FIRST SEARCH FOR POINT SOURCES OF HIGH-ENERGY COSMIC NEUTRINOS WITH THE ANTARES NEUTRINO TELESCOPE^*

The data presented here were collected between 2007 January 31 and 2008 December 30. During this time, the construction of the ANTARES detector was still in progress. The detector consisted of 5 lines for most of 2007 and of 9, 10, and 12 detector lines during 2008. The total live time of the data used for the analysis is 304 days (144, 38, 48, and 74 days with 5, 9, 10, and 12 detector lines, respectively.)

The online event selection identifies triplets of OMs that detect multiple photons, either as a high-charge hit or as hits separated by less than 20 ns on adjacent OMs. At least four such triplets are required throughout the detector, with the relative photon arrival times being compatible with the hypothesis that light is emitted along the track of a relativistic particle.

The arrival times of the hits are calibrated as described in Aguilar et al. (2011a). The inter-line timing has been measured in an iterative procedure by comparing the expected hit times to those measured in a large sample of reconstructed downgoing muons. Compatible results were obtained using the calibration system consisting of pulsed laser and LED beacons to measure the relative timing delays.

The positions and orientations of the OMs vary because of the sea currents. An acoustic positioning system, combined with compasses and tiltmeters located along the detector lines, measures the positions and orientations of the OMs, with an accuracy of ∼10 cm.

From the timing and position information of the hits, muon tracks are reconstructed using a multi-stage fitting procedure (Heijboer 2004). The initial fitting stages provide the hit selection and starting point for the final fit. The final stage consists of a fit of the likelihood $\cal {L}$ to the observed hit times and includes the contribution of optical background hits. Several starting points of the procedure are tried to increase the probability of finding the global likelihood maximum. The reconstruction quality of the final track is quantified by a parameter $\Lambda = {\cal L}^{\rm final}/N_{\rm dof} + 0.1(N_{\rm conv}-1)$, where N_dof = N_hits − 5 is the number of degrees of freedom in the fit, and N_conv is the number of starting points that converged to the same final fit. The second term in the Λ definition is an ad hoc reward for fits with N_conv > 1.

Neutrino candidates are selected from upgoing events using criteria that have been determined in a "blind" manner, i.e., before performing the search analysis on the data. The criteria are chosen to optimize the expected median value of the upper limit on the neutrino flux (i.e., sensitivity).

The angular uncertainty obtained from the likelihood fit of the muon track is required to be smaller than 1 deg. This cut removes 75% of the upward reconstructed atmospheric muons.

The cumulative distribution of Λ for muons that are reconstructed as upgoing is shown in Figure 1 along with the simulated contributions from atmospheric muons and neutrinos. The simulation uses Agrawal et al. (1996) for the atmospheric neutrino flux; see Barr et al. (2006) for the flux uncertainty. The atmospheric muons are simulated by the QGSJET (Kalmykov & Ostapchenko 1993) and CORSIKA (Heck et al. 1998) packages with the primary cosmic-ray flux from Nikolsky et al. (1984). Comparisons between different simulation chains resulted in a muon flux uncertainty of 50% (Aguilar et al. 2010a).

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The final sample of neutrino candidates consists of 2190 upgoing events with Λ > −5.4 and an angular uncertainty <1 deg. This is compatible with the simulation, which predicts 763 ± 381 muon and 1130 ± 339 neutrino events to pass these cuts, for a total of 1893 ± 509. Hence, the sample is expected to consist of about 60% atmospheric neutrinos and 40% misreconstructed muons.

The cumulative distribution of the angle between the reconstructed muon direction and the neutrino direction is shown in Figure 2 (left panel) for neutrino events with a neutrino spectrum proportional to E⁻²_ν, where E_ν is the neutrino energy. The median of this angular error is 0.5 ± 0.1 deg. For the subset of data in which the full 12 line detector was operational, the resolution is estimated to be 0.4 ± 0.1 deg.

While the deficit of atmospheric muons caused by the Moon shadow is currently observed by ANTARES at the 2.7σ level (Rivière 2011), significantly more data are required to stringently constrain the angular resolution. Instead, the systematic uncertainty on this quantity has been estimated by varying the time resolution of the OMs Δ_t in the simulation. The allowed range of Δ_t is determined by requiring that the resulting simulated number of neutrino events, as determined by selecting events in the neutrino dominated region, Λ > −5, be compatible with the number observed in data. The best agreement between data and simulation is obtained for Δ_t = 2.5 ns, which is somewhat larger than the nominal expected resolution of 1.5 ns. Hence, this value is used for all simulations in this analysis, in particular for extracting the central value of the allowed range of angular resolutions. For a simulated timing resolution of 3.4 ns, the number of observed neutrinos exceeds the simulation by 60%, which is twice the amount allowed by the systematic neutrino flux uncertainty of 30% (Barr et al. 2006). This discrepancy thus places a 2σ upper bound on the time resolution, which translates into a 1σ systematic uncertainty on the angular resolution of 0.1 deg. This uncertainty incorporates, to first order, all effects which have a net result of degrading the time resolution, such as possible mis-alignments of the detector, inaccuracies in the simulation of light propagation in the water or in the transit time distribution of the PMT. A similar analysis with analogous results has been performed using downgoing muon data instead of upgoing neutrino candidates.

The absolute orientation of the detector is known with an accuracy of about 0.1 deg (Halladjian 2010); this uncertainty is taken into account as an independent effect.

