511th WE-Heraeus-Seminar

From the Heliosphere into the Sun– Sailing against the Wind –

Collection of presentationsEdited by Hardi Peter (peter@mps.mpg.de)

Physikzentrum Bad Honnef, GermanyJanuary 31 – February 3, 2012

http://www.mps.mpg.de/meetings/heliocorona/

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: GMann@aip.de

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)

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

Bad Honnef, Febr. 2, 2012 3

IInnvveerrssiioonn ooff PPhhoottoonn SSppeeccttrraa iinnttoo EElleeccttrroonn SSppeeccttrraa

(forward fitting method, Holman et al. 2003)

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

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)

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)

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 �=�>�

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

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

�� �����=

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.

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 !!!

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)

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

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!

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)

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

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.

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.

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

�

��

���

�

��

���

�

��

�

��

���

��

���

�

��

� ���

��

��

�

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..-���������������,