Simona ToscanoSimona ToscanoIFIC (Instituto de Física Corpuscular) CSIC-Universitat de València, SpainIFIC (Instituto de Física Corpuscular) CSIC-Universitat de València, Spain

on behalf of the ANTARES collaborationon behalf of the ANTARES collaboration

TeV Particle Astrophysics IV 24-28 September 2008, IHEP, Beijing

Point-like source searches with the Point-like source searches with the ANTARES neutrino telescope ANTARES neutrino telescope

Neutrino telescopes

??

~MeV~MeV GeV-100 GeVGeV-100 GeV GeV-TeVGeV-TeV TeV-PeVTeV-PeV PeV-EeVPeV-EeV > EeV> EeV

Scientific scope of a Cherenkov Neutrino Telescope:

ANTARES is a powerful tool to search for neutrino point like sources:ANTARES is a powerful tool to search for neutrino point like sources:

Search for point-like sources is

one of the main motivations to

build a Neutrino Telescope

12-Line detector Angular resolution better than 0.3° above a few TeV

Galactic Centre visible 63 % of time

Sky coverage in Galactic coordinates for a detector located in the Mediterranean Sea and at the South Pole. The locations of recently observed sources of very high energy (VHE) -rays are also 𝜸indicated.

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ANTARES detectorANTARES completed in May 2008ANTARES completed in May 2008

ANTARES LAYOUT:ANTARES LAYOUT:

12 lines (875 PMTs) +1 line for 12 lines (875 PMTs) +1 line for environmental parameters environmental parameters 25 storeys / line25 storeys / line 3 PMTs / storey3 PMTs / storey

(See Zornoza’s talk in plenary session for details.)(See Zornoza’s talk in plenary session for details.)

Footprint of the 12-line detector in atmospheric muons

Positions of reconstructed tracks at Positions of reconstructed tracks at time of first triggered hittime of first triggered hit

a neutrino-induced muon a neutrino-induced muon crossing the detectorcrossing the detector

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Heig

ht o

f hit

OM

Time of hit

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−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 simulate a number of experiments to

infer the test statistic distribution.

−They are well-known and very robust.−They do not have a strong dependence on the detector performances.−Significances are easily computed and analytically derived

(Feldman-Cousins upper limit). −They need a bin/cone optimization.

CONE METHODCONE METHOD

EM ALGORITHMEM ALGORITHM

Methods for the search of point-like sources

Different methods have been developed within ANTARES collaboration for the search of point-like sources:

Signal-like

Background-like

Sky is divided in a grid of bins (to perform a full-sky survey) or cones around the source position (for a fixed-source search). The optimum size of the bins/cones is calculated for maximum sensitivity.

The optimum search cone radius optimum search cone radius (calculated for each ) corresponds to the minimum MRFMRF (model rejection factor) .

The average upper limit (aka sensitivity) is calculated assuming that no true signal is present (ns=0) and only the expected background (nb) ofatm and atmis observed.

For a Poisson distribution of the background, the average upper limit is:

MRF is defined as:MRF is defined as:

)n()!(n

)(n),n(nμ)(nμ bobs

nb

nbobsb

obs

obs

exp9090

Upper limit Poisson weight

sn90

CONE METHODCONE METHOD EM ALGORITHM

RA

Source position

55

The background The background pdf is extracted pdf is extracted from MC or real from MC or real RA-scrambled RA-scrambled data.data.

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).

CONE METHOD EM ALGORITHMEM ALGORITHM

),;()()( Σμxx SSBGBG PPp

cos2

exp2

cosexp2

1);( 2

2

2

22

Σμx ,PS

Signal pdf model is selected to be 2D-GaussiansSignal pdf model is selected to be 2D-Gaussians

Initial valuesfor the signal pdf-source coordinates - det. angular resolution-S cluster elements

EM algorithm Most of the time, there are no events in the given direction which yields a null likelihood

Background like Signal like

Test Statistic:

BICBIC

Flowchart of the EM-based methodFlowchart of the EM-based method)log()|(log2),|(log2BIC 101

