Studying magne-c turbulence from polarized mul-frequency...
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Studying magne-c turbulence from polarized mul--frequency synchrotron emission Hyeseung Lee 1 with Jungyeon Cho 1 , A. Lazarian 2 1 Chungnam Na;on University, South Korea 2 University of Wisconsin-Madison, USA KNAG 2016
Transcript of Studying magne-c turbulence from polarized mul-frequency...
Studyingmagne-cturbulencefrompolarizedmul--frequencysynchrotronemission
HyeseungLee1
withJungyeonCho1,A.Lazarian21ChungnamNa;onUniversity,SouthKorea
2UniversityofWisconsin-Madison,USA
KNAG2016
Outline0
KNAG2016
Topic1spa-ally–coincidentregions
Topic2spa-ally–separatedregions
LOS LOS
inprogress
powerspectrumofPolariza-onP(or)ofitsderiva;vedP/dλ2fromspa-ally-coincidentregions
anisotropy
ofPolariza-onP
fromspa-ally-separatedregions
Sta-s-cs
Quan-ty
Geometry
Mo;va;on
MagnetohydrodynamicTurbulence
starforma;onMagne;c
reconnec;on
Cosmicrays
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PDF Structurefunc-on
(RainerBeck&RichardWielebinski2013)
Magne-cField
���
Synchrotronemission
Faradayrota-on
I ∝B⊥γ
Φ∝B||
1
PowerspectrumKNAG2016
Mo;va;on
MagnetohydrodynamicTurbulence
starforma;onMagne;c
reconnec;on
Cosmicrays
��� ���
PDF Powerspectrum Structurefunc-on
(RainerBeck&RichardWielebinski2013)
Magne-cField
���
Synchrotronemission
Faradayrota-on
I ∝B⊥γ
Φ∝B||
1
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sta;s;caldescrip;on:powerspectrum1-0
||
+
+
+��� ||E(k)
k[Hz]
real-spacedistribu;onofv(r),b(r),ρ(r),…
��� ���
Powerspectrum:E(k)e.g)E(k)~k5/3(Kolmogorovspectrum)
wavenumber(k∝1/λ)
Amplitude(S)
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Fouriertransform
Synthe;cData
B!"(x") = B0 + A(k
")eiχ
k =2
kmax−1
∑ ,B0=0
N3=5123
1 10 100k
0.0001
0.0010
0.0100
0.1000
1.0000
E(k)
k-5/3
InFourierspace
|A(k)|2∝k-m
m=11/3forKolmogorov
(Cho&Lazarian2010)
2π
Method–Data
Spectrumofmagne;cfieldfollowsaKolmogorovspectrum
1-2-1
wherekmax=N/2(N=resolu;on)
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Synthe;cData
B!"(x") = B0 + A(k
")eiχ
k =2
kmax−1
∑ ,B0=0
N3=5123
Method–Data
wherekmax=N/2(N=resolu;on)
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1 10 100k
10-5
10-4
10-3
10-2
10-1
100
E(k)
mB=-1.67mρ=-1.00
k-5/3formagne;cfield
k-1fordensity
1-2-1
1 10 100k
10-5
10-4
10-3
10-2
10-1
100
E(k)
mB=-1.67mρ=-1.67
TurbulenceData:basedona3rdorderaccuratehybridnon-osciallatory(ENO)schemeinaperiodicboxofsize2π(Cho&Lazarian2002)
δρ δt +∇⋅ (ρv!) = 0
δv!δt + v!⋅∇v!+ ρ−1∇(a2ρ)− ∇×B
!"( )×B
!"4πρ = f
!"
δB!"−∇× (v
"×B!"
) = 0MA=v/VA~0.7MS=v/a~0.7
Method–DataSynthe;cData
B!"(x") = B0 + A(k
")eiχ
k =2
kmax−1
∑ ,B0=0
wherekmax=N/2(N=resolu;on) N3=5123
KNAG2016
1-2-2
Φ(X, z) = 0.81 ne(z)1cm3
⎛
⎝⎜
⎞
⎠⎟Bz (z)1µG
⎛
⎝⎜
⎞
⎠⎟dz1pc⎛
⎝⎜
⎞
⎠⎟radm−2
0
z∫
§ Polarizedintensityobservedata2Dposi;onXontheplaneoftheskyatwavelengthλ
P X,λ 2( ) = dzPj X, z( )0
L∫ e2iλ
2Φ X,z( ),
Intrinsicpolariza;ondefinedbytheStokesparametersQandU:
Pj=Qj+iUj
z
Method:Polariza;onfromsynchrotronrad.
