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511th WE-Heraeus-Seminar
From the Heliosphere into the Sun– Sailing against the Wind –
Collection of presentationsEdited by Hardi Peter ([email protected])
Physikzentrum Bad Honnef, GermanyJanuary 31 – February 3, 2012
http://www.mps.mpg.de/meetings/heliocorona/
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Bad Honnef, Febr. 2, 2012 1 1
Particle Acceleration and Plasma Kinetics in the Corona and Wind
Gottfried Mann Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, D-14482 Potsdam, Germany
e-mail: [email protected]
The Sun is a giant particle accelerator.
MHD is not appropriate to describe these phenomena.
Plasma kinetics is needed !!!
Flare: - enhanced emission of electromagnetic waves (radio - �-ray range) - acceleration of particles (e, p, and heavy ions)
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Bad Honnef, Febr. 2, 2012 2
XX--RRaayy EEmmiissssiioonn DDuurriinngg SSoollaarr FFllaarreess
Basic problem: How are electrons accelerated up to high energies (> 20 keV) within a fraction of a second during solar flares? (� RHESSI) Energetic electrons carry a substantial part of the energy released during a flare. (Lin & Hudson 1971, 1976; Emslie et al. 2004)
RHESSI mission
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Bad Honnef, Febr. 2, 2012 3
IInnvveerrssiioonn ooff PPhhoottoonn SSppeeccttrraa iinnttoo EElleeccttrroonn SSppeeccttrraa
(forward fitting method, Holman et al. 2003)
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Bad Honnef, Febr. 2, 2012 4
RRHHEESSSSII RReessuullttss IIII
FFlluuxxeess aanndd PPoowweerr ooff EEnneerrggeettiicc EElleeccttrroonnss
Fe Pe mean energy
moderate flares 4.7 �1034 s-1 2.8 �1020 W 37 keV
large flares (Fe > 1036 s-1) 1.5 �1036 s-1 9.1 �1021 W 38 keV
(Mann & Warmuth, 2010)
sample of 25 flares
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Bad Honnef, Febr. 2, 2012 5
TThhee SSttaannddaarrdd FFllaarree MMooddeell
� filament becomes instabil
� it is rising up
� a current sheet is establisted
� magnetic reconnection takes place
� outflow shock (Forbes, 1986; Tsuneta & Naito, 1998; Aurass, Vrsnak & Mann, 2002; Aurass & Mann, 2004)
(Carmichael, 1964; Sturrock, 1996; Hiroyama, 1974; Kopp & Pneumann, 1976) (or CSHKP-model)
electron acceleration at the termination shock
(Mann et al., 2007, 2009)
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Bad Honnef, Febr. 2, 2012 6
RReellaattiivviissttiicc SShhoocckk DDrriifftt AAcccceelleerraattiioonn II
reflection in the de Hoffmann-Teller frame Lorentz-transformations:
laboratory frame �� shock rest frame �� HT frame �� back
�� motional electric field has been removed
� conservation of kinetic energy:
� conservation of magnetic moment:
const2HT,
2HT,II =�+� �
constB
constB
p
HT
2HT,
HT
2HT, =
��= ��
fast magnetosonic shock � magnetic field compression
� moving magnetic mirror
� reflection and acceleration
non-relativistic approach (Ball & Melrose, 2003; Mann & Klassen, 2005)
relativistic approach (Mann et al., 2006)
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Bad Honnef, Febr. 2, 2012 7
� transformation of the particle velocities
( )downuplc
II,is2s
Ic,i
sII,i
B/Bsinarc:angleconeloss
)(1
tan
=��
�����
�>�
���
�
RReellaattiivviissttiicc SShhoocckk DDrriifftt AAcccceelleerraattiioonn IIII
};{}{ ,rII,r,i;II,i �� �����
c/secv
ß21
)1(
21
)1(2
ss
,i2ssII,i
2s
,r
2ssII,i
2sII,is
II,r
��=�
��+���
��=�
�+���
�+���=�
��
� reflection conditions:
� only particles with are accelerated for 0II,i >� lc*ss cos �=�>�
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Bad Honnef, Febr. 2, 2012 8
SShhoocckk DDrriifftt AAcccceelleerraattiioonn aatt tthhee TTeerrmmiinnaattiioonn SShhoocckk
resulted differential fluxes
T = 10 MK MA = 2.3 vs = 1500 km/s 87°
88°
89° � reflection and acceleration of e at the TS
� substantial decrease of the pitch angle
� transmission into the downstream region
at the 2nd shock encounter
� moving towards the dense chromosphere
� hard X-ray emission
W � sdrift
12 keV 86° 6 m
50 keV 88° 25 m
20 MeV 89° 10 km
E = V � B = 2 kV/m
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Bad Honnef, Febr. 2, 2012 9
coronal parameters from radio observations (at 150 MHz):
shock parameters:
comparison: theory � observations
CCoommppaarriissoonn ooff TThheeoorryy aanndd OObbsseerrvvaattiioonnss
MK40TG6.4B
cm108.2N
o
38e
=
=
�= �
220s
sA
updownupdown
cm109.2A
s/km2000v5.3M
2B/BN/N
�=
��=�
=�
)RHESSIbyobserveds107.1(s102F 136136e
�� ���=
The theory can approximately explain the observations.
