Radio-emission distribution functions

Lateral distribution functions

Geomagnetic and charge-excess

See: I3RbGeoCe class

The observed radio emission is parameterized based on the energy fluence, split into the vxB and vxvxB directions (motivated by the main emission mechanisms for radio). The function has been tuned for the analysis of radio emission at the South Pole in the frequency range of 70-350 MHz, see this proceeding. The logarithm of geomagnetic energy fluence is described by the sum of two modified gaussians on the vxB axis along with a sigmoid for distances within the Cherenkov ring. The Askarian emission is described by a skew-normal distribution. These two LDFs are summed together with a parameterized relative normalization. The LDF also includes an overall normalization such that the integral of the energy fluence out to r=inf is E = unity (in IC units). Thus, the “shower size parameter” is the amount of radiated energy in the relevant frequency band.

The LDF loads in the special numbers from a text file (see rock_bottom/resources/data/geo_ce_param) and these can be updated by simply specifying different formatted ASCII files by using the loaders in the I3RbGeoCe class.

Two-Gaussian

See: I3RbTwoGauss class

For this LDF, the emission is described as the sum of two Gaussians that are offset by a variable amount. The two Gaussians have opposite signs such that the sum produces the “bean” shape that is created by the interference between the two emission mechanisms. As such, the LDFs are offset along the vxB axis. For a given point, only one value is returned so this could be used to describe e.g. the total fluence. The normalization has no correspondence to a physical quantity.

Timing functions

Hyperbolic wavefront

See: I3RBTimeHyperbola class

The radio wavefront is approximately a hyperbola where far from the emission point the emission follows a Cherenkov-like emission with an opening angle of ~1 degree. However, close the the shower, the emission can no longer be treated like a point source and the emission arrives on a curved shape. This function approximately captures that and includes parameters which describe the cone pitch angle, the width of the curved part, and an overall time delay.