Prominence Dynamics: the Key to Prominence Structure

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

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

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

plasma is NOT static model must be dynamic

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

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

Evaporation: the Thermal Nonequilibrium Model Hypothesis: condensations are caused by heating localized above footpoints of long, low-lying loops, with heating scale  << L from Tmax to apex: N2(T) L >> Q  from footpoint to Tmax: N2(T)  ~ Q  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

Why do condensations form? • chromospheric evaporation increases density throughout corona increased radiation • 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 • rapid cooling  local pressure deficit, pulling more plasma into the condensation • a new chromosphere is formed where flows meet, reducing radiative losses

Why does thermal nonequilibrium occurwith asymmetric heating? • Constraints: P1 = P2 , L1 + L2 = L, E1 E2 • Scaling Laws: E ~ PV ~ T7/2 L ~ P2 L T-(2+b) • Key Result: P ~ E(11+2b)/14 L (2b-3)/14 • e.g., for b = 1, P ~ E13/14 L -1/14 • equilibrium position: L1 / L2 = (E1 / E2 ) (11+2b)/(3-2b) • for b = 1, L1 / L2 = (E1 / E2 ) 13 !! • for b 3/2, no equilibrium is possible

Requirements 1D hydrodynamics Solar gravity Coronal heating Radiation and thermal conduction 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 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 Modeling Thermal Nonequilibrium (T)  N2 T-b

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

60-Mm chromospheres* T = 3x104 K mass source/sink heat flux sink maintain correct relationship between coronal pressure and chromospheric properties Closed ends v=0, g=0 T=const., dT/ds=0 Nonuniform g|| 285-Mm corona Tapex ~ 3 MK Napex ~ 6 x 108 cm-3 Uniform small “background” heating Range of flux tube geometries Initial and Boundary Conditions *Note: presence of deep chromosphere strongly influences results (as in 1D loop models)

Shallow Dip NRK run

Deep Dip NLK run

Very Shallow Dip Loop D run

Very Shallow Arch Loop A run

Impulsive Heating + Very Shallow Dip <dt> = 500 s

Impulsive Heating + Very Shallow Dip <dt> = 2000 s

Condensations always form (for loop length and heating scales used in simulations) Condensation remains at midpoint and grows unless footpoints are heated unequally 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 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 Steady vs Impulsive Heating

Summary of Results • Plasma dynamics provide important constraints on prominence magnetic structure and coronal heating • 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 • Long threads only form in highly flattened loops • Impulsive heating produces condensations IF • Average interval is < radiative cooling time (~2000 s) OR • No uniform background heating exists

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

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

Prominence Dynamics: the Key to Prominence Structure