Prominence Dynamics: the Key to Prominence

Structure

Judy KarpenNaval Research Laboratory

http://solartheory.nrl.navy.mil/

judy.karpen@nrl.navy.mil

SVST HSVST H image imagecourtesy of Y. Lin courtesy of Y. Lin

OutlineOutline

• Constraints on Plasma StructureConstraints on Plasma Structure

• Plasma ModelsPlasma Models LevitationLevitation

InjectionInjection

Evaporation (thermal nonequilibrium)Evaporation (thermal nonequilibrium)

• Physics of Thermal NonequilibriumPhysics of Thermal Nonequilibrium

• Implications for Magnetic StructureImplications for Magnetic Structure

• Crucial Observations by Solar B and STEREOCrucial Observations by Solar B and STEREO

Plasma Structure: ConstraintsPlasma Structure: Constraints

ObservationalObservational

•Spine and barbsSpine and barbs

•Knots and threadsKnots and threads

•Appearance varies with TAppearance varies with T

TheoreticalTheoretical

•Mass comes from Mass comes from chromospherechromosphere

•Mass traces magnetic Mass traces magnetic structure (frozen in)structure (frozen in)

•|||| >> >>

•Hg ~ 500 kmHg ~ 500 km

•Energy input consistent Energy input consistent with coronal heatingwith coronal heating

10 Mm10 Mm

Threads: length ~ 25 Mm, Threads: length ~ 25 Mm, width ~ 200 km width ~ 200 km (SVST, (SVST, courtesy of Y. Lin)courtesy of Y. Lin)

plasma is NOT static plasma is NOT static model must be model must be dynamicdynamic

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LevitationLevitation

Converging bipolesConverging bipoles Photospheric reconnection sitePhotospheric reconnection site

Cool chromospheric plasma is lifted into the corona Cool chromospheric plasma is lifted into the corona by reconnected field lines, during flux cancellationby reconnected field lines, during flux cancellation

see Galsgaard & Longbottom 1999, Pecseli & Engvold 2000, Litvinenko & Wheatland 2005see Galsgaard & Longbottom 1999, Pecseli & Engvold 2000, Litvinenko & Wheatland 2005

InjectionInjection

Photospheric reconnection between arcade and Photospheric reconnection between arcade and cancelling bipole drives cool, field-aligned jetscancelling bipole drives cool, field-aligned jets

corona

photosphere

see Chae et al. 2004, Liu et al. 2005see Chae et al. 2004, Liu et al. 2005

Evaporation: the Thermal Evaporation: the Thermal Nonequilibrium ModelNonequilibrium Model

Hypothesis:Hypothesis: condensations are caused by heating condensations are caused by heating localized above footpoints of long, low-lying loops, localized above footpoints of long, low-lying loops, with heating scale with heating scale << L << L

References (all ApJ):References (all ApJ): Antiochos & Klimchuk 1991; Dahlburg et al. 1998; Antiochos & Klimchuk 1991; Dahlburg et al. 1998; Antiochos et al. 1999, 2000; Karpen et al. 2001, 2003; Karpen et al. 2005, 2006Antiochos et al. 1999, 2000; Karpen et al. 2001, 2003; Karpen et al. 2005, 2006

from Tmax to apex: N2(T) L >> Q from footpoint to Tmax: N2(T) ~ Q

Why do condensations form?Why do condensations form?

• chromospheric evaporationchromospheric evaporation increases density increases density throughout corona throughout corona increased radiationincreased radiation

• T is highestT is highest within distance ~ within distance ~ from site of from site of maximum energy deposition (maximum energy deposition ( i.e.,i.e., near basenear base))

• when L > 8 when L > 8 , conduction + local heating , conduction + local heating cannot balance radiation near apex cannot balance radiation near apex

• rapid cooling rapid cooling local pressure deficit, local pressure deficit, pullingpulling more plasma into the condensationmore plasma into the condensation

• a a new chromospherenew chromosphere is formed where flows is formed where flows meet, reducing radiative lossesmeet, reducing radiative losses

Why does Why does thermal nonequilibriumthermal nonequilibrium occur occurwith asymmetric heating?with asymmetric heating?

• Constraints: P1 = P2 , L1 + L2 = L, EE11 E E22

• 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

Modeling Thermal NonequilibriumModeling Thermal Nonequilibrium• RequirementsRequirements

1D hydrodynamics1D hydrodynamics

Solar gravitySolar gravity

Coronal heatingCoronal heating

Radiation and thermal Radiation and thermal conductionconduction

• AssumptionsAssumptions One flux tube among many One flux tube among many

in filament channelin filament channel

Low plasma Low plasma (rigid walls) (rigid walls)

Optically thin radiation (no Optically thin radiation (no radiative transport)radiative transport)

Volumetric coronal heating Volumetric coronal heating localized near footpointslocalized near footpoints

(T) (T) N N2 2 TT-b-b

• Simulations:Simulations: ARGOS, 1D hydrodynamic code with1D hydrodynamic code with

adaptive mesh refinement adaptive mesh refinement (AMR) -- (AMR) -- REQUIREDREQUIRED

MUSCL + Godunov finite-MUSCL + Godunov finite-difference schemedifference scheme

thermal conduction, solar thermal conduction, solar gravity, optically thin radiation gravity, optically thin radiation (Klimchuk-Raymond (Klimchuk-Raymond [T])[T])

spatially and/or temporally spatially and/or temporally variable heatingvariable heating

