sophie musset , eduard kontar , nicole vilmer - … · sophie musset1, eduard kontar2, nicole...
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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
𝛾𝐿𝑇 − 𝛾𝐹𝑃 ≠ 2
Need additional
mechanism to
collisional transport
2
Battaglia & Benz (2006)
Simoes & Kontar (2013)
Photon spectral index
𝛾𝐿𝑇 − 𝛾𝐹𝑃 ≠ 2
Need additional
mechanism to
collisional transport
2
Battaglia & Benz (2006)
Simoes & Kontar (2013)
Photon spectral index
𝛾𝐿𝑇 − 𝛾𝐹𝑃 ≠ 2
Electron spectral index
𝛿𝐿𝑇 − 𝛿𝐹𝑃 < 0 Ratio of electron rate
𝑁 𝐿𝑇
𝑁 𝐹𝑃> 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
𝛿 = 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
𝛿 = 4.2 ± 0.2
𝑁 = 0.12 ± 0.03 × 1035 s−1
𝛿 = 4.4 ± 0.2
𝛿 = 5.2 ± 0.4
𝑁 = 0.06 ± 0.02 × 1035 s−1
12-25 keV
25-50 keV
50-100 keV
6
Thick target
Electron spectral index: 𝜹
Electron rate above 25 keV: 𝑁
Thin target
Electron spectral
index: 𝜹
Integrated electron
mean flux spectrum
above 𝐸0=25 keV
𝑛𝑉𝐹0 = 𝑛𝑉𝐹 𝐸 𝑑𝐸∞
𝐸0
𝑛𝑉𝐹0 = 0.46 ± 0.08 × 1055 𝑐𝑚−2𝑠−1
X-ray imaging spectroscopy
Musset et al, in prep
𝛿 = 4.2 ± 0.2
𝑁 = 0.12 ± 0.03 × 1035 s−1
𝛿 = 4.4 ± 0.2
𝛿 = 5.2 ± 0.4
𝑁 = 0.06 ± 0.02 × 1035 s−1
12-25 keV
25-50 keV
50-100 keV
6
Thick target
Electron spectral index: 𝜹
Electron rate above 25 keV: 𝑁
Thin target
Electron spectral
index: 𝜹
Integrated electron
mean flux spectrum
above 𝐸0=25 keV
𝑛𝑉𝐹0 = 𝑛𝑉𝐹 𝐸 𝑑𝐸∞
𝐸0
𝑛𝑉𝐹0 = 0.46 ± 0.08 × 1055 𝑐𝑚−2𝑠−1
Distance between the footpoints and the looptop source: ~17 and ~15 × 108 cm
Length of the loop 𝐿 ~ 3.2 × 109 cm
X-ray imaging spectroscopy
Musset et al, in prep
7
𝑁 𝐿𝑇 = 𝐴𝐿𝑇 𝐹 𝐸 𝑑𝐸 = 𝐴𝐿𝑇 𝑛𝑉𝐹(𝐸)
𝑛𝑉
∞
𝐸0
𝑑𝐸∞
𝐸0
𝑵 𝑳𝑻 = 𝟏
𝒏𝑳𝑳𝑻 𝒏𝑽𝑭 𝑬 𝒅𝑬∞
𝑬𝟎
X-ray imaging spectroscopy
Musset et al, in prep
7
𝑁 𝐿𝑇 = 𝐴𝐿𝑇 𝐹 𝐸 𝑑𝐸 = 𝐴𝐿𝑇 𝑛𝑉𝐹(𝐸)
𝑛𝑉
∞
𝐸0
𝑑𝐸∞
𝐸0
𝑵 𝑳𝑻 = 𝟏
𝒏𝑳𝑳𝑻 𝒏𝑽𝑭 𝑬 𝒅𝑬∞
𝑬𝟎
𝐿𝐿𝑇 = 9.6 × 108 𝑐𝑚
𝑉𝑡ℎ = 1.5 × 1026 𝑐𝑚3
𝑛 = 𝐸𝑀 𝑉𝑡ℎ = 1.2 ± 0.2 × 1011 𝑐𝑚−3
𝑵 𝑳𝑻 = 0.4 ± 0.2 × 1035 s−1 𝑵 𝑳𝑻
𝑵 𝑭𝑷= 2.2
Spatial distribution of electrons
<nVF(E,z)> at 25 keV
Electron mean spectra <nVF(E,z)>
in the different parts of the loop
Looptop source
Footpoints
8
𝑛𝑏𝐸𝑚𝑖𝑛 =
𝐹(𝐸)
𝑣(𝐸)𝑑𝐸
∞
𝐸𝑚𝑖𝑛
