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\begin{document}
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\title{NEUTRINO ASTRONOMY\footnote{Talk given at the XXXIInd Rencontres de Moriond, Very High Energy Phenomena in the Universe, Les Arcs, France (January 18-25, 1997) } }
\author{ L. MOSCOSO }
\address{DSM/DAPNIA/SPP, CEA/Saclay, 91191-Gif-Sur-Yvette CEDEX, France}
\maketitle\abstracts{The sky survey with high energy neutrinos is complementary to the survey with photons. The method of the detection of ${\nu}_{\mu}$ is described and the expected sensitivity to galactic and extra-galactic sources with a km$^3$ detector is estimated. The status of the current under-water(ice) detector projects is reported.}
\section{Introduction}
The intense activity on the conception and realization of large high energy neutrino detectors is motivated by the
observation of cosmic ray flux extending up to few $10^{20}$\,eV.
The origin of these cosmic rays and the nature of mechanisms capable to
explain
the observed energies and luminosities
are presently unknown. In order to
progress in the understanding of this phenomenon, it is necessary to extend
our knowledge by observing high energy cosmic rays of different natures. Therefore, it is important to study both
the energy spectra of $\gamma$-rays and of neutrinos.
Because these particles have no electric charge they are not deflected by the
galactic or by the extra-galactic magnetic field.
Several examples of detection of cosmic neutrinos exist: solar neutrinos, below 10\,MeV, and neutrinos from the supernova SN1987a, above 20\,Mev. It is of major interest to try to detect signals at higher energies. Several attempts have been made with underground detectors, originally devoted to the detection of
proton decay. The modest dimensions of these detectors allowed to determine only upper limits on the neutrino luminosities of several celestial bodies.
In order to improve the sensitivity to high energy neutrino fluxes the
construction of a detector of a km$^3$ scale is now foreseen.
Among the possible sources in the Galaxy X-ray binary systems could emit high energy neutrinos. They consist in a compact body, like a neutron star or a black hole, which
accretes the matter of its non compact companion. The presence of a very high
magnetic field rotating with high frequency and the presence of plasma flow could yield to particle acceleration. The interaction of the accelerated particles with matter could produce mesons which decay in neutrinos.
Another source of high energy neutrinos could be the remnants of young
supernov\ae. Protons could be accelerated by the explosion wind and, again, the
neutrino emission could be due to the interactions of the accelerated protons
with matter. The typical time duration of this emission would be of the order
of 1-10\,years.
Very high energy neutrinos could be emitted by active galactic nuclei (AGN).
These potential sources are supposed to be galaxies containing a black hole in
the central region. The acceleration power is
supplied by the accretion onto the black hole.
The emission of gamma-rays up to $\approx$ 10\,GeV from Active Galactic Nuclei and from galactic sources has been well established a large number of them are reported in the Second EGRET Catalog. Nevertheless, only two AGNs (Mrk 421 and Mrk 501) and two pulsars (PSR1706-44 and the Crab) have been also observed as emitters of high energy gammas (above 300\,GeV). A possible explanation is that high energy gamma-rays are absorbed by interacting with infra-red and cosmic background radiations. It is worth noting that high energy neutrinos are immune to this phenomenon.
\section{Detection of high energy neutrinos}
High energy muon neutrinos can be detected by observing long range muons produced
in charged current neutrino nucleon interactions in the matter surrounding the detector.
Due to the increase of the $\nu N$ cross-section with the neutrino energy and to the increase of the muon path-length with the muon energy the ratio of the event rate to the neutrino flux ${\Phi}_{\nu}^{-1}(E_{\nu}){\mathrm d}N/{\mathrm d}E_{\nu}$ is an increasing function of the neutrino energy $E_{\nu}$. This means that high energy neutrinos will be statistically enhanced.
The higher the energy of the neutrino, the lower the scattering angle between the neutrino and the produced muon is. At energies above 1\,TeV the average of this angle is lower than 1$^{\circ}$. So, the direction of the parent neutrino is well determined.
Despite its increase with the neutrino energy the $\nu N$ cross-section remains small. So, the detector area must be large enough to provide a sufficient sensitivity in any direction. For this reason a volume of 1\,km$^3$ is needed.
