Sophie Musset1, Eduard Kontar2, Nicole Vilmer1

15th RHESSI Workshop, 26-30 July 2016, Graz

1 LESIA, Observatoire de Paris 2 School of Physics and Astronomy, University of Glasgow

1. RHESSI Imaging Spectroscopy: a new tool to study electron

transport during solar flares

2. The 2004 May 21 solar flare

3. The diffusive transport model (Kontar et al, 2014)

4. Comparison between observations and model predictions

5. Conclusions

1

Battaglia & Benz (2006)

2

Battaglia & Benz (2006)

Photon spectral index

2

Need additional

mechanism to

collisional transport

2

Battaglia & Benz (2006)

Simoes & Kontar (2013)

Photon spectral index

2

Need additional

mechanism to

collisional transport

2

Battaglia & Benz (2006)

Simoes & Kontar (2013)

Photon spectral index

2

Electron spectral index

< 0 Ratio of electron rate

> 1

Need additional

mechanism to

collisional transport

2

Need additional

mechanism to

collisional transport

Radio observations : Kuznetsov & Kontar (2015)

3

Radio observations : Kuznetsov & Kontar (2015)

Spatial distribution of the density of

energetic electrons with E > 60 keV

= 2.1

3

X-ray imaging spectroscopy

Musset et al, in prep

12-25 keV

25-50 keV

50-100 keV

4

Thick target

Thin target Thick target

X-ray imaging spectroscopy

Musset et al, in prep

5

X-ray imaging spectroscopy

Musset et al, in prep

= 4.2 0.2

= 0.12 0.03 1035 s1

= 4.4 0.2

= 5.2 0.4

= 0.06 0.02 1035 s1

12-25 keV

25-50 keV

50-100 keV

6

Thick target

Electron spectral index: Electron rate above 25 keV:

Thin target

Electron spectral

index: Integrated electron

mean flux spectrum

above 0=25 keV

0 =

0

0 = 0.46 0.08 1055

21

X-ray imaging spectroscopy

Musset et al, in prep

= 4.2 0.2

= 0.12 0.03 1035 s1

= 4.4 0.2

= 5.2 0.4

= 0.06 0.02 1035 s1

12-25 keV

25-50 keV

50-100 keV

6

Thick target

Electron spectral index: Electron rate above 25 keV:

Thin target

Electron spectral

index: Integrated electron

mean flux spectrum

above 0=25 keV

0 =

0

0 = 0.46 0.08 1055

21

Distance between the footpoints and the looptop source: ~17 and ~15 108 cm Length of the loop ~ 3.2 109 cm

X-ray imaging spectroscopy

Musset et al, in prep

7

= = ()

0

0

=

X-ray imaging spectroscopy

Musset et al, in prep

7

= = ()

0

0

=

= 9.6 108

= 1.5 1026 3

= = 1.2 0.2 1011 3

= 0.4 0.2 1035 s1

= 2.2

Spatial distribution of electrons

at 25 keV

Electron mean spectra

in the different parts of the loop

Looptop source

Footpoints

8

=

()

()

Energetic electron density above Emin cm-3

Energetic electron density

above 25 keV

9

=

()

()

Energetic electron density above Emin cm-3

Energetic electron density

above 25 keV

Energetic electron density

above 60 keV

From radio (Kuznetsov

& Kontar 2015)

From

X-rays

9

Energetic electron density above Emin cm-3

= ()

()

Energetic electron density

above 25 keV

Energetic electron density

above 60 keV

From radio (Kuznetsov

& Kontar 2015)

From

X-rays

Distribution deduced from gyrosynchrotron emission is more peaked than

the distribution deduced from X-rays

,25

,25 ~1.6 3.8

,60

,60 ~7.7 9

9

1

()

=

+ 0()

Diffusion Collisions Source

Kontar et al (2014)

()

=

3 : mean free path

Strong pitch angle scattering due to small scale magnetic fluctuations

diffusive transport of energetic electrons

10

1

()

=

+ 0()

Diffusion Collisions Source

Kontar et al (2014)