Energetic electron density above Emin cm-3
Energetic electron density
above 25 keV
9
𝑛𝑏𝐸𝑚𝑖𝑛 =
𝐹(𝐸)
𝑣(𝐸)𝑑𝐸
∞
𝐸𝑚𝑖𝑛
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 𝑛𝑏𝐸𝑚𝑖𝑛 =
𝐹(𝐸)
𝑣(𝐸)𝑑𝐸
∞
𝐸𝑚𝑖𝑛
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
𝑛𝑏,𝐿𝑇25
𝑛𝑏,𝐹𝑃25 ~1.6 𝑒𝑡 3.8
𝑛𝑏,𝐿𝑇60
𝑛𝑏,𝐹𝑃60 ~7.7 𝑒𝑡 9
9
1
𝑣
𝜕
𝜕𝑧𝐷𝑧𝑧(𝑇) 𝜕𝐹
𝜕𝑧=
𝜕
𝜕𝐸
𝑑𝐸
𝑑𝑥𝐹 + 𝐹0𝑆(𝑧)
Diffusion Collisions Source
Kontar et al (2014)
𝐷𝑧𝑧(𝑇)
=λ𝑣
3 λ : mean free path
Strong pitch angle scattering due to small scale magnetic fluctuations
diffusive transport of energetic electrons
10
1
𝑣
𝜕
𝜕𝑧𝐷𝑧𝑧(𝑇) 𝜕𝐹
𝜕𝑧=
𝜕
𝜕𝐸
𝑑𝐸
𝑑𝑥𝐹 + 𝐹0𝑆(𝑧)
Diffusion Collisions Source
Kontar et al (2014)
𝐹𝐷 𝐸, 𝑧 =𝐸
𝐾𝑛0 𝑑𝐸′
𝐹0 𝐸′
4𝜋𝑎 𝐸′2 − 𝐸2 + 2𝑑2exp −
𝑧2
4𝑎 𝐸′2 − 𝐸2 + 2𝑑2
∞
𝐸
𝐷𝑧𝑧(𝑇)
=λ𝑣
3 λ : mean free path
Suppose λ constant
10
𝑖𝑛 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠 𝑐𝑚2 𝑠 𝑘𝑒𝑉
1
𝑣
𝜕
𝜕𝑧𝐷𝑧𝑧(𝑇) 𝜕𝐹
𝜕𝑧=
𝜕
𝜕𝐸
𝑑𝐸
𝑑𝑥𝐹 + 𝐹0𝑆(𝑧)
Diffusion Collisions Source
Kontar et al (2014)
𝐹𝐷 𝐸, 𝑧 =𝐸
𝐾𝒏𝟎 𝑑𝐸′
𝑭𝟎 𝐸′
4𝜋𝒂 𝐸′2 − 𝐸2 + 2𝒅2exp −
𝑧2
4𝒂 𝐸′2 − 𝐸2 + 2𝒅2
∞
𝐸
𝐷𝑧𝑧(𝑇)
=λ𝑣
3 λ : mean free path
𝒏𝟎 density of the medium
𝒅 size of the acceleration region
𝒂 α λ/𝑛0
𝑭𝟎 injected electron spectrum
Acceleration region
Suppose λ constant
10
1
𝑣
𝜕
𝜕𝑧𝐷𝑧𝑧(𝑇) 𝜕𝐹
𝜕𝑧=
𝜕
𝜕𝐸
𝑑𝐸
𝑑𝑥𝐹 + 𝐹0𝑆(𝑧)
Diffusion Collisions Source
Kontar et al (2014)
𝐹𝐷 𝐸, 𝑧 =𝐸
𝐾𝒏𝟎 𝑑𝐸′
𝑭𝟎 𝐸′
4𝜋𝒂 𝐸′2 − 𝐸2 + 2𝒅2exp −
𝑧2
4𝒂 𝐸′2 − 𝐸2 + 2𝒅2
∞
𝐸
𝐷𝑧𝑧(𝑇)
=λ𝑣
3 λ : mean free path
Spatial distribution of electrons at 20 keV
collisional
𝜆 = 109cm
𝜆 = 108cm
𝜆 = 107cm
𝑛𝑉𝐹𝐷
𝑛𝑉𝐹𝐷
𝑛𝑉𝐹𝐷
𝑛𝑉𝐹𝐶
10
1
𝑣
𝜕
𝜕𝑧𝐷𝑧𝑧(𝑇) 𝜕𝐹
𝜕𝑧=
𝜕
𝜕𝐸
𝑑𝐸
𝑑𝑥𝐹 + 𝐹0𝑆(𝑧)
Diffusion Collisions Source
Kontar et al (2014)
𝐹𝐷 𝐸, 𝑧 =𝐸
𝐾𝒏𝟎 𝑑𝐸′
𝑭𝟎 𝐸′
4𝜋𝒂 𝐸′2 − 𝐸2 + 2𝒅2exp −
𝑧2
4𝒂 𝐸′2 − 𝐸2 + 2𝒅2
∞
𝐸
𝐷𝑧𝑧(𝑇)
=λ𝑣
3 λ : mean free path
Spatial distribution of electrons at 20 keV Looptop and footpoint spectra
collisional
𝜆 = 109cm
𝜆 = 108cm
𝜆 = 107cm
𝜆 = 109cm
𝜆 = 108cm
𝜆 = 107cm
looptop
footpoint
𝑛𝑉𝐹𝐷
𝑛𝑉𝐹𝐷
𝑛𝑉𝐹𝐷
𝑛𝑉𝐹𝐶
λ Mean free path
𝑑 Size of acceleration region
𝐿 ~ 3.2 × 109 cm
Length of the loop
Spatial distribution at 25 keV Coronal and footpoint spectra
𝑛 = 1.2 ± 0.2 × 1011 𝑐𝑚−3; λ = 109 𝑐𝑚 ; 𝑑 = 3 × 108 𝑐𝑚
