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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
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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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
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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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
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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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).
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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Corona & Solar Wind
SOHO/LASCO
MOVIE HERE
Steady Winds from the Polar Regions
Time-Dependent Outflow from the Equatorial Regions
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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Coronal Holes / Active Regions / QuietRegions
YOHKOH
Black Area in Poles : Coronal Holes (Low Density)Bright in Low-Latitude : Active RegionsOthers : Quiet Regions
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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Overview (during Solar Minimum)
by Tom Dunne _
FIGURE HERE (CREDIT MATTER)
(Roughly) Dipole Magnetic fieldOpen Poles : Steady Stream
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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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
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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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
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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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
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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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
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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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
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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Chromosphere/Corona/SW
n(cm-3)
1017
109
10
106
104
Rs1 1.003 215
(1AU)
Chr
omosph
ere
CoronaSolar Wind
T(K)
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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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)
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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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.
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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Comparison with Obs
Observations(r8Rsun) : Inter-Planetary Scintillation (Nagoya-STE;EISCAT)
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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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
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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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)
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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On Acceleration
p * v is plotted
not Thermal-driven but Wave-Driven Wind
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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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
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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r-t diagram (raw data)
Various Waves!
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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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
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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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 &
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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r-t diagram (Vperp)
Both Outgoing & Incoming Alfven Waves
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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r-t diagram (Bperp/Br)
Both Outgoing & Incoming Alfven Waves
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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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 )
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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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
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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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
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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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
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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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
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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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
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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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.