It is generally assumed that the neutrino flux emitted by a galactic source is proportional to ( 2 from ray observations above 10 GeV.)
In order to calculate the sensitivity of a detector to a given proton luminosity , the number of expected muons with energies above a given energy threshold during the exposure time has to be compared with the background due to atmospheric neutrinos.
This calculation has been performed with a Monte Carlo program. It shows that better sensitivities can be obtained for the highest values of the muon energy threshold. So, a cubic kilometer detector is particularly well aimed at the detection of sources with total proton luminosities of 10-10ergs at distances of 1kpc and between 10-10ergs for the whole Galaxy (10kpc).
For individual known sources, the calculation of the detectable luminosity has been performed by taking into account the distance of each individual source, the fraction of time during which the source is below the horizon, the latitude of the detector and the flux of the background atmospheric neutrinos averaged along the apparent path of the source. Results are shown in .
The models of AGN generated neutrino fluxes differ in their production sites and production mechanisms. We considered three types of models [22,23,24] which do not contradict existing measurements ( e.g. the Fréjus upper limit at 2.6 TeV ).
The corresponding diffuse fluxes of muon neutrinos for these models is shown in fig. together with the angle-averaged atmospheric neutrino flux (ATM) .
The rates of neutrino induced muons are calculated from these fluxes using the CTEQ3-DIS parton
distribution functions and a Monte Carlo propagation of the muons.
The results for a 1km effective area
detector are summarized in
table , for muon energy thresholds E ranging from
1 TeV to 100 PeV. Above 10TeV the event rates
predicted for neutrinos coming from AGNs become larger
than for atmospheric neutrinos.
If some of the AGNs are powerful enough sources, they could be detected individually. A possible method to estimate the fluxes from individual AGNs is to select all AGN sources of the Second EGRET Catalog and to assume that the neutrino flux is equal to the gamma-ray flux. The basic assumption used is that all gamma-rays are of hadronic origin. In the case where an important fraction of gamma-rays are of electromagnetic origin the values that we quote for neutrinos must be scaled down. Results of this estimate are given in .
It is shown that, due to the low background level ( per year and per km for an angular cut of 1), for each one of the three different methods of calculation there are several sources for which a statistically significant signal could be detected in one year with a km detector.
From Gamma Ray Burst sources, in  the rate of upcoming muons from neutrinos above 100 TeV in an underwater detector is expected to be between 10 and 100 /km/year. These neutrinos would be distinguished from the atmospheric ones due to their correlation to GRB's, which can be precise thanks to the brief emission interval of the gammas.
We considered three models: BHSl and BHSh (with GeV, and respectively)  and SIG (with GeV, p = 1, constrained by the 1-10 GeV -ray observational data assuming an extra-galactic magnetic field of G) . The corresponding expected diffuse neutrino fluxes are displayed in fig. and the corresponding induced muon rates for a km effective area detector are shown in table . Only the most optimistic amongst these three models (BHSh) gives rise to a detectable signal in one year with a km detector.
The signal will consist of an excess of neutrino flux coming from the Sun or from the center of the Earth.
The calculation of the sensitivity of a detector depends on the parameters of the theoretical model and the atmospheric neutrinos background.
This calculation has been performed in [21,17,26] in terms of the sensitive area required to detect a 4 standard deviations signal as a function of the neutralino mass. The results of this calculation shows that a detector with an area of 1km running for one year would be sensitive to a range of neutralino masses extending up to a few TeV.
For all subjects described above, the atmospheric neutrinos constitute a source of background which is suppressed by using an energy threshold of 10 TeV. Nevertheless, atmospheric neutrinos may be an interesting subject of study by lowering the energy threshold to 10GeV.
In this case, the analysis of the angular distribution of muon neutrinos will allow the study of the flux as a function of the thickness of matter crossed through the Earth which varies from a few tens of km to 13000km depending on the zenith angle. This should allow to look for neutrino oscillations in a domain of the oscillation parameter space where Kamiokande and Superkamiokande have shown some evidence of such an effect [27,28].