Monte Carlo Simulations of Timing Structure: Morphology

4. Shower Morphology

We now discuss the ways that we expect the timing structure the Cherenkov light producedby real gamma ray generated air showers to differ from that of a single track of isotropicallyemitting point sources. In an atmospheric cascade, the number of Cherenkov emitting particlesvaries with altitude. The shower particles have a distribution of directions due to various processesincluding multiple scattering, bending in the Earth's magnetic field, and any change indirection dueto the process which created the particle. Further, the emission along the particle track is directedaccording to the Cherenkov emission angle, and is definitely not isotropic as in our model. Finally,due to the statistical nature of the shower development the exact distribution of particles variesconsiderably, and we can expect the shower to shower fluctuations to be quite large. This will be especially true for low energy showers.

Even with these factors contributing to the complexityof real air showers, the predominant factor in determining the shape of the wavefront is the geometryas described in our model. Figure 5 shows the arrival times of a 50GeV gamma ray from zenith.The colors indicate the altitude of emission of the Cherenkov photons: photons emitted above10,000 m are purple ,those emitted from 6000 m to 10,000 m are colored blue, and photons emittedbelow 6000 m are colored black. Comparison of this figure to Figure 1 shows that the overallstructure of the wavefront is readily understood in term of the emission altitude of the photons.

Equation 8 shows that the timing structure of the shower core reflectsthe distribution of the altitudes of emission.Figure 6 is a series of plotsshowing the particle tracks,the wavefront, the timing structure in a 25 m x 25 m area centered at the core, the distribution ofemission altitudes and a scatter plot of timing vs. emission altitude. The plots are shown for 2different gamma ray showers each at energies of 20, 50, 100 and 300 GeV. The peak of the timingdistribution is correlated to the altitude of maximum emission. Note that this is true only near thecore. Due to the focusing effect mention earlier, we would not expect the envelope of the timingstructure to be much affected at the timing annulus radius. The timing structure at the annulusradius is to first order independent of the altitude of emission distribution. This is important since itimplies that any method of direction determination using the timing AT THE ANNULUS ONLYwill be effective, accurate and independent of the energy of a shower and its altitude of emission distribution.

Figure 7 shows a sample of timing wavefronts for gamma rayshowers with primaryenergies of 20, 50, 100, and 300 GeV. These plots were chosen to show the range of wavefrontsexpected due to fluctuations in shower development. A packet with an unbiased sample of showersis available to scan. The important point to note is that at lower energies, the timing wavefrontsshow a greater diversity in shape and structure. At the low light levels of low energy showers,fluctuations in the shower development are better reflected in the wavefront.