The main source of background is the flux of neutrinos produced in the cascades initiated by primary cosmic rays in the atmosphere. This is a physical unavoidable background.
The flux of downward-going atmospheric muons is about 10 order of magnitude higher than the flux of muons induced by atmospheric neutrinos. In order to suppress this high flux the detector must be well shielded.
The most economic way to realize a km-scale well shielded detector is to build a 3-D array of optical modules in ocean deep or under the polar ice. High energy muons crossing the detector medium will produce \u{C}erenkov light at an angle ${\theta}_C \simeq 43^{\circ}$. The reconstrucion of the muon direction is performed by using the informations on the arrival times of the photons recorded by the optical modules. All simulations show that an angular resolution of $1^{\circ}$ is easily reachable. To avoid the high flux of atmospheric muons only upward-going muons will be considered.
\section{Fluxes and rates}
Event rates are calculated by using a Monte~Carlo technique taking into account of the neutrino flux, the $\nu N$ cross-section~\cite{botts} and the muon propagation in the matter surrounding the detector. The uncertainties on quoted number depend on the uncertainties on these parameters. The most relevant parameter for the error propagation is the $\nu N$ cross-section which is now well constrained at energies below 100\,TeV but becomes badly known for energies far above 100\,TeV.
No error estimate are reported on the predicted fluxes given by different authors for extra-galactic sources. For atmospheric neutrinos an uncertainty of about 20\% is likely.
Therefore an overall uncertainty of the order of 30\% is expected on the predicted sensitivities to galactic sources and an overall uncertainty of one order of magnitude may be estimated on predicted event rates for extra-galactic sources.
\subsection{Galactic sources}
It is generally assumed that the number of neutrinos emitted by a galactic
source per time unit and per energy unit is given by:
\[ \frac{{\mathrm d}^2 N_{\nu}}{{\mathrm d}E_{\nu}{\mathrm d}t} =
A {E_{\nu}}^{-\gamma}. \]
The spectral index is $\gamma \approx 2$ as measured in gamma-ray
observations in the region below 10\,GeV.
The normalization factor $A$ is related to the luminosity of the source by:
\[ {\cal L}_{\nu} = \int_{E_0}^{E_C} \frac{{\mathrm d}^2 {N}_{\nu}}{{\mathrm d}
E_{\nu} {\mathrm d} t} E_{\nu} {\mathrm d}E_{\nu} = \epsilon {\cal L}_p, \]
where ${\cal L}_{\nu}$ and ${\cal L}_p$ are respectively the luminosities
for neutrino and proton emissions for the whole energy spectrum between the
minimal value $E_0$ and the cut-off energy value $E_C$ and where $\epsilon$ is the ratio of the total neutrino luminosity to the total proton luminosity.
It is then easy to derive the neutrino flux at the detector for a source which
is at a given distance $D$:
\[ \frac{{\mathrm d} {\Phi}_{\nu}}{{\mathrm d} E_{\nu}} =
\frac{A}{4 \pi D^2} {E_{\nu}}^{-\gamma}. \]
In order to estimate the sensitivity of the detector to the total
luminosity ${\cal L}_p$ it is necessary to calculate the number of expected
muons with energies above the energy threshold during the exposure time for any given value of ${\cal L}_p$ and
to compare it to the expected background due to atmospheric neutrinos.
The expected number of
muons is given by:
\[ N_S ={\Phi}_0 \left( \frac{1\,{\mathrm{kpc}}}{D} \right)^2
\left( \frac{\epsilon}
{0.1} \right) \left( \frac{{\cal L}_p}{10^{38}{\mathrm{erg\,s}}^{-1}}
\right) ST. \]
The values of ${\Phi}_0$ are given in table~\ref{lmtb:tab1} for two different values of the differential spectral index $\gamma$ and for different muon energy thresholds. The detector exposure $ST$ is a covolution of the effective area, which is supposed to be independent of the muon direction, with the running time, calculated by taking into account the on source duty factor. The fluxes of muons induced by atmospheric neutrinos, averaged over the detectable hemisphere, have been calculated by using the neutrino flux given in ref.~\cite{volkova} and are also given in the last column of
table~\ref{lmtb:tab1}. This flux allows us to calculate the background which contaminates the signal:
\[ \begin{array}{ll} N_{\mathrm{BK}} & = {\Phi}_0^{\mathrm{atm}}
2{\pi} (1-\cos {\theta}_c)ST \\
& \simeq {\Phi}_0^{\mathrm{atm}}
ST {\pi} {\theta}_c^2, \end{array} \]
where ${\theta}_c$ is the angular cut used to define the direction of the
source.
