takeru suzuki- a solution to the coronal heating and solar wind acceleration in the coronal holes :...

8/3/2019 Takeru Suzuki- A Solution to the Coronal Heating and Solar Wind Acceleration in the Coronal Holes : Non-linear Alfven Waves

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A Solution to the Coronal Heating and Solar WindAcceleration in the Coronal Holes :

Non-linear Alfven Waves

Takeru Suzuki

Dept.of Physics, Kyoto University

Collaborator : Shu-ichiro Inutsuka


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My Brief CV / Research Summary

Name : Takeru K. SuzukiPhD : Astronomy Dept., Tokyo (Mar. 2003)Now : JSPS Fellow, Physics Dept. Kyoto

Interests : Plasma Astrophysics (Theory)

Solar Corona/Wind

Suzuki(2002;2004)Suzuki & Inutsuka(2005)

Stellar Coronae/WindsSuzuki,Yan,Lazarian & Cassinelli(2005)

Neutron Star Winds

Suzuki & Nagataki(2005)

Galaxy ClustersFujita,Suzuki & Wada(2004)Fujita & Suzuki(2005)

Cosmic Rays & NucleosynthesisGalaxy Evolution

Suzuki,Yoshii & Kajino(1999)

Suzuki,Yoshii & Beers(2000)

Suzuki & Yoshii(2001)

Structure Formation

Suzuki & Inoue(2002):Applicaiton

:Connection


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Outline

IntroductionSolar Corona/Wind & General Astrophysical PlasmaWhat is the Problem ?

Our Simulation

Results Suzuki & Inutsuka 2005, ApJL, 632, L49First Direct Realization of the Formation of the Corona and Solar Wind

Nonlinear Dissipation of Alfven Waves

Applications (if enough time)Suzuki & Inutsuka 2005 in preparation (for J. Geophys. Res.)

Disappearance of Solar (& Stellar) WindsUnification of Fast/Slow Solar Winds


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Solar Corona

Jul.11th, 1991 Full Eclipse in Hawaii(NASA & ESA); YOHKOH/SXT _

Photosphere(Surface) : 6000KCorona : > 10^6KHow to Heat up?

Hot plasma streams out (Solar Wind).


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Corona & Solar Wind

SOHO/LASCO

MOVIE HERE

Steady Winds from the Polar Regions

Time-Dependent Outflow from the Equatorial Regions


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Coronal Holes / Active Regions / QuietRegions

YOHKOH

Black Area in Poles : Coronal Holes (Low Density)Bright in Low-Latitude : Active RegionsOthers : Quiet Regions


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Overview (during Solar Minimum)

by Tom Dunne _

FIGURE HERE (CREDIT MATTER)

(Roughly) Dipole Magnetic fieldOpen Poles : Steady Stream


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Fast/Slow Solar Wind

Property (1 AU) Slow Wind Fast Wind

Flow Speed ~400km/s ~750km/sDensity ~7 cm-3 ~3 cm-3Origin Low-Lat.Holes(??) Polar Holes

Mass Flux (rho*v) is similarRam Pressure (rho * v^2) : Fast > Slow


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Application to General Astrophysical Plasma

Before going on to specific Solar Topics, Id like to address...Solar Plasma (Reference frame)

=> Astrophysical PlasmaExamples

Coronae in Usual Stars (with surface convections)Main Sequence Stars with


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Energetics of Corona

T(K)

106

104

Fm,0

Fm

HeatingFc

Conduction

RadiationFr

Ff

Mass Loss

Chromo-

sphereCorona

Transition

Region

~2000kmPhoto-

sphere

r

Energy LossSolar WindRadiative CoolingDownward Conduction

Fm,0 1057erg cm2s1

( L1046

)can keep the hot corona.0.05 - 5% of the surfaceturbulent energy.

Energetics : O.K., But

How to Heat up?Lift up the surface turbulence energy => Dissipate in CoronaHow to Accelerate?

Gas Pressure of 1MK plasma => Wind with ~


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General Consensus

Important IngredientsB-field

Corona : P_gas/P_mag (plasma beta) ~ 0.01(Photosphere : ~100)

Surface Convection~1km/s Motions of B-field (Poynting Flux)=> (Uplift) => (Dissipation) => Plasma Heating/Acceleration


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Waves vs. Reconnections (AC vs.DC)

Waves : Alfven Wave is promising in Open regiontravel long distance to heat outer (SW) as well as inner (Corona) regions

Turbulent

Motions

Wave Propagation

along B-Fields

Reconnections : Probably Important in Closed Region

Tsuneta et al.1992


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Open vs. Closed Waves vs.Reconnections (?)

