The charged current interaction of UHE electron neutrinos and the neutral current interactions of UHE neutrinos of all active flavors will produce large localized depositions of energy in the IceCube detector. The signature of these electromagnetic or hadronic showers (cascades) is a bright, pointlike source of Cherenkov light4 as shown in fig. 24. To be detected, cascades must occur near or within the active detector volume, and consequently the effective volume for their detection is substantially smaller than that of muons. However, cascades have the advantage that their energies can be measured more accurately than muon events, making it easier to separate UHE cascades from background. This is especially true for νe charged current and "double bang" ντ interactions, where the resulting cascades give a fairly accurate measure of the energy of the parent neutrino.
Cascade events were generated using one of three generators depending on the study:
These vertices are then passed to the detector simulation package, amasim, which generates PMT hits in the array and builds them into events. Triggers were generated on a coincidence of five hits in 2.5 μs. Additionally, a feature of amasim was enabled that preserves pulse amplitude information for each pulse in the event that a single OM receives multiple hits. 5 This additional information approximated waveform readout in IceCube.
Applying algorithms developed for AMANDA on simulated IceCube data, we have estimated the vertex, direction, and energy resolutions of cascades in IceCube. We have also estimated these resolutions using newly developed algorithms tailored to IceCube data. Estimates using AMANDA algorithms are conservative since they rely primarily on the arrival times of the first photons in each PMT, while in IceCube we will have access to much more detailed waveform information. Estimates using new algorithms are also conservative since we anticipate using the waveform information in a more complete manner than presented here.
The AMANDA algorithm for reconstructing the vertex position and time is based on a model of the scattering and absorption of Cerenkov light in the ice. It maximizes a likelihood function which depends on a parametrization of the probability distribution of observing one photon with a given time delay at some distance from the source. The AMANDA algorithm for reconstructing direction and energy is also a maximum likelihood fit which uses a parametrization of the expected number of photons at each PMT as a function of cascade energy and the relative cascade-PMT direction.
Applying these algorithms to simulated IceCube cascades with contained vertex positions (vertices at least 100 m from the edge of the detector), resulted in energy and zenith angle resolutions which were better than in AMANDA. The resolutions are as follows:
These resolutions are illustrated in fig. 25.
Ultimately, we anticipate that we will construct a likelihood function which uses the full waveform information from each PMT, maximizing the probability that each PMT observed a particular waveform as a function of cascade (r,t,E, d). Moreover, waveform readout will dramatically increase the dynamic range of the PMTs. Cascade reconstructions in particular would benefit from this enhancement due to the nature of the cascade signal: OMs very close to the cascade vertex are expected to receive thousands of Cherenkov γs, but simultaneously the detector must be able to resolve the single γ hits at large distances for accurate energy reconstruction.
Techniques for suppressing the cosmic ray muon events in IceCube have been borrowed from AMANDA cascade analyses. The very large instrumented volume of IceCube makes cosmic-ray muon rejection very efficient using quick algorithms based on event topology and total charge information. Once these fast filters have reduced the data volume down to manageable levels, maximum likelihood fits are performed to reconstruct the cascade vertex, direction, and energy and further cuts are made on these output quantities.
It should be noted that these cuts were contructed to optimize HE events (E > 10 TeV) and consequently, they are not efficient at passing the lower energy atmospheric neutrinos. In fact, in a search for high energy galactic or extragalactic neutrinos, atmospheric neutrinos themselves constitute a background.
The selection criteria are now explained. First, the tensor of inertia is evaluated about the center of gravity of the hits and is diagonalized to find its eigenvalues. The ratio of the smallest eigenvalue to the sum of the eigenvalues, L1/ΣLi, provides an estimate of the sphericity of the event: muons tend towards elongated hit patterns while cascades produce hits more or less spherically symmetric about their centers. Next, a line fit is performed. The line fit is an analytic approximation that all hits lie along a straight line moving at the speed of light. This heuristic provides a measure of the time flow of the hits in an event. Cascades and muons separate into two clearly distinct populations via the parameter jvLF j, the velocity of the linefit. Monte Carlo simulations indicate that cuts on these two variables suppress much of the background and accept most of the cascade signal.
While the above criteria reduce the background by almost two orders of magnitude there still remain at least four orders before the level of the signals is approached. An additional cut on the total charge generated by the detected photoelectrons, ΣQ, is applied which reduces even the high-energy Corsika-generated cosmic-ray muons almost another two orders of magntiude at the expense of loss of signal sensitivity below about 10 TeV. A cut was applied on the likelihood of the cascade reconstruction, Lcas < 6, eliminating all but two events of the (admittedly small) simulated high energy background sample. Finally, a containment cut was made which required the center of gravity of the hits, weighted with ADC amplitude, to fall within a cylindrical volume centered on the detector center, 750 m in height, 450 m in radius (0.48 km3). This eliminates all background events in the sampled sets.
