Magne&c Reconnec&on. Its role in CMEs & flares part II Lecture 4 Jan. 30, 2017

Transcription

1 Magne&c Reconnec&on Its role in CMEs & flares part II Lecture 4 Jan. 30, 2017

2 Last Time: Reconnec&on paradox Ideal region E = - u B 0 External E set by inner solu&on diffusion region E + u B 0

3 How reconnec&on works: details of the diffusion region E 0 u o u i 2δ 2Δ Mass conserva&on: u i Δ = u o δ M Ai = u i v A = δ Δ Aspect ra&o of diffusion region

4 Fast reconnec&on: Δ << L E 0 2L 2Δ 2δ How does small region affect external field? It creates bent field lines what next?

5 Response to bend Lin & Lee 1994 Riemann problem for 1D current sheet (CS) t=0 B CS J F = J x B B Riemann problem: ini&alize w/ 2 uniform regions separated by discon&nuity (CS) Find subsequent &me- evolu&on Solu4on: discon&nuity decomposes into traveling shocks and rarefac&on waves Lots & lots of bent field lines

6 Response to bend t=0 CS fast magnetosonic rarefac&on wave FMRW SMS Lin & Lee 1994 Riemann problem for 1D current sheet (CS) slow magnetosonic shock switch- off limit SMS FMRW B J F = J x B B u u u u

7 Response to bend Lin & Lee 1994 Riemann problem for 1D current sheet (CS) t=0 CS FMRW SMS hot & dense SMS FMRW B J F = J x B u u u u B ρ SMS SMS T FMRW FMRW

8 How it works in 2d Lin & Lee 1999 SS p

9 Petschek reconnec&on u i SMS SMS SMS v A 2Δ v A SMS P η!e M ~ Δ L <<1 2L External solu&on requires current - current appears in SMSs Released energy is converted to heat & KE by SMSs - very lidle is Ohmically dispated

10 Petschek reconnec&on SMS u i SMS v A 2Δ v A 2L What happens here? 1. FMS if the local FMS speed is below ouflow speed: Fast Mode Termina4on Shock 2. Otherwise: a smooth region of flow decelera&on u

11 How it works in a flare Tsuneta and Naito 1998 Forbes, T.G., and Malherbe 1986

12 B y t=0 B z B May 18, 2015 B z CS B y J F = J x B B Δθ " tan Δθ % $ ' = B y # 2 & B z FMRW v Riemann problem in 2.5d RD v z SMS v hot & dense v SMS v z RD Lin & Lee 1994 v FMRW

13 Q: Will resis&vity always result in slow (Sweet- Parker) reconnec&on? A: Yes, if η is uniform in space But not, when η(x) is locally enhanced* Biskamp & Scwartz 2001 J z SMS η enhanced *as by micro- instability

14 SMS SMS ρ FMS ρ Yokoyama & Shibata 2001 ρ

15 SMS SMS T FMRW ρ Takasao et al FMS

16 m e dv e dt Anomalous resis&vity Electron momentum eq. à generalized Ohm s law = e(e + 1 c u B) 1 n e P e + 1 n e c J B + m eν ei (v i v e ) Q: What is this drag force? A: An average force from random E fields origina&ng from the ions. Classical drag: E is experienced during close encounters with individual ions = collisions cross sec&on σ ei ~ ν ei = n e v th,e σ ei drag from ions = m eν ei en e e 4 m 2 4 e v th,e J = eη e J η e ~ η sp ~ v 3 th,e ~ T 3/2

17 Anomalous resis&vity Electron momentum eq. à generalized Ohm s law m e dv e dt = e(e + 1 c u B) 1 n e P e + 1 n e c J B + m eν ei (v i v e ) Other source of random electric field: plasma instability Expect ν ei ~ γ growth rate drag from ions = m eν ei en e J = eη e J If instability draws energy from rela&ve e/i mo&on then η e = " $ # % $ γ ~ v i v e α when v i - v e > v cr η sp, J < J cr = en e v cr η sp + C( J / J cr 1) α, J > J cr can lead to η e >> η sp and Δ << L

18 Ugai 1996 v D = v i v e J ρ

19 Energy budget E = u B +ηj Work done by changing B: J E = 1 c J (u B)+η e J 2 work by = u ( 1 J B) = u F c L Lorentz force Mag. Kin. Q: does dissipated energy End up as heat (i.e. increased T in Maxwellian)? Ohmic dissipa&on t Mag. internal ( 3 p ) 2 =!+η J 2 η from par&cle- par&cle collisions classical resis&vity YES see 2 nd law of thermo η from wave- par&cle interac&on anomalous resis&vity??? non- Maxellian dist n

20 Evolu&on via reconnec&on CS will change topology Transfer flux across CS Dissipate energy at site of CS Can facilitate erup&on (overcome obstacle presented by Aly- Sturrock) Evolu&on can lead to LoE Rapid ideal energy release Development of more intense CS S&ll more reconnec&on

21 Erup&on via reconnec&on Assume E CS (more later) è Φ beneath CS increases Downward force decreases (reconnec&on reduces overlying flux) Flux rope rises Flare signatures produced by E

22 Erup&on via reconnec&on

23 η=0 Mikic & Linker 1994 E M η 0 E 0

24 Aly- Sturrock conjecture: E M < E open E M E open Linker & Mikic 1995

25 Slightly more complex toy model* quadrupolar AR w/ flux rope y two null points h x *from Longcope & Forbes 2014

26 ψ 5 : overlying flux A B ψ 1 : arcade flux null points è 2 CSs 2 CSs è 2 sites for reconnec&on: A: breakout reconnec&on: decreases ψ 5 B: tether- cuyng reconnec&on: increases ψ 1 Reconnec&on changes equilibrium

27 ψ 5 ψ 1 ψ 5 2- parameter space of equilibria: reconnec&on produces mo&on

28 Slow evolu&on via breakout reconnec&on: Decreases overlying flux ψ 5 Leaves unchanged arcade flux ψ 1

29 Loss of equilibrium through reconnec&on E M F z =0 decrease ψ 5 break- out reconnec&on

30 Numerical solu&on from Karpen et al. 2012

31 Flux ropes Reconnec&on: produced flux rope which erupts

32 Twisted flux ropes Nishida et al d Reconnec&on: produces twisted flux rope

33 AND 3d reconnec&on Longcope & Beveridge 2007

34 Reconnec&on can create twisted flux rope before erup&on Van Ballegooijen & Martens 1989

35 Reconnec&on w/ subduc&on: Amari et al. 1999

36 Amari et al. 2000

37 Summary Large scales è ideal evolu&on (E =0) Can develop CSs è small scales è E 0 in CS Non- ideal evolu&on: reconnec&on Releases magne&c energy Converts to heat, KE,? Can lead to LoE è more CSs & more reconnec&on Reconnec&on can produce twisted flux ropes which erupt