TRACE 171A (T~1MK)_

MOVIE HERE

Transient Brightening : Reconnections (Maybe)Steady Open Regions : Waves (Maybe)


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Alfven Waves

2 TypesHigh-freq (ion-cyclotron; 10^4Hz) wavesHeating of Heavy Ions (Large m/q) Kohl et al.1998; Cranmer et al.1999Difficult to heat P & e

No sufficient PowerHeavy ions (lower-resonant freq.) absorb energy before protons

Cranmer 2000_

Low-Freq waves( 1 (Non-Linear)

(Note) Wave action, instead of energy flux, is an adiabatic constantin moving media


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Previous Works

To Study various non-linear wave processes,(Time-dependent) Simulation : Straightforward

Most Previous Works Based on Analytic/Steady-state ModelingBut They need TOO MUCH Simplification

However, a lot of Difficulties even in simulationsHuge Density Contrast : > 15 orders of mag.

Previous simulations : Separate Regions

From coronal base to outward (No Coronal Heating)Oughton et al.2001, Ofman 2004_

Only in chromosphere & low corona (No SW Acceleration)Kudoh & Shibata 1999; Bogdan et al. 2003

_

Outgoing boundary condition at Outer BoundaryBoth Material and Waves

No one has successfully done simulations

from photosphere to >a few Rsun even in 1D


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Chromosphere/Corona/SW

n(cm-3)

1017

109

10

106

104

Rs1 1.003 215

(1AU)

Chr

omosph

ere

CoronaSolar Wind

T(K)


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Simulation

65Rs=0.3AU

HeatingAcceleration

Yohkoh/SXT

Region : Photosphere ~ 64 Rsun (0.3AU)Both Coronal Heating and Wind Acceleration

Transverse(Alfven) fluctuations from the BottomAppropriate dv (~1km/s), spectrum(1/f; 20sec - 30min)

Outgoing Boundary Condition1D ; SuperRadial expansion of Flux tube (mimic dipole B)Ideal MHD with radiative cooling & thermal conduction


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Basic Eqns.

Ideal (Non-Relativistic) MHD (a ratio of specific heats = 5/3)

(mass)d

dt+

r2f

r(r2fvr) = 0 (1)

(Momentum, ) dvr

dt = p

r1

8r2f

r (r2

fB2)+

v22r2f

r (r2

f)GM

r2

(2)

(Momentum,) ddt

(rfv) =

Br

4

r(rfB) (3)

(Total Energy)

d

dt(e+

v2

2+

B2

8)+

1

r2f

r[r2f{(p+B

2

8)vrBr

4(B v)}]+ 1

r2f

r(r2fFc)+qR = 0,

(4)where Fc is conductive flux, qR npne is radiative cooling

(Induction eq.)B

t

=1

rf

r

[rf(vBr

vrB)] (5)

(No Monopole) Br2f = const. (6)


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Characters of our Simulation

AdvantageBroadest Region(Photosphere - 0.3AU)Self-Consistent;Waves/Heating/Cooling : Automatic(Waves with P>20s)

Minimal ParametersPhotospheric PerturbationSuper-radial flux tube (mimic dipole B-field)

Disadvantage

1-fluid ideal MHDPlasma Heating : only by MHD shock; No Collisionless processesActually, observed ion/electron T are different.

1D

Wave Propagation : Restricted to B-direction(B//k)(In spite of 1D MHD)Our approach is the most Self-Consistent at the moment.


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Comparison with Obs

Observations(r8Rsun) : Inter-Planetary Scintillation (Nagoya-STE;EISCAT)


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Interpretation of Result

Forward Simulation with Minimal Input Parameters =>Observed Corona & Fast Solar Wind (as Natural Outcome)

"A Solution to the Heating & Acceleration of the main part ofthe plasma in the Coronal Holes"(?)