The effective area for muon neutrinos A^eff_ν is defined as the ratio between the selected neutrino event rate and the cosmic neutrino flux. It is determined from simulations and is shown in Figure 2 (right panel) as a function of the neutrino energy for three declination intervals. Throughout this Letter, the cosmic neutrino flux is assumed to consist of an equal amount of ν_μ and $\bar{\nu }_{\mu }$.

In the search, limits are set on the constant ϕ in the flux parameterization dN/dE_ν = ϕ × [E_ν/GeV]⁻² GeV⁻¹ cm⁻² s⁻¹. The acceptance A for such a flux is defined as the constant of proportionality between the number of selected signal events and the flux intensity ϕ. It can be computed by convoluting A^eff_ν(E) with dN/dE_ν(E). For declinations δ < −48 deg, A and A^eff_ν are approximately constant in declination. For −48 deg  <  δ < 48 deg, the functions decrease because of the requirement that the tracks are upgoing. For a source declination of −90 (0) deg, A = 3.2 (1.8) × 10⁷ GeV cm² s. This means a total of 3.2(1.8) neutrinos would be detected and selected from a point source with a flux of 10⁻⁷ GeV⁻¹ cm⁻² s⁻¹. For this flux model, the energy of 80% of the selected signal is in the range 3 TeV <E_ν < 700 TeV.

To constrain the systematic uncertainty on the acceptance, the atmospheric neutrino data have been compared to a simulation in which the efficiency of each OM is reduced. A 15% effect was observed, which is applied as the systematic uncertainty on the acceptance in the limit calculations.

The search method is based on the likelihood of observing the events, defined as

$$\begin{equation} \log {\cal L}_{\rm s+b} = \sum _i \log [ \mu _{\rm sig} \times {\cal F}(\beta _i(\delta _s,\alpha _s)) + {{\cal B}(\delta _i) } ] - \mu _{\rm sig} - N_{\rm bg}, \end{equation} \tag{ 1 }$$

where the sum is over the neutrino candidate events, and $\cal F$ is a parameterization of the point-spread function. This is defined as the probability density to find the reconstructed muon i an angle β away from the declination δ_s and right ascension α_s of the source; it is closely related to the angular resolution (see Figure 2). ${\cal B}(\delta)$ is a smooth parameterization of the background rate derived from the observed declination distribution of the 2190 selected events. The mean number of selected signal events produced by the source is μ_sig. The term N_bg represents the total number of expected background events, which is constant and therefore does not influence the maximum-likelihood fits or the likelihood ratio.

In the candidate list search, the likelihood is maximized for each candidate by numerically fitting the source intensity μ_sig to the events located within 20 deg of the source, with the source coordinates fixed to the known position. In the full-sky search, potentially significant clusters are first identified using a loose cone selection, which requires at least four events in a cone of 3 deg diameter. For each cluster, the likelihood is maximized by fitting the source coordinates and the intensity, yielding maximum-likelihood estimates for these quantities.

The next step is to compute the test statistic, which is defined as the logarithm of the likelihood ratio:

$$\begin{equation} Q = \log {\cal L}^{\rm max}_{\rm s+b} - \log {\cal L}_{\rm b}, \end{equation} \tag{ 2 }$$

where ${\cal L}^{\rm max}_{\rm s+b}$ is the maximum value of the likelihood found in the fit and ${\cal L}_{\rm b}$ is the likelihood computed for the background-only hypothesis (μ_sig = 0). A large (small) value of Q indicates that the data are compatible with the signal (background).

Pseudo-experiments are generated by randomly sampling the declination from the background parameterization ${\cal B}$ and the right ascension from a uniform distribution. Events from a neutrino point source are added and distributed around the desired coordinates according to the point-spread function. The systematic uncertainties on the angular resolution and orientation of the detector are incorporated by varying the simulated characteristics of the signal events within the assigned uncertainties.

Distributions of Q obtained by applying the search method to the pseudo-experiments are used to extract p-values and limits corresponding to the observed Q in the data. The limits are obtained following Feldman & Cousins (1998).

As no significant point sources are observed, 90% confidence level limits are obtained for the intensity, ϕ^90%CL, of an E⁻²_ν neutrino flux from each of the source candidates. They are listed in Table 1 and are shown in Figure 4 as a function of the source declination. Figure 4 also shows the sensitivity of this analysis. It is in agreement with the median value of the actually observed limits. For the area of the sky that is always visible (δ < −48 deg), the sensitivity is about $7.5 \times 10^{-8} { (E_{\nu } \rm /GeV)^{-2} \,GeV^{-1} \,s^{-1} \,cm^{-2}}$.

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The present limits are more stringent than those obtained for the northern hemisphere by previous multi year experiments (also indicated in the figure) and are competitive with those set by the IceCube collaboration (Abbasi et al. 2011) for δ < −30 deg. It should be noted that even though each experiment sets limits on the intensity of an assumed E⁻²_ν spectrum, the experiments are sensitive in different energy ranges. For this spectrum, ANTARES detects most events at energies in a broad range around 10 TeV, which is the relevant energy range for several galactic sources (Crocker et al. 2005). Southern hemisphere limits shown from the IceCube experiment probe the neutrino flux predominantly in the region above 1 PeV (Abbasi et al. 2011).

The event selection and the search method have been cross-checked with an independent analysis using the same selection criteria and a search method based on the expectation-maximization algorithm (Dempster et al. 1977; Aguilar & Hernandez-Rey 2008). In this method, the angular spread of the signal events is a free parameter in the likelihood and the maximization is performed analytically. The results of both the full-sky and the candidate list search are consistent with the results discussed earlier.