Lecture 9 Prominences and Filaments

Lecture 9 Prominences and Filaments Filamentsare 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. September 23, 1999 SoHO-EIT H (http://spaceweather.com/glossary/filaments.html) Physics 777 Week 12 2004

Physics 777 Week 12 2004

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 : 1016 ~ 1017 m-3 Height: 15,000 ~ 100,000 km Formation of Filament Consider a hot plasma, with T0 , 0 and thermal equilibrium under a balance between heat h and radiation  0 : 0 = h -  0 Physics 777 Week 12 2004

Lecture 9 Prominences Physics 777 Week 12 2004

Lecture 9 Prominences 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. If conduction is absent, w>0, plasma is thermally unstable Presence of conduction stabilizes the plasma, provided 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. Physics 777 Week 12 2004

 to field // To field Energy Equation: Linear field solution: Boundary condition: Lecture 9 Prominences 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: Modeling depends on 5 parameters 0, T0, h, L, . It is found that when 0 exceeds a critical value ~ 1015 m-3, the plasma can not have a hot equilibrium --- cool down to form prominence. Physics 777 Week 12 2004

Lecture 9 Prominences 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: c decreases as L or  increases Neglecting heating term, energy balance equation becomes: Physics 777 Week 12 2004

Lecture 9 Prominences Equations 11.18, 11.20, & 11.21 determine 20, B20, T20 in term of L and B. Fig. 11.7a shows that when L > Lmax, 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, Lmax = 50, 000 km --- height of quiescent prominence. Colling time : pressure balance: Time dependent energy equation: Assume L = Lmax ( 1 + ), solution is shown in Fig. 11.7b. T decreases slowly first, then drops suddenly. , cooling time decreases. E.g., = 10-2.  ~ 105 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, 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 Bx, By are uniform, Bz 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 hmin. hmin  as Bx increases, so active region filaments are lower. Also, there exists a maximum share ~ 75° to 83° Lecture 9 Prominences Homework: derive these 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: Bz = Solution. Averaged lorenz Force Bx = g(z) x = 0, 0  z  H FL = J Bx0. J = 2 Bzd / . Current flowing through prominence FL > 0 for z > 17,000 km, can support a reasonable plasma mass of nd  1.8 x 1024 m-2. MHD stability Using energy principle, condition for stability: Current-free: Bz with x, for stable configuration, fields must be concave upwards. Lecture 9 Prominences Physics 777 Week 12 2004

Helical structure B has uniform Bx0, By0 and a pure azimuthal pinch field. resulting field lines depend on the value of C < 1, field has a dip; 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 =  R2  Balance between them: Support in a horizontal Field B field has the form . Prominence has a radius of R0 and its axis is located at x = 0, z = h Lecture 9 Prominences Physics 777 Week 12 2004

Outside prominence, magmetic field is potential, Boundary conditions: BR, 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 1015 g, energy up to 1032 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. Lecture 9 Prominences 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 Bl is surrounded by an azimuthal field Baz, speed of CME is constant. force balance: magnetic pressure tension gravity Conservation of longitudinal field: Be h2 = const. `` of azimuthal `` : Baz h R = const. `` of mass `` : n h2 R = const. Also assume Baz / Bl = const. Then: h ~ R, Rc ~ R, Bl ~ R-2 Background field in solar wind ~ R-3, so, CME magnetic field is dominant. In a more general equation: Lecture 9 Prominences 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. Lecture 9 Prominences Physics 777 Week 12 2004

Lecture 9 Prominences and Filaments