This document describes a conceptual design for the proposed IceCube Neutrino Observatory at the South Pole. An Executive Summary is provided in section 2. Section 3 gives the scientific motivation for constructing a kilometer-scale device optimized for detection of cosmological neutrinos with ultrahigh energies in the TeV to PeV range. Section 4 briefly reviews the current status of the field of neutrino astronomy, and section 5 details the expected performance of the IceCube neutrino telescope, with emphasis on the scientific goals outlined in section 3.
Most of the remainder of the document focuses on technical aspects of the IceCube detector. Section 6 lists the technical requirements the IceCube detector must meet in order to attain the desired scientific goals, and section 7 gives a complete conceptual description of the IceCube detector itself. Section 8 describes how the data produced by this detector will be processed and made available for high-level analysis, and section 9 shows how the collaboration will organize itself to perform these analyses.
An explanation of how drilling, deployment and the associated logistics will be handled is given in section 10. Section 11 describes what quality assurance procedures will be implemented to ensure initial and continued success in deployment, data acquisition and data processing. Finally, section 12 shows how the AMANDA and IceCube detectors will be integrated to maximize the overall science output.
This document describes a conceptual design for the proposed IceCube Neutrino Observatory at the South Pole. An Executive Summary is provided in section 2. Section 3 gives the scientific motivation for constructing a kilometer-scale device optimized for detection of cosmological neutrinos with ultrahigh energies in the TeV to PeV range. Section 4 briefly reviews the current status of the field of neutrino astronomy, and section 5 details the expected performance of the IceCube neutrino telescope, with emphasis on the scientific goals outlined in section 3.
Most of the remainder of the document focuses on technical aspects of the IceCube detector. Section 6 lists the technical requirements the IceCube detector must meet in order to attain the desired scientific goals, and section 7 gives a complete conceptual description of the IceCube detector itself. Section 8 describes how the data produced by this detector will be processed and made available for high-level analysis, and section 9 shows how the collaboration will organize itself to perform these analyses.
An explanation of how drilling, deployment and the associated logistics will be handled is given in section 10. Section 11 describes what quality assurance procedures will be implemented to ensure initial and continued success in deployment, data acquisition and data processing. Finally, section 12 shows how the AMANDA and IceCube detectors will be integrated to maximize the overall science output.
This and other documents are on the Web at http://www.icecube.wisc.edu.
The IceCube Project at the South Pole is a logical extension of the research and development work performed over the past several years by the AMANDA Collaboration. The optical properties of ice deep below the Pole have been established, and the detection of high-energy neutrinos has been demonstrated with the existing detector. This accomplishment represents a proof of concept for commissioning a new instrument, IceCube, with superior detector performance and an effective telescope size at or above the kilometer-scale.
IceCube scientific goals require that the detector have an effective area for muons generated by cosmic neutrinos of one square kilometer. The detector will utilize South Pole ice instrumented at depth with optical sensors that detect the Cherenkov light from secondary particles produced in interactions of high-energy neutrinos inside or near the instrumented volume.
The design for the IceCube neutrino telescope is an array of 4800 photomultiplier tubes (PMTs) each enclosed in a transparent pressure sphere to comprise an optical module (OM) similar to those in AMANDA. In the IceCube design, 80 strings are regularly spaced by 125 m over an area of approximately one square kilometer, with OMs at depths of 1.4 to 2.4 km below the surface. Each string consists of OMs connected electrically and mechanically to a long cable, which brings OM signals to the surface. The array is deployed one string at a time. For each string, a hot-water drill creates a hole in the ice to a depth of about 2.4 km. The drill is then removed from the hole and a string with 60 OMs spaced by 17 m is deployed before the water freezes. The signal cables from all the strings are brought to a central location, which houses the data acquisition electronics, other electronics, and computing equipment.
Each OM contains a PMT that detects individual photons of Cherenkov light generated in the optically clear ice by muons and electrons moving with velocities near the speed of light. Signal events consist primarily of upgoing muons produced in neutrino interactions in the bedrock or the ice. In addition, the detector can discriminate electromagnetic and hadronic showers ("cascades") from interactions of νe and ντ inside the detector volume provided they are sufficiently energetic (a few 100 TeV or higher). Background events are mainly downward-going muons from cosmic ray interactions in the atmosphere above the detector. The background is monitored for calibration purposes by the IceTop air shower array covering the detector.
Signals from the optical modules are digitized and transmitted to the surface such that a photon's time of arrival at an OM can be determined to within a few nanoseconds. The electronics at the surface determines when an event has occurred (e.g., that a muon traversed or passed near the array) and records the information for subsequent event reconstruction and analysis.
At the South Pole site (see fig. 1), a computer system accepts the data from the event trigger through the data acquisition system. The event rate, which is dominated by down-going cosmic ray muons, is estimated to be 1–2 kHz. This will produce a large amount of data and requires filtering and compression of this data stream at the South Pole. There are two ways for the data to be transported to the Northern Hemisphere. The first and preferred method is via satellite transmission. The second method is by hand-carrying the data tapes north once the station reopens in the austral summer. Even in this case, a reduced set of data must be transferred daily by satellite to monitor the detector and to access important data. Once at the data archive, the data are catalogued, unpacked, checked, filtered, and calibrated. Interesting events are reconstructed and distributed to the collaboration for scientific analysis.
The technology that will be employed in IceCube has been developed, tested, and demonstrated in AMANDA deployments, in laboratory testing, and in simulations. This includes the instrument architecture, technology, deployment, calibration, and scientific utilization of the proposed detector. There have been yearly improvements in the AMANDA system, especially in the OMs, and in the overall quality of the information obtained from the detector. In the 1999/2000 season, a string was deployed with optical modules containing readout electronics inside the module. The information is sent digitally to the surface over twisted-pair electrical cable. This option eliminates the need for optical fiber cables and simplifies calibration of the detector elements. This digital technology is the baseline technology of IceCube.
For more details and references, see http://www.icecube.wisc.edu.
The construction of neutrino telescopes is overwhelmingly motivated by their discovery potential in astronomy, astrophysics, cosmology and particle physics. To maximize this potential, one must design an instrument with the largest possible effective telescope area to overcome the small neutrino cross section with matter, and the best possible angular and energy resolution to address the wide diversity of possible signals. A well-designed neutrino telescope can
In practice, the observed fluxes of cosmic-rays and gamma rays set the scale of a neutrino telescope. With minimal model-dependence, one can estimate the very high energy cosmic neutrino fluxes by scaling to the observed energy density in high-energy cosmic-rays, or to the measured fluxes of non-thermal high-energy gamma rays. The basic assumption in calculating the expected neutrino fluxes is that some fraction of cosmic-rays will interact in their sources to produce neutrinos.
Although they are not yet identified, the sources of the highest energy cosmic radiation very likely involve extremely dense regions with exceptional gravitational forces such as supermassive black holes, collapse of massive stars or mergers of black holes and neutron stars. With accretion and intense radiation fields as ingredients, some fraction of the particles accelerated in such environments will likely produce pions in hadronic collisions with ambient gas and/or by photoproduction. In either case, the neutral pions decay to photons, while charged pions include neutrinos among their decay products with spectra related to the observed gamma-ray spectra. In the first part of this section, we discuss estimates based on this relationship and conclude that a km-scale detector is needed to observe neutrino signals from known classes of high energy astrophysical sources.
The baseline design of the detector maximizes sensitivity to νμ-induced muons from below with energies in the TeV to PeV range, where the acceptance is enhanced by the increasing neutrino cross section and muon range but the Earth is still largely transparent to neutrinos. Good angular resolution is required to distinguish possible point sources from background, while energy resolution is needed to enhance the signal from astrophysical sources, which are expected to have flatter energy spectra than that of the atmospheric neutrino background.
A standard technique to search for high energy neutrinos of astrophysical origin is to look for upgoing muons induced by νμ that have penetrated the Earth. The signal is given by the convolution
Signal ∼ Area ⊗ RμNA⊗σν⊗φν,
where Rμ is the muon range in g/cm2 and NA is Avogadro's number. The range and cross section both increase linearly with energy into the TeV region, after which the rate of increase slows. Neutrinos with Eν < 100 TeV are not strongly attenuated by the Earth, and much of the solid angle away from the nadir remains accessible up to 1 PeV [16]. Thus the optimum range for νμ-induced upgoing muons is from a TeV to a PeV. Also in this energy range the muon energy loss is greater than minimum ionizing, which is a potential way to discriminate against the background of atmospheric neutrinos, which have a steeply falling spectrum. We will return to the importance of energy measurement further on.
