Modelling the Initiation of Solar Eruptions. Tibor Török. LESIA, Paris Observatory, France

Transcription

1 Modelling the Initiation of Solar Eruptions Tibor Török LESIA, Paris Observatory, France

2 What I will not talk about: global CME models Roussev et al., 2004 Manchester et al., 2004 Tóth et al., 2007 numerical simulation of CME propagation to Earth (and beyond) important to understand space weather study shocks, interaction with solar wind and magnetosphere, etc. long-term aim: real-time simulation of solar eruptions initiation mechanism(s) not yet treated properly

3 Solar Eruptions largest energy release processes in solar system main driver of space weather disturbances observed as flares, filament eruptions & CMEs often all three components observed together ( eruptive flares ) different observational manifestations of one underlying process: dynamic reconfiguration of (a part of) the solar corona

4 Basic Constraints T. Forbes, 2000 consensus: eruptions are magnetically driven (details not well known) photospheric magnetic field largely unaffected by eruptions energy for eruption stored in corona force-free currents sudden onset, rapid (exponential) acceleration & huge expansion rapid energy release ( 1032 ergs within first few minutes)

5 Further constraint: Distinct Eruption Phases Schrijver et al Sterling et al Zhang & Dere (2006) before eruption: slow build-up phase (energy storage) during eruption: activation: slow rise of filament; weak soft X-ray / EUV signatures acceleration: rapid exp.-like acc.; huge expansion; flare onset propagation: const. speed; interaction with solar wind; flare decay observations suggest different mechanisms in activation and acceleration phases

6 Basic Theoretical Concept Courtesy T. Forbes initiation main phase Yokoyama et al., 2001 Standard (CSHKP) Model of eruptive flares: phase 1 = initiation and opening (includes impulsive flare phase ) phase 2 = main phase : formation of large-scale vertical current sheet reconnection re-closes active region field flare + plasma & flux ejection into interplanetary space standard model for initiation of eruption does not exit yet!

7 Models & Limitations (see Forbes 2000, 2001) models comprised of: system of differential equations (mostly MHD approximation) set of physical boundary conditions (well constrained by observations) initial state (poorly constrained by observations) coronal field not known initial states idealized & complexity removed equations difficult to solve numerical simulations required computer power limited cannot cover full equations & length scale range models still valuable to test proposed physical mechanisms storage and release : initial arcade or flux rope + boundary driven evolution

8 Tether Cutting / Flux Cancellation Moore et al., 2001 Amari et al simulation 1997 May 12 event (PSI) initial slow reconnection within sheared arcade ( tether cutting ) fast runaway reconnection follows (flux rope formed & flare) ejection if overlying tension is weak enough; otherwise compact flare provides model for pre-flare phase & flux rope formation does not clearly address flux rope ejection mechanism

9 Magnetic Breakout Antiochos et al., D model, courtesy Ben Lynch (central) magnetic arcade is sheared and expands feedback between expansion and breakout reconnection initial driver flare reconnection drives eruption in main phase (Lynch et al. 2008) most large eruptions originate in multipolar source regions cannot work in bipolar active regions

10 Catastrophic Loss of Equilibrium / Ideal MHD Instability Forbes, Lin, Isenberg, Priest, Démoulin, et al. Roussev et al. 2003, Titov & Démoulin 1999 Török & Kliem 2005 Fan & Gibson 2007 start with flux rope configuration LoE: no neighbouring equil. in sequence of stable equilibria kink instability: occurs for supercritical flux rope twist torus instability: occurs for sufficient drop of overlying field torus instability is the physical mechanism behind catastrophic LoE

11 Helical Kink Instability Titov & Démoulin (1999) Török et al. (2004) Török & Kliem (2005) 2002 May 27 (confined eruption) occurs if flux rope twist exceeds critical value helical deformation of flux rope axis morphology of filament eruptions reproduced possible trigger & initial driving mechanism Williams et al. (2005) 2004 Nov 10 (fastest CME ever)

12 Torus Instability what about eruptions without helical deformation (majority of events)? kink instability expected to saturate early on huge expansion of CMEs? hoop force : restoring force: I2 fi = ( L + µ 0 R 2) 4π 2 a 2 R 2 I Bex fb = π a2 current ring + external field: can be unstable against expansion n instability threshold (free ring): Bext ( R ) = B0 R ncrit 3 / 2 Bateman (1978) Kliem & Török (2006)

13 Torus instability (partial current ring) 2005 June 16 Schrijver et al. (2008) similar ncr for line-tied flux ropes (Török & Kliem, Fan & Gibson, Isenberg & Forbes; all 2007) stable at low heights rope needs to rise until field drops fast enough (consistent with slow rise of prominences prior to eruption)

14 Summary KI & TI torus instability kink instability threshold: critical twist (Φ 3π ) helical shape no significant expansion threshold: critical ambient field drop (n 3/2 no helical shape huge expansion good quantitative match with certain eruption properties predict thresholds for eruption onset (twist & external field slope) do not include pre-eruptive evolution

15 Similarities & Differences tether cutting / flux cancellation magnetic breakout MHD instability all models include a twisted flux rope at relatively early stage of eruption all models produce a vertical CS below flux rope flare reconnection models mainly differ in trigger mechanism, otherwise evolution similar distinguish rather between trigger and driving mechanisms!

