Probing Coronal and Chromospheric Magnetic Fields with Radio

Probing Coronal and
Chromospheric Magnetic Field
with Radio Imaging Polarimetry
Kiyoto Shibasaki, Kazumasa Iwai
(Nobeyama Solar Radio Observatoy, NAOJ)
Presented by Kiyoshi Ichimoto
(Hida Observatory, Kyoto University)
2014/12/04
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Outline
1. Introduction
2. References
3. Circular Polarization Measurements by the
Nobeyama Radioheliograph
4. Post flare arcade of loops on Oct. 22,2000
5. Magnetic field in the Chromosphere
6. Summary
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1. Introduction
• Interaction of moving charged particles with B due to Lorenz force
( F = q v x B)
• gyration motion around B
• Cyclotron frequency is in microwave range
f H (MHz) = 2.8 x B (Gauss) (17GHz ~ 6,000 G)
• Circularly polarized EM wave interacts with gyrating electrons
• Classical treatment (no Quantum Mechanics !)
• simple inversion (pol. deg -> B||)
• Continuum emission (no lines)
• No Doppler effect
• magnetic fields in Hot, Turbulent and Moving plasma can be measured
• B|| only, low spatial resolution
2. References
• Studies of interaction between EM waves and
magnetized media developed in the field of the
terrestrial Ionosphere
• “The Magneto-Ionic Theory and its Applications to the
Ionosphere” by J. A. Ratcliffe, Cambridge University Press,
1962
• Applications to the Sun and Planets are in:
• “Radio Emission of the Sun and Planets” by V. V.
Zheleznyakov, Pergamon Press, 1970 (English translation)
• Simplified formulae for applications can be found in:
• “Radio Emission from the Sun and Stars” by G. A. Dulk,
Ann. Review Astron. Astrophys. 1985. 23: 169-224
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Thermal free-free emission
TB: Observed brightness temperature
=
TB ∫ T exp( −τ )dτ
T: plasma temperature
=
=
τ ∫ κ dl,
κ const × ne2T −3/2
TB ~ Tτ ~ EM / T (τ << 1, optically thin uniform cloud)
EM = ∫ ne2dl
• In magnetic field:
κ o=
κ (1 ± f H cos(α ) / f )
,x
(for ordinary and extraordinary mode)
=
TB o ,x ~ TB ( f ± f H cos(α ) )
(TB x TB o ) / (TB x + TB o ) ~ n( f H / f ) cos(α )
p =−
where n = −∂ (ln(TB )/∂ (ln(f)) , Bogod and Gelfreikh, 1980)
Inversion at 17 GHz
• Polarization degree and magnetic field
p=
n × ( f H / f ) cos(α ) ,
TB ∝ f − n
=
) 60 / n × p(%) at 17 GHz
B|| (Gauss
• Optically thin case:
TB ∝ f −2
B|| (Gauss=
) 30 × p(%)
(1% ~ 30 Gauss )
n=0
• Optically thick case:
(uniform temperature) p = 0
Instruments: Nobeyama radioheliograph
Table Specifications of Nobeyama radioheliograph.
Frequency
17 GHz (I and V)
34 GHz (I)
Field of view
Full disk
Spatial
resolution
10 arcsec (17GHz)
5 arcsec (34GHz)
1 frequency band for polarization
2 frequency bands for intensity
𝐵𝐵𝑙𝑙 𝐺𝐺 = 10700
1 𝑉𝑉
𝑛𝑛𝜆𝜆 𝑐𝑐𝑐𝑐 𝐼𝐼
2-D Radio magnetic filed
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4. Post flare arcade of
loops
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Event on Oct. 22, 2000
Upper Left：17GHz intensity (I)
Loop like structure corresponds to bright
arcade top. Each flare loop is in the plane
of line of sight.