Faradayrota;onmeasure
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1-2-3
kz
ky
kx
E3D (k) = P3D (k)dkk−0.5
k+0.5∫
= v!k
2dk
k−0.5
k+0.5∫
shell-integrated1Dspectrumfora3Dvariable
Ky
Kx
E2D (K ) = P2D (K )dKK−0.5
K+0.5∫
= S!K
2dK
K−0.5
K+0.5∫
Ring-integrated1Dspectrumfora2Dvariable
Sta;s;cs–Powerspectrum
k k+1
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1-2-4
γ=2.0
The varia;ons of the spectral index of rela;vis;c electron energydistribu;on change the amplitude of the fluctua;ons, but not thespectralslopeofthesynchrotronpowerspectrum.
Result1–spectralindexofEED(γ)
EED(ElectronEnergyDistribu;on):N(E)dE=N0E-γdEKNAG2016
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5γ
0
1
2
3
4
5
6
E 2D/E
2D,γ=
2
(b)
LP12Our results
1 10 100K
0.01
0.10
1.00
10.00
100.00
1000.00
10000.00
E 2D(K)
γ=4.0γ=3.5γ=3.0γ=2.5γ=2.0γ=1.5
K-8/3
(a)
1-3-1
γ=1.5~4.0
Dγ ≈ C ⋅2γ−2!B2γ−4 Γ 1+γ[ ]− Γ 1+ 1
2γ
⎡
⎣⎢⎤
⎦⎥
2⎛
⎝⎜⎜
⎞
⎠⎟⎟×Dγ=2
(Lazarian&Pogosyan2012)
Φ(X, z) = 0.81 ne(z)1cm3
⎛
⎝⎜
⎞
⎠⎟Bz (z)1µG
⎛
⎝⎜
⎞
⎠⎟dz1pc⎛
⎝⎜
⎞
⎠⎟radm−2
0
z∫
§ Polarizedintensityobservedata2Dposi;onXontheplaneoftheskyatwavelengthλ
P X,λ 2( ) = dzPj X, z( )0
L∫ e2iλ
2Φ X,z( ),
Intrinsicpolariza;ondefinedbytheStokesparametersQandU:
Pj=Qj+iUj
z
Method:Polariza;onfromsynchrotronrad.2-3
Faradayrota;onmeasure
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1-2-3
Fixedintrinsicsynchrotronemission(Q/I=1,U/I=0)
EffectofFaradayrota-on
Result2-synchrotronradia;onorFaradayrota;on1-3-2
P1P2P3P4
xn-4 xn-2 xn-1 xn
P1Φ1Φ2
Φ3
P1=P2=P3=P4
Φ1≠Φ2≠Φ3
P2Φ2
Φ3
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λ 2 ~ Kmax
2π ne B||P X,λ 2( )∝ e2i λ 2 Φ X,z( )
thesynchrotronemissiongetsuncorrelated
1 10 100K
10-6
10-4
10-2
100
102
104
106
E 2D(K)
λ=0.020λ=0.14λ=0.36λ=0.66λ=1.3λ=2.5
K-8/3
(a)λ~1
Fixedintrinsicsynchrotronemission(Q/I=1,U/I=0)
EffectofFaradayrota-onUniformFaradayroata;on
(ne(z)=1,Bz(z)=1)
Effectofsynchrotronemission
Result2-synchrotronradia;onorFaradayrota;on1-3-2
intrinsicsynchrotronemission
P1P2P3P4
xn-4 xn-2 xn-1 xn
P1Φ1Φ2
Φ3
P1P2P3P4
xn-4 xn-2 xn-1 xn
Φ1 P1Φ2Φ3
P1=P2=P3=P4 P1≠P2≠P3≠P4
Φ1=Φ2=Φ3Φ1≠Φ2≠Φ3
P2Φ2
Φ3
Φ2Φ3P2
KNAG2016
Fixedintrinsicsynchrotronemission(Q/I=1,U/I=0)
EffectofFaradayrota-onUniformFaradayroata;on
(ne(z)=1,Bz(z)=1)
Effectofsynchrotronemission
Result2-synchrotronradia;onorFaradayrota;on
KNAG2016
1 10 100K
10-6
10-4
10-2
100
102
104
106
E 2D(K)
λ=0.020λ=0.14λ=0.36λ=0.66λ=1.3λ=2.5
K-8/3
(a)
1 10 100K
10-2
10-1
100
101
102
103
104
105
E 2D(K)
λ=0.020λ=0.12λ=0.30λ=0.56λ=0.90λ=2.0λ=3.2λ=4.7λ=6.3λ=17.
