1. Lecture 9 Prominences and Filaments Filaments are formed in magnetic loops that hold relatively cool, dense gas suspended above the surface of the Sun," explains David Hathaway, a solar physicist at the NASA Marshall Space Flight Center. "When you look down on top of them they appear dark because the gas inside is cool compared to the hot photosphere below. But when we see a filament in profile against the dark sky it looks like a giant glowing loop -- these are called prominences and they can be spectacular. Physics 777 Week 12 2004 Physics 777 Week 12 2004 September 23, 1999 SoHO-EIT HH (http://spaceweather.com/glossary/filaments.html)

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3. Lecture 9 Prominences Filaments  Disk Prominences  Limb Quiescent: high Active Region: low Quiescent prominence is a huge, almost vertical sheet of dense cool plasma, surrounded by a hotter and rarer coronal environment. T: 5,000 ~ 8,000 K H: 60,000 ~ 600,000 km  : 10 16 ~ 10 17 m -3 Height: 15,000 ~ 100,000 km Formation of Filament Consider a hot plasma, with T 0,  0 and thermal equilibrium under a balance between heat h and radiation   0 : 0 = h -   0 Physics 777 Week 12 2004 Physics 777 Week 12 2004

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5. Lecture 9 Prominences If conduction is absent, w>0, plasma is thermally unstable Presence of conduction stabilizes the plasma, provided Physics 777 Week 12 2004 Physics 777 Week 12 2004 Formation in a loop: Active Region prominence energy equation: If  or L is large, h is small, state of thermally non-equilibrium ensures, loops cool down to a new equilibrium of prominence temperature. Use force equation to derive T,  structure Solutions are shown in Fig. 11.1 -------- formation of a cool core, , T droops quicker in the core.

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7. Lecture 9 Prominences Physics 777 Week 12 2004 Physics 777 Week 12 2004 Formation in a coronal Arcade When coronal pressure becomes too great, force-free equilibrium ceases to exist and plasma cools to form a quiescent prominence The arcade is in equilibrium under force balance:  to field // To field Energy Equation: Linear field solution: Boundary condition: Modeling depends on 5 parameters  0, T 0, h, L, . It is found that when  0 exceeds a critical value ~ 10 15 m -3, the plasma can not have a hot equilibrium --- cool down to form prominence.

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9. Lecture 9 Prominences Physics 777 Week 12 2004 Physics 777 Week 12 2004  c decreases as L or  increases Neglecting heating term, energy balance equation becomes: Solution has the form: Fig. 11.4 shows the solution. Formation in a current sheet: For a T & , characteristic of lower corona, a neutral sheet becomes thermally unstable when L > 100,000 Km. Horizontal force balance and thermal equilibrium:

10. Lecture 9 Prominences Physics 777 Week 12 2004 Physics 777 Week 12 2004 Equations 11.18, 11.20, & 11.21 determine  20, B 20, T 20 in term of L and B. Fig. 11.7a shows that when L > L max, a hot equilibrium condition does not exist, plasma cools down along a dotted line to a new equilibrium at prominence temperature. E.g., at B = 1 G, L max = 50, 000 km --- height of quiescent prominence. Colling time : pressure balance: Time dependent energy equation: Assume L = L max ( 1 + ), solution is shown in Fig. 11.7b. T decreases slowly first, then drops suddenly. , cooling time decreases. E.g., = 10 -2.  ~ 10 5 sec ( 1 day ) Line – Tying : During the condensation of plasma in a vertical current sheet, lorentz force will tend to oppose the transverse motions because the magnetic field lines are anchored in the dense photosphere. The effect of line-tying is to favour the formation of thin wedges. If heating balances radiation outside the sheet,

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12. Lecture 9 Prominences Physics 777 Week 12 2004 Physics 777 Week 12 2004 Magnetohydrostatics of support in a simple arcade Kippenhahn --- Schlüter model Fig. 11.9 Field lines are bowed down by dense plasma in prominence. Magnetic tension provides upward force to balance gravity to support plasma; magnetic pressure increases with distance from z-axis to provide transverse force to compress plasma and balance plasma pressure gradient Force balance: Assume B x, B y are uniform, B z is a function of x.  x, z direction equations: Boundary conditions: Solutions: More complete treatment includes magnetic shear and heat transfer conclusion: prominence can not exist below h min. h min  as B x increases, so active region filaments are lower. Also, there exists a maximum share ~ 75 ° to 83 ° Homework: derive these

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14. Lecture 9 Prominences Physics 777 Week 12 2004 Physics 777 Week 12 2004 External Fields Fig. 11.2 shows a typical magnetic configuration of a prominence --- thin current sheet PLUS surrounding fields which are potential in x-z plane. The problem is to solve. with boundary conditions: B z = Solution. Averaged lorenz Force B x = g(z) x = 0, 0  z  H F L = J B x0. J = 2 B zd / . Current flowing through prominence F L > 0 for z > 17,000 km, can support a reasonable plasma mass of nd  1.8 x 10 24 m -2. MHD stability Using energy principle, condition for stability: Current-free: B z  with x, for stable configuration, fields must be concave upwards.

15. Lecture 9 Prominences Physics 777 Week 12 2004 Physics 777 Week 12 2004 Helical structure B has uniform B x0, B y0 and a pure azimuthal pinch field. resulting field lines depend on the value of C 1, closed field lines in x – z plane. Support of current sheet Fields are treated by vertical current sheet together with a current filament field ( Fig. 11.3 ) supporting force is the force of repulsion between two line current, This force supports a prominence of mass m =  R 2  Balance between them: Support in a horizontal Field B field has the form. Prominence has a radius of R 0 and its axis is located at x = 0, z = h

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18. Lecture 9 Prominences Physics 777 Week 12 2004 Physics 777 Week 12 2004 Outside prominence, magmetic field is potential, Boundary conditions: B R, B  continuous at ( y, z ) Solution: Inside prominence: A field component aling filament is necessary to produce prominence-like temperature. Coronal Mass Ejections ( coronal transient ) mass 10 15 g, energy up to 10 32 ergs. Speed is 100 to 1,000 km/s consequence: geomagnetic storms solar energetic particles may be related to filament eruptions and or flares. Typical structure includes: Front, Cavity & Core.

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20. Lecture 9 Prominences Physics 777 Week 12 2004 Physics 777 Week 12 2004 They may have limb events or halo events ( Earth directed ). A CME may produce magnetic cloud in interplanetary space. They may cause coronal dimming. Let’s discuss two simple models of CMEs. ( Fig. 11.15 ) Twisted loop Model Longitudinal field B l is surrounded by an azimuthal field B az, speed of CME is constant. force balance: magnetic pressure tension gravity Conservation of longitudinal field: B e h 2 = const. `` of azimuthal `` : B az h R = const. `` of mass `` : n h 2 R = const. Also assume B az / B l = const. Then: h ~ R, R c ~ R, B l ~ R -2 Background field in solar wind ~ R -3, so, CME magnetic field is dominant. In a more general equation:

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22. Physics 777 Week 12 2004 Physics 777 Week 12 2004 At certain twist  =  c, CME speed is constant,  >  c, acceleration  <  c, deceleration Untwisted loop Models Conservation of flux: `` of mass : This model also explain that CMEs are accelerated to a certain speed and then keeps constant speed. More recent Models S.T. Wu MHD model J. Chen ejecting flux rope model Magnetic clouds and Ace data.

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