Search for point-like source in ANTARES

1. Search for point-like source in ANTARES Juan Antonio Aguilar Sánchez IFIC (Instituto de Física Corpuscular) CSIC-Universitat de València, Spain on behalf of the ANTARES collaboration

2. ANTARES: • Very good angular resolution • Galactic Centre visible 63 % of time Motivation Scientific scope of a Cherenkov Neutrino Telescope: Search for point-like sources is one of the main motivations to build a Neutrino Telescope ? ANTARES: See talk from A. Kouchner Background: Mostly Atmospheric neutrinos

3. EM algorithm ML Ratio Grid/Cluster Signal-like Background-like Methods for the search of point-like sources • Different methods have been developed within ANTARES collaboration for the search of point-like sources: Unbinned techniques Binned techniques • They are more powerful than binned techniques. • They use the precise configuration of the events. • No optimization is needed in unbinned methods • They require more CPU time and Monte Carlo experiments • They are well-known and very robust • They do not have a strong dependence on the detector performances • They need a bin/cone optimization • Significances are easily computed and analytically derived.

4. EM algorithm EM algorithm ML Ratio ML Ratio Grid/Cluster Grid/Cluster d RA Grid and Cluster Methods • Sky is divided in a grid of squared bins or cones around each sample event. • The optimum size of the bins/cones is calculated for maximum sensitivity, with the additional criteria of having the same number of background events per bin/cone (uniform sensitivity) Significance: Si=log10(Pi) Grid method Pi is the probability for the background to produce Ni or more events if there are Ntotal events in the declination band Pi is the probability of the background to produce the observed number of events N0 or more (up to the maximum number Ntotal).  is each element of the set CnNtotal of combinations of Ntotal elements in groups of n elements. Cluster method

5. As a discriminator observable (test statistic) the likelihood ratio is used: Two hypotheses: • H0: only atmospheric neutrinos • H1: background and some signal likelihood if there is signal+bg likelihood for bg-only Knowledge of detector: EM algorithm ML Ratio Grid/Cluster point spread function Pdf muon energy reconstruction detector acceptance Parameters to fit: flux magnitude source position flux spectral index Likelihood Ratio Method Try to develop a method that uses all available information: 1.- Event distribution 2.-Energy information 3.-Energy dependence of the angular resolution Likelihood is expressed as a sum over the events Background density: Signal density:

6. EM algorithm ML Ratio Grid/Cluster source position Gaussian width Parameters to fit: The EM algorithm • The EM method is a pattern recognition algorithm that analytically maximizes the likelihood in finite mixture problems, which are described by different density components (pdf) as: signal: αRA,  bg: only  position of event: x = (αRA, δ) Point-like sources pdf proportion of signal and background Selected model: • The background pdf is extracted from MC data or real RA-scrambled data when available • Signal pdf model is selected to be 2D-Gaussians

7. INCOMPLETE data set EM algorithm ML Ratio Grid/Cluster COMPLETE data set L(Ψ) Q(Ψ,Ψ(m+1))+hm+1 Q(Ψ,Ψ(m))+hm Ψ Ψ(m) Ψ(m+1) Ψ(m+2) General procedure • The idea is to assume that the set of observations forms a set of incomplete data vectors. The unknown information is whether the observed event belongs to a component or another. The vector zi is a class indicator that indicates if the event i belongs to the background or the source. Easily differentiable! • E-Step (Expectation-step): • Start with a set of initial parameters Ψ(m) = {π1,π2,µ,Σ} • Expectation of the complete data log-likelihood, conditional on the observed data {x} • M-Step (Maximization-step): • Find Ψ =Ψ(m + 1)that maximizes Q(Ψ, Ψ(m)) Successive maximizations of the function Q(Ψ,Ψ(m)) lead to the maximization of the log-likelihood

8. Background like Signal like BIC3σ BIC5σ EM algorithm ML Ratio Grid/Cluster where Nσ = 3σ, 5σ Searching procedure Pre-clustering algorithm Initial valuesY(m): -mcluster barycenter -s cluster size -pS cluster elements As a discriminator observable we use the Bayesian Information Criterion (BIC) used in a frequentist fashion: E-step: Compute Q(Y,Y(m)) 10000 experiments m = m +1 M-step: FindY* = arg max Q(Y,Y(m)) Y(m+1) = Y* The discovery power of the test (or discovery potential) is the percentage of success in detecting a source over the background No Q(Y(m+1),Y(m)) – Q(Y(m),Y(m-1)) ≤x Yes YML = Y(m+1)

9. EM algorithm ML Ratio Grid/Cluster Results and Comparison • Results with different neutrino Monte Carlo and muon track reconstruction strategies. Direct comparison is not completely fair. • Unbinned methods show better performance. More information is included (event distributions, angular error estimate and the energy in the MLR method). • Among unbinned methods, the Expectation Maximization show better results (or at least equivalent) without using the expected performances of the detector. It is a reliable and robust method. EM algorithm Comparison among methods Probability to detect a source at 5σ and 3σ as a function of the observed average number of events from a source located at -80º per year. Power @ 50%: <8 events (<6 events) with 5σ (3σ). Discovery power as a function of the mean number of observed events (after track reconstruction and quality cuts)

10. EM algorithm ML Ratio Grid/Cluster Discovery potential and sensitivity • The expected sensitivity of ANTARES in 365 days is of the same order that the present limits set by AMANDA (for the Northern Hemisphere), since the better angular resolution allows a better background rejection Sensitivity to a E-2 neutrino spectrum from a δ = - 60º declination point-like source for ANTARES, and NEMO (astro-ph/0611105) and averaged over all declinations in the Northern Sky for IceCube (astro-ph/0305196v1) with a 90% C.L. as a function of the exposure of the detector

11. Conclusions • ANTARES has a good opportunity to detect point-like neutrino sources. Its good angular resolution, and its privileged location (Galactic Centre visible 63% of the time) make it a very promising neutrino telescope. • However theoretical models of cosmic neutrino production, and experimental data from other experiments like AMANDA, suggest that expected neutrinos fluxes are very low. Hence powerful searching algorithms have to be developed. • In ANTARES several searching algorithms were devised. Among them, unbinned methods show a better discovery potential and sensitivity. The Expectation-Maximization algorithm is a pattern recognition algorithm that can be applied to the search of point-like neutrino sources with very good results. • In one year, ANTARES is expected to reach the same sensitivity as AMANDA after 1001 days of duty cycle due to the better angular resolution of ANTARES.