Download Hard X-Ray Polarization – a Diagnostic of Electron

Hard X-Ray Polarization– a
Diagnostic of Electron
Acceleration Processes in Solar
Flares
Gordon Emslie
Department of Physics, UAH, Huntsville, AL
Polarization in Solar Flares
• Impact polarization on neutrals (e.g. Hα)
• Fluorescence
• Continuum polarization (hard X-rays)
Accelerated Electrons in Flares
• Revealed by bremsstrahlung signature
• Cross-section for bremsstrahlung ~ 10-5
× cross-section for energy loss
(principally Coulomb losses on ambient electrons)
• ⇒Electron (flux, energy) ~ 105 × hard
X-ray (flux, energy)
• Electron energy can be 1032 – 1033 ergs
in large events
Number & Current problems
• Rate of e- acceleration ≈ 105 × rate of photon production ≈
1037 s-1 in large flare
– But: number of electrons in flare volume ≈ 1037
⇒ source would be emptied in ~ 1 s!
– Need for recycling and current closure
.
.
.
Number & Current problems
• Rate of e- acceleration ≈ 105 × rate of photon production ≈
1037 s-1 in large flare
– But: number of electrons in flare volume ≈ 1037
⇒ source would be emptied in ~ 1 s!
– Need for recycling and current closure
• Associated Current ≈ 1037 e- s-1 ≈ 1018 A
– Ampère law ⇒ B = µoI/2πr ~ 108 G
– Faraday law ⇒ V = L dI/dt ~ (µol) I/τ ~ 1019 V
“Resolution” of Current Problem?
• Current density j ~ 104 A m-2
• Maximum radius of current channel from
(Ampère) ∇× B ~ B/r = µo j ⇒ r = B/ µo j ~ 10 m
(Faraday) V= µo L(πr2j)/τ ⇒ r ~ 1 m (!)
• ⇒ Number of channels ~ 1012 (1014)
• ⇒ Aspect ratio of loop ~ 106-7
• Complicated current closure pattern
Electron Energization Methods
• Large-Scale Direct Electric Field:
– Sub-Dreicer
– Super-Dreicer
• Stochastic
• Thermal
Direct Electric Field Acceleration
m dv/dt = e E - ν mv
(cf. m dv/dt = m g - ν mv)
• skydiver: “collision frequency” ν ~ v, drag force ~ v2
⇒ stable terminal velocity vt = g/ν
• current in wire: ν ~ v ⇒ vd = eE/mν
⇒ j = ne vd = (ne2/mν) E, i.e. j = σ E (Ohm’s Law)
• But, electrons in a dilute plasma: ν ~ 1/v3 for v > vt
⇒ “terminal velocity” concept not valid
⇒ runaway acceleration at sufficiently high speeds
vcrit = vt √(ED/E) (ED ~ 10-8 n(cm-3)/T(K) V cm-1)
Accelerated Spectrum
F(E )
background Maxwellian
runaway tail;
height ~ dn/dt
eεL
ε
Super-Dreicer Acceleration
• Involves large electric fields
– E = - (v/c) × B
• Driven by external flow field
• All electrons in distribution are rapidly
accelerated
Super-Dreicer Acceleration Geometry
y
Bx
v
By
Ez 
Bz 
v
By
Bx
x
Super-Dreicer Acceleration Geometry
y
Reconnecting B component
Bx
v
By
Ez 
Bz 
v
By
Bx
x
Super-Dreicer Acceleration Geometry
Inductive E
y
Reconnecting B component
Bx
v
By
Ez 
Bz 
v
By
Bx
x
Super-Dreicer Acceleration Geometry
Inductive E
y
Reconnecting B component
Bx
v
By
Ez 
Bz 
v
By
Bx
In-sheet guiding B
x
Super-Dreicer Acceleration Geometry
Inductive E
y
Reconnecting B component
Bx
v
By
Ez 
Bz 
v
By
Bx
In-sheet guiding B
Out-of-sheet B component –
limits acceleration time
x
Super-Dreicer Acceleration
• Electric field E= (v/c) × B
– v=108 cm s-1; B=103 G ⇒ E=103 V cm-1 ~ 106 ED
– Acceleration length ~ 1 m; time ~ 10-8 s
• Particles remain in acceleration region for very
short time and escape along magnetic field
component perpendicular to sheet
• Rapid reconnection in a very thin (1 m) current
sheet – stability?
Accelerated Spectrum
F(E )
ε
Electron Energization Methods
• Large-Scale Direct Electric Field:
– Sub-Dreicer
– Super-Dreicer
• Stochastic
• Thermal
Stochastic Acceleration
• Alfvén waves accelerate electrons out of
thermal distribution through gyroresonance
acceleration
• Fast mode waves continue acceleration to
high energies through “transit-time”
acceleration (Fermi acceleration between
moving magnetic mirrors)
Accelerated Spectrum
F(E )
ε
Electron Energization Methods
• Large-Scale Direct Electric Field:
– Sub-Dreicer
– Super-Dreicer
• Stochastic
• Thermal
Thermal Source?
• Bulk heating to several × 108 K
• Isotropic?
.
.
.
.
.
Thermal Source?
• Bulk heating to several × 108 K
• Isotropic?
