4.2. Astronomy on Ice

IceCube is, perhaps, the most promising route for neutrino detection [495]. This telescope will consist of 80 kilometer-length strings, each instrumented with 60 10-inch photomultipliers spaced by 1.7 m. The deepest module is 2.4 km below the ice surface. The strings are arranged at the apexes of equilateral triangles 125 m on a side. The instrumented detector volume is a cubic kilometer. ⁽⁴³⁾ A surface air shower detector, IceTop, consisting of 160 Auger-style Cerenkov detectors deployed over 1 km² above IceCube, augments the deep-ice component by providing a tool for calibration, background rejection and air-shower physics. Muons can be observed from 10¹¹ eV to 10¹⁸ eV. Cascades, generated by _e, _e, , and can be observed above 10¹¹ eV and reconstructed at energies somewhat above 10¹³ eV. The angular resolution is 0.7° at TeV energies.

As an example of the IceCube potential, in what follows we briefly discuss its sensitivity to probe the neutron hypothesis of UHECRs via observation of the antineutrino beam n p + e^- + _e, expected from the Cygnus direction [54]. To this end, we first estimate the background signal. As discussed in Sec. 2.1, the TeV -ray flux,

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reported by HEGRA Collaboration [139] in the vicinity of Cygnus OB2 is likely due to hadronic processes. Since ⁰'s, ⁺'s, and ^-'s are produced in equal numbers, we expect two photons, two _e's, and four _µ's per ⁰. On average, the photons carry one-half of the energy of the pion, and the neutrinos carry one-quarter. For dF / dE E^-2, the energy-bins dE scale with these fractions, and we arrive at

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for the fluxes at the source, where denotes any one of the three pion charge-states. Terrestrial experiments (see e.g. [504]) have shown that _µ and are maximally mixed with a mass-squared difference ~ 10^-3 eV². This implies that the _µ's will partition themselves equally between _µ's and 's on lengths large compared to the oscillation length _osc ~ 1.5 × 10^-3 (E / PeV) pc. From these remarks, one finds a nearly identical flux for each of the three neutrino flavors (j = e, µ, ), which is equal to [155]

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Although TeV neutrinos are copiously produced, because they are weakly interacting the detection probability on Earth is tiny, about 10^-6 [466]. In particular, the expected event rate at IceCube associated with the unidentified HEGRA source is < 1 yr^-1 (D. Hooper, private communication). Such an event rate is even smaller than the atmospheric neutrino background. ⁽⁴⁴⁾ Moreover, existing limits on TeV -ray fluxes in this region of the sky are near the HEGRA sensitivity [505]. In light of this, we take as background the atmospheric neutrino event rate, and so Poisson statistics implies that a signal 3.5 events is significant at the 95% CL.

Antineutrinos take only a very small part of the energy of the parent neutron, typically ~ 10^-3. Hence, to estimate the event rate of TeV antineutrinos at IceCube, the relevant nucleus population at the source has an energy per nucleon E_{N, PeV} ~ 1 PeV. Nuclei with Lorentz factor ~ 10⁶ are synthesized in all supernovae. Hadronic interactions with the HII population (density < 30 cm^-3 [140]) and photodisintegration processes provide the flux of PeV neutrons. In this energy regime, the target photons at photodisintegration threshold energies are in the ultraviolet, ~ 5 eV. This includes the entire emission spectrum of the O stars and about 60% of photons from B stars (with average temperature 28,000 K). From the photon emission rate F_UV the number density n_UV at the surface of a sphere of radius R from the core center is given by

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For the O-star population, the photon emission rate in the Lyman region is found to be F_L 10⁵¹ photons s^-1 [192]. The Lyman emission corresponds to 60% of the entire O star spectrum. Furthermore, as mentioned above, 60% of the B star spectrum is also active for photodisintegration in this energy region, and the B star population is about 20 times greater than that of the O stars [192]. Now, from the H-R diagram [506] one can infer that the energy luminosity of a B-star is about 0.1 that of an O star. Additionally, the B star temperature is about 0.5 the O star temperature, giving a number luminosity ratio of about 0.2. All in all, for photodisintegration resulting in PeV nucleons, the relevant photon density in the core of the Cygnus OB2 association is n_UV ~ 230 cm^-3. The nucleus mean free path is 35 kpc, corresponding to a collision time = 10⁵ yr. Thus, the collision rate for photodisintegration in the core region is comparable to the hadronic interaction rate. ⁽⁴⁵⁾

Since one is interested in neutrinos, it is still necessary to compare the production rate for charged pions in the hadronic case to the overall rate for generating neutrons. To assess this ratio, we made use of available high energy event simulations showing spectator nucleon and pion spectra for Fe-N / p-N collisions at 10¹⁵ and 10¹⁶ eV [507] (summarized in [508]). The pion rapidity spectra in the central plateau are roughly energy independent, except for the widening of the plateau with energy whereas there is a slow increase of spectator neutrons as one reaches the region of interest (E_N 1 PeV). Allowing for sizeable differences in hadronic interaction models, the secondary populations are roughly 35% ^±, 45% , 10% nucleons, and 10% K [508]. In the energy range yielding PeV neutrons, only about 30% of the rapidity plateau contributes charged pions above 2 TeV. Since only half the nucleons are neutrons, we arrive at a ratio

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in the hadronic interactions.

