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Study of the Response of the ANTARES Detector instrumented with Direction-Sensitive Optical Modules
M. Anghinolfi, A.Bersani, K. Fratini, M. Osipenko, M. Taiuti
Dipartimento di Fisica del l'Universitґ di Genova or Istituto Nazionale a di Fisica Nucleare, sezione di Genova, I-16146 Genova, Italy

V. Kulikovsky, A. Plotnikov, E. Shirokov
Institute of Nuclear Physics, Moscow State University, 119899 Moscow, Russia We studied the p erformances of the underwater neutrino telescop e ANTARES equipp ed with direction-sensitive optical modules. The main feature of these optical modules is to detect the direction of the incoming Cherenkov light. In this note we show that the effective area of the underwater neutrino telescop e ANTARES could b e improved at low neutrino energies (E < 10 TeV) by adding in the reconstruction procedure the information on the direction of the detected Cherenkov light.

I.

INTRODUCTION

We investigated how the response of the underwater neutrino telescope ANTARES [1] could be improved by introducing the additional information of the direction of the detected Cherenkov light. We designed a prototype of a direction-sensitive optical mo dule (DOM) and we accordingly mo dified the simulation and reconstruction codes [2] currently used by the ANTARES Collaboration to study the response of the detector. The DOM is based on a position-sensitive photomultiplier coupled to a light guide system such that all the Cherenkov light arriving from the same direction is fo cussed on a reduced area of the photo catho de. The basic working principles have been discussed in [3]. In Figure 1 it is summarized how the device would work: all photons arriving from the same direction are collected on a single sector of the multi-anodic photomultiplier.

x

x

R

R

FIG. 1: Left: b ehaviour of the classical optical module: the Cherenkov light illuminates the whole photocathode surface. Right: the mirrors concentrates the light on a single sector of the photocathode surface.

The realization of a prototype of the direction-sensitive optical is in progress. A cross section of the DOM prototype is shown in Figure 2. The prototype is based on a 4-ano ds 10" photomultiplier position-sensitive. In order to match the refraction index of the photomultiplier and the glass sphere, the volume between the photomultiplier and the glass sphere must be filled with a transparent material like plexiglas or optical gel. A set of mirrors realized with highly reflective 3M plastic material with a reflectivity in the blue region better than silver or aluminum concentrate the light on a single sector of the photo catho de surface. Two prototypes of such a photomultiplier have been manufactured by Hamamatsu and the measurement of their optical properties is in progress. We will not discuss in this paper the structure of the DOM, but we simply assume that the solid angle (close to 2 ) covered by each standard optical mo dule can be subdivided into four independent quadrants. Therefore the new optical mo dule has been implemented in the simulation co de using four smaller photomultiplier with reduced angular acceptance. The size of the photocathode area and the cut in the angular acceptance have been defined in order to maintain the same amount of collected light. The way how the DOM has been implemented in the simulation software is discussed in section II; in section III we discuss how we modified the reconstruction program and we show that the response of the telescope based on this solution improves for low energy muons (E < 10 TeV).


FIG. 2: The prototyp e of a direction-sensitive optical module based on a 4-anodic photomultiplier coupled to a light-guide system. The main comp onents are the photocathode surface (blue), the mirror system (gray) and the optical gel (yellow).

II.

THE RESPONSE OF THE DIRECTION-SENSITIVE OPTICAL MODULE

In this section we briefly verify that the description of the DOM is correctly implemented in the simulation program. The standard optical mo dule and the DOM configuration have the same sensitive area, therefore the collected light should also be the same. We report in Figure 3 the comparison between the simulations of the amount of light collected with the assumption of zero background (top panel), and with the assumption of 40 kHz background (bottom panel; in Figure 4 the comparison between the number of active optical mo dules with the assumpion of zero background (top panel), and the same with the assumption of 40 kHz background (bottom panel). The four plots show that there are no differences between the two configurations.
III. THE TELESCOPE RESPONSE

