25/04/23 1

Energetic electrons acceleration: combined radio

and X-ray diagnostics

Hamish Reid1,2 Nicole Vilmer2

Eduard Kontar1

1University of Glasgow 2Observatoire de Paris

1

25/04/23 2Where are electron accelerated ?

25/04/23 3

April 15th 2002 Solar Flare.

Background is SOHO/EIT 195

Small Red contours are

RHESSI 15-30 kev

Coloured Contours are NRH 432 MHz Blue to 164 MHz Yellow

Where are electron accelerated ?

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• Assume a common acceleration region for upward and downward propagating energetic electron beams (e.g. Ashwanden et al 1995)

• Use the X-ray data from HXR emission to constrain parameters of downward and upward electron beams

• Estimate parameters regarding the common acceleration region.

Basic Concept

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Consider an electron cloud with size d, spectral index located at initial acceleration site r=0 described by:

Langmuir waves are generated when their growth rate is larger than the background Maxwellian plasma collisional absorption.

Basic Concept

dr

vgtrvf exp)()0,,( 00vvg ~)(0

cpe

c vfv

n

2 ln4 3

22

Tee

pec vm

e

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onacceleratitypeIII hdh

Basic Concept

Langmuir waves are expected to grow at distance r = htypeIII – hacceleration. We can constrain r from the growth rate for Langmuir waves

1

0 )(vvgndrpe

c

The collisional absorption is small so we can derive the simple relationship

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April 15th 2002 Solar Flare.

TOP: Phoenix-2 spectral radio data from 700 – 100

MHz

MIDDLE: NRH radio flux from 432 – 164 MHz

BOTTOM: RHESSI HXR flux at 25, 13, 6 keV

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Take the spectral index of HXR

every 2 seconds

Take the starting frequency of radio

emission with criteria of 2x the

quiet background level

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Starting Frequency vs Photon Spectral Index

Scatter plot of the starting

frequency vs the photon

spectral index

Points have an anti

correlation with a

coefficient of -0.65

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Assume an exponential electron density model for the solar corona (Paesold

et al 2001).

Assume the thick target model to get

the electron spectral index from the photon

spectral index.

onacceleratitypeIII hdh

Starting Distance vs Spectral Index

d = 10.5 ± 1.6 Mm hacceleration = 52.3 ± 21.2 Mm

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April 15th 2002 Solar Flare.

Background is SOHO/EIT 195

Small Red contours are

RHESSI 15-30 kev

Coloured Contours are NRH 432 MHz Blue to 164 MHz Yellow

Acceleration Region

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Simulation Initial Conditions

The initial electron beam (at time=0) is dependent on position (as a Gaussian) and velocity (as a power-law)

drvgtrvf ||exp)()0,,( 0

vv

vnvg beamo

min

min

)1()( ovvv min

The initial, thermal spectral energy density is:

t

peeb

vv

vTktrvW log4

),,( 2

2

2

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One Dimensional QL equations

One dimensional quasilinear equations (e.g. Drummond and Pines, 1962) describing the kinetics of energetic electrons and Langmuir waves (Kontar, 2001) (Reid and Kontar 2010 in press ApJ)

tsLcw

e

peTe

vvvFW

vFWv

nrW

vv

vW

Lv

tW log)(3 2

22

Wave Generation and Absorption

Spontaneous Emission

22

222

020

4)()( v

fdvd

vF

vW

vmefrr

rrrv

tF

c

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Sample Simulation

Electron Flux Plasma Waves

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Sample Simulation

Assume Langmuir waves are induced at a certain level

above the thermal background W/WTh

A linear fit recovers the value for hacceleration and d

onacceleratitypeIII hdh

d = 14.9 ± 0.75 Mm hacceleration = 49.4 ± 8.61 Mm

104 W/WTh gives the best fit

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Conclusion

• Combined analysis of HXR and radio observations provided reasonable insight into the acceleration region height and size.

• Numerical simulations validated the results and shows the main starting height dependence comes from the spectral index and acceleration region size.

d = 10.5 ± 1.6 Mm hacceleration = 52.3 ± 21.2 Mm