The generic cosmic accelerator is believed to produce neutrinos in the flux ratio νe : νμ : ντ :: 1 : 2 : 0. With neutrino oscillations, however, at the detection point this ratio becomes 1 : 1 : 1. This is especially interesting for neutrino telescopes because the ντ is not absorbed in the Earth like the νe and νμ due to the charged current regeneration effect (as discussed below). Instead, ντ's with energies exceeding roughly 1 PeV pass through the Earth and emerge with an energy of roughly 1 PeV. IceCube is well-suited to detecting neutrinos in this energy range and will have full 4π sensitivity to this potential signal.
In the second part of this section we discuss several other important scientific goals which depend on the sensitivity of the detector to neutrinos of much higher energies and of much lower energies. On the one hand, we will discuss detecting and measuring the energy of PeV–EeV νe, νμ and ντ interactions. On the other, we will consider the detection of low energy muon-neutrinos from the annihilation of dark matter particles and the detection of MeV electron-antineutrinos from galactic supernovae. We describe how the baseline design can address these objectives as well.
We estimate the range of possible neutrino signals in three ways: first on the basis of an energetics argument, second by referring to some particular models, and third by comparing to known sources of TeV photons.
Models for the origin of the highest energy cosmic-rays typically predict associated neutrino fluxes. A requirement on the sources is that they must provide sufficient power to supply the observed energy in the galactic or extragalactic component of the cosmic radiation. The assumption that comparable amounts of energy go into high-energy neutrinos allows an estimate of the corresponding neutrino signal that is independent of the specific nature of the sources, but which depends only on their distribution in the universe.
In the case of galactic cosmic-rays, the energy flux carried by neutrinos is much lower than that carried by the parent cosmic-rays because the charged particles are trapped locally as they propagate diffusively in the turbulent galactic magnetic fields. Thus an observer inside the galaxy has several chances to see a given cosmic ray particle, but only one chance to see a neutrino that passes directly out of the galaxy. Nevertheless, there is a chance that some nearby galactic sources could be visible in neutrinos in a km-scale detector. Examples will be discussed in the next section.
In contrast, the neutrino energy flux for a cosmological distribution of sources can be comparable to or larger than the observed cosmic-ray energy flux. The flux depends on how the sources have evolved over cosmological time scales{provided that the fraction of accelerated protons that interact near the source is large. One natural scenario that gives comparable energy in neutrinos and cosmic rays occurs when protons remain trapped in the acceleration region until they suffer inelastic collisions, while secondary neutrons escape and decay to become cosmic-ray protons. It is generally believed that sources of the ultra-high energy cosmic-rays are indeed extragalactic, or at least not confined to the plane of the galaxy. There is some evidence for a transition from one particle population to another somewhere above 1018 eV as well as for a trend from heavy toward lighter composition. Measurements of the cosmic-ray spectrum above 1017 eV are summarized in fig. 2.
We now wish to estimate the neutrino signal expected if the energy in neutrinos is comparable to the energy in the extra-galactic component of the cosmic radiation. The first step is to determine what fraction of the observed spectrum is the extra-galactic component. It is generally assumed that the acceleration processes produce a power-law spectrum α E-α with differential index α = 2 or slightly higher [8, 10]. But the measured spectrum has an index close to α = 3, so it is not clear just how to normalize with an extra-galactic component with a much harder spectrum.
As an illustration, the lower heavy line in fig. 2 shows a spectrum with α = 2 and an exponential cutoff at 5 × 1019 eV to represent the Greisen-Zatsepin-Kuzmin (GZK) effect [11]. Particles with energies above the GZK cutoff have interaction lengths in the microwave background of order 50 Mpc or less and must therefore be from a local or exotic component (indicated by Super-GZK in the figure), which we do not consider for the moment. If the excess of data above the curve for E < 1019 eV in fig. 2 is attributed to the tail of the galactic cosmic-ray spectrum, then the energy in a universal component of the cosmic radiation may be estimated. Integrating the energy content under the α = 2 curve gives for the energy density in cosmic rays of extragalactic origin, ρEG ∼ 2 × 10-19 eV. The estimated power calculated from ρEG is
consistent with that observed from AGN and GRBs.
Shifting the normalization point lower (or higher) by half a decade in energy would increase (decrease) this estimate by roughly a factor of two. This is comparable to the systematic differences among the different measurements of the spectrum. If the spectrum is steeper (indicated by the upper solid curve in fig. 2, as expected for acceleration by relativistic shocks [12, 13, 14]) then the energy content will be somewhat [15] larger.
Using our estimate of the energy in the extragalactic component of the cosmic-ray spectrum and assuming a spectral index α ∼ 2:0 for the neutrinos as well as the cosmic-rays, one predicts a neutrino event rate of f × 30 events/km2/yr [17], where f is the efficiency for production of neutrinos relative to cosmic rays. For f = 0:3 this estimate gives a diffuse flux at the level of E2νdN/dEν ∼ 10-8 GeVcm-2sr-1, which is comparable to the "upper bound" estimate of Waxman & Bahcall [8] before accounting for the likely effect of evolution of sources over cosmological times.
In a sense, this estimate is conservative, and there are several ways in which the neutrino flux could be larger:
The above discussion is summarized in Fig. 3.
We may summarize the previous paragraphs by saying that an argument based on energetics coupled with a natural association between cosmic particle accelerators and their secondary neutrino beams suggests that a km-scale detector will be needed to see the neutrinos. A similar conclusion is reached by relating the neutrino flux to the source of the highest energy cosmic-rays in the context of specific models.
In a recent review [19] Learned and Mannheim have summarized recent work on models of AGN, GRB and other sources of high energy astrophysical neutrinos. As relevant examples, we quote here just two new papers that appeared since ref. [19]. Schuster, Pohl and Schlickeiser [20] work out the consequences of a model of AGN blazars [21] in which the TeV γ-rays come from decay of neutral pions produced in proton-proton collisions as a relativistic cloud of dense plasma plows into the ambient interstellar medium of the host galaxy. In this picture, there is a similar flux of TeV neutrinos from decay of charged pions. They conclude that the neutrino flux from a typical bright TeV γ-blazar would be detectable at the 3 σ level above atmospheric background in an exposure of a km2-year. During an extended flare, such as occurred for Mrk501 from March to September of 1997 [22, 23, 24], the rate would be correspondingly higher in this model (see below).
The frequently quoted estimates [25, 26] of neutrino production in GRB sources by collisions of extremely energetic protons with MeV photons in the gamma-ray jets typically produces ∼ 100 TeV neutrinos at a level sufficient to produce a few events per km2-year. Now Mészáaros and Waxman [27] argue that in gamma-ray bursts that involve collapse of massive progenitors, there will be an earlier phase of production of multi-TeV neutrinos from collisions of energetic protons with X-rays as the jet pushes through the envelope of the progenitor. They predict that there may also be a class of collapses so massive that the jets do not emerge. These would not appear as visible gamma-ray bursts but would generate neutrino bursts. The event rates estimated range from a few hundred to a thousand per year over the whole sky, depending on the ratio of "choked" to "bursting" fireballs. The northern hemisphere bursts would be detectable by IceCube.
The question whether the intriguing sources of TeV γ-rays such as Markarian 421, 501 are cosmic proton accelerators has not yet been answered. Most experts argue that the photons are produced by radiative processes from accelerated electrons. There are, however, some hints that this may not be the case. For example, the spectrum of Mrk501 during the extended (six month) flare in 1997 [22] entends to above 20 TeV, which strains the electronic models because of the short synchrotron loss time for electrons. However, only neutrinos can provide incontrovertible evidence of proton acceleration.
For the case of the Mrk501 flare, it is possible to estimate the associated neutrino flux and signal that would be expected if the observed photons are produced from decay of neutral pions. The neutrino flux is closely related to the photon flux at the source. If the pion production mechanism is photoproduction by protons, then the energy in muon neutrinos will be about 1/4 the energy in photons. If the pions are produced in proton-gas collisions, then the energy in muon neutrinos and the energy in photons will be comparable. To obtain the source spectrum of photons, it is necessary first to account for the attenuation of photons during propagation through the infrared background radiation. This has been estimated by Konopelko et al. [28]. They find a source photon spectrum that extends from below a TeV to above 20 TeV with a power law differential spectral index of α = 2. Starting from the six-month average flux in Ref. [22] and correcting for the infra-red absorption, one would expect 10–100νμ events per km2 of effective area in four months, depending on the origin of the produced pions (photo-production or proton-gas interactions).