Important Results(Nonlinear) Dissipation of Alfven Waves (discuss later)Not Thermal-driven but Wave-driven Wind

Corona(10^6K) Chromosphere(10^4K)

Importance of Thermal Instability

Outflow Velocity2.5Rsun (~ Sonic Point) : ~150km/s

(No difficulty in time-dependent Simulation at the sonic point.)10Rsun : 500-800km/s (Acceleration : r


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Energy Transfer

Energy Flux of Each Component

Wave => Thermal (+ radiation loss)(inner)Wave, Thermal => Kinetic (outer)


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Energy Flux, Pressure

Steady State Energy Equation :1

r2fr

[r2f{vr(v2r+v22

+ e + p GM

r) +

B24

vr BrBv

4+ Fc}] + qR = 0

f: Geometrical Expansion, Fc: Conductive Flux,qR: Radiative Loss (Optically Thin)

Alfven Wave Energy Flux :

FA = v2(vA + vr) + pAvr = BrBv

4 + (

v22

+B28

)vr + B28

vr(Energy Density)*(Phase Speed) + (Pressure)*(Advection)


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On Acceleration

p * v is plotted

not Thermal-driven but Wave-Driven Wind


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Reason of 1MK

-23

-22.8

-22.6

-22.4

-22.2

-22

-21.8

-21.6

-21.4

-21.2

-21

4 4.5 5 5.5 6 6.5 7

cooling(ergcm^3/s)

log(T)

cooling.dat

Thermal Instability at T~10^5KA few 10^4 K => Jump to 1MKIf T>1MK, T settles down by thermal cond.


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Downward Thermal Conduction

T(K)

106

104

Fm,0

Fm

HeatingFc

Conduction

RadiationFr

Ff

Mass Loss

Chromo-

sphereCorona

Transition

Region

~2000kmPhoto-

sphere

r


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r-t diagram (raw data)

Various Waves!


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MHD Waves

7 Characteristics;(Fast,Alfven,Slow)x2+Entropy Waves

v-vF

v-vAv-vs

v v+vs

v+vA

v+vF

t

r

(footnote)MHD eqns

Evolutionary Eqns.Mass(+1) Momentum(+3) Energy(+1) Induction(+3)

Constraint Eqnno Monopole(-1)

=> 7 hyperbolic (wave) eqns

Magnetically dominated plasma with B//k=> Alfven & Fast degenerate=> (effectively) 5 characteristics


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MHD Waves (Low-beta & B//k)

v-vs

v v+vs

v+vA

t

r

v-vA

Alfven (=Fast) : Transverse

Appear in v & BSlow (~= Sound) : Longitudinal

Appear in vr &


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r-t diagram (Vperp)

Both Outgoing & Incoming Alfven Waves


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r-t diagram (Bperp/Br)

Both Outgoing & Incoming Alfven Waves


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r-t diagram (density)

Slow Waves & Contact Surface (Flow)


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r-t diagram (Vr)

Slow Waves & Contact Surface (Flow)

M d D i i


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Mode Decomposition

Extract each mode quantitatively (Cho & Lazarian 2002; 2003)Alfven mode

Outgoing/Incoming Alfven Correlation between v & Bz = v

B/

4 (Elsasser var.)

FA,out/in = z2vA (vA = Br/4)

(Positive Correlation : Left-going)

v_|_

B_|_

Outgoing Incoming

Similar for Slow modeCorrelation between & vr (Positive Corr.: Right-going)

W Di i i


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Wave Dissipation

(Normalized at 1.02Rs for Superradial Expansion of Flux Tube)

only < 0.1% of the initial Outgoing Alfven Wave Energy Fluxremains at 0.3AU

Ch h & T iti R i


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Chromosphere & Transition Region

Outgoing Alfven : Reflection by Density GradientVariation of Alfven speed(~B/sqrt(rho))( Shape Deformation = Partial Reflection ("Non-WKB")

~15% of the input energy => the coronac.f. Cranmer & van Ballegooijen 2005

_

This flux (5x10^5 erg/cm^2/s) is sufficient for the coronalhole heating!

E l (W R fl ti )


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Example (Wave Reflection)

MOVIE HERE

In Corona & Solar Wind


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In Corona & Solar Wind

key process in Alfven Wave Dissipation:

Generation of MHD slow waves(Kudoh & Shibata99; Moriyasu et al.04)

_

Prediction : Longitudinal motions in Solar Wind

c.f. Sakurai et al.(2002)

Generation of Slow Waves


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Generation of Slow Waves

dB Pm:large

Pm=0

Pm:large

Pm=dB2

/8

Variation of Magnetic Pressure, dB^2

=> Longitudinal Motions=> MHD Slow (Sound) Waves=> Steepen to Shocks

Exmp (Compressive Mode Generation)


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Exmp.(Compressive Mode Generation)

MOVIE HERE

Coronal Heating / Wind Acceleration


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Coronal Heating / Wind Acceleration

The most important process in Alfven Wave DissipationGeneration of MHD Slow (Sound) WavesSlow Waves => (Steepen) => Slow Shocks

Slow shock : magnetic and kinetic energy => heat.