\begin{table}[p]
\caption{Values of ${\Phi}_0$ (see the text) for different energy
thresholds and for two different spectral
index, $\gamma = 2$ and $\gamma = 2.2$,
and flux of muons induced by atmospheric neutrinos
averaged over the whole $2 \pi$ downward hemisphere for the same thresholds.}
\label{lmtb:tab1}
\vspace{0.4cm}
\begin{center}
\begin{tabular}{|r|c|c|c|}
\hline
& & & \\
Energy & $\gamma = 2$ & $\gamma = 2.2$ & Atm. neutrinos \\
threshold & (cm$^{-2}$\,s$^{-1}$) & (cm$^{-2}$\,s$^{-1}$) &
(cm$^{-2}$\,s$^{-1}$\,sr$^{-1}$) \\
& & & \\
\hline
& & & \\
10\,GeV & $3.0 \cdot 10^{-13}$ & $1.3 \cdot 10^{-13}$ &
$1.5 \cdot 10^{-13}$ \\
100\,GeV & $2.8 \cdot 10^{-13}$ & $1.2 \cdot 10^{-13}$ &
$5.3 \cdot 10^{-14}$ \\
1\,TeV & $1.7 \cdot 10^{-13}$ & $6.6 \cdot 10^{-14}$ &
$5.9 \cdot 10^{-15}$ \\
10\,TeV & $5.2 \cdot 10^{-14}$ & $1.5 \cdot 10^{-14}$ &
$1.4 \cdot 10^{-16}$ \\
& & & \\
\hline
\end{tabular}
\end{center}
\end{table}
The luminosity that can be detected as a signal (of at least 10 events) exceding 5 standard deviations from the atmospheric neutrinos background is:
\[ {\cal L}_p = {\cal L}_0 \left( \frac{0.1}{\epsilon} \right)
\left( \frac{1\,{\mathrm{km}}^2 {\mathrm y}}{ST}\right)^{1/2}
\left( \frac{D}{1\,{\mathrm{kpc}}}\right)^2
\left( \frac{{\theta}_c}{1^{\circ}} \right), \]
with:
\[ \frac{{\cal L}_0}{10^{38} {\mathrm{erg\,s}}^{-1}} =
2.75 \cdot 10^{-10} \left( \frac{{\Phi}_0^{\mathrm{atm}}}{1\,{\mathrm{cm}}^{-2}
{\mathrm s}^{-1} {\mathrm{sr}}^{-1}} \right)^{1/2}
\left( \frac{1\,{\mathrm{cm}}^{-2}{\mathrm s}^{-1}}
{{\Phi}_0} \right). \]
As an example the detectable luminosities for sources located at 5\,kpc
are given in table~\ref{lmtb:tab2} for two different spectral
index values and for different energy thresholds. This table clearly shows that
better sensitivities can be obtained for the highest values of the muon energy
threshold.
\begin{table}[p]
\caption{Example of minimum detectable proton luminosities for $D=5\,{\mathrm{kpc}}, ST = 1\,{\mathrm{km}}^2{\mathrm y}$.}
\label{lmtb:tab2}
\vspace{0.4cm}
\begin{center}
\begin{tabular}{|r|c|c|c|}
\hline
& & & \\
Energy & Background & $\gamma = 2$ & $\gamma = 2.2$ \\
threshold & (atmosph. $\nu$) & (erg\,s$^{-1}$) & (erg\,s$^{-1}$) \\
& & & \\
\hline
& & & \\
10\,GeV & 30 & 10$^{36}$ & 2\,10$^{36}$ \\
100\,GeV & 10 & 6\,10$^{35}$ & 1.3\,10$^{36}$ \\
1\,TeV & 1 & 4.8\,10$^{35}$
& 1.2\,10$^{36}$ \\
10\,TeV & 0.03 & 1.5\,10$^{36}$ & 5.3\,10$^{36}$ \\
& & & \\
\hline
\end{tabular}
\end{center}
\end{table}
For individual known sources the calculation of the detectable luminosity can be
performed by taking into account of the distance of each individual source, the
fraction of time ${\epsilon}_t$ 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. As an example
these values are given in table~\ref{lmtb:tab3} for
detectors of 1\,km$^2$ located at $45^{\circ}$N and $90^{\circ}$S running for one year
and for a threshold energy of 1\,TeV.