In principle, high-energy neutrino astronomy has the potential to discriminate between hadronic and electromagnetic origin of the TeV emission from objects as diverse as supernova remnants, gamma-ray bursts and active galactic nuclei. The fluxes are likely to be low, however. Estimates for a variety of sources show that reasonable expectations are at the level of a few events per km2-year. Moreover, the estimates depend on how many interactions the photons experience in the source as well as whether all observed photons are hadronic in origin. As an example of the latter point, the hadronic model of Bednarek and Protheroe [29] for the CRAB nebula attributes only the high-energy end of the photon spectrum to decay of neutral pions. For a range of parameters their model predicts a signal from < 1 to as much as 4 events per km2·yr with Eμ > 1 TeV. The corresponding rate from atmospheric background within a 1° cone is ≈ 0:4.
So far we have focussed on detection of muons from below the horizon produced by muon neutrinos in the TeV-PeV regime, such as may be associated with GRB sources, AGN or other cosmic accelerators observed as TeV gamma-ray emitters. Neutrinos of both higher and lower energies can also be measured with IceCube. This capability will allow us to address other science that ranges from WIMP annihilation and supernova explosions to ντ appearance to neutrinos from topological defects of supermassive relic particles.
So far we have assumed an IceCube energy threshold of 0.4 TeV or higher. It is important to note that it will be possible to detect muon-neutrinos of significantly lower energy. If the track of the secondary muon is close to an individual string, its length can be deduced from the arrival times of Cherenkov photons detected by nearby PMTs. A good measurement requires nanosecond timing in several modules. Requiring, conservatively, signals in five modules separated by 17 m, the minimum tracklength is ∼ 70 m for a muon energy of ∼ 15 GeV. Requiring further that the distance from the string to the track is significantly less than the scattering length, 10 m for instance, yields a detection volume of 25 megaton with a threshold of less than 20 GeV for a source directly below the detector, in particular for neutrinos from annihilation of WIMPS trapped in the center of the Earth. For other directions the energy threshold is higher and the efficiency for a given energy is correspondingly lower. The cuts on track-length and proximity to a string can be relaxed if the detector would be exposed to an accelerator beam. During the short beam spills the detector is free of background and requirements on track measurement can be reduced thus increasing the target volume. On the other hand, the neutrino beam would be at some angle to the strings, depending on the location of the accelerator, which would reduce the acceptance.
Several science missions would benefit from a reduced threshold in a limited volume, e.g. the search for dark matter. If Weakly Interacting Massive Particles (WIMPs) make up the dark matter of the universe, they would also populate the galactic halo of our own Galaxy. They would be captured by the Earth or the Sun where they would annihilate pairwise, producing high-energy muon neutrinos that can be detected by neutrino telescopes. A favorite WIMP candidate is the lightest neutralino which arises in the Minimal Supersymmetric Model (MSSM). In general, IceCube's reach as a dark matter detector is complementary to that of direct search detectors because of its good sensitivity to larger neutralino masses, typically higher than a few hundred GeV. In addition, the rates depend on the capture and annihilation rates of the WIMPs in the Earth or Sun rather than their cross sections for interaction in the detector. High energy neutrinos produced in the annihilation of galactic neutralino dark matter have characteristic energies of 1/4 ∼ 1/6 the mass of the parent particles. A reduction in neutrino threshold therefore results in increased sensitivity to lower masses. The standard IceCube geometry presents an effective area of 0.7 km2 for WIMPs with mass = 50 GeV annihilating in the core of the Earth. For WIMPS in the Sun, because of the less favorable geometry, the effective area increases from ∼ .01 km2 for mw = 50 GeV and approaches 0.7 km2 for TeV WIMPS. The situation is most favorable for WIMPS above the threshold for decay into weak intermediate bosons, where IceCube is competitive with specialized future detectors such as GENIUS and CRESST in the search for neutralino dark matter anticipated in supersymmetric theories [45].
Another reason for maintaining sensitivity to ∼ 10 GeV neutrinos is that these may be produced in GRBs along with high energy neutrinos. Bahcall and Meszaros [46] have argued that a gamma-ray burst "fireball" is likely to contain an admixture of neutrons, in addition to protons, in essentially all progenitor scenarios. Inelastic collisions between protons and neutrons in the fireball produce muon neutrinos (antineutrinos) of ∼10 GeV energy as well as electron neutrinos (antineutrinos) of ∼5 GeV, which could produce ∼7 events/year in km-scale detectors, if the neutron abundance is comparable to that of protons. With a reduced threshold and exploiting coincidence in timing with the GRB, this flux may be observable.
A low threshold also preserves the capability discussed in connection with AMANDA (see sec. 12) to detect secondary muons from TeV-energy gamma rays produced in the atmosphere above the detector. These are guaranteed fluxes, calculable from the observed fluxes. The technique could be particularly revealing in GRB studies.
Neutrinos produced locally by interactions of cosmic-rays in the atmosphere constitute the foreground for neutrinos of astrophysical origin. They are both background and calibration source. The energy spectrum of atmospheric neutrinos is steep, falling approximately like E-3 and steepening to E-3.7 for E>>1 TeV. Above ∼ 10 GeV the flux of νe falls even more quickly, and above ∼ 100 effects of oscillations are also negligible. Thus atmospheric muon-neutrinos are a known calibration source up to a TeV and beyond. There is a characteristic factor of two excess of neutrinos from near the horizontal as compared to the vertical. Measuring the rate and angular dependence of atmospheric νμ-induced muons is therefore a benchmark measurement for IceCube.
The component of "prompt" νμ from charm decay has a harder spectrum than the component from decay of charged kaons and pions. It is expected to become the dominant source of atmospheric neutrinos above an energy of perhaps 100 TeV. The exact level of the prompt component is rather poorly known, and it could present a significant background for diffuse astrophysical neutrinos. If it is sufficiently large, it could be measured by IceCube as a hardening the neutrino energy spectrum by one power of the energy.
With a sufficiently low energy threshold, IceCube could also play a role in confirming the compelling indications that atmospheric neutrinos oscillate. Studies of systematics and backgrounds show, however, that significant progress would require smaller spacing of OMs along a string than presently planned. Such a specialized effort would be warranted only if ongoing experiments fail to prove oscillation of atmospheric neutrinos before IceCube construction.
The interactions of neutrinos with PeV energies and higher will have spectacular signatures in IceCube. (The simulated 6 PeV neutrino in fig. 16 illustrates this point.) Since the Earth becomes increasingly opaque to neutrinos with energy in the PeV range and higher, it is necessary to use events from horizontal and downgoing neutrinos. Fortunately, setting an energy threshold in the PeV energy region is high enough to be above atmospheric backgrounds. In this energy region the observed muon events in IceCube will be dominated by muon neutrinos interacting in the ice or atmosphere above the detector and near the horizon. PeV cascades from νe interactions in the detector volume also contribute at a somewhat lower rate. Tau neutrinos will also show up as cascades, as described below. Upgoing neutrinos are suppressed by an order of magnitude. Due to the Earth's opacity, the zenith angle distribution of neutrinos associated with EeV signals will have a striking signature. For a detailed discussion, see [36, 38].
With a threshold for cascades below the PeV region, IceCube will be complementary to detectors such as Auger, OWL and RICE which have thresholds of 10 EeV and higher. The lower threshold means that comparable event rates may be possible with IceCube even though its effective volume is much smaller.
The high-energy capability of IceCube will allow us to attack a major scientific problem, the existence of particles whose energy apparently exceeds the GZK cutoff. Speculations regarding their origin include heavy relics from the early Universe and topological defects which are remnant cosmic structures associated with phase transitions in grand unified gauge theories [30, 31, 32]. Interactions of ultra-high energy neutrinos with massive neutrinos in the galactic halo is also a possibility [33]. Such models would predict a sizeable flux of neutrinos in a much higher range of energy than the neutrinos associated with the GRB and AGN models mentioned above. Some limits on the highest predictions of neutrino fluxes are emerging from analysis of horizontal air showers, but there is still considerable phase space for exploration. Detection of neutrinos produced in interactions leading to the GZK cutoff is also a possibility, although their level is relatively low. Specific examples include:
Interest in detection of τ neutrinos is motivated by the evidence for neutrino oscillations from SuperKamiokande [39] and SNO [40]. Production of ντ in hadronic interactions or photoproduction is suppressed relative to νe and ντ by several orders of magnitude. In the absence of new physics, ντ of astrophysical origin would therefore be virtually undetectable. If, however, there is large mixing in the νμ↔ντ channel, then over astrophysical distances fluxes of ντ would be comparable to νμ.
