3-dimensional Evolution of an Emerging Flux Tube in the Sun. T. Magara

Transcription

1 3-imensional Evolution of an Emerging Flux Tube in the Sun T. Magara (Montana State University) February 6, 2002 Introuction of the stuy Dynamical evolution of emerging fiel lines Physical process working on emerging fiel lines Some implications base on the result Summary

2 Emerging magnetic fiel... sometimes relate to energetic events on the sun, such as Rust an Kumar (1996) Canfiel, Huson, Pevtsov (2000), etc. Sigmois, Prominence eruptions, CMEs, etc. About this stuy... We have one 3-imensional MHD numerical simulations of a magnetic flux tube emerging through the solar atmosphere with a special attention pai to the ynamics of emerging fiel lines.

3 About the simulation... Simulation moel backgroun atmosphere: 4 layers (convection zone, photosphere, chromosphere, an corona) magnetic flux tube: Gol-Hoyle type magnetic fiel ( r = 2, L w = 2π) simulation box: (nx, ny, nz) = (149, 167, 168) 100 x 100, 100 y 100, 10 z 100 x: , y: , z: (Nonuniform mesh system) Initial state z y x Initial perturbation Vertical istribution ρ = ρ p, p = p p, T = T p = 5000 K We impose an upwar motion in the mile of flux tube an a ownwar motion at both ens of tube uring the initial phase (0 t 5). L = 2 Λ p = 300 km

4 Evolution of an emerging flux tube

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7 So far, we obtaine... Structure of emerging fiel lines Abbett (2001) Sigmois Magara & Longcope (2001) Photospheric velocity fiel & magnetic fiel Fan (2001)

8 Toay s main topic is the ynamical behavior of emerging magnetic fiel in the solar atmosphere with a focus on the axis fiel of flux tube. Black line: axis fiel line Sie view Magara & Longcope (2001)

9 Let us start to see the time variation of the height of axis fiel line. z axis fiel line The axis fiel line tens to stop rising at first, but start rising later.

10 Velocity fiel along iniviual emerging fiel lines (outer fiel line & axis fiel line) at several istinct times outer fiel line inner fiel line Outer fiel line Axis fiel line

11 Each fiel line (outer fiel line & axis fiel line) has a istinct evolutionary character. Outer fiel line (emerging earlier) Expansion phase Graual phase Expansion phase Axis fiel line (emerging later)

12 We fin two kins of phases: expansion phase an graual phase. Next, let us investigate how forces ( P g, P m, T m, ρ g) work at these phases. Outer fiel line Expansion phase Upwar force: P m time = 16.0 time = 40.0 Downwar force: ρ g (early phase) Tm (late phase)

13 Axis fiel line Expansion phase: upwar force: P m, ownwar force: Tm time = 40 Graual phase... unulation time = 18 time = 26 time = 34 Quasi-static stage: P g ρ g Expansion stage: upwar force: P m ownwar force: ρ g Regression stage: upwar force: T m ownwar force: ρ g

14 From the simulation result, we foun for the outer fiel line (emerging early) a magnetic loop simply continues to expan for the axis fiel line (emerging late) a magnetic loop is in graual phase at first, an then enters a expansion phase later

15 Now let us consier the physical process working on the iniviual fiel lines. In orer to come out to the atmosphere, fiel lines must satisfy the emergence conition. λ > B2 2 ρ g : critical wavelength for magnetic Rayleigh-Taylor instability T m = B2 4 π 1 R c ~ B2 4 π 1 λ B ρ g Magara (2001) for instability T m < ρ g λ > ~ B2 ρ g

16 axis fiel line outer fiel line The ifference in evolution between outer fiel line an axis fiel line comes from the fact that they have a ifferent istance between footpoints when they emerge. For the outer fiel line, the emergence istance between footpoints is < 2 In this case, the emerge fiel line can expan without waving. For the axis fiel line, the emergence istance between footpoints is In this case, the emerge 2 λ fiel line is subject to RT < unulation. The fiel line oes not make a simple expansion but takes a waving behavior with graual rise.

17 graual rise expansion ρ: large transition What causes the transition from the graual phase to the expansion phase? The point is that the critical wavelength for the R-T instability changes inversely with the gas ensity. = B2 2 ρ g ρ 1 : small» As a magnetic loop graually rises, ρ is ecreasing ρ: small is increasing : large 2 > 2 When becomes comparable to, then the loop can keep a convex shape an starts expaning continuously.

18 Shibata s self-similar solution (1989, 1990) In the nonlinear phase of Parker instability, v z ~ ω l / 2 z, ρ z 4, an B z z 1. = B2 2 ρ g z2 ω l: linear growth rate z Magara (2001)

19 Evolution of emerging fiel lines When the istance between footpoints of a magnetic loop is comparable to at the appearance stage, the loop simply follows an expansion phase. Outer fiel line 2 > Axis fiel line > 2 When the istance between footpoints of a magnetic loop is much larger than at the appearance stage, the loop becomes unulate an takes a graual phase. 2 > During the graual phase, the loop rises upwar an the gas sustaine on the loop rains ownwars. This makes the local value of larger an finally becomes comparable to, leaing to the expansion phase.

20 Some implications from the simulation result... Prominence Eruption Graual phase The problem is there is a huge gap in scale (time & space) between the simulation moel an the actual prominence. Simulation moel 1200 km erupts in 20 min. after the emergence Expansion phase 4000 km Prominence typical lifetime is between a ay an several months 20,000 km 100,000 km

21 How can we overcome this gap? Here we focus on the istance between footpoints an compare this with the critical wavelength of R-T instability. height km 1200 km simulation moel prominence The height to erupt h is relate to. 20 min. The key parameter controlling the length of graual phase is. ay ~ months time simulation moel ~ ~ 4000 km» prominence 100,000 km 100,000 km

22 Simple emergence??» Graual phase Evaporation Conensation? We have not yet known the precise mechanism of prominence formation, but the lifetime of them (the length of graual phase) coul be relate to parameter, that is, the ratio of to may control the evolution of prominences.

23 CMEs... a manifestation of the ynamical evolution of magnetic loops that have a istinct evolutionary character Outer fiel lines... expansion phase Inner fiel lines... graual phase expansion phase Stratifie structure outer layer... helmet streamer inner layer... compact, ense structure (prominence) height height expansion phase graual phase time voi area of magnetic fiel P m time When the inner fiel line enters an expansion phase, they are ejecte by a strong magnetic pressure graient force an show a CME. Pre-eruption stage Eruption stage

24 Summary Objective of the stuy to investigate the ynamics of emerging magnetic fiel Dynamical evolution of emerging fiel lines expansion phase an graual phase Physical process working on emerging fiel lines the relation between the footpoint istance an Some implications from the result prominence eruption an CMEs