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

• 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)

neutrino TauShower

Radio waveCherenkov radiationFluorensence lightCharged particles

t1

t2

t3

t4

t5

Shower front Shower max

Air shower

Longitudinal distribution

• 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 ± .

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

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

€

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.

)),,((),()( 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

Blue is fitting curveRed is simulated curve

Shower Structure:

Shower Structure:particle energy distribution

Shower Structure:particle energy distribution

Shower Struture:Angle of Emission

• 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 ± .

50MHz75MHz100MHz

R

dAntenna distance d

R=10km

10^17eV10^17.5eV10^18eV

R

dAntenna distance d

R=10km

10^16.5eV10^17eV10^17.5eV10^18eV

R=10kmd=0

Radiation Spectra

Scaling Behavior

at centerd=500m

d=1000m

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

Shower Struture:Emission Position

Effect of Curvature Radius

10^16.5 eV

10^17 eV

10^17.5 eV

10^18 eV

10^18.5 eV

10^17eV10^17.5eV10^18eV

R

d R=10kmd=0

Pulse Expectation

at core500m1000m

R

d

Antenna distance d

R=10km

Pulse Expectation

10km

15km

20km

30km

40km

observation distance R

R

d

Antenna distance d

Pulse Expectation

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.