Tau neutrinos of sufficiently high energy can in principle be identified in several ways in a km-scale neutrino detector. Perhaps the most striking signature would be the characteristic double bang events [41] in which the production and decay of a τ lepton would be seen as two separated bursts in the detector. It may also be possible to identify "lollipop" events in which a ντ with energy > PeV creates a long minimum-ionizing track that enters the detector and ends in a huge burst as the τ lepton decays to a final state with hadrons or an electron. The entering τ, because of its large mass, would emit fewer bremsstrahlung photons than a muon of similar energy. Such events would be detected from above or near the horizontal since the Earth is opaque to neutrinos with energies at or above the PeV region.
At still higher energies, the Earth becomes completely opaque to νe and νμ fluxes but it remains transparent to ντ flux [42]. In essence, ντ charged current interactions create a tau lepton, which decays before losing all its energy, and which always has a ντ as one of its decay products. This ultimately results in an upgoing ντ flux in the 100 TeV energy range. In what follows we discuss only the "double-bang" signature, which gives a conservative estimate of possible rates.
In a charged current ντ deep inelastic scattering (DIS) interaction with a nucleus, a τ lepton of energy (1-y)Eντ is produced as well as a hadronic shower of energy yEντ which is initiated in the fragmentation of the nucleus. Here y is the fraction of energy transferred to the hadronic vertex in the interaction. The τ lepton travels on average a distance Rτ along the medium before decaying given by:
| Rτ= | Eτ | ct0= | (1-y)Eντ | ct0 |
| mτ | mτ |
where Eτ and mτ are the energy and mass of the τ respectively and t0 is its rest lifetime. In its decay it produces another ντ and an electromagnetic or hadronic shower ∼; 82% of the times. Assuming a typical detector dimension D, there are several conditions that have to be fulfilled for the detection of a double bang event induced by aντ:
Using these criteria we can estimate the probability of detecting a double bang event in a neutrino telescope of linear dimension D = 1 km such as IceCube using a simple Monte Carlo. We take the energy threshold for detecting showers to be Eshower ∼ 1 TeV and fix 250 m as the minimum distance the τ has to travel to distinguish the Cherenkov light from both showers. This (conservative) number is mainly determined by the 125 m separation between strings since detection by separated strings is needed to establish the double burst for a horizontal event. This distance corresponds to a minimum energy of ∼ 5 PeV for the τ lepton. The requirement that both bursts occur inside the detector sets an upper limit of ∼ 20 PeV. With these constraints, one would expect at most a few events per year given current limits on neutrino fluxes from AMANDA. This conclusion is consistent with the result of Athar et al. [43], who find some tens of double bang events per year in the original AGN model [44] which is somewhat above current limits.
A high energy neutrino telescope in deep Antarctic ice is sensitive to the stream of low energy neutrinos produced by a galactic supernova Although 10-20 MeV energy is far below the AMANDA/IceCube trigger threshold, a supernova would be detected by higher counting rates in individual PMTs over a time window of 5-10 s. The enhancement in rate of a single PMT is buried in PMT dark noise. However, by summing the signals from all PMTs a significant excess would be observed. Limits obtained with AMANDA have been submitted for publication [47]. Relatively low background counting rates in ice (relative to water) make this possible.
Most of the energy released by a supernova is liberated in a burst lasting about ten seconds. Roughly equal energies are carried by each neutrino species with a thermal spectrum of temperature 2-4 MeV. Since the νe cross-section on protons in the detector is significantly larger than the interaction cross sections for the other neutrino flavors, νe events dominate the signal by a large factor after detection efficiency is taken into account. In this reaction, free protons absorb the antineutrino to produce a neutron and a positron which is approximately isotropically emitted with an energy close to that of the initial neutrino. A thermal spectrum of temperature 4 MeV, when folded with an inverse beta decay cross section which increases with the square of the neutrino energy, yields an observed positron energy distribution which peaks in the vicinity of 20 MeV. The track-length of a 20 MeV positron in ice is roughly 12 centimeters and therefore over 3000 Cherenkov photons are produced.
AMANDA and IceCube can contribute to the SuperNova Early Warning Network [48]. A recent analysis [47] shows that 70% of the galatic disk can be monitored for a supernova like SN1987A using a selected set of low noise AMANDA PMTs. Given a known template for time evolution of the pulse, the resulting accuracy in timing could be 14 ms for AMANDA-II and as good as 1-3 ms for IceCube. The resulting angular resolution depends on the orientation of the triangulation grid with respect to the supernova. The three detectors SuperK, SNO and IceCube will achieve typical resolution of 5 to 20 degrees. This is to be compared with the accuracy of about 5° achieved from the measured electron direction in a detector like SuperK.
Simultaneous detection of high energy and lower energy MeV neutrinos from a supernova is an exciting capability of a high energy neutrino telescope with supernova sensitivity. Loeb and Waxman [49] have shown that when a type II supernova shock breaks out of its progenitor star, it becomes collisionless and may accelerate protons to TeV-energy or higher. Inelastic nuclear collisions of these protons produce a ∼1 hr long flash of TeV neutrinos about 10 hr after the thermal neutrino burst from the cooling neutron star. A Galactic supernova in a red supergiant star would produce a neutrino flux of ∼ 10-4 erg/cm2 s. A km2 neutrino detector will detect ∼100 muons, thus allowing one to constrain both supernova models and neutrino properties. All these opportunities will be greatly enhanced by a low threshold associated with short tracks detected by individual strings.
The main goal of the IceCube project is the detection of extraterrestrial sources of very high energy neutrinos [19, 50, 51].
IceCube is a multi-purpose detector. Beside high energy neutrino astronomy, it can be used to investigate a series of other questions:
Discovery of any single one of the high energy signals listed above would unquestionably make IceCube a resounding success. However, as a detector one hundred times larger than AMANDA and one thousand times larger than any underground detector, IceCube will be opening a new window on the universe, and as such holds out even greater promise: the exciting discovery of unanticipated phenomena.
The science of high energy neutrino astronomy is compelling. The main challenge is therefore to develop a reliable, expandable and affordable detector technology. The diagram in fig. 4 shows
schematically the range of various detectors in the space of volume vs. neutrino energy. IMB and Kamioka are so far the only detectors that have observed neutrinos from outside the solar system, with the detection of SN1987A. With its large volume and great sensitivity, Super-Kamiokande has pushed the frontiers of the study of atmospheric neutrinos in the sub-GeV and multi-GeV energy range, SNO and Super-Kamiokande have done the same with solar neutrinos, with SNO recently providing the first clear evidence of solar neutrino oscillations. There is significant activity with several underground detectors, including Borexino and KamLand, pushing toward lower energy and higher energy resolution on the solar neutrino frontier. Super-Kamiokande, along with Frejus, MACRO and Soudan, have also provided important limits on fluxes of high energy neutrinos.
With the termination of the pioneering DUMAND experiment, the efforts in water are, at present, spearheaded by the Baikal experiment [71]. The Baikal Neutrino Telescope is deployed in Lake Baikal, Siberia, 3.6 km from shore at a depth of 1.1 km. An umbrella-like frame holds 8 strings, each instrumented with 24 pairs of 37-cm diameter QUASAR photomultiplier tubes (PMT). Two PMTs in a pair are switched in coincidence in order to suppress background from natural radioactivity and bioluminescence. Operating with 144 optical modules since April 1997, the NT-200 detector has been completed in April 1998 with 192 optical modules (OM). The Baikal detector is well understood, and the first atmospheric neutrinos have been identified.
The Baikal site is competitive with deep oceans, although the smaller absorption length
of Cerenkov light in lake water requires a somewhat denser spacing of the OMs. This does, however, result in a lower threshold which may be a definite advantage, for instance for oscillation measurements and WIMP searches. They have shown that their shallow depth of 1 km does not represent a serious drawback. By far the most significant advantage is the site with a seasonal ice cover which allows reliable and inexpensive deployment and repair of detector elements from a stable platform.
With data taken with the Baikal NT-200 detector, the Baikal collaboration has shown that atmospheric muons can be reconstructed with sufficient accuracy to identify atmospheric neutrinos, as illustrated in fig. 5. The neutrino events are isolated from the cosmic ray muon background by imposing a restriction on the chi-square of the Cerenkov fit, and by requiring consistency between the reconstructed trajectory and the spatial locations of the OMs reporting signals.
In the following years, NT-200 will be operated as a neutrino telescope with an effective area between 103∼ 5 × 103 m2, depending on energy. Presumably too small to detect neutrinos from extraterrestrial sources, NT-200 will serve as the prototype for a larger telescope. For instance, with 2000 OMs, a threshold of 10 ∼ 20 GeV and an effective area of 5 × 104 ∼ 105 m2, an expanded Baikal telescope would fill the gap between present underground detectors and planned high threshold detectors of km3 size. Its key advantage would be low threshold.