Background was estimated using two different physics generators for cosmic ray muons: the basiev program generates proton primaries up to energies of 1 PeV. Beyond that, heavier elements constitute a large portion of the cosmic-ray primaries and the Corsika air shower package is used which accurately simulates the composition of the cosmic-ray primaries and the high-energy interactions up to very high energies, exceeding 1020 eV. The calculated live times of the atmospheric muon samples are 80 seconds and 16 hours, respectively for the basiev and Corsika sets. Therefore, background was estimated for higher cut levels which left no background in the sample sets. This was done by fitting background versus a cut variable well below threshold and integrating the extrapolated variable above threshold. Clearly, a more thorough study necessitates additional background sampling. The results of the background suppression cuts on these data sets as well as signal acceptance on diffuse (E-2) and atmospheric neutrino fluxes are presented in table 9.
| Cut Level | Diffuse Signal | ATM ν Signal | basiev ECR < 1 PeV | Corsika ECR > 1PeV |
|---|---|---|---|---|
| Trigger | 981 | 22500 | 1.17 × 1011 | 2.22 × 108 |
| L1/ΣL | 842 | 10650 | 8.03 × 108 | 7.76 × 106 |
| |νLF| | 676 | 5470 | 1.47 × 108 | 2.34 × 106 |
| ΣQ | 461 | 470 | 13 | 5.68 × 104 |
| Lmpe < 6 | 447 | 397 | ∼ 0 | 1.96 × 103 |
| ρ < 450m, |z| < 375m | 180 | 217 | ∼ 0 | ∼ 50 |
Table 9: Event rates of various sources of signal and background versus cut level. The numbers quoted are in units of expected events per year. In the case of the diffuse neutrino flux, the rate is scaled for a flux of E2Φν = 10-7 (GeV · cm · s · sr)-1.
There is also the possibility for strong cosmic-ray muon background suppression with the surface array, IceTop. In the high-energy region where muon bremsstrahlung begins to look like a signal the surface array becomes relevant in two ways. Air showers with energy in the PeV range and above will trigger the surface array with high efficiency, and this trigger can be used to veto and study this source of background. At higher energy the surface array will also have some veto power for showers with cores outside the physical boundary of the array.
The effective trigger volume, Veff , is defined as the equivalent volume in which the detector achieves 100% efficiency and is calculated from a simulation of cascades thrown in a much larger volume, Vgen, by
| Veff(Ecas) = | ntrig(Ecas) | × Vgen |
| ngen(Ecas) |
and ranges from about 1 km3 at 1 TeV to 4 km3 at 100 PeV (see fig. 26). A more realistic effective volume has been calculated that takes into account the background rejection criteria discussed in the previous section. "Background Rejection I" refers to cuts made that remove background that is expected to remain after vetoing cosmic-ray events that trigger the IceTop surface array. The effective volume drops to zero below about 1 TeV because of a high charge requirement, reaches 1 km3 at 10 TeV, and grows to about 2.5 km3 at 100 PeV. "Background Rejection II" cuts further require that the center of gravity of the hits be contained well inside the detector instrumented volume. This additional cut reduces cosmic-ray muon background to zero independent of any IceTop veto at the cost of reducing the fiducial volume to ∼ 0.5 km3.
Examination of table 9 shows that there is a very prominent signal of atmospheric ν (ATM ν) at trigger level (fig. 27). Since they are produced with a much softer spectrum than the expected spectra of extragalactic neutrinos, most of this signal populates the medium and high energy regions from the lower energy threshold of IceCube (∼ 100 GeV to several tens of TeV) and is reduced by more than 90% by the PQ cut. It may possible to recover some of this lost signal by tuning the cuts for low energy neutrinos. For example, the high charge cut could be lowered and supplemented with a cut on the zenith angle of the muon reconstruction to reject downgoing fakes.
With present reconstruction techniques, the poor angular resolution of ν-induced cascades in the IceCube detector makes it difficult to perform a point source search in these channels. However, new reconstruction techniques which take advantage of waveform information may improve upon this situation.
Earth absorption plays a significant role in the UHE neutrino flux at the IceCube detector. Figure 28 shows the zenith angle dependence on the event rate and demonstrates the effect: Earth shadowing begins attenuating the event rate below the horizon at several tens of TeV. The shadowing steepens with energy until, above energies Eν > 10 PeV, the earth is almost totally opaque to neutrinos. Fold into this the fact that the target volume for ν → cascade, being closer to the detector than for ν → μ vertices, is symmetrically distributed both above and below the detector so that cascades do not suffer a reduced amount of target material for downgoing events. These two observations together imply that the upper hemisphere is especially important for the detection of UHE ν-induced showers and the ability to cleanly separate UHE neutrino-induced showers from cosmic-ray muon background is another trump held by cascade analyses. The differential event rate of UHE cascades in IceCube versus energy for a flux of E2Φν = 10-7 (GeV · cm · s · sr)-1 is shown in fig. 29. The squares represent the trigger rate and the triangles represent the event rate after all background rejection cuts have been applied.
GRBs are another hypothesized source of UHE extragalactic neutrinos. For these sources, Waxman and Bahcall [127, 128] propose a flux that is very soft, falling as E-1 until a break energy of several hundred TeV when the spectrum turns down to fall as E-2. Folding in the ν cross-section, one obtains the result of an increasing interaction rate (in log E) until the break energy, and thus a very high-energy source of ν-induced cascades in the detector visible above the background (fig. 30). The authors also predict that the ν and γ bursts are very closely correlated in time so that the IceCube detector can restrict searches to time windows centered on burst events observed by one of the several gamma-ray satellites. However, if the GRB fluence is close to the W&B prediction, IceCube could still detect a cluster of cascade events from such a burst without "triggering" on satellite observations.
A GRB search in the cascade channel has a distinct advantage over the muon channel search which offsets the smaller effective volume of high-energy cascades versus muons: background rejection is based on event topology. That is, cascades do not look like atmospheric muons, therefore the upper hemisphere does not need to be excluded from a cascade GRB search, making IceCube sensitive to both northern and southern hemisphere GRBs.
High energy cascade reconstruction will benefit greatly from the waveform readout of IceCube which is not yet fully simulated. Many improvements could be made to the reconstruction algorithms which are currently not equipped to make use of the detailed hit information that comes with waveform readout. These are likely to improve cascade identification at high energies. At lower energies, better cuts need to be developed that reject background but preserve the neutrino signal. Containment cuts that use the outer portion of IceCube as a veto shield should allow sub-TeV cascade events to be identified.