• But, region is still connected magnetically
to cool (~104 K) chromosphere
⇒ strong thermal gradients present
⇒ anisotropy
⇒ polarization
Accelerated Spectrum
F(ε )
ε
Comparison of Accelerated Spectra
F(E)
Sub-Dreicer
Strongly anisotropic
E
ε
F(E)
Comparison of Accelerated Spectra
Super-Dreicer
Sub-Dreicer
F(E)
Strongly anisotropic
Strongly anisotropic
E
E
ε
F(E)
Comparison of Accelerated Spectra
Super-Dreicer
Sub-Dreicer
F(E)
Strongly anisotropic
Strongly anisotropic
F(E)
Stochastic
E
E
Weakly anisotropic
ε
E
F(E)
Comparison of Accelerated Spectra
Super-Dreicer
Sub-Dreicer
F(E)
Strongly anisotropic
Strongly anisotropic
F(E)
Stochastic
E
E
F(E)
Weakly anisotropic
Thermal
Weakly anisotropic
ε
E
E
Bremsstrahlung Cross-Section
• Q = Z2 Qep + Z Qee
• Qee normally negligible
• For fixed direction of emergent photon, and
integrated over directions of outgoing electron,
Qep = Qep (ε,E,θ,φ, //,⊥)
ε = energy of photon
E = energy of incoming electron
(θ,φ) = direction of incoming electron
(//,⊥) = polarization of photon
(relative to collision plane)
Cross-Section (Gluckstern & Hull 1953)
Effect of Magnetic Field
•Electrons spiral around magnetic
field lines
•Must average over θ and φ
•Result is that bremsstrahlung
cross-section really depends on
–ε and E
–direction (θ’,φ’) of guiding
magnetic field
–polarization relative to plane
containing B and line to
observer
Effect of Magnetic Field
•Electrons spiral around magnetic
field lines
•Must average over θ and φ
•Result is that bremsstrahlung
cross-section really depends on
B
–ε and E
–direction (θ’,φ’) of guiding
magnetic field
–polarization relative to plane
containing B and line to
observer
Earth
Effect of Magnetic Field
•Electrons spiral around magnetic
field lines
•Must average over θ and φ
•Result is that bremsstrahlung
cross-section really depends on
B
–ε and E
–direction (θ’,φ’) of guiding
magnetic field
–polarization relative to plane
containing B and line to
observer
–For vertical field, this is radial
direction on the solar disk
Earth
Dilution of Polarization
• Maximum bremsstrahlung occurs at same
location of maximum collisional scattering
• This reduces the observed polarization,
unless we can image the highly polarized
segment of the source separately
• Need to consider (energy-dependent) targetaveraged angular distribution of electrons
Non-Thermal Source Schematic
Predictions for Solar Flare Polarization
Predictions for Solar Flare Polarization
Single point within a loop
Predictions for Solar Flare Polarization
Single point within a loop
Langer and Petrosian (1977)
Predictions for Solar Flare Polarization
Single point within a loop
radial
Langer and Petrosian (1977)
Predictions for Solar Flare Polarization
Single point within a loop
transverse
radial
Langer and Petrosian (1977)
Predictions for Solar Flare Polarization
Single point within a loop
transverse
radial
Langer and Petrosian (1977)
Bai and Ramaty (1978)
Predictions for Solar Flare Polarization
Single point within a loop
Source-integrated
transverse
radial
Langer and Petrosian (1977)
Bai and Ramaty (1978)
Leach and Petrosian (1983)
Spectral Index
Spectral Index
Angular width of beam
Spectral Index
Angular width of beam
Magnetic field convergence
Thermal Source Polarization
Geometry
Thermal Source Polarization
Geometry
Polarizatio
n
Complications
• Photospheric albedo backscatter
– Downward photons can multiple Compton
scatter back toward observer
– Can reduce or induce polarization
• Actual measurement includes
– Earth backscatter
– Instrumental polarization
Backscatter Polarization – Polarized Primary
Backscatter Polarization – Unpolarized Primary
Complications
• Photospheric albedo backscatter
– Downward photons can multiple Compton
scatter back toward observer
– Can reduce or induce polarization
• Actual measurement includes
– Earth backscatter
– Instrumental polarization
RHESSI as a Polarimeter (20 – 100 keV)
A small (3 cm diam by 3.5 cm high) cylinder of Be serves as
scattering element.
The Ge detectors measure the distribution of the scattered radiation.
The rotation of the spacecraft rotation provides an effective method
for fine sampling of the scatter distribution.
An Initial Approach to RHESSI Analysis
Three pairs of detectors with similar background :
detectors 8/9, detectors 3/5 and detectors 4/6.
The data from detectors 3-6 can be used as background estimate
for the polarimeter mode detectors 8/9.
An Initial Approach to RHESSI Analysis
Three pairs of detectors with similar background :
detectors 8/9, detectors 3/5 and detectors 4/6.
The data from detectors 3-6 can be used as background estimate
for the polarimeter mode detectors 8/9.
Can also use detector-detector
scatterings
Available Data
• X4.8 flare of July 23, 2002
Coronal
source C
Footpoints
North (N)
Middle (M)
South (S)
Available Data
• X4.8 flare of July 23, 2002
Available Data
• X4.8 flare of July 23, 2002
• Series of great flares of October & November, 2003
Conclusions
• A definitive measurement of polarization of
hard X-ray solar flare bremsstrahlung would
be a powerful constraint on models
• RHESSI, while not designed as a
polarimeter, does have some capability in
this area
• Data exists for several large flares