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GeoSynchrotron Radiation from Tau Neutrino Induced Shower
Kwang-Chang Lai
collaborate with C.-C. Chen, G.-L. Lin, T.-C. Liu and J. Nam
Institute of Physics, NCTU, Hsinchu, TaiwanLeung Center for Cosmology and Particle Astrophysics,
NTU, Taipei, Taiwan
Dept. of Phys., CYCU, 2009.04.28
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• Ultra high energy particles are detected by measuring the induced air showers.
• Detecting radio emission is one way to measure the air shower.
• Radio emission can be produced by charged particles gyrating the geomagnetic field.
• An earth-skimming tau neutrino will induce an air shower after turning into tau.
• Resulted emission is calculated in the coherent geosynchrotron model.(Huege and Falcke, A&A, 2003)
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neutrino TauShower
Radio waveCherenkov radiationFluorensence lightCharged particles
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t1
t2
t3
t4
t5
Shower front Shower max
Air shower
Longitudinal distribution
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• The shower comes from em cascades of tau decay products, dominantly
• We simulate electron showers at energies of 10^16.5, 10^17, 10^17.5, 10^18 and 10^18.5 eV.
• These energies correspond to comogenic neutrinos.• Shower structure, angular and energy distribution, is
adapted to calculate the synchrotron radiation.• The pattern of the radiation field and the radio pulse
are presented.
€
e±, μ ±, and π ± .
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Geometry
ϑ
ϕ ),( ϕϑθ
),( ϕϑR||e
)
Front of shower max.
Bv
10km0≡ηk =1000m
θ ||e)
⊥e)
off d
istance d
observation distance R
x
y
z
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emission position, k(curvature radius)
€
ϑ€
ϑ
Shower front is modeled as a part of a spherical surface.Each particle is assumed to emit radially from the center. is thus defined. So is curvature radius k.
Shower frontp()(r)
p(): particle energy distribution(r): particle lateral distribution
shower core
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€
vE (R,ω) =
4π
c
⎛
⎝ ⎜
⎞
⎠ ⎟
1/ 21
R
ω e
8cπA||(ω)(−
) e ||), A|| > A⊥
€
A||(ω) = i2ρ
3cγ −2 + θ 2
( )K2 / 3
ωρ
3cγ −2 + θ 2
[ ]3 / 2 ⎛
⎝ ⎜
⎞
⎠ ⎟.
Synchrotron radiation for one particle
ω, γ, ρ, θ: frequency of radiation, Lorentz factor and gyroradius, line-of-sight angle. Electron-positron pair coherence assumed.
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)),,((),()( 1
),( ωϕϑϕϑω REpddN
RES ∫ Ω=
Total yield by superposition over shower profile:
p, ρ: energy distribution and lateral profile generated from simulation.
)0,0(),( |||| ee)) ≡ϕϑ is approximated.
Electron-positron coherence helps to eliminate . ⊥A
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Blue is fitting curveRed is simulated curve
Shower Structure:
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Shower Structure:particle energy distribution
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Shower Structure:particle energy distribution
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Shower Struture:Angle of Emission
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• The shower comes from em cascades of tau decay products, dominantly
• We simulate electron showers at energies of 10^16.5, 10^17, 10^17.5, 10^18 and 10^18.5 eV.
• These energies correspond to cosmogenic neutrinos.
• Shower structure, angular and energy distribution, is adapted to calculate the synchrotron radiation.
• The pattern of the radiation field and the radio pulse are presented.
€
e±, μ ±, and π ± .
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50MHz75MHz100MHz
R
dAntenna distance d
R=10km
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10^17eV10^17.5eV10^18eV
R
dAntenna distance d
R=10km
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10^16.5eV10^17eV10^17.5eV10^18eV
R=10kmd=0
Radiation Spectra
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Scaling Behavior
at centerd=500m
d=1000m
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emission position, k(curvature radius)
€
ϑ€
ϑ
Shower front is modeled as a part of a spherical surface.Each particle is assumed to emit radially from the center. is thus defined. So is curvature radius k.
Shower frontp()(r)
p(): particle energy distribution(r): particle lateral distribution
shower core
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Shower Struture:Emission Position
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Effect of Curvature Radius
10^16.5 eV
10^17 eV
10^17.5 eV
10^18 eV
10^18.5 eV
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10^17eV10^17.5eV10^18eV
R
d R=10kmd=0
Pulse Expectation
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at core500m1000m
R
d
Antenna distance d
R=10km
Pulse Expectation
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10km
15km
20km
30km
40km
observation distance R
R
d
Antenna distance d
Pulse Expectation
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Summary
• We analyzed the radio property of tau neutrino induced shower.
• Shower profile has universal features.• The universal Lorentz and lateral distributions allow to
adapt fitting formulae in calculation.• The coherent geosynchrotron model, though
incomplete, rendered a picture for detecting tau neutrino by radio emission.
• This work provide a basis to develop a realistic simulation.
• It also is a good reference for experiments design.