Next : Detector design

Detection principle

Since the Earth acts as a shield against all particles except neutrinos, a neutrino telescope uses the detection of upward-going muons as a signature of muon neutrino interactions in the matter below the detector. The muon detection medium may be a natural body of water or ice through which the muon emits Cherenkov light. Its detection allows the determination of the muon trajectory.

A neutrino telescope uses the detection of upward-going muons as a signature of muon neutrino interactions in the matter below the detector (Click to enlarge)

This detection technique requires discriminating upward going muons against the much higher flux of downward atmospheric muons (see figure below). To simplify the discrimination, the detector is installed in a deep site where a layer of water or ice would shield it.

In order to correlate the measured muon spectrum with the original neutrino spectrum, it is necessary to understand the dynamics of neutrino interactions, the opacity of the Earth, the energy loss of muons and the resolution of the detector over a wide range of angles and energies.

Different types of neutrino interactions in ANTARES

Charged-current $\nu _e$ interactions give rise to electromagnetic and hadronic showers with longitudinal dimensions of no more than a few metres, because the radiation length and the nuclear interaction length of water are below 1 m. On the scale of ANTARES, these are nearly point-like events. At energies above 100 GeV, the energy resolution of these events is expected to be better than for muon events because they leave all of their energy inside the detector volume. On the other hand, their angular resolution will be poor compared to muon events, due to the point-like character of the showers. Charged-current $\nu _e$ interactions will be contaminated by neutral-current interactions of both $\nu _e$ and $\nu _\mu$ (and $\nu_\tau$ , if present).
The number of neutral-current interactions is about 1/3 of the number of charged-current interactions. The neutrino type is not identified in the neutral-current interactions, the energy resolution is poor due to the missing final-state neutrino, and the angular resolution is poor due to the point-like character.

Charged-current $\nu _\mu$ interactions produce $\mu^\pm$ leptons as well as a point-like hadronic shower.
The $\nu _\mu$ energy can be estimated from the measured $\mu^\pm$ energy. In $\nu_\mu d \rightarrow \mu^- u$ interactions, the average $\mu^-$ energy is 1/2 of the $\nu _\mu$ energy; in $\bar\nu_\mu u \rightarrow \mu^+ d$ interactions, the average $\mu^+$ energy is 3/4 of the $\bar\nu_\mu$ energy.
The $\mu^\pm$ energy can be determined from the range for E<100 GeV, or from dE/dx for E>1TeV (see below). For $\nu _\mu$ interactions inside the detector, additional information on the $\nu _\mu$ energy is available from the hadronic shower. The ANTARES detector is designed for the detection of these charged-current $\nu _\mu$ interactions.

Charged-current $\nu_\tau$ interactions produce $\tau^\pm$ leptons with electronic, muonic and hadronic decay modes. The $\nu_\tau$ interaction vertex and the $\tau^\pm$ decay vertex cannot be separated for energies below around 100 TeV. The electronic and hadronic modes will look like $\nu _e$ charged-current or neutral-current interactions. The muonic decays $\tau^- \rightarrow \mu^-\bar\nu_\mu\nu_\tau$ , with branching ratio 17%, will be visible in ANTARES, but they cannot be distinguished from $\nu _\mu$ interactions.

Cherenkov light emission

Charged particles emit light under a characteristic angle when passing through a medium if their velocity exceeds the speed of light in the medium. The Cherenkov angle $\theta$ is related to the particle velocity $\beta$ and the refractive index of the medium n:

In the energy range interesting for ANTARES (E > 10 GeV), particles will generally be ultra-relativistic with $\beta=1$ . The refractive index of sea water is n=1.35 for a wavelength of 450 nm therefore the Cherenkov light is emitted under $42^\circ$ for this wavelength. This easy geometrical pattern of light emission allows a precise reconstruction of tracks from the measurement of only few hits at different space points.

The number of photons produced along a flight path dx in a wave length bin $d\lambda$ for a particle carrying unit charge is :

$\begin{displaymath}\nonumber \frac{d^2N}{d\lambda dx} = 2\pi \alpha \sin^2\theta / \lambda^2 \end{displaymath}$

At wavelengths of 400-500 nm the efficiency of the photomultipliers as well as the transparency of the water are maximal. Within 1 cm flight path 100 photons are emitted in this wavelength bin. Between 285-400 nm twice as many photons are emitted, however they contribute less to the detected signal. At a perpendicular distance of 40 m from a charged track the density of photons between 400-500 nm is still 1 per 340 cm², neglecting absorption and scattering effects. The effective area of the photomultipliers being considered is in the same range (300-500 cm²). This gives an indication of the active detector volume around each photomultiplier.

For $\beta=1$ the Cherenkov light yield is independent of the energy of the charged particle. This means the light output of a single particle does not allow its energy to be measured. However when hadronic or electromagnetic showers are produced (which might occur at the neutrino vertex as well as for radiative processes along a muon track) the total light yield of the shower will be proportional to the total track length in the shower and therefore to its initial energy. This allows some calorimetric measurements if the neutrino vertex is inside the active detector volume or for muon tracks above 1 TeV where radiative processes dominate its energy loss.

Light propagation in sea water

The processes of absorption and scattering characterise the transmission of light in water. They are parameterised by the absorption length $\lambda_{a}$ , the scattering length $\lambda_{s}$ , and the scattering function $\beta(\theta)$ which describes the angular distribution of the scattering. The relevant window of wavelengths for a sea water Cherenkov detector is centred on blue light. Deep sea water transparency is maximal in the blue, with typical values of 60 m for $\lambda_{a}$ and $\lambda_{s}$ , and a scattering function peaked in the forward direction with an average value for the cosine of the scattering angle $\langle \cos(\theta)\rangle \simeq 0.9$ . Seasonal variations are expected to affect these values, especially the scattering parameters which are governed by the amount of suspended particulate matter. Some in situ measurements of optical properties have been done at the ANTARES site.

Observable sky

Sky map with the sources from the 3^rd Egret catalogue. The grey area is never seen by ANTARES, the area within the red line is observable 24 hours a day.

The ANTARES neutrino telescope, situated at a latitude of 43° North, can observe upward-going neutrinos from most of the sky (about $3.5\pi$ sr), due to the rotation of the Earth. Declinations below -47° are always visible, while those above +47° are never visible. Declinations between -47° and +47°are visible for part of the sidereal day (see figure).

Most of the Galactic plane is visible, and the Galactic centre is visible most of the sidereal day. Since the AMANDA telescope at the South pole is sensitive to positive declinations, the two detectors will have a reasonable area in common for cross-checks (about $1.5\pi$ sr).

At energies greater than about 40 TeV, the interaction length becomes smaller than the Earth's diameter for $\nu _\mu$ traversing the dense core of the Earth. Above 10 PeV, only nearly horizontal $\nu _\mu$ are visible. If the field of view can be extended to 10° above the horizon at these energies where the background is greatly diminished, a non-negligible fraction of the sky can be kept observable even at these energies.

Like other underground detectors, neutrino telescopes can observe the sky independently of the time of day, the phases of the moon or the weather. Existing underground experiments have usually reached 80% duty cycle after the initial debugging phase. ANTARES aims for even higher values for the off-shore facilities because the access is complicated and time-consuming.

Next : Detector design

Author : Thierry Stolarczyk