In order to better understand the results, we first remind that the reconstruction program is mainly based on the time response of the photomultipliers. For a given timing value, each active photomultiplier defines in the space an hemi-spherical surface with a thickness proportional to the photomultiplier time resolution as shown in the left panel of Figure 5, representing all the possibile emission points of the detected light. At least one point of the muon tra jectory belongs to the surface and the reconstruction uncertainties clearly increase with the radius of the hemi-spherical surface. For high energy neutrinos (E > 10 TeV) the number of active mo dule is large enough to minimize the uncertainties; but for lower energy neutrino the number of active optical mo dules decreases and this compensation cannot always o ccur. The use of the DOM configuration reduces this uncertainty and we anticipate that the effect is particularly evident at neutrino energies smaller than 10 TeV as shown in Figure 9. In fact the surface representing all the possibile emission points of the detected light has now a triangular shape as shown in the right panel of Figure 5. As a consequence, the error on the emission point lo cation is drastically reduced. The presently available reconstruction software is based on the AART Strategy [4] developed by Aart Heijbo er. We included the description of the DOM mo difying few steps of the recostruction co de. To better explain the mo dification we first summarize the AART Strategy.
A. The AART Strategy

The strategy identifies a reasonable track TI to be used as the seed for the fit of the data. TI is estimated by a procedure that includes the following steps: a) the linear fit, b) the M-estimator and c) the fit of the time residuals without noise contribution. As TI is determined, it is used as input to the final PDF (Probability Density Function) fit that includes the effect of the background. The AART strategy utilizes for each i-th optical mo dule the lo cal co ordinates in the detector, the orientation, the time signal ti and the collected charge hi . To better describe the invidual steps of the strategy we now define h0 the largest hit that provides the reference time t0 and ci the flag that identifies the i-th hit that is in coincidence within


10

3

Directional Detector

Standard Detector

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2

10

1 0 20 40 60 80 100 Photoelectrons per event

10

3 Directional Detector

Standard Detector

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1 0 500 1000 1500 2000 2500 3000 Photoelectrons per event

FIG. 3: The comparison b etween the distributions of the light collected in a single event by a detector equipp ed with standard optical module (dotted histogram) and with DOM (continuous histogram) b oth with the sensitive area of a 10" photomultiplier with zero background (top panel) and with 40 kHz background (b ottom panel).

20 ns with any other hit in nearby photomultiplier. With this definition we allow, in the case of DOM, coincidences in the same optical module.


1200
Directional Detector

1000 800 600 400 200 0 0

Standard Detector

5

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15 20 25 Number of fired OM

600 500 400 300 200 100 0

Directional Detector

Standard Detector

400

600

800

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1200 1400 1600 Number of fired OM

FIG. 4: The comparison b etween the numb er of active optical modules in the standard configuration and in the DOM one with zero background (top panel) and with 40 kHz background (b ottom panel).


FIG. 5: The graphical description of the location of the p ossible emission p oint of the Cherenkov light detected by an optical module at fixed timing. The thickness of the gray region corresp onds to the photomultiplier time resolution. Left: standard optical module; right: DOM.

B.

The Linear Fit

The first step aims to identify a reduced set 0 of informations that includes h0 and all hits hi that have a time difference ti = t0 - ti such that the following three constraints are simultaneously satisfied distance(h ,h ) i 0 - 500 ns < ti c distance(hi ,h0 ) (1) - 20 ns < ti v distance(hi ,h0 ) < 10 km where c is the muon velocity and v the speed of light in water. This is a reasonally small set of hits that includes most of the signal hits. However the number of noise hits included in 0 is to o large and therefore a subset L is derived from 0 choosing all hits with hi > 2.5 photoelectrons .OR. ci = .T RU E . (2)

The obtained reduced set L is the input for the linear fit based on the closest approach distance of the muon track compatible with the hits. Assuming the following muon track equation y (t) = p + d · ct the parameters p and d that define the track are evaluated minimizing the following sum Ci - y (ti )
i
L

(3)

2

(4)

where the closest approach point Ci is evaluated from hi using a table, defined a priori, that connects Ci to the hit amplitude, and ti is the measured time. The output of the linear fit is the track TL that is then utilized as the starting track of the second step of the reconstruction algorithm.
C. The M-estimator

