4.1. Bounds on the energy spectrum
The basic operational system of neutrino telescopes is an array of strings with photo-multiplier tubes (PMTs) distributed throughout a natural Cerenkov medium such as ice or water. The largest pilot experiments (~ 0.1 km in size) are: the now defunct DUMAND (Deep Underwater Muon and Neutrino Detector) experiment [470] in the deep sea near Hawaii, the underwater experiment in Lake Baikal [471], and AMANDA (Antarctic Muon And Neutrino Detector Array) [472] in the South Pole ice. Next generation neutrino telescopes aim towards an active volume in the range of 1 km3 of water. Projects under construction or in the proposal stage are: two deep sea experiments in the Mediterranean, the French ANTARES (Astronomy with a Neutrino telescope Abyss environment RESearch) [473] and NESTOR (Neutrino Experiment SouthwesT Of GReece [474]), and ICECUBE [475], a scaled up version of the AMANDA detector.
The traditional technique to observe cosmic neutrinos is to look
for muons (along with a visible hadronic shower if the
is of
sufficient energy) generated via charged-current interactions,
(µ,
µ)
N 
(µ-, µ+) + anything,
in the rock below the detector. The Cerenkov light emitted by
these muons is picked up by the PMTs, and is used for track
reconstruction. The muon energy threshold is typically in the
range of 10 - 100 GeV. However, besides the desired
extraterrestrial neutrinos, below ~ 103 GeV there is a
significant background of leptons (produced by CRs interacting in
the atmosphere)
[476,
477]
and so the task of developing diagnostics for neutrino sources becomes
complicated. With rising energy
(
106 GeV) the three neutrino flavors can be identified
[478].
The spectacular neutrino fireworks (in the 10 MeV range) from supernova 1987A constitute the only extragalactic source so far observed [479, 480]. The Fréjus [481], Baikal [482], MACRO [483], and AMANDA [484] collaborations reported no excess of neutrinos above the expected atmospheric background, enabling significant limts to be set on the diffuse neutrino flux. (39) These limits are shown in Fig. 9.
 |
Figure 9. The horizontal solid lines
indicate current 90% CL upper limits on the neutrino fluxes
|
Upward going neutrinos with energies
108 GeV are typically
blocked by the Earth. This shadowing severely restricts the high
energy event rates in underground detectors. However, neutrinos
may also induce extensive air showers, so current and future air
shower experiments might also function as neutrino detectors. The
neutrino interaction length is far larger than the Earth's
atmospheric depth, which is only 0.36 km water equivalent (kmwe)
even when traversed horizontally. Neutrinos therefore shower
uniformly at all atmospheric depths. As a result, the most
promising signal of neutrino-induced cascades are quasi-horizontal
showers initiated deep in the atmosphere. For showers with large
enough zenith angles, the likelihood of interaction is maximized
and the background from hadronic cosmic rays is eliminated, since
the latter shower high in the atmosphere. These
-showers will
appear as hadronic vertical showers, with large electromagnetic
components, curved fronts (a radius of curvature of a few km),
and signals well spread over time (on the order of microseconds).
The event rate for quasi-horizontal deep showers from ultra-high energy neutrinos is [492]
 |
(70) |
where the sum is over all neutrino species i =
e,
e,
µ,
µ,
,
, and all final states
X. NA = 6.022 × 1023 is Avogadro's
number, and
d
i /
dEi is the source flux of neutrino species i,
as usual denotes the cross
section, and 
is the
exposure measured in cm3 w.e. sr
time. The Fly's Eye and the AGASA Collaborations have searched for
quasi-horizontal showers that are deeply-penetrating, with depth
at shower maximum
Xmax > 2500 g/cm2 (see e.g.
[498,
499]).
There is only 1 event that
unambiguously passes this cut with 1.72 events expected from
hadronic background, implying an upper bound of 3.5 events at
95%CL from neutrino fluxes. Note that if the number of events
integrated over energy is bounded by 3.5, then the same limit is
certainly applicable bin by bin in energy. Thus, using
Eq. (70) one obtains
 |
(71) |
at 95% CL for some energy interval
. Here, the sum over
X takes into account charge and neutral current processes. In a
logarithmic interval
where a single
power law approximation
 |
(72) |
is valid, a straightforward calculation shows that
 |
(73) |
where 
=
(
+ 1)
/ 2 and
<A> denotes the quantity A evaluated at the center
of the logarithmic interval. The parameter
= 0.363 +
-
, where
0.363 is the power law index of the SM neutrino cross sections
[500] and
and -
are the power
law indices (in the interval
) of the exposure
and flux
di /
dEi, respectively. Since
sinh /
> 1, a
conservative bound may be obtained from Eqs. (71) and (73):
 |
(74) |
By taking = 1 as a
likely interval in which the single power law behavior is
valid (this corresponds to one e-folding of energy), and setting
<Ei d
i /
dEi> = 1/6
<E
d /
dE>
(
total neutrino
flux) from Eq. (74) it is straightforward to obtain 95%CL upper limits
on the neutrino flux. The limits are shown in
Fig. 9.
These bounds will be improved in the near future. In particular, each
site of PAO will observe ~ 15 km3we sr of target mass around
1019 eV
[501].
Moreover, the study of radio pulses from electromagnetic
showers created by neutrino interactions in ice would provide an increase in
the effective area up to 104 km2. A prototype of
this technique is the Radio Ice Cerenkov Experiment (RICE)
[502].
Similar concepts are used by the Goldstone Lunar ultrahigh energy
neutrino Experiment (GLUE),
(40)
the ANtartic Impulse Transient Array (ANITA),
(41)
and the Fast On-orbit Recording of Transient Events (FORTE).
(42)
Existing limits on -fluxes
from RICE, GLUE and FORTE, as well as the projected sensitivities of
forthcoming experiments are collected in Fig. 9.
39 The Frejus experiment, located in an underground laboratory, measured the energy of muons produced by neutrino interactions in the rock above the detector. The detector itself comprised a calorimeter made from a vertical sandwich of over 900 iron slabs interspersed with flash chambers. Geiger tubes embedded in the structure provided the trigger [485]. The extensive air shower array on top of the Gran Sasso Laboratory (EAS-TOP) [486] and MACRO [487] used similar techniques. Back.
40 This experiment observes microwave Cerenkov pulses from electromagnetic showers induced by neutrinos interacting in the Moon's rim [493] Back.
41 A balloon-borne payload that will circle the continent of Antartica at 35,000 meters, scanning the vast expanses of ice for telltale pulses of radio emission generated by the neutrino collisions [http://www.ps.uci.edu/~anita/]. Back.
42 The FORTE satellite records bursts of electromagnetic waves arising from near the Earth's surface in the radio frequency range 30 to 300 MHz with a dual polarization antena [494]. Back.
E-2 as reported by the EAS-TOP
[