Simulations of radio emission from cosmic ray air showers

Tim Huege &Heino Falcke

ARENA-WorkshopZeuthen, 17-03-2005

A new modelling approach

historical works were not detailed enough for application to LOPES

refractive index of atmosphere ~1.0geomagnetic mechanism favoured over

Askaryan-type Cherenkov radiation approach: geosynchrotron emission

electron-positron pairs gyrating in the earth’s magnetic field: radio pulses

coherent emission at low frequencies earlier: analytic calculations presented here: Monte Carlo simulations

based on analytic parametrisations of air shower properties

in progress: Monte Carlo simulations based on CORSIKA-simulated air showers

Monte Carlo simulations of geosychrotron radiation

time-domain MC no far-field

approximations full polarisation info thoroughly tested compared with

analytics and data takes into account:

longitudinal & lateral particle distributionsparticle track length & energy distributionsair shower and magnetic field geometryshower evolution as a whole

Monte Carlo, Analytics & Data:Radial dependence

vertical 1017 eV shower

good agree-ment in spite of very different methods

Data fromAllan et al. (1971)

Results:Spectra for a vertical shower

spectra steeper at higher distances

55 MHz: coherence only up to ~ 300 m (vertical showers)

10 MHz: very coherent

55 MHz

incoherent regime:need better air shower model(inhomogeneities, pitch angles)

incoherent regime:need better air shower model(inhomogeneities, pitch angles)

Results:A vertical shower at 10 MHz

Total field strength pattern of a vertical 1017 eV shower: total field strength

emission pattern highly symmetrical in spite of intrinsic asymmetry introduced by geomagnetic field

only small effect of geomagnetic field inclination on total emission

distance east-west [m]

dist

ance

nor

th-s

outh

[m

]

Results: Emission patternfor inclined showers at 10 MHz

projection effects along the shower axis, but: pattern gets broader as a whole (distance to shower max)!

Vertical 1017 eV shower 45° inclined 1017 eV shower

distance east-west [m]

dist

ance

nor

th-s

outh

[m

]

dist

ance

nor

th-s

outh

[m

]

distance east-west [m]

Results: Coherence as a function of zenith angle

peak emission levels slightly lower, but:coherence up to much higher distances

20 m

500 m

Vertical 1017 eV shower 45° inclined 1017 eV shower

Results:Zenith angle dependence

1017 eV, 10 MHz

flattening with zenith angle

weak B-field de-pendence

not simple projection effect

Results: Linear polarisation

most power in polarisation directionperpendicular to B-field and shower axes

distance EW [m]

dist

ance

NS

[m

]

distance EW [m]

dist

ance

NS

[m

]

45° zenith angle, shower alongnorth-south direction

45° zenith angle, shower alongeast-west direction

Results: Scaling with Ep

for 10 MHz

nearly linear scaling

flatter at higher distan-ces

Parametrisation formula

derived formula parametri-sing dependence on:frequencyobserving positionair shower geometryprimary particle energydepth of shower maximum

very useful for the interpretation of experimental data

accuracy better than~ 15 - 20% in thecoherent regime

available as an online calculator

The next steps

work in progresssubstitution of analytically parametrised air

shower with CORSIKA-based model, including a realistic pitch-angle distribution and intrinsic inhomogeneities

inclusion of atmospheric electric fields in the near future

inclusion of Askaryan-type Cherenkov effects (time-domain)

detailed comparison of simulated events with events measured by LOPES

Conclusions

detailed emission model for the first time model thoroughly verified (analytics/MC) important results so far:

emission pattern intrinsically symmetricpolarisation characteristics (verify geomagnetic origin)radial dependencespectral dependence (low frequencies!)scaling with primary particle energyzenith angle dependence (inclined showers!)all incorporated in a useful parametrisation formula

overall result: signal well interpretable and explainable by geosynchrotron emission