However, photodisintegration also takes place in the outer regions of the OB association as long as: (i) the density of the optical photons propagating out from the core allows a reaction time which is smaller than the age of the cluster ~ 2.5 Myr [509] and (ii) the diffusion front of the nuclei has passed the region in question. From Eq. (78) we estimate an average photon density n_UV 25 cm^-3 out to 30 pc, which gives a reaction time of 10⁶ yr. The diffusion time (~ 1.2 Myr) is a bit smaller than the age of the cluster, and somewhat higher than the reaction time, allowing about 90% of the nuclei to interact during the lifetime of the source. Thus, the production rate of neutrons via photodisintegration is amplified by a volume factor of 27 over the rate in the 10 pc core. The net result of all this consideration is that the PeV neutron population is about an order of magnitude greater than that of the TeV charged pions [54].

With this in mind, we now discuss the prospects for a new multi-particle astronomy: neutrons as directional pointers + antineutrinos as inheritors of directionality. The basic formula that relates the neutron flux at the source (dF_n / dE_n) to the antineutrino flux observed at Earth (dF / dE) is [54]:

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The variables appearing in Eq. (80) are the antineutrino and neutron energies in the lab (E and E_n), the antineutrino angle with respect to the direction of the neutron momentum, in the neutron rest-frame (), and the antineutrino energy in the neutron rest-frame (). The last three variables are not observed by a laboratory neutrino-detector, and so are integrated over. The observable E is held fixed. The delta-function relates the neutrino energy in the lab to the three integration variables. ⁽⁴⁶⁾ The parameters appearing in Eq. (80) are the neutron mass and rest-frame lifetime (m_n and _n), and the distance to the neutron source (D). dF_n / dE_n is the neutron flux at the source, or equivalently, the neutron flux that would be observed from the Cygnus region in the absence of neutron decay. Finally, dP / d is the normalized probability that the decaying neutron in its rest-frame produces a _e with energy . Setting the beta-decay neutrino energy equal to its mean value ₀, we have dP / d = ( - ₀). ⁽⁴⁷⁾ Here, the maximum neutrino energy in the neutron rest frame is just the neutron-proton mass-difference Q m_n - m_p = 1.29 MeV, and the minimum neutrino energy is zero in the massless limit. ⁽⁴⁸⁾ The expression in parentheses in Eq. (80) is the decay probability for a neutron with lab energy E_n, traveling a distance D. In principle, one should consider a source distribution, and integrate over the volume d³ D. Instead, we will take D to be the 1.7 kpc distance from Earth to Cygnus OB2; for the purpose of generating the associated neutrino flux, this cannot be in error by too much.

Putting all this together, normalization to the observed "neutron" excess at ~ 10¹⁸ eV leads to about 20 antineutrino events at IceCube per year [54]. A direct TeV _e event in IceCube will make a showering event, which, even if seen, provides little angular resolution. In the energy region below 1 PeV, IceCube will resolve directionality only for _µ and _µ. Fortunately, neutrino oscillations rescue the signal. Since the distance to the Cygnus region greatly exceeds the _e oscillation length _osc ~ 10^-2(E / PeV) pc (taking the solar oscillation scale m² ~ 10^-5 eV²), the antineutrinos decohere in transit. The arriving antineutrinos are distributed over flavors, with the muon antineutrino flux F_µ given by the factor 1/4 sin²(2 ) 0.20 times the original F_e flux. The flux is the same, and the _e flux is 0.6 times the original flux. Here we have utilized for the solar mixing angle the most recent SNO result 32.5° [510], along with maximal mixing for atmospheric _µ- neutrinos and a negligible _e component in the third neutrino eigenstate. All in all, for a year of running at IceCube, one expects 4 _µ showers with energies 1 TeV to cluster within 1° of the source direction, comfortably above the stated CL [54].

IceCube is not sensitive to TeV neutrinos from the Galactic Center, as these are above the IceCube horizon, where atmospheric muons will dominate over any signal. However, other kilometer-scale neutrino detectors, such as those planned for the Mediterranean Sea, may see the Galactic Center flux.

In summary, in a few years of observation, IceCube will attain 5 sensitivity for discovery of the Fe n _{e µ} cosmic beam, providing the "smoking ice" for the Galactic Plane neutron hypothesis.

⁴³ Extension of these aperture is in the proposal stage [503]. Back.

⁴⁴ For a year of running at IceCube the expected background from atmospheric neutrinos (with energy 1 TeV) within 1° circle centered in the Cygnus direction (about 40° below the horizon) is < 1.5 events. Back.

⁴⁵ This estimate takes into account a hadronic cross section, _{Fe p} ~ A^0.75 _pp 6 × 10^-25 cm², and the generous upper limit [138] of the nucleon density ~ 30 cm^-3 [140]. Back.

⁴⁶ Note that E = _n( + cos = E_n (1 + cos / m_n,

where _n = E_n / m_n is the Lorentz factor, and (as usual) 1 is the particle's velocity in units of c. Back.

⁴⁷ The delta-function in the neutron frame gives rise to a flat spectrum for the neutrino energy in the lab for fixed neutron lab-energy E_n = _n m_n:

with 0 E 2 _{n 0}. Back.

⁴⁸ The massless-neutrino approximation seems justifiable here: even an eV-mass neutrino produced at rest in the neutron rest-frame would have a lab energy of m _n GeV, below threshold for neutrino telescopes. Back.