K-8/3
(b)
1-3-2
small-K large-K
Faradaydepolariza;oneffect negligible
smallλ
dPdλ 2
=P λ1( )−P λ2( )
λ12 −λ2
2
dP/dλ2isalsousefultorecoverthesta;s;csofFaradayrota;on!
(Lazarian&Pogosyan2016)
Result2-synchrotronradia;on&Faradayrota;on
incodeunitΦ(X, z)∝ Bz (X, z)ρ(X, z)z=1
N
∑ N
electronnumberdensity(ne)
KNAG2016
1 10 100K
10-2
100
102
104
E 2D(K)
αb=1.67αρ=1.67
λ=0.020λ=0.29λ=0.90λ=1.4λ=2.0λ=2.5λ=3.2λ=3.9
K-8/3
(a)
1 10 100K
0.001
0.010
0.100
1.000
10.000
100.000
1000.000
Spec
trum
of d
P/dλ
2
λ=1.163λ=1.420λ=1.735λ=2.119λ=2.588λ=3.162
αB=1.67αρ=1.67K-8/3
(a)
1 10 100K
0.001
0.010
0.100
1.000
10.000
100.000
1000.000
Spec
trum
of d
P/dλ
2
λ=1.163λ=1.420λ=1.735λ=2.119
αB=1.67αρ=1.00K-2
(b)
1-3-3
synchrotronemissionF.R.effect
Faradaydepolariza;oneffect
fluctua;onsinF.R.measure
★
Ky
Kx
WecanobtainspectruminFourierspaceforcertainwave-vectorsthroughinterferometricobserva;ons!
1 10 100k
0.0001
0.0010
0.0100
0.1000
1.0000
E(k)
k-5/3
Telescoperesolu;on
numberofbaselines
noise
Interferometricmethod
KNAG2016
1-4
0.0753
0.5314
0.9875
1.4437
1.8998
2.3559
2.8121
-1.5185
-1.0666
-0.6148
-0.1629
0.2890
0.7408
1.1927
★
★
Result3–effectoftelescoperesolu;on
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1 10 100K
0.1
1.0
10.0
100.0
1000.0
E 2D(K)
synthetic
λ=0.750
θFWHM=2.0θFWHM=4.0θFWHM=6.0θFWHM=8.0θFWHM=10.θFWHM=30.θFWHM=50.
1-4-1
θFWHM=3’
★
Ky
Kx
numberofbaselines
Result3–numberofbaselines
KNAG2016
1-4-2
1 10 100K
10-5
10-4
10-3
10-2
10-1
100
101
102
P 2D(K)
Nbase,30.(a)
1 10 100K
10-5
10-4
10-3
10-2
10-1
100
101
102
P 2D(K)
Nbase,60.(b)
NBASE=30
★
noise
Result3–effectofnoise
KNAG2016
1-4-3
1 10 100K
10-5
10-4
10-3
10-2
10-1
100
101
102
P 2D(K)
1.%10%20% S/N=1/5
1 10 100K
10-8
10-6
10-4
10-2
100
P 2D(K
)
λ=0.90cmnoise level=20.%
m=-3.67m=-4.00m=-3.34
(b)
K-11/3
K −me−K2 2σK
2
Results3–usingMHDturbulencedata
KNAG2016
1-4-3
θFWHM=3’,NBASE=30,S/N=1/5
sta;s;caldescrip;on:anisotropy
KNAG2016
R⊥
R||
R⊥
R||
Structurefunc-on
Quadrupolemoment
M~n (R) = 1
2πe−inφ D
~I R,φ( )dφ
0
2π∫
2-1
DI (!R) = I(
!X)− I(
!X +!R)( )
2, !R =!R|| +!R⊥
2-ndorderstructurefunc-on
R||
R⊥
B0
Ii(X)-Ii(X+R)
M~2 (R)
M~0 (R)
φ
Modedecoupling:Alfven,fast,slow2-2
KNAG2016
OurnumericalresultsshowthatwecanstudyMHDturbulencethroughpolarizedsynchrotronemission.Thisstudycanbeperformed• inthepresenceofFaradayrota;onanddepolariza;oncausedby
turbulentmagne;cfield,• intheseungswhenonlyFaradayrota;onisresponsibleforthe
polariza;onfluctua;ons,• inthepresenceofeffectsoffinitebeamsize,noise,andafew
baselinesèOurpresentstudypavesthewayforthesuccessfuluseof
spectrumwithobserva-onaldata.
Summary3
KNAG2016
Thankyouforyouracen-on!
Anyques-ons?