, =

0

0

4 2 2 + 22exp

2

4 2 2 + 22

()

=

3 : mean free path

Suppose constant

10

2

1

()

=

+ 0()

Diffusion Collisions Source

Kontar et al (2014)

, =

4 2 2 + 22exp

2

4 2 2 + 22

()

=

3 : mean free path

density of the medium size of the acceleration region /0 injected electron spectrum

Acceleration region

Suppose constant

10

1

()

=

+ 0()

Diffusion Collisions Source

Kontar et al (2014)

, =

4 2 2 + 22exp

2

4 2 2 + 22

()

=

3 : mean free path

Spatial distribution of electrons at 20 keV

collisional

= 109cm

= 108cm

= 107cm

10

1

()

=

+ 0()

Diffusion Collisions Source

Kontar et al (2014)

, =

4 2 2 + 22exp

2

4 2 2 + 22

()

=

3 : mean free path

Spatial distribution of electrons at 20 keV Looptop and footpoint spectra

collisional

= 109cm

= 108cm

= 107cm

= 109cm

= 108cm

= 107cm

looptop

footpoint

Mean free path Size of acceleration region ~ 3.2 109 cm Length of the loop

Spatial distribution at 25 keV Coronal and footpoint spectra

= 1.2 0.2 1011 3; = 109 ; = 3 108

= 3 1010 3; = 3 108 ; = 3 108

11

Spatial distribution of energetic electron density

with energy > 25 keV

= 1.2 0.2 1011 3 ; = 3 108

= 3 1010 3 ; = 3 108

= 109 = 3 108

12

Spatial distribution of energetic electron density

with energy > 25 keV

= 1.2 0.2 1011 3 ; = 3 108

= 3 1010 3 ; = 3 108

= 109 = 3 108

12

The diffusive transport model

(Kontar et al. 2014) is

consistent with the X-ray

observations (spectral and

spatial distribution).

What about the radio

observations of Kuznetsov and

Kontar (2015) ?

Spatial distribution of energetic electron density

with energy > 25 keV with energy > 60 keV

= 1.2 0.2 1011 3 ; = 3 108

= 3 1010 3 ; = 3 108

= 109 = 3 108

= 6 107 = 2 107

7

The distribution is more

peaked: need a smaller

Trapping can be caused by magnetic

field convergence.

The trapped fraction of particles is

And in the case of isotropic pitch-

angle distribution,

Where 0 is the loss cone angle

With = the magnetic ratio. (Simoes & Kontar 2013)

= 1

= cos (0)

0 = sin1 ( 1/)

13

Trapping can be caused by magnetic

field convergence.

The trapped fraction of particles is

And in the case of isotropic pitch-

angle distribution,

Where 0 is the loss cone angle

With = the magnetic ratio. (Simoes & Kontar 2013)

= 1

= cos (0)

0 = sin1 ( 1/)

= . = .

13

Magnetic field strength along the

loop (Kuznetsov & Kontar 2015)

Trapping can be caused by magnetic

field convergence.

The trapped fraction of particles is

And in the case of isotropic pitch-

angle distribution,

Where 0 is the loss cone angle

With = the magnetic ratio. (Simoes & Kontar 2013)

= 1

= cos (0)

0 = sin1 ( 1/)

= . = .

. < < .

13

Magnetic field strength along the

loop (Kuznetsov & Kontar 2015)

Trapping can be caused by magnetic

field convergence.

The trapped fraction of particles is

And in the case of isotropic pitch-

angle distribution,

Where 0 is the loss cone angle

With = the magnetic ratio. (Simoes & Kontar 2013)

= 1

= cos (0)

0 = sin1 ( 1/)

= . = .

. < < .

But how to explain the spectral

hardening in the footpoints?

Imaging spectroscopy is used to study the spatial distribution of electrons and

the comparison of spectral distribution in different parts of the loop

Diffusive transport model (Kontar et al 2014) can explain the X-ray observations

Diffusive transport model can also explain the gyrosynchrotron observations,

but with a smaller mean free path

Mean free path is energy dependant

First comparison between radio and X-ray observations to probe energetic

electrons tra