1. Prominence Dynamics: the Key to Prominence Structure Judy Karpen Naval Research Laboratory http://solartheory.nrl.navy.mil/ judy.karpen@nrl.navy.mil SVST H  image courtesy of Y. Lin

2. Outline Constraints on Plasma Structure Constraints on Plasma Structure Plasma Models Plasma Models  Levitation  Injection  Evaporation (thermal nonequilibrium) Physics of Thermal Nonequilibrium Physics of Thermal Nonequilibrium Implications for Magnetic Structure Implications for Magnetic Structure Crucial Observations by Solar B and STEREO Crucial Observations by Solar B and STEREO

3. Plasma Structure: Constraints Observational Spine and barbs Spine and barbs Knots and threads Knots and threads Appearance varies with T Appearance varies with T Theoretical Mass comes from chromosphere Mass traces magnetic structure (frozen in)  || >>   Hg ~ 500 km Energy input consistent with coronal heating 10 Mm Threads: length ~ 25 Mm, width ~ 200 km (SVST, courtesy of Y. Lin)

4. plasma is NOT static model must be dynamic

5. Levitation Converging bipoles Photospheric reconnection site Cool chromospheric plasma is lifted into the corona by reconnected field lines, during flux cancellation see Galsgaard & Longbottom 1999, Pecseli & Engvold 2000, Litvinenko & Wheatland 2005

6. Injection Photospheric reconnection between arcade and cancelling bipole drives cool, field-aligned jets corona photosphere see Chae et al. 2004, Liu et al. 2005

7. Evaporation: the Thermal Nonequilibrium Model Hypothesis: condensations are caused by heating localized above footpoints of long, low-lying loops, with heating scale << L References (all ApJ): Antiochos & Klimchuk 1991; Dahlburg et al. 1998; Antiochos et al. 1999, 2000; Karpen et al. 2001, 2003; Karpen et al. 2005, 2006 from T max to apex: N 2  (T) L >> Q from footpoint to T max : N 2  (T) ~ Q

8. Why do condensations form? chromospheric evaporation increases density throughout corona  increased radiation chromospheric evaporation increases density throughout corona  increased radiation T is highest within distance ~ from site of maximum energy deposition (i.e., near base) T is highest within distance ~ from site of maximum energy deposition (i.e., near base) when L > 8, conduction + local heating cannot balance radiation near apex when L > 8, conduction + local heating cannot balance radiation near apex rapid cooling  local pressure deficit, pulling more plasma into the condensation rapid cooling  local pressure deficit, pulling more plasma into the condensation a new chromosphere is formed where flows meet, reducing radiative losses a new chromosphere is formed where flows meet, reducing radiative losses

9. Why does thermal nonequilibrium occur with asymmetric heating? E 1  E 2 Constraints : P 1 = P 2, L 1 + L 2 = L, E 1  E 2 Scaling Laws : E ~ PV ~ T 7/2 L ~ P 2 L T -(2+b) Key Result : P ~ E (11+2b)/14 L (2b-3)/14   e.g., for b = 1, P ~ E 13/14 L -1/14   equilibrium position: L 1 / L 2 = (E 1 / E 2 ) (11+2b)/(3-2b)   for b = 1, L 1 / L 2 = (E 1 / E 2 ) 13 !!   for b  3/2, no equilibrium is possible

10. Modeling Thermal Nonequilibrium Requirements Requirements  1D hydrodynamics  Solar gravity  Coronal heating  Radiation and thermal conduction Assumptions Assumptions  One flux tube among many in filament channel  Low plasma  (rigid walls)  Optically thin radiation (no radiative transport)  Volumetric coronal heating localized near footpoints  (T)  N 2 T -b Simulations: ARGOS, 1D hydrodynamic code with  adaptive mesh refinement (AMR) -- REQUIRED  MUSCL + Godunov finite- difference scheme  thermal conduction, solar gravity, optically thin radiation (Klimchuk-Raymond  [T])  spatially and/or temporally variable heating

11. 1D Hydrodynamic Equations ideal gas mass momentum energy “No meaningful inferences on the heating process can be obtained from static models.” - Chiuderi et al. 1981

12. Initial and Boundary Conditions 60-Mm chromospheres * 60-Mm chromospheres *  T = 3x10 4 K  mass source/sink  heat flux sink  maintain correct relationship between coronal pressure and chromospheric properties Closed ends Closed ends  v=0, g=0  T=const., dT/ds=0 Nonuniform g || Nonuniform g || *Note: presence of deep chromosphere strongly influences results (as in 1D loop models) 285-Mm corona  T apex ~ 3 MK  N apex ~ 6 x 10 8 cm -3  Uniform small “background” heating  Range of flux tube geometries

13. Shallow Dip NRK run

14. Deep Dip NLK run

15. Very Shallow Dip Loop D run

16. Very Shallow Arch Loop A run

17. Impulsive Heating + Very Shallow Dip = 500 s = 500 s

18. Impulsive Heating + Very Shallow Dip = 2000 s = 2000 s

19. Steady vs Impulsive Heating Condensations always form (for loop length and heating scales used in simulations) Condensations always form (for loop length and heating scales used in simulations) Condensation remains at midpoint and grows unless footpoints are heated unequally Condensation remains at midpoint and grows unless footpoints are heated unequally Highly repetitive behavior: Highly repetitive behavior:  condensation formation times, masses, and lifetimes  adjacent corona can develop periodic unsteady flows Condensation speeds ~ 10 km/s, faster when falling vertically or a pair is merging Condensation speeds ~ 10 km/s, faster when falling vertically or a pair is merging Condensations form if pulses are < 2000 s apart, on average, or if background heating is absent Shorter pulses cause stronger flows but don’t affect condensing process Although total energy input at both footpoints is equal, condensations do not always remain static and growing Entire system is more chaotic, but quasiperiodicities appear at times Condensation speeds comparable or lower, but motions are much less predictable Length of condensation varies more; wider range of sizes/masses per run

20. Summary of Results Plasma dynamics provide important constraints on prominence magnetic structure and coronal heating Plasma dynamics provide important constraints on prominence magnetic structure and coronal heating Steady footpoint heating produces no (significant) condensations in Steady footpoint heating produces no (significant) condensations in  Loops shorter than ~8 x heating scale (e.g., overlying arcade)  Loops higher than the gravitational scale height No dynamic condensations on deeply dipped loops No dynamic condensations on deeply dipped loops Long threads only form in highly flattened loops Long threads only form in highly flattened loops Impulsive heating produces condensations IF Impulsive heating produces condensations IF  Average interval is < radiative cooling time (~2000 s) OR  No uniform background heating exists

21. Where is the plasma in the sheared arcade? red = too short green = too tall black = too deep blue = just right

22. Crucial Observations STEREO STEREO  Estimate prominence mass  3D view of plasma dynamics and structure Solar B Solar B  Proper motions and Doppler signatures of plasma dynamics  Origin of filament-channel shear  Coronal heating scale, location, variability