In order to find the best track, the arrival times of the Cherenkov light tth (T ), evaluated from a generic track T, i are compared to the measured time ti and the differences (time residuals) ri (T ) = tth (T ) - ti minimized. In order i


to find a solution TM almost independent from the starting track TL the M-estimator fit is applied. It minimizes the following function of the residuals ri and of the photomultiplier angular acceptance G=
i
M

2 -2 1+ hi ri /2 - (1 - )f

ang

(cosi )

(5)

where = 0.05, i is the angle of arrival of the light with respect to the axis of the photumultiplier, and the angular acceptance fang (cosi ) is reported in Figure 6.
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.2 0 0.2 0.4 0.6 0.8 1 cos()

FIG. 6: The standard photomultiplier angular acceptance used in the reconstruction.

The set

M

of hits used with the M-estimator fit is the reduced set of 0 that satisfies the following constraints -150 ns < ri (TL ) < 150 ns .OR. hi > 2.3 photoelectrons (6) distance(h ,T ) < 100 m i L

D.

The Time Residuals Fit

The track TM obtained from the M-estimator fit is the seed of the likeliho o d minimization of the Probability Density Function (PDF) P (ti |tth ) of the residuals ri , shown in Figure 7 with the assumption of no background. The set PDF i of hits used with the PDF-fit is the reduced set of M that satisfies the following constraints -0.5r < ri (TM ) < r distance(h ,T ) < 300 m i M .OR. (7) hi > 2.5 photoelectrons .OR. ci = .T RU E . where r is the RMS value of the distribution of the residuals ri referred to TM . In order to further reduce the dependence from the starting track TL , the M-estimator and PDF pro cedures are repeated several times using different starting tracks TL obtained from rotation or translation of the original TL , pro ducing every time a new TPDF track. The TPDF track that shows the best minimization becomes TI , input track for the final fit.


P(ti|ti )

th

1

10

-1

10-2

10-3

10-4

10-5 -10

0

10

20

30

40 50 time residual r i (ns)

FIG. 7: The Probability Density Function (PDF) used in the reconstruction.

E.

The Improved Time Residuals Fit

The final step is based on the likelihood minimization of the improved Probability Density Function (PDF) of the residuals ri defined as P (ti |tth ) = wsig Psig (ti |tth )+(1 - wsig )Pbkg (ti |tth ) i i i (8)

where Psig (ti |tth ) represents the PDF for signal, Pbkg (ti |tth ) represents the PDF for the background noise, and i i wsig , that depends on the amplitude of the read-out, the orientation and lo cation of the optical mo dule, represents the probability that hi is a signal hit. The used set I is the subset of 0 that satisfies the following constraints: -250 ns < ri (TI ) < 250 ns distance(h ,T ) < 300 m i I .OR. (9) hi > 2.5 photoelectrons .OR. ci = .T RU E .
F. Implementing the Direction-sensitive Optical Module

The intro duction of the direction-sensitive optical mo dule required several changes in the fitting pro cedure, particularly in the definition of the tables and functions used. First of all the data in the table used in the linear fit have been changed in order to represent the most probable light emission point rather than the closed approach distance. Consequently the linear fit of Eq.(4) has been corrected in order to minimize the light emission point as follows: Ci - y(ti )
i 2

(10)

where ti is obtained from the measured time ti correcting for the light propagation from the most probable emission point to the optical mo dule.


Aeff (m2)

10

1

10-1

10-2

10-3 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 log E(GeV)
10

FIG. 8: The effective area of the standard ANTARES detector (crosses) and ANTARES equipp ed with DOM (black squares) for muonic neutrinos assuming < 5 . The full triangles represent the result of the standard reconstruction procedure applied to the standard ANTARES detector.

