Simulations of radio emission from cosmic ray air showers Tim Huege & Heino Falcke ARENA-Workshop Zeuthen,

A new modelling approach historical works were not detailed enough for application to LOPES refractive index of atmosphere ~1.0 geomagnetic 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 distributions particle track length & energy distributions air shower and magnetic field geometry shower evolution as a whole

Monte Carlo, Analytics & Data: Radial dependence vertical eV shower good agree- ment in spite of very different methods Data from Allan 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 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] distance north-south [m]

Results: Emission pattern for inclined showers at 10 MHz projection effects along the shower axis, but: pattern gets broader as a whole (distance to shower max)! Vertical eV shower45° inclined eV shower distance east-west [m] distance north-south [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 eV shower45° inclined eV shower

Results: Zenith angle dependence eV, 10 MHz flattening with zenith angle weak B- field de- pendence not simple projection effect

Results: Linear polarisation most power in polarisation direction perpendicular to B-field and shower axes distance EW [m] distance NS [m] distance EW [m] distance NS [m] 45° zenith angle, shower along north-south direction 45° zenith angle, shower along east-west direction

Results: Scaling with E p for 10 MHz nearly linear scaling flatter at higher distan- ces

Parametrisation formula derived formula parametri- sing dependence on: frequency observing position air shower geometry primary particle energy depth of shower maximum very useful for the interpretation of experimental data accuracy better than ~ % in the coherent regime available as an online calculator

The next steps work in progress substitution 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 symmetric polarisation characteristics (verify geomagnetic origin) radial dependence spectral dependence (low frequencies!) scaling with primary particle energy zenith angle dependence (inclined showers!)  all incorporated in a useful parametrisation formula overall result: signal well interpretable and explainable by geosynchrotron emission

Results: Polarisation for 10 MHz eV, 45° zenith angle total field strength: pattern simply rotates with  but:  de- pendence in polarisation components

Results: Polarisation is linear emission indeed strongly linearly polarised, as predicted in analytics east-west north-south vertical

Results: Wavefront curvature radio front curved only appro- ximate fit by sphere seen by LOPES spherical surface with 6.3 km radius

Results:  NKG vs. radio pulse strength electron-positron density filtered pulse amplitude pulse amplitude falls off flatter than particle density in shower centre region