The Baikal experiment represents a proof of concept for deep ocean projects. These have the advantage of larger depth and optically superior water. Their challenge is to find reliable and affordable solutions to a variety of technological challenges for deploying a deep underwater detector. Several groups are confronting the problem; both NESTOR and ANTARES are developing rather different detector concepts in the Mediterranean. The NESTOR collaboration [74], as part of a series of ongoing technology tests, is testing the umbrella structure which will hold the OMs. They have already deployed two aluminum "floors," 34 m in diameter, to a depth of 2600 m. Mechanical robustness was demonstrated by towing the structure, submerged below 2000 m, from shore to the site and back. These tests should soon be repeated with fully instrumented floors. The actual detector will consist of a tower of 12 six-legged floors vertically separated by 30 m. Each floor contains 14 OMs with four times the photocathode area of the commercial 8 inch photomultipliers used by AMANDA and ANTARES.
The detector concept is patterned along the Baikal design. The symmetric up/down orientation of the OMs will result in uniform angular acceptance and the relatively close spacings in a low threshold. NESTOR does have the advantage of a superb site off the coast of Southern Greece, possibly the best in the Mediterranean. The detector can be deployed below 3.5 km relatively close to shore. With the attenuation length peaking at 55 m near 470 nm the site is optically superior to that of all other deep water sites investigated for neutrino astronomy.
The ANTARES collaboration [72] is investigating the suitability of a 2400 m-deep Mediterranean site off Toulon, France. The site is a trade-off between acceptable optical properties of the water and easy access to ocean technology. Their detector concept indeed requires remotely operated vehicles for making underwater connections. First results on water quality are very encouraging with an attenuation length of 40 m at 467 nm and a scattering length exceeding 100 m. Random noise exceeding 50 khz per OM is eliminated by requiring coincidences between neighboring OMs, as is done in the Lake Baikal design. Unlike other water experiments, they will point all photomultipliers sideways in order to avoid the effects of biofouling. The problem is significant at the Toulon site, but only affects the upper pole region of the OM. Relatively weak intensity and long duration bioluminescence results in an acceptable deadtime of the detector. They have demonstrated their capability to deploy and retrieve a string, and have reconstructed down-going muons with 8 OMs deployed on the test string.
With the study of atmospheric neutrino oscillations as a top priority, they had planned to deploy in 2001-2003 10 strings instrumented over 400 m with 100 OMs. After study of the underwater currents they decided that they can space the strings by 100 m, and possibly by 60 m. The ANTARES detector will consist of 13 strings, each equipped with 30 storeys and 3 PMTs per storey. The large photocathode density of the array will allow the study of atmospheric neutrino oscillations in the range 255 < L=E < 2550kmGeV??1 with neutrinos in the energy range 5 < Eν < 50 GeV. This detector will have an area of about 3 × 104m2 for 1 TeV muons–similar to AMANDA-II–and is planned to be fully deployed by the end of 2003.
A new R&D initiative based in Catania, Sicily has been mapping Mediterranean sites, studying mechanical structures and low power electronics. One must hope that with a successful pioneering neutrino detector of 10-3 km3 in Lake Baikal, a forthcoming 10-2km3 detector near Toulon, the Mediterranean efforts will converge on a 10-1km3 detector possibly at the NESTOR site.
As in many other fields, high energy neutrino astronomy would ideally have two or more independent experiments sensitive to the same energy regime. Such redundancy allows one to perform vital crosschecks and (hopefully) discovery verification. It is therefore in the best interests of the community that projects other than AMANDA and IceCube succeed. In addition, a detector in the northern hemisphere would provide the community with full TeV–PeV neutrino sky coverage, while at the same time having considerable coverage overlap regions.
The AMANDA-B10 results presented below provide a proof-of-concept for a high energy neutrino telescope at the South Pole. We focus first on the detection of neutrinos and compare them to the predicted flux of atmospheric neutrinos. Possible backgrounds will be discussed. We then apply the results to the search for high energy neutrinos of astrophysical origin, such as a diffuse flux of HE neutrinos, point-like sources and gamma-ray bursts.
It is important to note that due to its size and shape, AMANDA-B10 is not highly sensitive to high energy neutrino fluxes expected from sources such as AGN and GRBs. The much larger AMANDA-II detector has significantly more sensitivity, and data from this device is currently being analyzed. However, only with IceCube will the sensitivity levels be high enough to reach predicted high energy neutrino flux levels.
The results presented here are based on data taken during the austral winter of 1997. The effective livetime has been determined to be 130.1 days for the selected data. The method of calibration and the characteristics of the optical sensors are very similar to the 4 string prototype array described in ref. [53]. Simulations predict a rate of a few tens of events per day from atmospheric neutrinos above a threshold of 30-50 GeV, compared to 6 · 106 events from cosmic ray muons, as shown in fig. 6.
The analysis of the atmospheric neutrino sample with the AMANDA-B10 array has been performed independently by two working groups in the collaboration. Both groups come to very similar and statistically consistent results while the methods are quite different and partially independent. The figures and the method presented here are based on one analysis [56].
Neutrinos are identified by looking for upward going muons. We use a maximum likelihood method [57], incorporating a detailed description of the scattering and absorption of photons in the ice, to reconstruct muon tracks from the measured photon arrival times. Events are reconstructed with a Bayesian method [58], in which the likelihood function is multiplied by a prior probability function. The prior function contains the zenith angle information in fig. 6. By accounting in the reconstruction for the fact that the flux of downgoing muons from cosmic rays is more than 5 orders of magnitude larger than that of upgoing neutrino-induced muons, the number of downgoing muons that are misreconstructed as upgoing is greatly reduced. A small
fraction of the downgoing muons (5 · 10-6) are reconstructed as upward and form a background to the neutrino-induced events. This background is removed by applying quality criteria to the time profiles of the observed photons as well as to their spatial distribution in the array. A measure of the event quality has been defined by combining six quality variables into a single parameter. A high event quality is reached when the values of all six parameters agree with the characteristics of a correctly reconstructed muon track. By making increasingly stringent cuts on the event quality the background of a total of 1:2 · 109 events is reduced by a factor of approximately 108, while retaining about 5% of the neutrino signal. The distribution of the single quality parameter for experimental data and for a Monte Carlo simulation of atmospheric neutrinos is shown in fig. 7. It compares the number of events passing various levels of cuts; i.e., the integral number of events above a given quality. At low qualities, the data set is dominated by misreconstructed downgoing muons, most of which are reproduced in the Monte Carlo. At higher cut levels, the passing rates of data closely track the simulated neutrino events, and the predicted background contamination is very low.
| Experimental Data | MC: Atmospheric Neutrinos | |
|---|---|---|
| Triggered | 1.2 · 109 | 4600 |
| Reconstructed upward | 5 · 103 | 571 |
| Upward going | 204 | 279 |
Table 1: Event numbers are given at various cutlevels: Experimental data and atmnospheric neutrino Monte Carlo.
We can investigate the agreement between data and Monte Carlo more systematically by comparing the differential number of events, rather than the total number of events passing various levels of cuts. This is done in fig. 7 (right), where the ratios of the number of events observed to those predicted from the combined signal and background simulations are shown. One can see that at low quality levels there is an excess in the number of misreconstructed events observed. This is mainly due to instrumental effects such as cross talk which are not well described in the detector Monte Carlo. There is also an excess, though statistically less significant, at very high quality levels, which is caused by slight inaccuracies in the description of the optical parameters of the ice. Nevertheless, over the bulk of the range there is close agreement between the data and the simulations, apart from an overall normalization factor. In the range where the line is shown the ratio of Data/MC is about 0.6. Counting all events above the quality cut (7.0) this ratio is 0.70. It should be emphasized that the quality parameter is a combination of all six quality parameters, and so the flat line in fig. 7 demonstrates agreement not only in individual cut parameters but also quantitative agreement in the correlations between cut parameters.
The zenith angle distribution for the 204 events is shown in fig. 6, and compared to that for the signal simulation. In the figure the Monte Carlo events were normalized to the observed events. The achieved agreement in the absolute flux of atmospheric neutrinos is consistent with the systematic uncertainties of the absolute sensitivity and the flux of high energy atmospheric neutrinos. The shape of the zenith distribution of data is statistically consistent with the prediction from atmospheric neutrinos. The zenith distribution reflects the angular acceptance of the narrow but tall detector. A skyplot of these events is shown in fig. 8. 223 events were found in an independent analysis. The overlap of 119 events with the sample presented here is within expectations. The observation of atmospheric neutrinos at a rate consistent with Monte Carlo prediction establishes AMANDA-B10 as a neutrino telescope.