)RHESSIbyobservedserg105.1(serg101P 129129e
�� �����=
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Bad Honnef, Febr. 2, 2012 10
CCoonncclluussiioonnss
�� The termination shock is able to efficiently generate energetic electrons. �� quantitative confirmations of Tsuneta & Naito��s (1998) suggestion �� quantitative agreement with RHESSI observations concerning the flux and power of energetic electrons (> 20keV) �� Electrons accelerated at the termination shock could be the source of nonthermal hard X- and ��-ray radiation in chromospheric footpoints as well as in coronal loop top sources.
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Bad Honnef, Febr. 2, 2012 11 11
Supra-Thermal Electrons in the Quiet Solar Corona
result of SOHO mission: differential heating (Te < Tp < THe)
(Wilhelm et al., 1998; Cranmer et al., 2002; Marsch & Tu, 2008) result of WIND and STEREO mission: F���core F���halo F���super-halo What creates supra-thermal tails?
Plasma kinetics is needed, again !!!
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Bad Honnef, Febr. 2, 2012
CCoorroonnaall FFuunnnneellss
(Hassler et al., 1999)
solar interior: magnetic field is confined to supergranular boundaries
solar corona: rapid expansion of magnetic flux tubes
(Gabriel, 1976; Hackenberg, Mann & Marsch, 2000 )
differential heating
F����4/>D6�?*>.;�*:.�0.6.:*<.-�*<�<1.�+*;.�7/�<1.�/=66.4�F���8:7<76;�*6-�276;�*:.�1.*<.-�+A�276�,A,47<:76�:.;76*6,.�F���;74*:�?26-�*,,.4.:*<276�
see: Axford & McKenzie (1991), Marsch & Tu (1997), Vocks & Marsch (2001)
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Bad Honnef, Febr. 2, 2012 13
EElleeccttrroonn AAcccceelleerraattiioonn bbyy WWaavveess
Ion cyclotron waves (LHP) are discussed for coronal heating and solar wind acceleration. (Marsch & Tu,1997; Vocks & Marsch, 2002) the model: resonant interaction between electrons and whistler (RHP) waves F���!�#�*6-�$�#�?*>.;�*:.�.52<<.-�/:75�<1.�+*;.�7/�<1.�/=66.4;�F���$�#�?*>.;��?12;<4.:;��:.;76*6<4A�26<.:*,<�?2<1�.4.,<:76; F���power law spectrum for the waves F���high-frequency tail of spectrum � electron frequencies � less wave energy for electrons than for ions
But bulk heating of electrons is not needed
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Bad Honnef, Febr. 2, 2012 14
WWhhiissttlleerr--EElleeccttrroonn IInntteerraaccttiioonn II
resonance condition: dispersion relation: waves away from the Sun:
frequency sweeping:
B and �e decrease with height
� Electrons with high v|| < 0
interact preferably with the waves
The thermal electrons does not absorb the waves!
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Bad Honnef, Febr. 2, 2012 15
WWhhiissttlleerr--EElleeccttrroonn IInntteerraaccttiioonn IIII
quasilinear theory: diffusion of electrons along lines of constant speed in the wave reference frame (Isenberg et al., 1999).
effect on electron distribution: F���26,:.*;.�7/�>�due to resonance F���.6.:0A�0*26� F���26,:.*;.�7/�>II due to mirror force
(vA,e = 0.5 c) (vA,e = 0.05 c)
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Bad Honnef, Febr. 2, 2012
SSoollaarr WWiinndd EElleeccttrroonn FFlluuxxeess aatt 11 AAUU
effects of waves: F���flux enhancement over wide energy range F���electron spectrum less steep (Vocks & Mann, 2003, 2008)
solid line: with waves dashed line: without waves dotted line: initial condition
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Bad Honnef, Febr. 2, 2012 17
SSuummmmaarryy
summary:
� a quiet stellar corona produces supra-thermal e- � same wave spectrum as for heating the corona common mechanism: � coronal heating
� solar wind acceleration � production of supra-thermal electrons
This mechanism is probably also acting in other stellar coronae.
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Bad Honnef, Febr. 2, 2012 18
TThhaannkk yyoouu ffoorr yyoouurr aatttteennttiioonn!!
Plasma kinetics are necessary to describe astrophysical phenomena (e.g. particle acceleration, non Maxwellian distributions), appropriately.
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Bad Honnef, Febr. 2, 2012
BBoollttzzmmaannnn -- VVllaassoovv EEqquuaattiioonn
gyrotropy: F���electron gyroperiods much shorter than other time scales F���1 spatial coordinate, s, along B F���2 velocity coordinates, vII and v�
Boltzmann - Vlasov equation for electrons:
right hand side: F���wave-particle interaction: quasilinear theory
F���Coulomb collisions, with protons and electrons:
Landau collision integral, collision partners with Maxwellian distribution
Coul.w.p.II
IIIIIIIIII t
f+tf=
vfv
vfv
sBln
B2v
vfE
meg+
sfv+
tf
�
��
���
�
��
���
�
��
�
��
���
��
���
�
��
� ���
��
��
�
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Bad Honnef, Febr. 2, 2012 20
EElleeccttrroonn DDiissttrriibbuuttiioonnss
height above coronal base: 1.06 R�
.4.,<:76��4/>D6�;8..-��������������,�height above coronal base: 6.5 R�
.4.,<:76��4/>D6�;8..-���������������,