1D Hydrodynamic Equations1D Hydrodynamic Equations

€

∂ρ∂t + 1

A∂∂sAvρ ⎛ ⎝ ⎜

⎞ ⎠ ⎟=0

∂ρv∂t

+ 1A∂∂sAv2ρ ⎛ ⎝ ⎜

⎞ ⎠ ⎟+∂p∂s

=ρg||

∂E∂t

+ 1A∂∂sA E+ p ⎡

⎣ ⎢ ⎤ ⎦ ⎥v

⎛

⎝ ⎜

⎞

⎠ ⎟=ρg||

v+Q(s)−n2Λ(T)

+ 1A∂∂sAκ

0T 5 /2 ∂T

∂s

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

E=12ρv2 + p

γ −1ideal gasideal gas

massmass

momentummomentum

energyenergy

“No meaningful inferences on the heating process can be obtained from static models.” - Chiuderi et al. 1981

Initial and Boundary ConditionsInitial and Boundary Conditions• 60-Mm chromospheres60-Mm chromospheres**

T = 3x10T = 3x1044 K K

mass source/sink mass source/sink

heat flux sinkheat flux sink

maintain correct relationship maintain correct relationship between coronal pressure and between coronal pressure and chromospheric propertieschromospheric properties

• Closed endsClosed ends

v=0, g=0v=0, g=0

T=const., dT/ds=0T=const., dT/ds=0

• Nonuniform gNonuniform g||||

*Note: presence of deep *Note: presence of deep chromosphere strongly influences chromosphere strongly influences results (as in 1D loop models)results (as in 1D loop models)

• 285-Mm corona 285-Mm corona

TTapexapex ~ 3 MK ~ 3 MK

NNapexapex ~ 6 x 10 ~ 6 x 1088 cm cm-3-3

Uniform small “background” Uniform small “background” heatingheating

Range of flux tube geometriesRange of flux tube geometries

Shallow DipShallow Dip

NRK runNRK run

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Deep DipDeep Dip

NLK runNLK run

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Very Shallow DipVery Shallow Dip

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Loop D runLoop D run

Very Shallow ArchVery Shallow Arch

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Loop A runLoop A run

Impulsive Heating + Very Shallow DipImpulsive Heating + Very Shallow Dip

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<dt> = 500 s<dt> = 500 s

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

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Steady Steady vsvs Impulsive Heating Impulsive Heating

• Condensations always form (for Condensations always form (for loop length and heating scales loop length and heating scales used in simulations)used in simulations)

• Condensation remains at Condensation remains at midpoint and grows midpoint and grows unlessunless footpoints are heated unequally footpoints are heated unequally

• Highly repetitive behavior:Highly repetitive behavior:

condensation formation times, condensation formation times, masses, and lifetimesmasses, and lifetimes

adjacent corona can develop adjacent corona can develop periodic unsteady flowsperiodic unsteady flows

• Condensation speeds ~ 10 km/s, Condensation speeds ~ 10 km/s, faster when falling vertically or a faster when falling vertically or a pair is mergingpair is merging

• Condensations form if pulses are < Condensations form if pulses are < 2000 s apart, on average, or if 2000 s apart, on average, or if background heating is absentbackground heating is absent

• Shorter pulses cause stronger flows Shorter pulses cause stronger flows but don’t affect condensing processbut don’t affect condensing process

• Although total energy input at both Although total energy input at both footpoints is equal, condensations do footpoints is equal, condensations do not always remain static and growing not always remain static and growing

• Entire system is more chaotic, but Entire system is more chaotic, but quasiperiodicities appear at times quasiperiodicities appear at times

• Condensation speeds comparable or Condensation speeds comparable or lower, but motions are much less lower, but motions are much less predictablepredictable

• Length of condensation varies more; Length of condensation varies more; wider range of sizes/masses per runwider range of sizes/masses per run

Summary of ResultsSummary of Results

• Plasma dynamics provide important constraints on Plasma dynamics provide important constraints on prominence magnetic structure and coronal heatingprominence magnetic structure and coronal heating

• SteadySteady footpoint heating produces no (significant) footpoint heating produces no (significant) condensations incondensations in Loops shorter than ~8 x heating scale (e.g., overlying arcade)Loops shorter than ~8 x heating scale (e.g., overlying arcade)

Loops higher than the gravitational scale height Loops higher than the gravitational scale height

• No No dynamicdynamic condensations on deeply dipped loops condensations on deeply dipped loops

• Long threads only form in highly flattened loops Long threads only form in highly flattened loops

• ImpulsiveImpulsive heating produces condensations IF heating produces condensations IF Average interval is < radiative cooling time (~2000 s) ORAverage interval is < radiative cooling time (~2000 s) OR

No uniform background heating existsNo uniform background heating exists

Where is the plasma in the Where is the plasma in the sheared arcade?sheared arcade?

red = too shortred = too shortgreen = too tallgreen = too tall

black = too deepblack = too deepblue = just rightblue = just right

Crucial ObservationsCrucial Observations

• STEREOSTEREO Estimate prominence massEstimate prominence mass

3D view of plasma dynamics and structure3D view of plasma dynamics and structure

• Solar BSolar B Proper motions and Doppler signatures of Proper motions and Doppler signatures of

plasma dynamicsplasma dynamics

Origin of filament-channel shearOrigin of filament-channel shear

Coronal heating scale, location, variabilityCoronal heating scale, location, variability