\begin{table}[p]
\caption{Detectable luminosities for several known sources. $\gamma = 2$.}
\label{lmtb:tab3}
\vspace{0.4cm}
\begin{center}
\begin{tabular}{|l|c|c|}
\hline
Sources & ${\cal L}_p$\,(erg/s) & ${\cal L}_p$\,(erg/s) \\
& $45^{\circ}$N & $90^{\circ}$S \\
\hline
{\underline{Pulsars}} & & \\
& & \\
Crab & $2 \cdot 10^{35}$ & $8 \cdot 10^{34}$ \\
Vela & $5 \cdot 10^{33}$ & - \\
PSR\,1937+21 & $10^{36}$ & $5 \cdot 10^{35}$ \\
PSR\,1953+29 & $7 \cdot 10^{35}$ & $2 \cdot 10^{35}$ \\
PSR\,1822-09 & $10^{34}$ & - \\
PSR\,1801-23 & $2 \cdot 10^{35}$ & - \\
& & \\
{\underline{Binary stars}} & & \\
& & \\
U0115+63 & - & $5 \cdot 10^{35}$ \\
Cyg-X3 & $(1-2) \cdot 10^{37}$ & $(2-3) \cdot 10^{36}$ \\
Her-X1 & $2 \cdot 10^{36}$ & $5 \cdot 10^{35}$ \\
Cyg-X1 & $5 \cdot 10^{35}$ & $10^{35}$ \\
Cen-X3 & $(5-20) \cdot 10^{35}$ & - \\
SS433 & $10^{36}$ & $5 \cdot 10^{35}$ \\
Vela-X1 & $5 \cdot 10^{34}$ & - \\
SMC-X1 & $5 \cdot 10^{37}$ & - \\
& & \\
{\underline{SN remnants}}& & \\
& & \\
Crab & $2 \cdot 10^{35}$ & $8 \cdot 10^{34}$ \\
1987a & $5 \cdot 10^{37}$ & - \\
\hline
\end{tabular}
\end{center}
\end{table}
This table clearly shows that there are more sources visible for a detector located at $45^{\circ}$N of latitude than for a detector located at $90^{\circ}$S. This is because, due to the Earth rotation, the solid angle seen by the first one is greater than that of the second one. But the value of ${\epsilon}_t$ is always 1 or 0 for the detector located at the South Pole because, if a source is below the horizon of the South Pole it decribe an apparent circle around the Earth axis and its elevation remains always equal to its declination. So, the source remains always detectable or undetectable. This also explain why for sources that may be detected at both latitudes the sensitivity of the detector located at $90^{\circ}$S is better than the sensitivity of the detector located at $45^{\circ}$N.
\subsection{Extra-galactic sources.}
The diffuse fluxes of neutrinos coming from AGNs have been calculated by
several authors~\cite{stecker,nellen,szabo,mannheim,protheroe}.
Other calculations give the neutrino flux of neutrinos originated by the
destructions of topological defects~\cite{bhs,sigl} (TD).
The predictions from ref.~\cite{szabo} and the most optimistic flux prediction from ref.~\cite{bhs} are in contradiction with the measurements made in the Fr\'ejus experiment~\cite{frejus}. Therefore they are not considered here.
