Coronal Heating Problemadhabal/V1/Reports/MHD... · Mani Chandra Arnab Dhabal Raziman T V PHY690C Course Project ... Our sincere thanks to our classmates for their presentation feedback,

Solar structureThe Problem

The ResolutionMHD turbulence

References

Coronal Heating Problem

Mani Chandra Arnab Dhabal Raziman T V

PHY690C Course Project

Indian Institute of Technology Kanpur

Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem



References

Outline

1 Solar structure

2 The Problem

3 The ResolutionSource of the energyMechanism of energy dissipationProposed mechanismsRegions of the corona

4 MHD turbulenceSpectrum: Kolmogorov or Kraichnan?




References

Structure

Source: Wikimedia commons




References

Zones

The Core

Upto 0.25 Solar radiiNuclear fusion occursTemperature as high as 13 million K

Radiative zone

0.25-0.7 solar radiiThermal radiation transfers heat energy outwardsTemperature falls from 7 million K to 2 million K

Convective zone

0.7-1 solar radiiPlasma not dense or hot enough for radiationThermal convections carries heat outwards




References

Zones

Photosphere

Visible surface of the sunBelow the photosphere sun is opaqueTemperature between 4500-6000K

Chromosphere

About 2000 km thickTemperatures upto 20,000 K

Corona

Extends to millions of kilometersTemperature ranges from 1 to 3 million K




References

Temperature variation

Source: Wikimedia commons




References

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




References

Essence

How does the corona maintain such high temperatures?




References

Source of the energyMechanism of energy dissipationProposed mechanismsRegions of the corona

Source

Less of a matter of contention

Photospheric and subphotospheric motions

Footpoints of coronal loops




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Mechanism

The �Real� problem

Many candidate processes have been proposed

No consensus yet

More accepted mechanisms involve MHD turbulence




References


Acoustic waves

Surface convection zones create a spectrum of acoustic waves

Density decrease in outer atmosphere results in rapid increaseof amplitude

Shock formation → Shock dissipation heats outer stellar layers

Shockless dissipation possible with radiative heating andionisation pumping




References


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 canexchange energy with the wave. This can transfer energy fromthe wave to the plasma




References


Alfvén body waves

Incompressible modes

Various dissipation mechanisms

Mode coupling: Transfer of energy to other modes whichdissipate more readilyResonant heating: Constructive interference of the re�ectedand propagating Alfvén wavesLandau dampingTurbulent heating: Kolmogorov-type cascadeViscous heating




References


Surface waves

At boundaries between media

Dissipation mechanisms

Resonant absorption: Kinetic waves receive energy fromsurface wavesMode couplingPhase mixing




References


Currents and �elds

Currents and magnetic �elds carry energy

Current sheets

Dissipations of currents:

Joule heatingNano�ares: Small �are events which happen in the coronaMagnetic reconnection

Source: Scholarpedia




References


Active regions

Ensembles of loop structures connecting points of oppositemagnetic 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




References


Quiet-sun regions

�Normal� regions


Compose 17.2% of total heating requirement




References


Coronal holes

Coronal regions that are dark in X-rays

Fast solar wind leaves the corona through coronal holes


Compose 0.4% of total heating requirement




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Coronal losses

Mainly three sources

Emission in resonance lines of ionized metals

Radiative recombinations due to the most abundant coronalions

Bremsstrahlung radiation at high temperatures




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Coronal losses

The total radiation loss per unit volume

L= nenHP(T )

ne = nH = 2×108cm−3, P(T ) = 10−21.94

L∼ 5×107W /m3

∼ 300W per unit area




References

Spectrum: Kolmogorov or Kraichnan?

MHD turbulence

Widely agreed to be leading a major role in coronal heatingprocess

Disagreement on whether the spectrum is Kolmogorov orKraichnan

Both found in literatureKraichnan: Dmitruk & GómezKolmogorov: Chae et al.




References


Kolmogorov Flux

Energy �ux:

E (k)∼ Cε23 k

−53

kE (k)∼ Cε23 k

−23

U2 ∼ Cε23 k

−53

Energy dissipation rate per unit mass

ε ∼ U3

L




References


Power dissipated per unit area:

P ∼ ρU3Lo

L

(L0 is the thickness of the corona)

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

We get P ∼ 400W /m2




References


Kraichnan Flux

E (k) ∼ A(εB0)12 k

−32

kE (k) ∼ A(εB0)12 k

−12

U2 ∼ ε12B0

12 k

−12

ε ∼ U4

B0L

P ∼ ρU4Lo

LB0

The Kraichnan �ux is found to be U

B0times the Kolmogorov �ux.

In the active regions, we have a large magnetic �eld around 1000G.

This gives P ∼ 0.2W /m2




References


Comparison

Kolmogorov �ux calculated falls in active region requirementrange

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~1200kmKraichnan injection scale length ~15kmKolmogorov-type turbulence is more preferred




References

Acknowledgements

We would like to thank Dr. M.K. Verma for guiding us through theproject. Our sincere thanks to our classmates for their presentationfeedback,




References

Bibliography I

Markus J. Aschwanden.An Evaluation of Coronal Heating Models for Active RegionsBased 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 onCoronal Heating Mechanisms.The Astrophysical Journal, Volume 505, Issue 2, pp. 957-973.

Daniel O. Dmitruk, Pablo; Gómez.Scaling Law for the Heating of Solar Coronal Loops.The Astrophysical Journal, Volume 527, Issue 1, pp. L63-L66.




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.Chromospheric and Coronal Heating Mechanisms II.Space Science Reviews, Volume 75, Issue 3-4, pp. 453-509.




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.[Online; accessed 14-April-2011].

Wikipedia.Sun � Wikipedia, the free encyclopedia, 2011.[Online; accessed 14-April-2011].


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Coronal Heating Problemadhabal/V1/Reports/MHD... · Mani Chandra Arnab Dhabal Raziman T V PHY690C Course Project ... Our sincere thanks to our classmates for their presentation feedback,