In order to establish AMANDA as a neutrino telescope, one more step is needed. That is the verification that AMANDA does indeed reconstruct the direction of events correctly in sky coordinates. This is done by analyzing events that are measured coincidently by AMANDA in the deep ice and by surface air shower detectors. In the 1997 data set we have three independent detectors at the surface in operation: the SPASE-1 air shower array, the SPASE-2 array, and the GASP air cherenkov detector. All three experiments agree on the average absolute pointing of the AMANDA array to within 1–2 degrees (sky coordinates) [55]. A full agreement with the true direction is achieved in azimuth, and a small offest of order 1 degree is observed in the in the zenith angle (data and Monte Carlo). The offset is relatively small compared to the size of a search bin (∼ 5 degrees half angle) for point sources. These instruments were also used to verify the angular resolution (median angular error) of about 3 degrees.
The observation of atmospheric neutrinos together with the verification of the angular resolution establishes AMANDA as a functioning neutrino telescope. From here we search the neutrino sky for various sources. Depending on the type of the investigated neutrino signal hypothesis (diffuse flux, point sources, GRB, WIMPs, etc.), we re-optimize the background rejection strategy.
The search for a diffuse neutrino flux of astronomical origin follows naturally from the observation of a diffuse flux of neutrinos generated in the atmosphere. Neutrinos from generic astrophysical sources are expected to extend to higher energies while the energy spectrum of atmospheric neutrinos falls off steeply with increasing energy. A very simple and robust measure of the energy of the observed muons is the number of optical modules (OM) that observed at least one photoelectron in a given event. Figure 9 shows the energy distribution of events that pass the neutrino filter as predicted for a) atmospheric neutrinos and b) an assumed energy spectrum for astrophysical neutrinos following a power law of dN/dEν = 10-5Eν-2 cm-2 s-1 sr-1 GeV-1. When using the number of fired OMs as a measure of energy we obtain the distributions given in fig. 9. The assumed astronomical neutrino flux would generate a significant excess at high multiplicities of fired photomultipliers. A preliminary analysis does not show such an excess. This leads to a preliminary upper limit [65] (90%C.L.) of dN/dEν ∼ 10-6Eν-2cm-2 s-1 sr-1 GeV-1. However, the systematics of this analysis with respect to the high energy sensitivity is still subject to further investigation. A re-analysis with an updated version of the Monte Carlo simulation is underway.
This sensitivity on the diffuse neutrino flux is below previously stated upper limits by experiments such as BAIKAL [71], SPS-DUMAND [66], AMANDA-A [67], and FREJUS [68], and comparable to a limit presented by BAIKAL [75].
It is comparable to the AGN prediction by Salamon and Stecker [63] and approaches the prediction of Protheroe [69].
The search for point sources allows us to measure the background off-source. Searches have been performed for specific point sources as well as all sky searches. The median angular resolution of the AMANDA-B10 array is 3 degrees. Thus, one hemisphere consists of 319 bins. Again the search strategy is optimized for the expected energy spectrum. The size of the search bins, the effective area and the livetime of the array enter the calculation of a neutrino flux limit. In absence of a signal we calculate upper limits to a neutrino flux from point sources. The preliminary average neutrino flux limits are at a level of dN/dEν ∼ 10-6Eν-2cm-2 s-1GeV-1.
The limit in case of Mrk501 is of particular interest. Here our neutrino flux limit is only about a factor of 10 above the gamma emission of this blazar, during its high state in 1997. The sensitivity of the AMANDA array is thus beginning to approach observed fluxes of gamma rays.
Figure 10 shows the expected neutrino fluxes from various sources, together with the current preliminary AMANDA upper limit (90% C.L.). The atmospheric neutrino background is given for a 2 × 2 degree bin. Detailed simulations have been performed of IceCube, the proposed kmscale neutrino array. The achievable upper limit for an assumed E-2-type spectrum for point sources is indicated in the figure.
According to the relativistic fireball model, gamma-ray bursts (GRBs) are expected to be astrophysical sources of high energy neutrinos. The expected neutrino event rate in AMANDA has been determined from a full MC simulation of the GRB signal and the detector. GRB neutrinos are generated following a broken power law energy-spectrum [78]. Figure 11 shows the energy spectrum of Monte Carlo events that triggered events in the AMANDA array. The search strategy has been optimized for this hypothetical signal. The number of expected events depends strongly on the assumed Lorentz factor. This scenario predicts event rates ranging from 10-4 events (Γ = 1000) to 1 event (Γ = 100) for the given data sample.
With ∼ 1/3 sky coverage, the BATSE satellite instrument detected 304 gamma-ray bursts in 1997. AMANDA data for 78 gamma-ray northern hemisphere bursts detected on-board the BATSE satellite were examined for coincident neutrino emission. Because the time window of coincidence is rather short, typically of order 10 seconds per burst, there is very little background from cosmic rays and atmospheric neutrinos. No excess of neutrinos has been found above a background of 17.2 events for all 78 bursts.
AMANDA can be used to search for non-baryonic dark matter in the form of weakly interacting massive particles (WIMPs). The non observation of an excess of vertically upgoing muons has been used to set a limit on the flux of neutrinos from WIMP annihilations in the center of the Earth [79]. With only 132 days of exposure in 1997, AMANDA has reached a sensitivity in the region of high WIMP masses (≥ 500 GeV) that begins to constrain the theoretically allowed parameter space. It is comparable in sensitivity to other detectors with much longer livetimes. Figure 12 shows the present AMANDA limit after 132 days observation time in comparison with the limits obtained from long-year exposure of MACRO, Baksan and SuperK [80]. Note that the AMANDA limit is determined including (currently) large systematic uncertainties (the other experiments did not include their comparatively small uncertainties).
By monitoring bursts of low energy neutrinos AMANDA can be used to detect the gravitational collapse of supernovae in the galaxy. This method takes advantage of the low noise characteristics (300–1500 Hz/PMT) of the optical sensors in the deep ice.
Figure 13 shows, for 215 days of live time in 1997/98 and all stable AMANDA-B10 PMTs, the distribution of the deviation Δμ of the average noise rate from its mean value. Each data point is the average over a 10 s interval. Accepting every 10 s interval with Δμ > 4 Hz (see the vertical line) as a supernova event, would result in one fake alarm per year. This corresponds to a 90% efficiency for a SN-1987A-like supernova event loacted at a distance of 9.8 kpc (the distance to center of Galaxy is about 8 kpc). A robust on-line monitor could be operated with a slightly higher threshold covering about 70% of the Galaxy. With AMANDA-II and an improved supression of non-Poissonian noise we will monitor more than 90% of the Galaxy.
A magnetic monopole with unit magnetic Dirac charge and a velocity of β close to 1 would emit Cherenkov light along its path, exceeding that of of a bare relativistic muon by a factor of 8300. From the non-observation of events with this clear signature, a limit of 0.62·10-16cm-2s-1sr-1 for highly relativistic monopoles has been derived. This limit, illustrated in fig. 53, is a factor of 20 below the Parker bound and a factor of four below other best limits.
The detection of atmospheric neutrinos in agreement with expectation and the calibration of downgoing muons with surface detectors establish AMANDA-B10 as a neutrino telescope. Since February 2000, the significantly larger and improved AMANDA-II array has been collecting data. Its effective area for high energy neutrinos is about three times that of the AMANDA-B10 array. At the same time improved angular resolution and background rejection potential are available. The analysis of these data is under way and will improve the given results significantly.
In this section we describe how well the IceCube detector will perform and show that it will reach the scientific goals described in Section 3. This performance depends crucially on signal detection efficiency, background rejection, and calibration of the detector response to high-level variables such as energy and direction and low-level variables such as hit times and amplitudes. Therefore, estimates of IceCube signal sensitivities and limit levels for a variety of potential signals are given, as well as descriptions of techniques for high-level calibration of the detector response (low-level calibrations are discussed separately in section 7). We also describe studies of the detector configuration in order to maximize detector performance.
The largest contribution to the ν flux from non-transient sources in the energy range of several hundreds of MeV to at least several hundreds of TeV is atmospheric neutrinos. The atmospheric ν flux is dominated by the muon component, increasing from a 2:1 νμ : νe ratio at low energies Eν ∼ 1 GeV to 30:1 at Eν ∼ 100 TeV so that the atmospheric ν "background" to UHE cascades is somewhat smaller than for UHE muons. The following sections will address the use of atmospheric neutrinos as a calibration source at lower energies, and their rejection as a background source at higher energies.