𝑛 = 3 × 1010 𝑐𝑚−3; λ = 3 × 108 𝑐𝑚 ; 𝑑 = 3 × 108 𝑐𝑚
11
Spatial distribution of energetic electron density
with energy > 25 keV
𝑛 = 1.2 ± 0.2 × 1011 𝑐𝑚−3 ; 𝑑 = 3 × 108 𝑐𝑚
𝑛 = 3 × 1010 𝑐𝑚−3 ; 𝑑 = 3 × 108 𝑐𝑚
λ = 109 𝑐𝑚 λ = 3 × 108 𝑐𝑚
12
Spatial distribution of energetic electron density
with energy > 25 keV
𝑛 = 1.2 ± 0.2 × 1011 𝑐𝑚−3 ; 𝑑 = 3 × 108 𝑐𝑚
𝑛 = 3 × 1010 𝑐𝑚−3 ; 𝑑 = 3 × 108 𝑐𝑚
λ = 109 𝑐𝑚 λ = 3 × 108 𝑐𝑚
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
𝑛 = 1.2 ± 0.2 × 1011 𝑐𝑚−3 ; 𝑑 = 3 × 108 𝑐𝑚
𝑛 = 3 × 1010 𝑐𝑚−3 ; 𝑑 = 3 × 108 𝑐𝑚
λ = 109 𝑐𝑚 λ = 3 × 108 𝑐𝑚
λ = 6 × 107 𝑐𝑚 λ = 2 × 107 𝑐𝑚
7
The distribution is more
peaked: need a smaller λ
Trapping can be caused by magnetic
field convergence.
The trapped fraction of particles is
And in the case of isotropic pitch-
angle distribution,
Where 𝛼0 is the loss cone angle
With 𝜎 = 𝐵𝐹𝑃 𝐵𝐿𝑇 the magnetic ratio.
(Simoes & Kontar 2013)
𝑇 = 1 −𝑁 𝐹𝑃
𝑁 𝐿𝑇
𝑇 = cos (𝛼0)
𝛼0 = sin−1 ( 1/𝜎)
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 𝛼0 is the loss cone angle
With 𝜎 = 𝐵𝐹𝑃 𝐵𝐿𝑇 the magnetic ratio.
(Simoes & Kontar 2013)
𝑇 = 1 −𝑁 𝐹𝑃
𝑁 𝐿𝑇
𝑇 = cos (𝛼0)
𝛼0 = sin−1 ( 1/𝜎)
𝑵 𝑭𝑷
𝑵 𝑳𝑻= 𝟐. 𝟐 𝝈 = 𝟏. 𝟒
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 𝛼0 is the loss cone angle
With 𝜎 = 𝐵𝐹𝑃 𝐵𝐿𝑇 the magnetic ratio.
(Simoes & Kontar 2013)
𝑇 = 1 −𝑁 𝐹𝑃
𝑁 𝐿𝑇
𝑇 = cos (𝛼0)
𝛼0 = sin−1 ( 1/𝜎)
𝑵 𝑭𝑷
𝑵 𝑳𝑻= 𝟐. 𝟐 𝝈 = 𝟏. 𝟒
𝟏. 𝟒 < 𝝈 < 𝟒. 𝟕
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 𝛼0 is the loss cone angle
With 𝜎 = 𝐵𝐹𝑃 𝐵𝐿𝑇 the magnetic ratio.
(Simoes & Kontar 2013)
𝑇 = 1 −𝑁 𝐹𝑃
𝑁 𝐿𝑇
𝑇 = cos (𝛼0)
𝛼0 = sin−1 ( 1/𝜎)
𝑵 𝑭𝑷
𝑵 𝑳𝑻= 𝟐. 𝟐 𝝈 = 𝟏. 𝟒
𝟏. 𝟒 < 𝝈 < 𝟒. 𝟕
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 trapping in the corona
Allows to probe two energy domains
14
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 trapping in the corona
Allows to probe two energy domains
Need to further develop the diffusive transport model with energy-dependent
mean free path, and for relativistic electrons
With imaging spectroscopy, model predictions about the spatial evolution of the
electron distribution are useful to compare to observations
14