Coronal Heating Problem

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1 Mani Chandra Arnab Dhabal Raziman T V PHY690C Course Project Indian Institute of Technology Kanpur

2 Outline Source of the energy Mechanism of energy dissipation Proposed mechanisms Regions of the corona 4 Spectrum: Kolmogorov or Kraichnan?

3 Structure Source: Wikimedia commons

4 Zones The Core Upto 0.25 Solar radii Nuclear fusion occurs Temperature as high as 13 million K Radiative zone solar radii Thermal radiation transfers heat energy outwards Temperature falls from 7 million K to 2 million K Convective zone solar radii Plasma not dense or hot enough for radiation Thermal convections carries heat outwards

5 Zones Photosphere Visible surface of the sun Below the photosphere sun is opaque Temperature between K Chromosphere Corona About 2000 km thick Temperatures upto 20,000 K Extends to millions of kilometers Temperature ranges from 1 to 3 million K

Chromosphere Corona About 2000 km thick Temperatures upto

6 Temperature variation Source: Wikimedia commons

7 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

thermodynamics : Heat cannot ow from a cold body to a hot body

8 Essence How does the corona maintain such high temperatures?

9 Source Source of the energy Mechanism of energy dissipation Proposed mechanisms Regions of the corona Less of a matter of contention Photospheric and subphotospheric motions Footpoints of coronal loops

corona Less of a matter of contention Photospheric

10 Mechanism Source of the energy Mechanism of energy dissipation Proposed mechanisms Regions of the corona The Real problem Many candidate processes have been proposed No consensus yet More accepted mechanisms involve

The Real problem Many candidate processes have been

11 Acoustic waves Source of the energy Mechanism of energy dissipation Proposed mechanisms Regions of the corona 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

outer atmosphere results in rapid increase of amplitude Shock formation Shock dissipation heats

12 Magnetoacoustic body waves Source of the energy Mechanism of energy dissipation Proposed mechanisms Regions of the corona 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

can dissipate via shocks Fast mode waves can dissipate via Landau damping Particles with velocities similar

13 Alfvén body waves Source of the energy Mechanism of energy dissipation Proposed mechanisms Regions of the corona 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 Turbulent heating: Kolmogorov-type cascade Viscous heating

to other modes which dissipate more readily Resonant heating: Constructive interference of the

14 Surface waves Source of the energy Mechanism of energy dissipation Proposed mechanisms Regions of the corona At boundaries between media Dissipation mechanisms Resonant absorption: Kinetic waves receive energy from surface waves Mode coupling Phase mixing

boundaries between media Dissipation mechanisms Resonant

15 Currents and elds Source of the energy Mechanism of energy dissipation Proposed mechanisms Regions of the corona Currents and magnetic elds carry energy Current sheets Dissipations of currents: Joule heating Nanoares: Small are events which happen in the corona Magnetic reconnection Source: Scholarpedia

energy Current sheets Dissipations of currents: Joule heating Nanoares:

16 Active regions Source of the energy Mechanism of energy dissipation Proposed mechanisms Regions of the corona Ensembles of loop structures connecting points of opposite magnetic polarity in the photosphere Location of phenomena linked to magnetic elds Heating requirement: W /m 2 Compose 82.4% of total heating requirements Low Alfvén timescales : DC processes are dominant

the photosphere Location of phenomena linked to magnetic elds Heating requirement: 2 10 2 2 10 3

17 Quiet-sun regions Source of the energy Mechanism of energy dissipation Proposed mechanisms Regions of the corona Normal regions Heating requirement: W /m 2 Compose 17.2% of total heating requirement

the corona Normal regions Heating requirement: 1 10

18 Coronal holes Source of the energy Mechanism of energy dissipation Proposed mechanisms Regions of the corona Coronal regions that are dark in X-rays Fast solar wind leaves the corona through coronal holes Heating requirement: W /m 2 Compose 0.4% of total heating requirement

in X-rays Fast solar wind leaves the corona through coronal holes

19 Coronal losses Source of the energy Mechanism of energy dissipation Proposed mechanisms Regions of the corona Mainly three sources Emission in resonance lines of ionized metals Radiative recombinations due to the most abundant coronal ions Bremsstrahlung radiation at high temperatures

in resonance lines of ionized metals Radiative recombinations due to

20 Coronal losses Source of the energy Mechanism of energy dissipation Proposed mechanisms Regions of the corona The total radiation loss per unit volume L = n e n H P(T ) n e = n H = cm 3, P(T ) = L W /m 3 300W per unit area

total radiation loss per unit volume L = n e n H P(T ) n e =

21 Spectrum: Kolmogorov or Kraichnan? 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.

22 Kolmogorov Flux Spectrum: Kolmogorov or Kraichnan? Energy ux: E(k) Cε 3 2 k 5 3 ke(k) Cε 2 3 k 2 3 U 2 Cε 2 3 k 5 3 Energy dissipation rate per unit mass ε U3 L

23 Spectrum: Kolmogorov or Kraichnan? Power dissipated per unit area: P ρu3 Lo L (L 0 is the thickness of the corona) Putting in numbers : ρ = kg/m 3, U = 50km/s, L 0 = m, L = km We get P 400W /m 2

24 Kraichnan Flux Spectrum: Kolmogorov or Kraichnan? E(k) A(εB 0 ) 1 2 k 3 2 ke(k) A(εB 0 ) 1 2 k 1 2 U 2 ε B 0 2 k 1 2 ε U 4 P B0L ρu 4 Lo LB0 The Kraichnan ux is found to be U times the Kolmogorov ux. B0 In the active regions, we have a large magnetic eld around 1000G. This gives P 0.2W /m 2

25 Comparison Spectrum: Kolmogorov or Kraichnan? 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 Kraichnan injection scale length ~15km Kolmogorov-type turbulence is more preferred

26 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,

27 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 Udo; Lemaire Chae, Jongchul; Schühle. SUMER Measurements of Nonthermal Motions: Constraints on Coronal Heating Mechanisms. The Astrophysical Journal, Volume 505, Issue 2, pp Daniel O. Dmitruk, Pablo; Gómez. Scaling Law for the Heating of Solar Coronal Loops. The Astrophysical Journal, Volume 527, Issue 1, pp. L63-L66.

28 Bibliography II Daniel O.; Martens Milano, Leonardo J.; Gomez. Solar Coronal Heating: AC versus DC. Astrophysical Journal v.490, p , 20 November P. Narain, U.; Ulmschneider. Chromospheric and coronal heating mechanisms. Space Science Reviews, vol. 54, Dec. 1990, p P. Narain, U.; Ulmschneider. Chromospheric and Coronal Heating Mechanisms II. Space Science Reviews, Volume 75, Issue 3-4, pp

29 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 Wikipedia. Coronal radiative losses Wikipedia, the free encyclopedia, [Online; accessed 14-April-2011]. Wikipedia. Sun Wikipedia, the free encyclopedia, [Online; accessed 14-April-2011].

Heating diagnostics with MHD waves

Heating diagnostics with MHD waves R. Erdélyi & Y. Taroyan Robertus@sheffield.ac.uk SP 2 RC, Department of Applied Mathematics, The University of Sheffield (UK) The solar corona 1860s coronium discovered