Waveform digitization will provide a wealth of information which undoubtedly will lead to improvements in many aspects of event reconstruction. Since work in this area has only just begun, this section presents a qualitative picture of what can be achieved with waveforms, with a focus on neutrino flavor differentiation. The signatures produced by electron, muon and tau neutrinos are as follows:
| Flux | Double Bang events | νμ + νμ (upgoing) events |
|---|---|---|
| 10-6 E-2(cm2 s sr)-1 | 6 | 10,779 |
| GRB (Fluctuation model) | ∼1 | 43 |
| TD, MX = 1014 GeV, Q0 = 6.31 × 10-35, p=0 | 146 | 58,665 |
| TD, MX = 1014 GeV, Q0 = 6.31 × 10-35, p=1 | 6 × 10-2 | 12 |
| TD, MX = 1014 GeV, Q0 = 6.31 × 10-35, p=2 | 1.5 × 10-2 | 3 |
| TD, MX = 1015 GeV, Q0 = 1.77 × 10-34, p=0 | 120 | 48,605 |
| TD, MX = 1015 GeV, Q0 = 1.58 × 10-34, p=1 | 5.5 × 10-2 | 9 |
| TD, MX = 1015 GeV, Q0 = 1.12 × 10-34, p=2 | 1.1 × 10-2 | 2 |
| Superheavy Relics MX = 1014 GeV | 3 × 10-2 | 4 × 10-4 |
Table 10: Double bang events per km2 per year in 2π stereoradian for representative νμ + νμ fluxes in the literature assuming Fντ/νμ = 0.5. Attenuation has been taken into account to calculate νμ events but not for ντ events. The GRB event rate takes into account fluctuations in distance, gamma factor and energy of the GRB's normalizing to 1000 GRB's/year. The TD's models correspond to maximal predictions of fig.2 in reference [103]. The neutrino flux from the decay of Superheavy Relics is taken from reference [104]. The numbers of double bang events grow by a factor of two if one takes into account recent neutrino oscillation results and uses instead Fντ/νμ = 1.
Tau events can have the characteristic "double bang" signature, which originates from the production and then decay of a tau particle. The first shower comes from the charged current interaction of the ντ with a nucleon. The products of this interaction are a tau lepton and a hadronic shower. The dissipation of the energy in the hadronic shower produces the first "bang."
The second shower happens when the tau travels a short distance and then decays into a tau neutrino. This reaction also causes a hadronic shower. The dissipation of this shower is what produces the second "bang." This energy range at which these event signatures are generated are from a few PeV to a few tens of PeV.
Alternatively, tau events can have the characteristic "lollipop" signature, which is created when the first bang described above is not detected but the tau lepton and the second bang caused by its decay are. These events can be distinguished from muons by the lower level of light produced by the heavier tau lepton in flight.
The energy regimes best-suited to the detection of each neutrino flavor are illustrated in fig. 35.
Figure 36 shows the average photoelectron density observed at an OM as a function of the distance of closest approach of the muon track. Stochastic energy losses have been excluded from the calculation. As expected, the closer the muon is to an OM, the more photoelectrons the OM sees.
Figure 37 shows the photoelectron density as a function of the distance between an OM and the high energy cascade vertex. In this case, the shower has inital energy of 1 PeV. Again, the closer the shower occurs to an OM, the more photoelectrons that module will see. At distances greater than 150 m, the photon flux drops by about one order of magnitude every 60 m.
In this section we discuss the spatial photon flux density distribution as generated by high energy cascades. The light profile of electromagnatic and hadronic cascades can be assumed to be identical as shown by [105]. Simulations in this report are based on electromagnetic cascades. Hadronic cascades differ only in the absolute light output, which is roughly 20% lower than for electromagnetic cascades. The simulations include the orientation of the optical sensor. The quantum efficiency is assumed to be 20% and the diameter of the PMT 25 cm. The spectral sensitivity is based on the Hamamatsu datasheet. The glass transmission of the pressure housing is based on the instrument housings manufactured by Benthos Co. which are currently in use by AMANDA.
In the following we focus on the integrated number of photoelectrons observed by an optical sensor in 2.5 μs of recording time. The time window of 2.5 μs is long enough to integrate over the full length of the expected pulses for cascades in the energy range discussed in this document (up to 100 PeV). (N.B.: The integrated number of photoelectrons scales linearly with the cascade energy.)