Muon events have been generated with the neutrino simulation package nusim [133, 134]. Neutrinos, sampled from an Eν-1 spectrum, are propagated through the earth, taking full account of the earth's density profile. Neutral current regeneration of the neutrinos is treated exactly using a recursive propagation algorithm. Simulation of a generic Eν-1 spectrum allows for the final events to be re-weighted to any desired neutrino source spectrum, whether it be an atmospheric neutrino spectrum (Eν-3.7), a generic Eν-2 spectrum for AGN neutrinos, or any other spectrum predicted in the literature.
The absorption of neutrinos in the Earth is an important effect, see fig. 14. For energies below a few tens of TeV, the full lower hemisphere is visible, whereas at energies above a few PeV the angular acceptance is reduced to zenith angles smaller than 30 degrees below horizon.
Neutrinos have been generated up to a maximum energy of 100 PeV which was set by technical limitations. Eight million events from downgoing muons which constitute the main source of background have been simulated and are used to demonstrate efficient background rejection. Muons were propagated with full simulation of stochastic energy loss. The detector simulation was performed with the AMANDA simulation package amasim. Ice inhomogenities have been neglected for this study but will be included in the future. We simulated PMTs of 10 in diameter but did not take into account the possible increase in light collection efficiency due to a proposed wavelength shifter coating applied to the outer OM surfaces. The noise of the PMTs has been conservatively assumed to be 500 Hz (i.e. higher than the design goal of 300 Hz). A trigger was defined by the condition of at least 5 hits in a local coincidence. A local coincidence is defined with respect to the four nearest neighbors, and for a time window of 1 μs. Signal Monte Carlo muon events are shown in figs. 15 and 16, where the muon energies are 10 TeV and 6 PeV, respectively.
The reconstruction was done in several steps using the AMANDA reconstruction package recoos. The start values for the full fit are obtained from two simple fast approximations called line-fit and dipole-fit (see [151] for details). As a first reduction step with respect to downgoing muons, relatively weak cuts on the zenith angle obtained from these fast approximations have been applied. These cuts have passing rates of 0.91, 0.78 and 0.04 with respect to the sample from AGN neutrinos, atmospheric neutrinos and downgoing muons, respectively.
Next, a full likelihood fit was performed (see [150] and [151]). This fit yields a series of parameters which can be used for selecting events with high quality reconstruction and for further reduction of background. The cuts chosen are the following:
Note that the standard cuts listed above result in a passing rate of 53% for AGN neutrinos and reduce the background from downgoing muons by 3 · 10-6. As shown in fig. 17, this background is concentrated close to the horizon. It can be easily rejected by a further zenith cut (if lower energies should be accepted), or by cuts on the number of channels (if one focuses to the separation of higher energies). Figure 17 also shows the background from uncorrelated coincident air showers (bottom right) which can produce two hit clusters, and earlier one at the bottom and a later one at the top of the array. Such events are not rejected by a simple angular cut, giving the relatively high passing rate after angular cuts compared to muons from single air showers. However, these events are easily identified by the subsequent cuts, in particular the cut on the smoothness.
Results are shown for the "standard configuration" (triangular pattern, 16 m vertical spacing2, 125 m interstring distance). Numbers at the top corner give the number of events and the passing rates. For AGN neutrinos, a flux of 2 × 10-7 · E-2 GeV-1 cm-2 s-1 sr-1 has been assumed, resulting in 4265 events.3
We have investigated the physics performance of the IceCube detector for different configurations, starting from the default configuration and going into the direction of both smaller and larger spacings [139]. Early results on similar IceCube simulations have been presented in [124, 125]. Whereas in [139] only configurations with about 5000 OMs and equidistant spacing are considered [124, 125] cover also options with twice or half the number of OMs, and nested configurations.
The basic pattern is shown in fig. 18. Apart from the triangular pattern, we also simulated rectangular patterns, which yield similar results. The circle in fig. 18 indicates an area of one square kilometer. The configuration includes 80 strings and 60 OMs per string. For a vertical spacing of 16 m, this results in an instrumented length of 944 m. The top layer of OMs was assumed to be at a depth of 1400 m. Table 2 summarizes the studied configurations.
The two following tables give the number of triggered and accepted events per year for the various configurations. Table 3 gives results for atmospheric neutrinos. Numbers in table 4 are for AGN neutrinos, again assuming a flux of 2 × 10-7·E-2 GeV-1 cm-2 s-1 sr-1. The upper numbers refer to triggered events, the lower numbers (in italics) to events after reconstruction and quality cuts.
| vertical/horizontal | 100m | 125m | 150m | 175m |
|---|---|---|---|---|
| 12m | X | X | X | - |
| 16m | X | X | X | - |
| 20m | X | X | X | X |
Table 2: Simulated configurations. Columns indicate different string spacings, rows different spacings of OMs along a string. An "X" indicates that the particular configuration was simulated.
| vertical/horizontal | 100 m | 125 m | 150 m | 175 m |
|---|---|---|---|---|
| 12 m | 2.9 k 1.5 k | 3.6 k 1.8 k | 4.3 k 2.2 k | - - |
| 16 m | 3.4 k 1.9 k | 4.3 k 2.3 k | 5.5 k 2.5 k | - - |
| 20 m | 4.0 k 2.1 k | 4.9 k 2.4 k | 5.7 k 2.6 k | 6.5 k 2.8 k |
Table 4: Number of triggered and accepted neutrino events per year (in thousands) assuming a flux of 2 × 10-7 · E-2 GeV-1 cm-2 s-1 sr-1. The upper numbers refer to triggered events, the lower numbers in italics to the events after quality cuts.
| vertical/horizontal | 100 m | 125 m | 150 m | 175 m |
|---|---|---|---|---|
| 12 m | 600 k 140 k | 620 k 130 k | 640 k 120 k | - - |
| 16 m | 590 k 140 k | 600 k 130 k | 620 k 110 k | - - |
| 20 m | 580 k 140 k | 590 k 110 k | 600 k 90 k | 560 k 60 k |
Table 3: Number of triggered and accepted events per year for atmospheric neutrinos (in thousands). The upper numbers refer to triggered events, the lower numbers in italics to the events after quality cuts.
Clearly, larger spacing is preferable for the AGN case but tends to suppress more atmospheric neutrinos after quality cuts. Going from 125 m string spacing to 150 m gives a 10% increase in accepted AGN events. The rectangular configuration gives a 5% increase in events rate. Decreasing the spacing to 12 m/100 m gives 30% loss in AGN neutrinos, but a slight increase for atmospheric neutrinos. The angular resolution for all configurations is ≤ 1 degree.
We calculate the sensitivity of the detector to diffuse fluxes of neutrinos with a generic E-2 spectrum, expected for sources such as active galactic nuclei (AGN). For the purposes of these calculations we assume a source strength for muon-neutrinos and antineutrinos of a level E2dN/dE = 10-7GeV cm-2 s-1 sr-1. We use the Model Rejection Potential formalism [132, 135], and the associated "model rejection factor" (MRF), to optimize the limit analysis. Figure 19 shows the results of the minimization of the MRF for the hit multiplicity (Nch) cut and an exposure time of three years. The top left figure shows the differential numbers of events expected for both the E-2 spectrum (blue solid line) and for the atmospheric neutrinos (red dashed line). The top right plot shows the same quantities as an integral distribution. Also shown is the Feldman-Cousins 90% confidence level average upper limit. As the background falls toward zero, this classical average upper limit converges toward a value of 2.44. The best limit is obtained where the model rejection factor, (μ(nb)/ns), is minimised (bottom left plot).This occurs for a cut of 168 channels, where 120.9 signal events would be expected upon a background of 17.2. The average upper limit for this background is 8.4, leading to a MRF = 6.9 × 10-2 ,and therefore to a flux limit of E2dN/dE = 6.9 × 10-7GeV cm-2 s-1 sr-1. The bottom right plot shows the parent neutrino energy distribution for those events with multiplicity above the optimal cut of 168 channels. The multiplicity cut corresponds to a minimum energy of about 30 TeV, and to a typical neutrino energy of 1 PeV. Table 5 summarizes the results of the MRF optimization for exposure times of one and three years.
| time (yrs) | Nch cut | S(≥ Nch) | B(≥ Nch) ν(B(≥ Nch)) | limit (= E-2dN/dE×ν/S)) | |
|---|---|---|---|---|---|
| 1 | 175 | 53.1 | 5.4 | 5.3 | 1.0 × 10-8 |
| 3 | 221 | 93.1 | 3.2 | 4.5 | 4.8 × 10-9 |
Table 5: IceCube model rejection factor for an E2dN/dE = 10-7cm-2s-1sr-1GeV2 flux as a function of exposure time.