In the simulation and reconstruction programs, the angular acceptance fang (cosi ) was set equal to that shown in Figure 6 for cos() > 0.71 and equal to zero for cos() < 0.71; and the value of has been optimized to 0.01; in the Improved Time Residual Fit the weight wsig has been mo dified taking into account also the new expected background rate. The value of wsig has been determined from a MonteCarlo simulation as described in the Aart strategy. In addition to the previous mo difications we implemented new constraints in order to efficiently use the information of the direction of the detected light and to optimize the response to low energy neutrino. The mo difications to the reconstruction program can be summarized as follows: a) for low energy neutrinos (E < 100 TeV ), the average number of hits is small and as a consequence the probability that the highest hit h0 is generated by the background is not negligible. Therefore, to improve the reconstruction efficiency, h0 is selected as follows: h0 = hM if the largest hit hM is larger that 3.0 photoelectrons, otherwise h0 is the largest hit with a coincidence signal (cM =.TRUE.); b) after every fitting procedure described in subsections III B to III E, the compatibility between the resulting track and the angular acceptance of the hits used in the reconstruction is verified, the hits not compatible are removed from the set and the fitting pro cedure is repeated. c) because in the new geometry the linear fit provides a solution closer to the real track, the range of the rotations used to pro duce new starting tracks are reduced.
G. ANTARES with the Direction-sensitive Optical Module

We now report the results of the study of the performance of ANTARES equipped with DOM. We first consider the simulation and reconstruction of neutrinos with energy below 104 GeV because in this energy interval the average number of signal hits is small and the information on the direction of the detected Cherenkov light can improve the reduction of the background contamination. To study the detector performances we selected the muonic tracks that have been reconstructed with go o d angular resolution, that is with an angular difference between the generated and recostructed muon directions better than 5 . This criteria is clearly not appliable in the real measurement because the value of is intrinsecally unknown. However, this is the first attempt to intro duce the directionality in the reconstruction pro cedure and we decided to begin with a qualitative estimate of the performances, thus postponing the task of finding the best pro cedure for low energy muons. In Figure 8 the results for the effective areas of the standard ANTARES detector and ANTARES equipped with DOM are reported. For sake of completeness we applied to both geometries the check on the compatibility between the resulting track and the angular acceptance of the hitted photomultiplier. For comparison we show also the results


A 1.3 1.2 1.1 1 0.9 2

eff dir

/A 1.4

eff std

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3

3.5

4

4.5

5

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6 6.5 7 log E(GeV)
10

FIG. 9: The ratio of the effective areas of ANTARES equipp ed with DOM and the standard ANTARES detector.

( o) 10 1 10-12

2.5

3

3.5

4

4.5

5

5.5

6 6.5 7 log E(GeV)
10

FIG. 10: The median of the angular error of the muon track reconstruction for the standard ANTARES detector (crosses) and ANTARES equipp ed with DOM (black squares) for all reconstructed muonic neutrinos.

obtained for the standard ANTARES detector reconstructed with the standard reconstruction program. In this case the reconstruction has been done by ... and we only applied the cut 5 to the angular reconstruction. The gain is reported in Figure 9 as the ratio between the effective areas of the two studied configurations: the effective area in the DOM configuration improves up to a factor 2 at E = 100 GeV and the effect is particularly evident at energies E < 1 TeV. The knowledge of the direction of the detected Cherenkov light improves the detector capability to reconstruct the muon tra jectories. This is shown in Figure 10 where we show, for all reconstructed tra jectories, the comparison between the medians of the angular error distribution for the standard ANTARES detector and ANTARES equipped with DOM. The DOM improves the reconstruction accuracy at neutrino energies below 10 TeV.


IV.

CONCLUSIONS

We implemented in the Antares reconstruction co de, starting from the AART strategy, the algorithm to reconstruct the muon tra jectory for a neutrino detector equipped with optical mo dule sensitive to the direction of the detected Cherenkov light. With the mo dified reconstruction co de we simulated the ANTARES geometry instrumented with DOM and we compared the performances with those of the standard ANTARES detector. It resulted that: · the check on the compatibility between the resulting track and the angular acceptance of the hitted photomultiplier increases the quality of the reconstruction; · the advantage of using the DOM consists in a better reconstruction efficiency of the shortest tracks that originate mainly from low energy neutrinos.

[1] [2] [3] [4]

E. Aslanides et al., the ANTARES prop osal, (1999), astro-ph/9907432, http://antares.in2p3.fr. www.antares2.in2p3.fr ANTARES-soft Internal notes. M. Taiuti, Nucl. Instrum. Meth. A 525 (2004) 137. "An algorithm for track reconstruction in ANTARES" Aart Heijb oer ANTARES-soft/20002-002.