Energy & Momentum Flux of Outgoing Alfven Wave=> Slow Waves => Slow Shocks => Plasma(Coronal Heating & Solar Wind Acceleration)

Density fluctuations(slow-mode) works as Mirrors against

Alfven Waves(3-wave interaction;Goldstein 1978)

_

=> Generation of Incoming Alfven Waves

=> Nonlinear wave-wave InteractionOther processes (less contribution)

Direct Steepening of Alfven Waves=>Fast Shock

Amplitude


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Amplitude

v2A,+

c2s =

B2

8P =

Pwave

Pgas

5 (Efficient mode conversion)

vS,+cS

1 (Dissipation by Slow Shocks)

Alfven Wave Nonlinearity,vA,+

vA

< 0.2

This value could be used in a simple model.

Discussion


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Discussion

Weak Point : 1D & MHD Approximation?Multi-dimensional effectsTurbulent cascade : Transverse Direction

Goldreich & Sridhar 1995; Matthaeus et al 1999; Oughton et al.2001

Phase Mixing Heyvaerts & Priest 1983

Refraction (angle of B & k changes) : Fast modeBogdan et al.2003

_

Interactions between field lines=> Nano-Flares (Katsukawa & Tsuneta 2001);

Wave Generation in the corona (Axford & Mckenzie 1997; Miyagoshi et al.2005)_

Kinetic effects(Not MHD but Boltzmann eqs.)Collisionless (Landau & ioncyclotron, Transit-Time) damping?

Conductive flux in collisionless plasma ?T difference in electron/ions

We need to study these issues via Local Simulations

Summary for Fast Wind


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Summary for Fast Wind

Our SimulationMost Self-Consistent; Everything is automatically includedwithin 1D MHD

Broadest Region(Density Contrast) : Photosphere - 0.3AU

Minimal Input Parametersdv & P(f) of Alfven Waves at PhotosphereGeometry of Flux Tube

Validity of 1D MHD needs to be examined

Results:Forward simulation of nonlinear Alfven Waves naturallyexplains the observed corona and fast wind.

Dissipation of Outgoing Alfven waves via

=> Slow waves => Slow shocks=> Incoming Alfven => wave-wave interaction

Universality & Diversity


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Universality & Diversity

We have studied various cases.Spectrum of dv(Photospheric Fluctuation)1/fwhite noiseSin wave, 3min

Polarization of dvLinear polarizationCircular Polarization

Amplitude of dv

B (photosphere) & f (flux tube expansion)

We skip the issues on the spectrum and polarization becausethe dependence is weak.

Dependence on dv


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Dependence on dv

Dependence on dv


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Dependence on dv

Disappearance of Solar Wind


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Disappearance of Solar Wind

dv Tmax np,1AU v0.1AU0.7(km/s) 1.0 106(K) 5(cm3) 550(km/s)0.4(km/s) 0.5 106(K) 0.05(cm3) 1200(km/s)

0.3(km/s) < 0.2 106

(K) 0.4km/s, Density => 1/100

Disappearance of Solar Wind!!(c.f.) On May 11, 1999, the observed solar wind

density becomes < 0.1(/cm^3), in contrast tothe usual value, 5(/cm^3)

(Note!) the stream interaction is also important for thisphenomena especially for V. Usamov et al.2000

Summary


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Summary

Our 1D MHD simulations covering from photosphere to 0.3AUshow :

The problem of the coronal heating and solar windacceleration in the coronal holes is solved by the nonlinear

low-frequency Alfven waves.Corona and transonic solar wind are natural consequence ofthe photospheric fluctuations of B-field, provided~>0.5km/s.

If becomes half, the solar wind disappears!Both fast & slow solar winds can be explained by the sameprocess, the nonlinear Alfven waves.

takeru suzuki- a solution to the coronal heating and solar wind acceleration in the coronal holes :...

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