Upper Right：17GHz circular polarization (V)
Lower Left：Circular polarization degree（V/I）
～ 0.3%
Mag. field distribution（~10 Gauss）
Post flare arcade of loops on Oct. 22,
2000
• optically thin thermal f-f (Tb ratio at 34 and 17 GHz
is about 1/4)
• Uniform circular polarization along the arcade with
0.3 % (~10 G)
• magnetic field increases upwards
(EM weighted mag. field strength)
• suggests loop structure, not cusp structure
Measured mag. field
strength increases
upwards
Measured mag. field
strength decreases
upwards due to Cusp
shape
YOHKOH
Observation
Soft X-ray Telescope（SXT)
Tsuneta (1997)
?
5. Magnetic field in the
Chromosphere
(optically thick case with
temperature gradient)
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Polarization at the chromosphere
Thermal bremsstrahlung
(Free-free emission)
at microwave range
At the chromosphere
𝜏𝜏 ≈ 1
Magnetic field
𝜏𝜏𝑜𝑜 ≠ 𝜏𝜏𝑥𝑥
penetrate into different layers
Temperature gradient
𝑇𝑇𝐵𝐵,𝑜𝑜 ≠ 𝑇𝑇𝐵𝐵,𝑥𝑥
𝑃𝑃 =
𝑇𝑇𝐵𝐵,𝑥𝑥 − 𝑇𝑇𝐵𝐵,𝑜𝑜
𝑇𝑇𝐵𝐵,𝑋𝑋 + 𝑇𝑇𝐵𝐵,𝑜𝑜
Polarization
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Observation: circular polarization
polarization
corresponds to
the
photospheric
magnetic field
Red：Radio pol (+)
0.5 1.0
％
Blue：Radio pol (-)
-0.5 -1.0 -1.5％
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Radio Magnetic filed
Green contours
n: =
circular polarization deg.
1 𝑉𝑉
𝐵𝐵𝑙𝑙 𝐺𝐺 = 10700
𝑛𝑛𝜆𝜆 𝑐𝑐𝑐𝑐 𝐼𝐼
𝜕𝜕log 𝑇𝑇𝐵𝐵
𝜕𝜕log 𝜆𝜆
＋ Green: n, Red: Mag. Field (N), Blue: (S)
HMI (G) Radio (G)
FP+
568
116
FP-456
-217
Radio Magnetic filed is derived
Ratio
0.20
0.47
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6. Summary
• Simple examples of magnetic field measurements are
presented using radio imaging instrument (NoRH)
• Coronal magnetic field in a post flare arcade of loops
(optically thin, uniform temperature)
• Chromospheric magnetic field in an active region
(optically thick with temperature gradient)
• There are other ways of measuring magnetic field
• Measurement of sunspot magnetic field using gyro-resonance
emission mechanism (highly polarized bright source above
sunspots)
• Measurement of very weak magnetic field in the upper corona or in
the inter-planetary space using Faraday rotation mechanism (linear
polarization position angle rotate with frequency)
• Measurement of magnetic field filled with non-thermal electrons
(accelerated in solar flares) due to gyro-synchrotron emission
• and others.
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END
Questions
 shibasaki.kiyoto@nao.ac.jp
Abstract
Circularly polarized radio waves interact with gyrating electrons in the magnetic
field due to the Lorentz force. Emissivity and absorption coefficients of right hand
circular polarization (RCP) and that of left hand circular polarization (LCP) are different.
This is the essence of magnetic field measurements with radio technique.
Inversion procedure is rather simple because these processes can be treated by
classical theory of electromagnetism and mechanics. In thermal plasma, emissivity
and absorption coefficient of radio waves are strongly coupled and their ratio is
approximated by Rayleigh-Jeans formula. Optical depths (line-of-sight integrated
absorption coefficient) of RCP and LCP differ in the presence of magnetic field. The
radio intensity difference between RCP and LCP (Stokes parameter V) can be used to
measure line-of-sight magnetic field strength.
Measurement of magnetic field strength in the corona is rather simple due to small
optical depth. Even in optically thick chromosphere, we can estimate magnetic field
strength due to steep temperature gradient. Examples of magnetic field distribution in
the corona and in the chromosphere observed by the Nobeyama Radioheliograph will
be presented. There are other methods to estimate magnetic field strength using
radio techniques in the solar atmosphere and also in the interplanetary space. These
methods will also be reviewed.
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