Figure 38 shows the spatial distribution of the integrated number of photoelectrons over a 2.5 μs time period. The light emission generated by the 1 PeV cascade is assumed to be cylindrically symmetric. Therefore we can project the density profile in a two dimensional graph, using cylindrical coordinates (rho, zet). In this and the following figures the light emission occurs at the origin (0,0). The shower itself is assumed to be pointlike. The direction of the shower points to the right (positive z). Thus the density is peaked in the forward direction. However, due to scattering of photons in the ice, the light is eventually distributed in all directions. On a scale of 400 m by 800 m as shown in the figure, which is very large compared to the effective scattering length of the ice (24 m) the emission becomes approximately spherical.
One can see that the symmetry of the light distribution is shifted in the forward direction by about one scattering length. The OMs are pointing downward in this simuation. A grid of OMs has been marked in the figure with a horizontal spacing of 125 m and a vertical spacing of 17 m, corresponding to the IceCube baseline design.
Figure 39 shows the maximum number of photoelectrons to strike a downward-facing OM per 10 ns bin for a 1 PeV shower. This figure can be used to derive the regions in which the PMT will saturate. For events relevant for IceCube the saturation depends primarily on the photocathode current. The figure gives the peak cathode current (in photoelectrons and ns). A dynamic range of 150 pe/ns can be used.
Figures 40, 41 and 42 show how pulse shapes increase with distance from the OM for a 100 TeV, 1 PeV and 100 PeV cascade. Therefore the peak amplitude (max pe) drops less strongly than the integrated number of photoelectrons. As these plots clearly show, waveforms will provide us with richly detailed information from which quantities such as cascade energy and direction can be estimated. IceCube OMs will be linear up to at least 150 pe per 10 ns bin, which means that a 100 TeV (1 PeV) cascade can be recorded linearly from distances as close as 30 m (50 m).
Tau neutrinos can produce distinctive "double bang" and "lollipop" signatures in IceCube, as described earlier in section 5.5. Waveform information is particularly well matched to the extraction of these signatures. Although detailed reconstruction algorithms have not yet been written, the following figures should make it clear that sufficiently energetic tau neutrinos can in principle be reconstructed and extracted from IceCube data.
Figure 43 shows the integrated number of photoelectrons from a double bang tau event of about 10 PeV primary energy as seen by downward facing OMs. The decay length of the tau lepton was 225 m. Figure 44 depicts the leading edge times of pulses from a tau lollipop event. Note how the incoming tau leaves a small but clearly distinguishable set of early pulses prior to its decay in to a large cascade. Figure 45 shows the pulse shapes as a function of time generated at various OMs for a double bang 10 PeV tau event. Note the distinctive double-peaked structure in OMs at z = 125 m from the first vertex: the first peak is from the interaction of the ντ; the second from the tau lepton decay. Figure 46 shows a tau event where the decay length of the tau was 300 m. At this distance, no single OM receives significant pulses from the two cascades, but timing measurements still show quite clearly that two distinct cascades were detected. Note that in figs. 43-46 the tau was generated travelling horizontally. That makes this analysis a conservative one because the horizontal orientation is the least favorable one for reconstructing such events.
The studies of individual events gives insight in the variety of pulse shapes that are expected in IceCube. The waveforms depend strongly on the following parameters:
Reconstruction methods that exploit this rich information are yet to be developed. However, based on the above simulations, we conclude that the characteristics of the pulse shapes show a strong correlation with fundamental physical parameters. It should therefore be a goal to record the pulse shapes with a precision sufficient to extract the important features.
It should be noted that the sampling depth of 4 μs can be exceeded in very rare cases (e.g., time profiles of tau events). Also, the dynamic range of existing large area PMTs will be exceeded if either the energy of the event is very high or the PMT is very close to the event. An increased dynamic range remains desirable. However, one should keep in mind that the detection volume at larger distances from the event is very large in these cases. For example, in case of 100 PeV energy cascades or higher, the PMTs will be saturated up to distances of more than 200 m. However there remains a very large shell of detector volume where hundreds of PMT will sample waveforms. This will compensate to a large extent the limited signal quality at closer distances.