The sensitivity of IceCube for point sources of neutrinos has been assessed. Since the background may be greatly reduced by cutting to a small angular region about the direction of the point source, the multiplicity cut (Nch) can be relaxed. The sensitivity has been checked in two ways, first by averaging the sensitivity over the upward going hemisphere, and second by looking at a point source from a specific zenith angle.
For each exposure time tested, we optimise in both angular bin size and Nch. Figure 20 shows the pointing accuracy of the array. Ninety percent of events reconstruct to within 4° of the true direction, and 60% to within 1°. The MRF results from varying angular bin and exposure time are shown in table 6. These show that a signal strength of the level dN/dE = 10-7cm-2s-1sr-1GeV2 would produce a very significant signal in IceCube, and in its absence, very constrained upper limits would be obtained. For both exposure times, the best choice of angular cut is about 1ffi, but the limit is ultimately not very sensitive to the choice of angular cut, suggesting that a smaller cut, to enhance the significance of a possible observation, may be warranted. Although the cuts have been optimised to minimise the MRF, thereby optimising the limit setting potential of the detector, we can make some basic estimates of the level of a point source flux needed to give a significant detection of a signal in the exposure time. A chance probability of ∼ 10-7 for a background fluctuation corresponds roughly to a "5 sigma" observation. For any quoted background level, we can calculate the number of events needed to get this chance probability. For the case of 1 year exposure with a 1° angular bin, the expected background is 0.53 events. If 8 events were observed, this would give the required chance probability of ∼ 10-7. A signal strength of 8 - 0.5 = 7.5 events is about 1/5 of the number of events expected from the dN/dE = 10-7cm-2s-1sr-1GeV2 flux, therefore a point source of level dN/dE ∼ 2 × 10-8cm-2s-1sr-1GeV2 would be required to produce a "5 sigma" observation in one year of live time. Of course, this analysis assumes that we only look at a single candidate source. If we do a full sky search, we must pay a penalty for statistical trials. There are about 6500 bins of 1° radius in a half sky (upgoing neutrino) search, so a significance of ∼ 10-9 would be needed for an unknown point source to give a ∼ 10-7 result after the trials are accounted for. This requires that about 10 events are observed (the chance probability to observe 10 or more events from a background of 0.53 is 3 × 10-10), increasing the required signal strength by about 30%.
Table 7 shows the MRF results for a point source at a zenith angle of 130° The limit setting potential is slightly less than the average seen in table 6. Figure 21 shows the model rejection potential optimization for a point source.
Recently, Waxman and Bahcall [94] have proposed that gamma-ray bursts (GRBs) might be sources of neutrinos. The search for neutrinos from GRBs is simplified over that of a point source, due to the time stamp available from satellite observations of the gamma rays from the burst. In the Waxman-Bahcall model the neutrinos are expected to arrive within approximately
| t(y) | ΔΨ | Nch cut | S(≥ Nch) | B(≥ Nch) | μ(B(≥ Nch)) | limit (= E-2dN/dE μ/S) |
|---|---|---|---|---|---|---|
| 1 | 0.5 | 25.5 | 43.1 | 0.53 | 2.9 | 6.7 × 10-9 |
| 1 | 1.0 | 32.5 | 60.6 | 0.91 | 3.2 | 5.3 × 10-9 |
| 1 | 2.0 | 42.5 | 55.6 | 1.10 | 3.4 | 6.0 × 10-9 |
| 1 | 5.0 | 55.5 | 43.9 | 2.20 | 4.0 | 9.0 × 10-9 |
| 3 | 0.5 | 32.5 | 110.2 | 0.67 | 3.0 | 2.7 × 10-9 |
| 3 | 1.0 | 42.5 | 137.6 | 0.82 | 3.1 | 2.3 × 10-9 |
| 3 | 2.0 | 53.5 | 128.8 | 1.25 | 3.5 | 2.7 × 10-9 |
Table 6: IceCube model rejection factor for a point source, averaged over zenith angles 90-180° with flux E2dN/dE = 10-7cm-2s-1GeV2. The optimum choice of cuts for both exposure times are highlighted in bold.
| time (yrs) | ΔΨ | Nch cut | S(≥ Nch) | B(≥ Nch) | μ(B(≥ Nch)) | limit (= E-2dN/dE × μ/S) |
|---|---|---|---|---|---|---|
| 1 | 0.5 | 24.5 | 36.6 | 0.71 | 3.0 | 8.2×10-9 |
| 1 | 1.0 | 33.5 | 47.7 | 1.0 | 3.3 | 6.9×10-9 |
| 1 | 2.0 | 41.5 | 45.8 | 2.2 | 4.0 | 8.8×10-9 |
| 1 | 5.0 | 64.5 | 25.6 | 1.6 | 3.7 | 1.4×10-8 |
| 3 | 0.5 | 29.5 | 98.0 | 1.2 | 3.4 | 3.5×10-9 |
| 3 | 1.0 | 33.5 | 143.2 | 3.0 | 4.4 | 3.1×10-9 |
| 3 | 2.0 | 42.5 | 132.8 | 5.8 | 5.5 | 4.1×10-9 |
Table 7: IceCube model rejection factor for an point source at 130° zenith angle, with flux E2dN/dE = 10-7cm-2s-1GeV2.
10 seconds of the gamma rays. The IceCube detector will reconstruct neutrino-induced muons from GRBs to less than ten degrees of the true direction (fig. 22).
The Waxman-Bahcall flux corresponds to the expected neutrino flux from 1000 GRBs. Within a 10° angular search bin and 10 second time window, we would expect a total of 15 upgoing muon events from 1000 GRBs after quality cuts were applied to remove the most obvious mis-reconstructed downgoing muons. The atmospheric neutrino background is negligible (total 0.32 events) but about 500 misreconstructed downgoing muons would remain. Tightening the cuts to the final cut set discussed previously removes the last of the muon background, reduces the atmospheric neutrino background to 0.23 events, and retains 12 GRB induced neutrino events. It should be noted that more Monte-Carlo simulations are needed to further check the belief that the background of mis-reconstructed downgoing muons is indeed zero.
Optimising the Nch cut leads to a cut of Nch = 12.5 and model rejection factor of 0.22, a severe constraint on the Waxman-Bahcall model. Since the GRB search is essentially background free, the improvement in the limit goes nearly linearly with the increasing number of GRBs searched. This behaviour is shown in table 8. It is interesting that the observation of only 210 GRBs is enough to rule out the Waxman-Bahcall model at 90% classical confidence.
Since the angular cut and time window search can be made so tight, the GRB searches are close to background-free. Then the observation of even a few events would be very significant. For 300 GRBs searched, and a 2°, window, the Waxman-Bahcall model predicts about 3 events, on an atmospheric neutrino background of 0.003. The chance probability of observing 3 or greater events given a background of 0.003 is about 5 × 10-9.
Table 8 shows that the MRF is insensitive to the choice of angular bin size. In this case, a choice of a smaller search window would be preferred, in order to reduce the background (for limited signal loss) and give a more significant observation of a potential signal. Ultimately however, the uncertainty in the knowledge of the GRB direction (from the satellite observation) will limit how small the angular search bin can be made. Figure 23 shows the model rejection potential optimization for GRBs.
| nbursts | ΔΨ | Nch cut | S(≥ Nch) | B(≥ Nch) | μ(B(≥ Nch)) | limit (= E-2dN/dE × μ/S) |
|---|---|---|---|---|---|---|
| 100 | 2.0 | 1.5 | 0.98 | 0.001 | 2.4 | 2.49 |
| 5.0 | 1.5 | 1.13 | 0.005 | 2.4 | 2.16 | |
| 10.0 | 1.5 | 1.19 | 0.02 | 2.46 | 2.06 | |
| 20.0 | 1.5 | 1.20 | 0.086 | 2.51 | 2.07 | |
| 30.0 | 12.5 | 1.22 | 0.19 | 2.60 | 2.12 | |
| 210 | 10 | 1.5 | 2.50 | 0.045 | 2.49 | 0.99 |
| 300 | 2.0 | 1.5 | 2.94 | 0.003 | 2.44 | 0.829 |
| 5.0 | 1.5 | 3.40 | 0.016 | 2.45 | 0.721 | |
| 10.0 | 1.5 | 3.51 | 0.065 | 2.46 | 0.70 | |
| 20.0 | 1.5 | 3.66 | 0.26 | 2.66 | 0.72 | |
| 1000 | 2.0 | 1.5 | 9.81 | 0.009 | 2.45 | 0.249 |
| 5.0 | 1.5 | 11.34 | 0.05 | 2.48 | 0.219 | |
| 10.0 | 12.5 | 11.9 | 0.215 | 2.62 | 0.22 | |
| 20.0 | 20.5 | 11.3 | 0.471 | 2.83</ |