AN EVALUATION OF CORONAL HEATING MODELS FOR ACTIVE REGIONS BASED ON Yohkoh, SOHO, AND TRACE OBSERVATIONSMarkus J. Aschwanden

Lockheed Martin Advanced Technology Center

ApJ. 560:1035-1044, 2001 Oct.20

Patrick Antolin

Kyoto University Solar Seminar

Introduction & Structure The Coronal heating problem, an unsolved

problem for more than 60 years. Theories tested by coronal heating

requirements or with help of scaling laws. → no strong conclusions for discrimination.

New set of observational constraints. → allow discrimination between models.

Discussion and comparison of theoretical models.

Conclusions.

Problems with the theories

Based on nonobservable parameters. Have not been fitted to observed data. Many approximate a coronal loop with a

straight cylindric tube, with homogeneous density and magnetic field along it. → inadequate for large-scale loops in EUV. (H , P « L).

I. Observational Constraints

Coronal Loops in AR have overdensity which can only be supplied by upflows of heated chromospheric plasma.

Chromospheric upflows. Coronal Heating Function localized in lower

corona with H10 Mm above photosphere.

→ They all involve a chromospheric role in the coronal heating process, rather than isolated coronal in situ mechanism.

The 3 observational constraints are derived for Active Region (AR) loops. → They don’t cover a major fraction of solar surface but the coronal volume that is topologically connected with AR completely dominates total heating requirement of the corona.

Examplen0, T0, T → PH PH = EHT ≈ -ER T

= n02Λ(T0)T.

Summing heating energy requirement: AR→82.4% QSR→17.2% CH→0.4% Total energy budget of CHP is dominated by heating requirement of AR loops during solar maximum

Overdensity of Coronal Loops

Only certain subsets of magnetic field lines are selected by the heating process and are loaded by hot plasma at a given time. ( Litwin & Rosner ‘93).

Density contrast of coronal loops with background: qn >10→overdensity of mass in CL.

→ Require mass supply from Chromosphere.

Chromospheric upflows in coronal loops Detection from feature tracking and Doppler shift

measurements→ Unidirectional or counterdirectional flows. In solar flares, brightening of EUV and soft X-ray

bright loops are explained by chromospheric evaporation in the form of heated upflows (precipitation of nonthermal particles or conduction fronts).

→ Observed also at cooler soft X-ray temp. (25MK to 6MK) and EUV temp.(up to 1-2MK). Manifested in small flares, microflares and nanoflares. (Feldmann et al.’96, Krucker & Benz, 2000).

Flows originated by: changes in coronal heating rate, asymmetries in loop structures, footpoint pressure.

The Coronal Heating Function

Measured using energy balance arguments that constrain spatial distribution of energy input EH(s) in: EH(s)=ER(s)+F(s).

Before: heating distributed uniformly along loop or near loop summit .(Priest et al.’98, 2000).

Now: opposite result → non uniform heating function concentrated near loop footpoints. sH=12 ± 5 Mm.(Aschwanden, Schrijver & Alexander, 2001).

For quiet-Sun corona or coronal holes, different heating mechanisms might apply.

II. Discussion of Coronal heating Mechanisms.

2 major categories {

1.Wave models (AC)

2. Stressing models (DC) (single-flux systems)

3. DC models with multiflux systems

Coronal heating ↔ multistage process

DC models: nanoflare model Subphotospheric convection, photospheric

horizontal flows, differential rotation → displacement of magnetic footpoints of CL.

→ build-up of nonpotential free magnetic energy.→ becomes eventually unstable.→ energy released by magnetic reconnection process. Heating expected to be uniformly distributed along

the loop (uniform twist and build-up of nonpotential energy).

→ not consistent with observations. Low (‘88) → generalization of nanoflare model.

