# First Year Performance Paper - Section 5.2

## 5.2 Shower reconstruction

Reconstruction of the direction and size of an air-shower proceeds from the arrival times of the shower front at the detectors on the ground together with a measure of the number of particles or amount of energy deposited in each detector. As evident from Fig. 23, typical air-shower signals produce hundreds or thousands of photoelectrons in IceTop tanks. Some examples of the resulting waveforms are shown in Fig. 14. The waveforms occasionally show structure that may reflect contributions of individual particles or groups of particles.

Several algorithms were developed to estimate the arrival time of the first particle in the shower front at an IceTop tank (leading edge). The most robust algorithm looks for the first pair of bins in the waveform with values above a fixed threshold between which the increment in voltage is locally at maximum (i.e. the steepest rise point). The intersection of the tangential line going through these points with the baseline is taken as an estimate of the leading edge. The sum of charges in all bins of the waveform above the threshold is taken as an estimate of total charge in the waveform. The time of the leading edge of the waveform can be determined to significantly better accuracy than From February to July 2005 the IceTop trigger required 10 DOMs within 2 μsec with signals above a voltage threshold equal to ten times the peak voltage of a single photoelectron. The trigger rate with this setting is approximately 0.7 Hz, about 40% of which involve all four stations, while the remainder have hits in only three stations. With only four stations, many of the triggers are from showers with cores outside the perimeter of the array, where the core location accuracy is poor. For the initial analysis we fit a plane wave to the shower front. By selecting showers with apparent cores (as determined by weighting the tank locations by the observed signals) within 45 m of the geometric center of the 4- station array, we obtain a subset enriched in "contained" events. Distributions of zenith and azimuth for this subset are shown in Fig. 24.

Reconstructed directions of showers measured with the surface array: (a) zenith angle. (A fit to the sec? law typical of atmospheric showers is shown.) (b) azimuth.

To obtain the most accurate possible determination of shower direction requires accounting for the delay of the leading edge behind a plane perpendicular to the trajectory of the cascade, which increases with core distance. Reconstruction accuracy is also limited by distribution of arrival times of the first particle in the shower front, which depends on shower size and distance from the shower core, and on accuracy of location of the core. More refined fits to shower direction and core location will become appropriate in future seasons when the array is larger.

(a) Showe-size spectrum in units equivalent to total visible energy deposited in the 8 tanks; (b) Times of 3 specific DOMs on String-21 in coincident events relative to the first IceTop DOM in the event. The peak near 0 is the time a specific IceTop DOM is hit.

Figure 25a shows the size-spectrum of showers measured by the IceTop array for a sample of events with apparent core location within 45 m of the center of the array. Shower size at the ground is measured here in terms of total visible energy summed over all tanks, based on the calibration with muons discussed above.

Studies of the cosmic-ray energy spectrum and composition require detailed simulations which are not yet available. A crude estimate using the ratio of the total area of the array to the total area of the 8 tanks leads to an estimate of total Nμ ↑ 4×104 at 10 GeV visible energy, which corresponds to showers with primary energy of 1 PeV. The visible energy spectrum of Fig. 25a has a power low behavior at high energy and a characteristic threshold shape at low energy. Given the spacing of the stations, IceTop with a 4-station threshold is expected to be 50% efficient at an energy of 300 TeV. This is consistent with the measurement shown in Fig. 25a, which includes 3-station hits as well as 4-station hits.