16 Trigger & Driver pre-eruptive configuration: stressed core field + stabilizing overlying field TRIGGER: any mechanism which slowly drives or dynamically perturbes the pre-eruptive configuration such that the core field erupts: tether cutting, breakout, kink instability converging, shearing, twisting flows obs: activation phase flux emergence / cancellation DRIVER: any mechanism which can account for rapid (exp.) acceleration and huge expansion of the core field / flux rope: flux rope (torus) instability / catastrophe flare-reconnection (below flux rope) obs: rapid acc. phase

17 Example 1: Flux Emergence & Torus Instability Titov & Démoulin (TD) Feynman & Martin 1995 Fan & Gibson (FG) Török, in preparation FG flux rope emerges kinematically into TD equilibrium reconnects with TD ambient field TD rope starts to rise linearly when onset criteria for torus instability are met TD rope erupts trigger: flux emergence driver: torus instability

18 Example 2: Flux Cancellation & Torus Instability Flux rope formed by BP reconnection due to flux cancellation Flux rope fed by tether-cutting reconnection Flux rope erupts freely, not before Aulanier, Török, Démoulin & DeLuca (2010) twisted bipolar field + photospheric diffusion rope formation & slow rise rope reaches height where torus instability sets in eruption if driving is stopped before TI criteria are met rope finds stable equilibrium trigger: BP + TC reconnection driver: torus instability

19 Steps Towards a Standard CME Model separate trigger & driver mechanisms (e.g. for breakout model) main acceleration: unify torus instability & catastrophic LoE role of flare reconnection activation phase: no model yet many possible triggers field geometry: arcade, flux rope, A FR transition?

20 Summary a standard model of CME initiation is emerging, it will include: ideal flux rope dynamics (instability / catastrophe) reconnection, probably in two stages: slow reconnection (trigger): e.g. breakout; flux rope formation fast reconnection in vertical current sheet flare; (can support eruption by pos. feedback with rising flux rope) path to formation of unstable / catastrophic flux rope equilibrium: (e.g.: flux emergence, flux cancellation, photospheric motions) probably elements of most current models

21 Geoeffectiveness of Solar Eruptions CMEs (and flares) are main driver of space weather disturbances important for geoeffectiveness: CME density, velocity & magnetic field orientation low corona: CME velocities ( ) km/s CME rotations up to 120 degree

22 CME Velocities (Fast & Slow CMEs) after MacQueen & Fisher (1983) Vršnak et al Yurchyshyn et al early observations indicated two types of CMEs: fast & slow (e.g., Sheeley et al. 1999) recent obs. (larger data sets) show continuous distribution (e.g., Vršnak et al. 2005) what determines CME velocity within this large range? CME driven by Lorentz force: ρ v 2 / 2 B 2 / 2µ 0 v v A (upper limit)

23 CME Velocities (Torus Instability) freely expanding current ring Kliem & Török (2006) line-tied flux rope Török & Kliem (2007) trajectory depends on slope of external field: n > 2: active regions, exp.-to-linear rise (fast CMEs) n nc: quiet sun, weak & nearly const. acc. (slow CMEs) yields large range of velocities unified model for fast & slow CMEs

24 CME Rotation (Observations) failed eruption Romano et al. (2003) slow CME (2009 June 14) fastest CME on record Williams et al. (2005) erupting filaments often exhibit a helical deformation during their rise include wide range of dynamic behaviour: failed eruption up to fast CME helical deformation can be described as writhing (or rotation)

25 CME Rotation (Some Quantitative Results) Thompson, Kliem & Török Fan (2005) Lynch et al. (2009) MC observations: mostly below 40, but sometimes much larger (up to 160 ) 3D reconstruction (STEREO) of erupting prominence: 120 kink-unstable flux rope model: up to 120 sheared arcade model: rotation of 50 (Fan & Gibson, Török & Kliem) (Lynch et al. 2009) observations: no large samples yet simulations: (Thompson) no parametric studies yet

26 CME Rotation (Kink Instability & Ambient Field) Isenberg & Forbes (2007) kink instability no kink instability Φ=5.7π ; B_tor=0 Φ=2.5π ; B_tor>0 several mechanisms may cause CME rotation (e.g., heliospheric CS) important in low corona: helical kink instability converts twist into writhe internal writhing ambient field parallel to flux rope bends its legs external writhing both yield the same sense of rotation difficult to disentangle

27 CME Rotation (Parametric Study; First Results) fix twist vary B_tor fix B_tor vary twist fix twist B_tor = 0 vary B(h) vary flux rope twist and ambient field in TD model flux rope apex rotations (20-140) obtained very strong rotations (>100 ) appear to require kink instability flux rope later on reconnects with ambient field (additional rotation)

28 SOTERIA projects observation: dynamic interaction of two filaments on 20 Nov 2003 simulation: reconnection of two coronal flux ropes

29 SOTERIA projects collaboration OBSPARIS, HVAR & UNIGRAZ observation: eruption nearby rotating sunspot simulation: flux rope eruption triggered by vortex motions

30 New SOTERIA Deliverable: Observations & Simulations