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# Expected performance

Cosmic accelerators are believed to produce neutrinos from the decay of charged pions in hadronic interactions. These interactions give 2 muon neutrinos for 1 electron neutrino (The tau neutrino fluxes are negligibly small). However because of neutrino oscillations, the expected flux at Earth is shared equally among the three flavours.

Among all neutrino flavours, muon neutrinos give the highest rates in Antares. This comes from the very long interaction length of muon in matter that increases the volume from which the neutrino interaction can be seen. A high energy muon travels through 10 kilometres of rock. Electrons or hadrons of the same energy are stopped after a few metres. The figure shows the neutrino interaction point (black dots in the Earth crust and in the sea) giving a detectable muon.

Contained interactions are expected to give much less events essentially because of the detector limited size. However these other channels would become competitive in a much larger detector.

## Pointing accuracy

The angular response of the detector with respect to the incoming neutrino direction is crucial for the identification of point sources of neutrinos. Three factors determine this response: the angle between the neutrino and the muon in the neutrino interaction, the deviation of the muon direction due to multiple scattering and the angular resolution of the detector with respect to the muon.

A muon going through or near the instrumented volume gives Cherenkov light that is detected by photomultipliers. The arrival time and amplitude of these photons, plus the PM positions, allow the reconstruction of the track. Because of the excellent water properties at the Antares site, the light diffusion is very limited and most of the Cerenkov photons arrives within a few nanoseconds of the expected arrival time.

The detector resolution will be determined by the quality of the alignment of the detector components, the time resolution of the photomultipliers, the global timing of the readout system and the quality of the muon reconstruction. The detector time resolution is mostly limited by the transit time spread in the photomultipliers which is about 3 ns (FWHM). As soon as the number of fired photomultipliers is enough, the track direction can be reconstructed with a very good accuracy.

The figure shows the error on angle determination obtained after several quality criteria from muon neutrino interactions as a function of the simulated neutrino energy. The bottom curve shows the angle difference between the reconstructed muon and the simulated one. The mismatch is always below 0.5 degree. The top curve shows the angular error between the reconstructed muon and the simulated neutrino. Below 1 TeV the error is dominated by the kinematics; Above 1 TeV the muon is emitted in the direction of the parent neutrino.

Above 10 TeV the Antares angular resolution is better than 0.3 degree. This angular resolution leads to a very good background rejection in point-like source searches.

## Effective area

The effective area is the surface the detector would have perpendicular to the incident particle beam if its detection efficiency was 100%. It is obtained from the ratio of the rate of detected events (s-1), muons in the following, over the incident flux (cm-2.s-1). For an incident muon flux at the detector, this gives the muon effective area. For an incident flux of neutrinos at the Earth surface, this gives the neutrino effective area.

### Muon effective area

The muon effective area gives the response function (detection rate) of the detector to an incident muon flux, whatever the process that gave rise to this flux. It is shown on the figure below (obtained from simulated charged current neutrino interactions).

The two first curves are respectively for reconstructed muons matching the neutrino angle at less than 1 degree and less than 3 degrees. They were obtained requiring explicitly these angular resolutions.

The last curve is the result of the selection criteria that lead to the angular resolution curve above, namely better than 0.3 degree above 10 TeV (thus explaining why the purple curve crosses the blue one at 10 TeV ). Below 100 GeV muon do not cross the instrumented volume anymore. This explains the drop below this energy.

The green line represents the geometrical surface, namely the ground surface covered by the instrumented volume. At high energies the effective area reaches or even exceeds the geometrical surface.

### Neutrino effective area

The muon-neutrino effective area is much smaller than the muon effective area since it takes into account the probability for a muon neutrino to interact and give a muon that can be seen by the detector. It never exceeds a few tens of square metres. It is shown for several angle ranges on the figure below. Around the vertical (0-30°, blue curve) and above 100 TeV, the Earth starts to become opaque to neutrinos : because of their larger cross section they interact early and the muon cannot reach the detector. At larger angles the rock thickness is smaller and this effect occurs later in energy. As a consequence the detector remains very efficient at very high energy for nearly horizontal neutrinos.

## Detector response to various spectral indices

The figure shows the differential event rates as a function of the simulated neutrino energy for three incoming neutrino spectra. Each spectrum is a power law, A.E-g, normalised to the same value, with the spectral indices,  g=2, g=2.2 and g=3.7. The first two values are what is expected from cosmic accelerators, while the last one is a good approximation of an atmospheric neutrino spectrum.

This figure was obtained from simulated charged current neutrino interactions. Muon were reconstructed and selected according to point-like source search criteria (purple curve in the angular resolution plot).

It shows were the event rate peak is expected for each hypothesis and how the cosmic accelerator spectrum can be separated from the atmospheric neutrino events.

## Energy response

The energy response is determined by the energy fraction transferred to the muon in the neutrino interaction, the energy lost by the muon outside the detector and the energy resolution of the detector. The muon energy determination requires different techniques in different energy ranges.

Below 100 GeV, the muons are close to minimum-ionizing, and the energy of contained events, with start and end points measured inside the detector, can be determined accurately from the range. The threshold for this method is about 5-10 GeV for vertical tracks, depending on the vertical distance between groups of optical modules, and about 15 GeV for more isotropic events, depending on the horizontal distance between lines.

Above 100 GeV, the range cannot be measured because of the limited size of the detector, but the visible range determines a minimum energy that can be used for the analysis of partially-contained events: starting events in which the vertex point is measured inside the detector, and stopping events in which the endpoint is measured.

Above 1 TeV, stochastic processes (bremsstrahlung, pair production, -rays) are dominant, and the muon energy loss becomes proportional to the energy. The muon range above 1 TeV increases only logarithmically with the muon energy. On the other hand, the detection efficiency increases with energy because of the additional energy loss. Monte Carlo studies have shown that the neutrino energy can be determined within a factor 3 above 1 TeV from the average energy loss.

Above 1 PeV, the Earth becomes opaque to upward-going vertical neutrinos. Higher energies are accessible closer to the horizon, however. Very high-energy tau neutrinos can be observed because the produced in interactions decay before they are absorbed, producing of lower energy which continue along the original flight path, but with decreasing interaction probability, resulting in an accumulation of events at the highest detectable energies.

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Author : Thierry Stolarczyk