to estimate the local anomalous resistivity h* I’ll try to derive informations on the m-CSs. But how can I compute h*? mass conservation (incompressible fluid) balance between inflow and diffusion Going from macro- to m-scales In the following I’ll test the feasibility of this scenario: observed high T plasma heated by reconnection occurring locally at m-scales in the macroscopic CS (from Lin et al. 2005)

  13. (Birn & Priest 1972) Estimate of h: current-aligned m-instabilities At small scales turbulence may be induced via current – aligned instabilities leading to anomalous resistivity. The main candidates are: 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). 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)

  14. 2) If the observed turbulence is due to plasma micro-instabilities, anomalous resistivity h* can be computed in the hypothesis of Ion-acoustic instability: Lower-hybrid drift instability: h* 3) MCS outflow velocity and magnetic field from an energy balance: Kinetic ener- gy increase Dek = D(rv2/2) Work by Lorentz force v·(j×B) 1/2 vflow Magnetic energy um = B2/2m Reconnection Thermal ener- gy increase Det = D(2nekTe) Ohmic dissip. j2/s 1/2 BMCS d, l Estimate of MCS and mCS parameters Given the observed turbulent speed we may estimate: 1) Fraction of turbulent energy density: 4) By assuming vout~ vflow and vin ~ vturb it is possible to estimate the mCSs sizes d, l

  15. Results IA instability: h*~ 2-3·105 m2/s ~ 0.3-0.4 Ωm lCS ~ 80 m dCS ~ 12 m LH instability: h*~ 2-3·108 m2/s ~ 300-400 Ωm lCS ~ 90 km dCS ~ 14 km vin ~ 40-50 km/s vout ~ 250-350 km/s MA ~ 0.15-0.16 B(MCS) ~ 1 G (Bemporad 2008)

  16. 2d L2 L2 2l D • By assuming B~ 1 G and D~ 104 km we get: • Ion-acoustic instability: 1010m-CS in a volume of (104)3 km3 • Lower-hybrid drift instability: 104m-CS in the same volume Energy balance: required number density of m-CS But how many m-CS we need? Let’s consider inside the macro-CS a box with volume L2D; the power dissipated by m-CSs with number density nmCS is At the same time the power required to heat the coronal plasma entering the macro-CS through 2L2 is

  17. where we assumed ve~ vturb. With values given above for nmCS , 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! Macro-CS broadened by turbulent reconnections Lazarian & Vishniac (1999): if in a turbulent CS em is injected on a scale length le with velocity ve, the MCS thickness D is where H >le is the MCS length and vA is the Alfvén speed. In a volume DL2 there are nmCS· DL2 micro-CS, the energy is injected over a surface nmCS· 8l 2 · DL2, hence over a length (Isobe 2003)

  18. 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 Macro vs. micro Is it possible to reconcile local micro-CS and global macro-CS reconnections? • At macroscopic 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 • hglob ~ 1010 - 5·1011 m2/s • ~ 104 – 6·105Ωm • At microscopic 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 • hloc ~ 105 – 108 m2/s • nmCS~ 104 – 1010mCS/(1012 km3) ???

  19. Post-CME hard X-ray emission (Saint-Hilaire et al. 2009) 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: • How heat transport occurs from 0.2 to 0.7 Ro through the turbulent CS medium? • X-ray source starts ~ 4 h before the CME start time → not post-CME reconnection! • Decays 8 h after the CME → cannot explain 2.3 days of high T UVCS emission…

  20. Summary • 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 resistivityh* >> hc 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 evolutionin 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 m-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 m-CSs is not demonstrated here, but this is a valid working hypothesis. • 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.

  21. Thank you!

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