The Shower Profile
Once the geometry of the event has been determined, the amount of light seen by the detector can be corrected for 1/r2 spread and attenuation losses to yield a shower size (in number of electrons, since most of the shower is dominated by the electromagnetic component.) as a function of the atmospheric depth penetrated. This function is referred to as a "shower profile".
Two important quantities can be extracted from the shower profile. First, the energy of the primary cosmic ray is proportional to the shower size. Second, the depth of the shower maximum can be read off the plot and gives a statistical measure of the composition of the primary cosmic ray. For the above event, there are ~6x108 particles at shower maximum. This translates to an energy of ~8x1017 eV for the primary particle. The shower maximum is measured at just over 800 g/cm2, which is more consistent with light composition for this energy. One should not attach too much significance to the measured value of Xmax, because the expected fluctuations are very large and conclusions should only be drawn from the average values over many events.
The actual shower profile fitting procedure is more complicated than the simplified description above would lead you to believe. The light observed by the detector includes several components in addition to the scintillation light. This is illustrated for a simulated 1018 eV event in the figure below. Here the shower development is parameterized in terms of altitude (top) and the "viewing angle" qi. The angle qi, introduced in the diagram above illustrating the timing fit, is the angle between the reverse direction of the shower and the pointing direction of the pixel in question. For example, those pixels which view the shower head-on would have qi values near zero.
Five distinct sets of curves are shown in the figure to the right. The curve marked Ne shows the shower size (relative to the scale on the right) as a function of shower development. The other four curves show the fractional contribution (left-hand side scale) to the total amount of light seen by the detector at each stage of shower development: (a) Cv: direct Cerenkov light for small viewing angles, (b) Sc: scintillation (fluorescence) light, (c) R: Cerenkov light from molecular (Rayleigh) scattering, and (d) M: Cerenkov light from particulate (Mie) scattering. All four components must be included when the observed light signal is fitted to a shower profile.