)(1 nvMDpMDp m

Likelihood ratio

Final pdf parameters that maximize the likelihood

penalty

66

[J.A. Aguilar & J.J Hernández. Astroparticle Physics doi:10.1016/j.astropartphys.2007.12.002]

mixing proportionsmixing proportions

For a point-like source:For a point-like source:

Analysis of ANTARES 5-Line dataReal data:Real data: Silver (Ag) Runs equivalent to 140 140 days live timedays live time(Ag: baseline < 120 kHz & burstfr < 40%)MC data:MC data:

x,y: track positions at time of first triggered hit

First neutrino with 5-Lines

First neutrino with 5-Lines

5-Line data from Jan to Dec 20075-Line data from Jan to Dec 2007

Muons simulated with CORSIKA

Primary ions -> p, He, N, Mg, Fe Primary energy -> 1 105 TeV/nucleon Primary zenith angles –> 0° 85° Primary spectrum E-2

Number of simulated showers 1010 Live time -> hours (or days) – years

(depending on the mass, energy and angle)

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Neutrinos

130 files of and anti- Spectrum of generated : E-1.4

Energy range: 10 – 107 GeV

88

Reconstruction of Reconstruction of trajectory from time, charge and position of PMT hits trajectory from time, charge and position of PMT hits

Track reconstruction method in two main steps:1) Linear pre-fit: first estimation of the track parameters is performed2) Final fit (ML method): PDF function of hit time residuals (t)

includes the full knowledge of the detector and the expected physics.

Reconstruction algorithm

bestbest

Quality cut of the reconstruction

Good agreement

between real data and MC

Declination distribution of both real data and MC for elevation < -10° && > -4.7

1)0.1(NNlog(L)Λ comp

DOF

Log-likelihood per degree of freedom Number of compatible solutions

5-Line detector performanceNeutrino angular resolution (angle between Neutrino angular resolution (angle between

the true neutrino and the reconstructed track) the true neutrino and the reconstructed track) for the 5-Line detector.for the 5-Line detector.

The angular resolution is better than 0.5better than 0.5° at high energies (E > 10 TeV)

Neutrino effective area for the 5-Lines detector, Neutrino effective area for the 5-Lines detector, averaged over the neutrino angle direction.averaged over the neutrino angle direction.

Selection of different nadir angles evidences the Earth opacity at higher energies.

AAeffeff ~ 4·10 ~ 4·10-2-2 @ 10 TeV @ 10 TeV

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Background estimation

Sample simulation #104 samples simulated. Each sample corresponds to 140 days (5-Line detector live time).

A fit of distribution, for given quality cuts, is performed from MC or real data

The background inside the cone, for increasing cone size, is estimated for a given declination.

EM

1. PBG fit from MC or real data gives the background pdf used in the algorithm.

2. Samples simulation

SignalSignal

1010

Signal simulation

The signal inside the cone is calculated from the angular error distribution

CONE METHODCONE METHOD EM ALGORITHMEM ALGORITHM

Neutrino (MC) Neutrino (MC) angular error angular error distribution for distribution for different different declination declination bands for a bands for a spectral index spectral index of 2of 2

The signal simulation has been done using theangular error distribution

Angular distances around the source location are randomized according to the angular error distribution

A declination band and the desirable number of events are selected.

Neutrino angular Neutrino angular resolution :resolution :

median angle median angle between the between the true neutrino true neutrino

track (from MC) track (from MC) and the and the

reconstructed reconstructed track.track.

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MRF as a function of cone radius for a MRF as a function of cone radius for a given declinationgiven declination

Optimization of the search cone radiusCONE METHODCONE METHOD EM ALGORITHM

Optimal cone Optimal cone radius for any radius for any declination.declination.

= -30°rmin= 3°

Expected Expected background background and fraction and fraction of signals in of signals in

the cone as a the cone as a function of function of declinationdeclination

The cone which minimizes the MRF The cone which minimizes the MRF is the optimum cone for point-like is the optimum cone for point-like sources searchsources search

declination (deg)

Signal in optimum radius

declination (deg)

Background in optimum radius

Optimum radius (deg)

declination (deg)

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Antares 5-Line SensitivityANTARES 5-Line sensitivity compared with ANTARES 5-Line sensitivity compared with the results presented by other neutrino the results presented by other neutrino experiments.experiments.