Other DC models

With current cascading: same problem because Joule heating is distributed more or less uniformly along the loops.(Van Ballegooijen’86)

With turbulence: model turbulent plasma in a homogeneous axial magnetic field and have a homogeneous electron density → produce uniform heating.

→ Only DC models that include chromosphere and TR zone, possibly causing enhanced ohmic dissipation in magnetic cannopies, can potentially explain obs.

AC models

Energy source: convectional or turbulent motion in subPH or PH layers → waves are generated there and propagate upward to heat the corona. Best candidates: Alfvén waves.

Alvénic resonance: Hollweg (‘84) calculates average Poynting flux along the loop (Alvénic wave energy converted to heat energy by turbulent heating) → 85% of energy that enters the loop remains, concentrated in looptop. → X

Other AC models

Resonant absorption. → nonuniformity of Alfvén velocity in CL (cross-sectional density variations…). Wave energy dissipated by ohmic heating or viscous turbulence. → Heating concentrated in multiple resonant layers that drift throughout the loop. → uniform heating → X (Ofman, Klimchuk, Davila ‘98).

Belien et al.’99 include vertical density and temp. structure of CL. Results:1. Only 5-10% of total Poynting flux is converted to Ohmic dissipation in corona.2. Ohmic dissipation in CH and TR is 4-8 times higher.3. In addition to density oscillation, there’s mass transport into the corona.

Other AC models

Alfvén waves dissipated by phase-mixing. Dissipation lengths are very large → maximum ohmic and viscous heating at large distances (≈1.4 R). →not satisfy heating scale heights of order H10 Mm. (Heyvaerts& Priest’83)

→ Only modified AC models that include CH and TR, where resonant absorption is much more effective than in the corona, can explain observed features.

Multiflux DC models

↔Magnetic reconnection models. Occur between magnetic field lines. Kinds:

Open-open (bipolar) Open-closed (tripolar) Closed-closed (quadrupolar)

Magnetic reconnection processes contributing to coronal heating may involve similar physical mechanisms observed on a larger energy scale in flares. Difference: heating efficiency.

Bipolar magnetic reconnection

X-point may occur in corona, CH or PH. Process leads to magnetic dipole config. Ends with

one overdense loop. → heating of plasma in closed loops:

- via nonthermal particles accelerated in EM fields that are created in reconnecting current sheets and precipitate to PH, or

- via thermal conduction fronts that propagate from high temp. current sheets to CH.

→ Heating of chromospheric plasma at footpoints→Overpressure pushes heated plasma up into CL by

chromospheric evaporation.

Tripolar magnetic reconnection

X-point may occur in corona, CH or PH. Emergence of a new dipole in open field region, or

collision of footpoint of open field line with adjacent dipole.

→ can carry plasma upward into corona.→ highly relevant for coronal heating, especially for

open field regions.→ applied for interpretation of explosive events (EUV

jets). (Chae et al. 2000)

Relaxation of new open field lines can accelerate acoustic waves or shock waves and heat plasma along the way.

Quadrupolar magnetic reconnection Prerequisites:

- pushing 2 closed field lines into physical contact.

- reconfiguration into a lower energy state. Plasma heating can occur in the separators of the

events (related flux transfer across separators provides free energy Longcope’98). This heating does not enhance local density

→cannot explain EM (or density) increase in observed soft X-ray brightenings.

Conclusions New set of observational constraints in AR allows clear

judging over theoretical models: Overdensity, upflows, localization of heating function near footpoint of coronal loops. → Chromospheric origin of heated plasma.

Conventional DC and AC models provide energy source of nonpotential magnetic energy and wave energy in the corona but cannot explain observations. → Only MHD models that include CH and TR.

→ Coronal heating problem cannot be solved without including the chromosphere.

Magnetic reconnection models may not only be applied to flares but also to AR heating (highest demand of heating) and quiet-Sun regions. Bipolar and quadrupolar reconnection have as an end product closed field lines thus cannot directly heat the open corona, but tripolar reconnection can.