Figure~\ref{fg:flux} shows the variations of the different neutrino fluxes
which are compared with the flux of atmospheric neutrinos~\cite{volkova}.
\begin{figure}[p]
\begin{center}
\mbox{
\epsfig{file=agn_flux_nb.eps,height=150mm}}
\caption{\label{fg:flux} Neutrino fluxes as function of the neutrino energy for different models: SDSS, NMB (continuous lines), MRLA, MRLB (dashed line), PRO (dotted line), BHSl, BHSh and SIG (dash-dotted lines). The lower continuous lines correspond to the calculation for atmospheric neutrinos. The black region is for different zenital angles. The fluxes have been multiplied by the neutrino energy. }
\end{center}
\end{figure}
The rates of upward muons induced by AGN neutrinos and by neutrinos from TD in a 1\,km$^3$ detector have been calculated by taking into account of the different neutrino fluxes and of the attenuation of neutrinos by the Earth and are compared to what expected from atmospheric neutrinos.
Table~\ref{lmtb:tab4} shows that the event rates for cosmic neutrinos decrease with the increasing energy threshold more slowly than the rate of events due to atmospheric neutrinos. The rates obtained by using the neutrino fluxes of ref.~\cite{stecker,nellen} for AGNs and of ref.~\cite{volkova} for atmospheric neutrinos with energy threshold of 1 and 10\,TeV are in good agrement with the calculations reported in ref.~\cite{gandhi}.
\begin{table}[p]
\caption{Number of upward-going induced muons expected per year in a km$^3$
detector for different models.}
\label{lmtb:tab4}
\vspace{0.4cm}
\begin{center}
\begin{tabular}{|l|c|c|c|c|c|c|}
\hline
& & & & & & \\
Models & $E_{\mu}^{\mathrm{min}} = 1$\,TeV & 10\,TeV & 100\,TeV & 1\,PeV & 10\,PeV & 100\,PeV \\
& & & & & & \\
\hline
& & & & & & \\
\underline{Atmospheric} & & & & & & \\
& & & & & & \\
Atm~\cite{volkova} & 12\,000 & 280 & 3.6 & 0.04 & 0.004 & - \\
& & & & & & \\
\underline{AGNs} & & & & & & \\
& & & & & & \\
SDSS~\cite{stecker} & 4\,200 & 2\,700 & 1\,100 & 180 & 12 & 0.2 \\
NMB~\cite{nellen} & 6\,300 & 1\,700 & 130 & - & - & - \\
& & & & & & \\
\underline{Blazars} & & & & & & \\
& & & & & & \\
MRLA~\cite{mannheim} & 330 & 50 & 5 & 0.7 & 0.2 & 0.02 \\
MRLB~\cite{mannheim} & 370 & 80 & 20 & 9 & 2.6 & 0.4 \\
PRO~\cite{protheroe} & 510 & 360 & 180 & 50 & 7.5 & 0.5 \\
& & & & & & \\
\underline{Defects} & & & & & & \\
& & & & & & \\
BHSl~\cite{bhs} & 3.8 & 2.6 & 1.4 & 0.6 & 0.2 & 0.05 \\
BHSh~\cite{bhs} & 700 & 340 & 135 & 42 & 10 & 2 \\
SIG~\cite{sigl} & 0.05 & 0.04 & 0.02 & 0.01 & 0.005 & 0.001 \\
& & & & & & \\
\hline
\end{tabular}
\end{center}
\end{table}
\section{Neutrinos from dark matter}
A neutrino telescope is well suited to the indirect detection of non baryonic
dark matter.
In the MSSM the supersymmetric partners of the neutral bosons are four
neutralinos: the two partners of the neutral SU(2) gauge bosons (gauginos),
and the two partners of the neutral Higgs particles (higgsinos). The lightest
neutralino is a linear combination of these four states.
The neutralinos remnants from the Big Bang move in the halo of the Galaxy with velocity of few hundreds of
km/s and loose energy by elastic scattering on the nuclei forming the matter of
the Sun and of the Earth when they cross them. This will result in a high
concentration of neutralinos in these celestial bodies enhancing the
annihilation rate per volume unit which will produce the neutrino emission.
The signal will, thus, consist in an excess of neutrino flux coming from the Sun
or from the center of the Earth.
The calculation of the sensitivity of a detector must take into account all
the parameters of the theoretical model and of the physical background of
atmospheric neutrinos.
This calculation has been performed in ref.~\cite{bottino} in terms of the sensitive
area required to detect a four standard deviations signal as a function of the
neutralino mass. The results of this calculation show (see figures 12
and 14 of ref.~\cite{bottino}) that a detector with an area of 1\,km$^2$
running for one year would
be sensitive to a range of neutralino masses extending up to few TeV.