Sensitivity in the integrated neutrino flux (above Sensitivity in the integrated neutrino flux (above EE= 10 GeV) for a spectral index of 2. = 10 GeV) for a spectral index of 2. The average increase of the unbinned method over the binned method is about 27%.

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Conclusions The ANTARES neutrino telescope has been completed in May 2008 with the installation of the last two lines. Its exceptional angular resolution, better than 0.3° above 10 TeV, makes of ANTARES a powerful tool to survey the sky and search for neutrino point-like sources. Since the fluxes from astrophysical neutrino emitters are expected to be low, several searching algorithms for the identification of signal excesses over the backgrounds have been developed within the ANTARES collaboration. The binned technique of cone search and the EM-based unbinned method have been applied to perform the analysis of data taken with the 5-Line detector. The better sensitivity for the 5-Line detector is achieved with the unbinned method. Its average increase over the binned method is about 27%. The expected sensitivity of ANTARES 5-Line in 140 days is of the same order that the limits published by other neutrino experiments .

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LAST NEWS from ANTARES meeting: LAST NEWS from ANTARES meeting: Unblinding proposal approved for the 5-Line analysisUnblinding proposal approved for the 5-Line analysis

ANTARES(12-Line) sensitivity

ANTARES expected sensitivity in one year of data-taking . We can compare the result in terms of sensitivity with respect to different experimental results and projected performances of several neutrino experiments.

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Sensitivities Unbinned 5-Line vs 12-Line with different quality cutsUnbinned 5-Line vs 12-Line with different quality cuts

Factor 7 Factor 10

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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:

g

jjj pp

1

);()( θxx

Point-like sources

• πj are the mixing proportions

• p(x;θj) are the different components

• g is the number of components

• θj is a parameter vector for each components

cos2

exp2

cosexp2

1);( 2

2

2

22

Σμx ,PS

1.The background pdf is extracted from MC data or real RA-scrambled data when available

2.Signal pdf model is selected to be 2D-Gaussians

),;()()( Σμxx SSBGBG PPp •We assumed only one source, g=1•Background only depends on declination•The reconstructed energy is not used

CONE METHOD EM ALGORITHMEM ALGORITHM

General procedure

• 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))

COMPLETE data set),,( }{ ra

iiii zyy INCOMPLETE data set

),( }{ raiii xx

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.

L(L(Ψ)Ψ)

Q(Ψ,Ψ(m))+hm

ΨΨ(m)(m) ΨΨ(m+1)(m+1) ΨΨ(m+2)(m+2) ΨΨ

Q(Ψ,Ψ(m+1))+hm+1

Successive maximizations of the function Q(Ψ,Ψ(m)) lead to the maximization of the log-likelihood

)]};({|))};({[log(E),(Q )()( mm pg ΨxΨyΨΨ

Easily differentiable!

CONE METHODCONE METHOD EM ALGORITHMEM ALGORITHM

zzii = = 1 if signal 1 if signal

0 if background 0 if background

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Searching procedureCONE METHOD EM ALGORITHMEM ALGORITHM

Initial values(m):-source coordinates - det. angular resolution-S cluster elements

E-step: Compute Q(,(m))

M-step: Find * = arg max Q(,(m))

(m+1)(m+1) = = **

QQ(((m+1)(m+1),,(m)(m)) – ) – QQ(((m)(m),,(m-1)(m-1)) ) ≤≤

MLML = (m+1)

m = m +1

No

Yes

Looking at a fixed Looking at a fixed direction in the sky.direction in the sky.

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Model Selection2020

We use the model testing theory to calculate the significances.As a test statistic we use the Bayesian Information Criterion (BIC):

Although it sounds bayesian is used in a frequentist fashion.

)log(),|(log2BIC )( nvMDp kkm

kk

)log()|(log2),|(log2BIC 101)(

1 nvMDpMDp m

In the case of two model testing (Only-background, M0, and background+signal, M1) is given by:

Likelihood ratio penalty

Confidence level

Discovery power

CONE METHOD EM ALGORITHMEM ALGORITHM