Coronal Heating Problem

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Solar structure The Problem The Resolution MHD turbulence References

Coronal Heating Problem

Mani Chandra Arnab Dhabal Raziman T V

PHY690C Course Project

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Solar structure The Problem The Resolution MHD turbulence References

Outline

1 Solar structure 2 The Problem 3 The Resolution

Source of the energy

Mechanism of energy dissipation Proposed mechanisms

Regions of the corona

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Solar structure

The Problem The Resolution MHD turbulence References

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Solar structure

Zones

The Core

Upto 0.25 Solar radii Nuclear fusion occurs

Temperature as high as 13 million K

Radiative zone

0.25-0.7 solar radii

Thermal radiation transfers heat energy outwards Temperature falls from 7 million K to 2 million K

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Solar structure

Zones

Photosphere

Visible surface of the sun

Below the photosphere sun is opaque Temperature between 4500-6000K

Chromosphere

About 2000 km thick Temperatures upto 20,000 K

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Solar structure

The Problem

The Resolution MHD turbulence References

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Solar structure

The Problem

From the core to the photosphere, temperature decreases However, beyond the photosphere the temperature increases Second law of thermodynamics : Heat cannot ow from a cold body to a hot body

Coronal temperature more than two orders of magnitude higher than photosphere

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Solar structure

The Problem

Essence

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Solar structure The Problem

The Resolution

MHD turbulence References

Mechanism of energy dissipation Proposed mechanisms Regions of the corona

Source

Less of a matter of contention

Photospheric and subphotospheric motions Footpoints of coronal loops

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The Resolution

Mechanism of energy dissipation

Proposed mechanisms Regions of the corona

Mechanism

The Real problem

Many candidate processes have been proposed No consensus yet

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The Resolution

Proposed mechanisms

Acoustic waves

Surface convection zones create a spectrum of acoustic waves Density decrease in outer atmosphere results in rapid increase of amplitude

Shock formation→ Shock dissipation heats outer stellar layers Shockless dissipation possible with radiative heating and ionisation pumping

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The Resolution

Proposed mechanisms

Magnetoacoustic body waves

Found in the bulk of the uid

Slow mode and fast modes : Compressible modes Slow mode waves can dissipate via shocks

Fast mode waves can dissipate via Landau damping

Particles with velocities similar to the wave velocity can exchange energy with the wave. This can transfer energy from the wave to the plasma

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The Resolution

Proposed mechanisms

Alfvén body waves

Incompressible modes

Various dissipation mechanisms

Mode coupling: Transfer of energy to other modes which dissipate more readily

Resonant heating: Constructive interference of the reected and propagating Alfvén waves

Landau damping

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The Resolution

Proposed mechanisms

Surface waves

At boundaries between media Dissipation mechanisms

Resonant absorption: Kinetic waves receive energy from surface waves

Mode coupling Phase mixing

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The Resolution

Proposed mechanisms

Currents and elds

Currents and magnetic elds carry energy Current sheets

Dissipations of currents:

Joule heating

Nanoares: Small are events which happen in the corona Magnetic reconnection

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The Resolution

Active regions

Ensembles of loop structures connecting points of opposite magnetic polarity in the photosphere

Location of phenomena linked to magnetic elds Heating requirement: 2×102−2×103W/m2

Compose 82.4% of total heating requirements Low Alfvén timescales : DC processes are dominant

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The Resolution

Quiet-sun regions

Normal regions

Heating requirement: 1×101−2×102W/m2

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The Resolution

Coronal holes

Coronal regions that are dark in X-rays

Fast solar wind leaves the corona through coronal holes Heating requirement: 5×100−1×101W/m2

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The Resolution

Coronal losses

Mainly three sources

Emission in resonance lines of ionized metals

Radiative recombinations due to the most abundant coronal ions

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The Resolution

Coronal losses

The total radiation loss per unit volume L=n_en_HP(T)

ne=nH=2×108cm−3, P(T) =10−21.94

L∼5×107W/m3

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Solar structure The Problem The Resolution

MHD turbulence

References

Spectrum: Kolmogorov or Kraichnan?

MHD turbulence

Widely agreed to be leading a major role in coronal heating process

Disagreement on whether the spectrum is Kolmogorov or Kraichnan

Both found in literature Kraichnan: Dmitruk & Gómez Kolmogorov: Chae et al.

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MHD turbulence

References

Kolmogorov Flux

Energy ux: E(k)∼Cε23k−35

kE(k)∼Cε23k−32

U2_∼_C_ε2 3k−35

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MHD turbulence

References

Power dissipated per unit area: P∼ ρU3L_o

L

(L0 is the thickness of the corona)

Putting in numbers : ρ=10−12kg/m3, U=50km/s, L0=7×108m, L=2×105km

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MHD turbulence

References

Kraichnan Flux

E(k) ∼ A(εB₀)12k−23

kE(k) ∼ A(εB₀)12k−21

U2 _∼ _ε1

2B₀12k−21

ε ∼ _BU4

0L

P ∼ ρU4Lo

LB0

The Kraichnan ux is found to be _BU₀ times the Kolmogorov ux. In the active regions, we have a large magnetic eld around 1000G.

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MHD turbulence

References

Comparison

Kolmogorov ux calculated falls in active region requirement range

Kraichnan ux falls below requirement More ne-tuning required for numbers? Similar calculation in Chae et al.:

Kolmogorov turbulence suggests an injection scale length of ~1200km

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Solar structure The Problem The Resolution MHD turbulence

References

Acknowledgements

We would like to thank Dr. M.K. Verma for guiding us through the project. Our sincere thanks to our classmates for their presentation feedback,

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References

Bibliography I

Markus J. Aschwanden.

An Evaluation of Coronal Heating Models for Active Regions Based on Yohkoh, SOHO, and TRACE Observations.

The Astrophysical Journal, Volume 560, Issue 2, pp. 1035-1044.

Udo; Lemaire Chae, Jongchul; Schühle.

SUMER Measurements of Nonthermal Motions: Constraints on Coronal Heating Mechanisms.

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References

Bibliography II

Daniel O.; Martens Milano, Leonardo J.; Gomez.

Solar Coronal Heating: AC versus DC.

Astrophysical Journal v.490, p.442-451, 20 November 1997.

P. Narain, U.; Ulmschneider.

Chromospheric and coronal heating mechanisms.

Space Science Reviews, vol. 54, Dec. 1990, p. 377-445.

P. Narain, U.; Ulmschneider.

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References

Bibliography III

P.; Matthaeus Oughton, S.; Dmitruk.

Coronal Heating and Reduced MHD.

Turbulence and Magnetic Fields in Astrophysics. Edited by E. Falgarone, and T. Passot., Lecture Notes in Physics, vol. 614, p.28-55.

Wikipedia.

Coronal radiative losses Wikipedia, the free encyclopedia, 2011.