\section{Status of the different projects}
Different projects are in progress:
\begin{description}
\item[AMANDA~\cite{price}] is a running project installed in the South Pole for which it has been demonstrated that deployment and logistics problems can be solved. In 1993-94 four strings were installed at 1000\,m depth (AMANDA A). The measurements of the ice transparency have shown that the light diffusion were too short (20-40\,cm). Four new strings (500\,m long) were deployed at 1500-2000\,m depth (AMANDA B). The measured atmospheric muon rate in AMANDA B is 25\,Hz and the coincidences AMANDA A-B occur with a frequency of 0.1\,Hz. The analysis of $5 \cdot 10^5$ coincidences A-B shows that there is no up/down confusion. The scattering length of \u{C}erenkov light in AMANDA B is two orders of magnitude larger than in AMANDA A. During winter 96-97 six new strings will complete AMANDA B.
\item[ANTARES~\cite{bertin}] is a project aiming at two goals: first the realization of a system capable to measure the environmental paremeters and, second, the realization of a ``demonstrator''.
A system to measure the optical background due to bio-luminescence and to the \u{C}erenkov light emission by electrons emitted in the $\beta$ decay of $^{40}$K present in the sea water is actually running. A system to measure the bio-fouling due to the sedimentation is also running. A system to measure the water transparency is under realization and will be operating next spring.
A string equiped with 30 Benthos spheres, several of them instrumented as optical modules, will be deployed with an electro-optical cable linked to the shore. This stage will be ready at the beginning of 1998. At the beginning of 1999 three strings with 30 optical modules each will be deployed, linked together and to the shore with an electro-optical cable (``Demonstrator'').
All these operations are performed off Toulon (France) at 30\,km from the shore and at 2400\,m depth. The guiding principle is that all operations performed with the demonstrator must be extrapolable to the km-scale detector.
Works on digital and analog signal transmission and on the optimization of the detector layout are in progress.
\item[Baikal~\cite{sokalski}] is a project installed in the lake Baikal (Siberia) at 100\,m depth. The final detector will consist in eight strings supporting 192 optical modules. This project started in April 93 by deploying 36 PMTs in three half strings. The system was recovered after 300 days of running time.
The main problem was the bio-fouling deposited on the glass spheres, mainly on the upward facing optical modules. In winter 96 four full strings were deployed (96 PMTs). Only two layers of PMTs are facing up.
The next stage will be the deployment of at least 144 PMTs this winter.
The analysis of $6.5 \cdot 10^7$ events recorded in 1993 gave an evidence of two upward-goung muons when 1.2 is expected from atmospheric neutrinos.
\item[DUMAND~\cite{learned}] was the pioneering project located at the Hawaii Islands. The funding
of this project has been cancelled in 1996 by DOE.
\item[NESTOR~\cite{resvanis}] is a project planned to be installed in a 3\,800\,m deep sea site offshore from Pylos (Greece). The project consists in one tower of 12 hexagonal floors of 16\,m in diameter supporting in total 168 PMTs.
Two aluminium floors and one titanium floor are ready for mechanical tests in shallow water.
The deployment is being studied, a digital transmission of the signal is being developed, a measurement of optical background has been recently performed.
\end{description}
\section{Conclusion}
The sky survey with high energy neutrinos is complementary to the survey with photons and will allow to better understand the mechanisms of emission and acceleration of cosmic rays. The detection of galactic and extra-galactic sources needs a huge under-water(ice) detector (1\,km$^3$).
Compared to the old generation detectors this represents a great improvement in volume ($\approx 20\,000 \times$\,SuperKamiokande) and a new method to work.
Several projects are working or are in project. They may be considered as the prototypes of the future detector.
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\bibitem{price} P.\,B.\,Price, {\em Last Results of the AMANDA Experiment}, talk given at this conference.
\bibitem{bertin} V.\,Bertin, {\em Status of the ANTARES Project}, talk given at this conference.
\bibitem{sokalski} I.\,Sokalski, {\em Last Results of the Baikal Experiment}, talk given at this conference.
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\end{document}