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Acoustic Detection of Extremely High Energy
Particles Off the French Riviera

Valentin NIESS CPPM-Marseille Workshop on
Acoustic detection, Stanford - Sep. 2003
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Contents

• Acoustic signal studies
• GEANT4 MC 3D studies of underwater shower Energy
  deposition (1-1000 TeV)
• Acoustic field at 400 m from the shower
• Parameterisation of the acoustic signal
• Compact array studies
• Event rates and Efficiency estimation
• Reconstruction Algorithms
• Monte-Carlo studies of some ANTARES like compact
  geometries
• On the way to a complete detector

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Computation of Energy Deposition

• Monte-Carlo simulations using GEANT4 package

e-, p

• Physical list from high energy hadronic
  calorimetry (100 TeV cut for p)
• 3D-rectangular binning of energy deposition
  (1 mm1mm1cm)

Computation time 8h _at_ 1 PeV on CCL farm (Lyon)
Interactions over rectangular box of water
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Longitudinal Energy Deposition

• Well studied for air-showers semi-empirical law
  for EM

1 TeV
10 TeV
100 TeV
100 TeV
10 TeV
1 TeV
EM Showers
Comparison with GEANT3 (Brunner)
Fit of mean longitudinal shower profile
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Energy Deposition Fluctuations
e-
e-
30
64
26
e-
100 TeV
10 TeV
1 TeV
31
p
p
110
p
128
6
Pressure Field Computation

• Instant-pressure field at time t computed by
  integration as

from Askariyan
Rcst
Integration over Spherical surface

• Numeric integration over energy deposition
  binning

Computation Time 8h On local computer
zoom
ds
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Absorption From Sea Water

• Local time-variations of pressure field computed
  from neighbourhood as
• Propagation approximated as orthogonal to shower
  axis
• Geometric spreading as
• Absorption computed from Fourier transform as

Direction of propagation
Distance to shower axis
Local variations neglected for time dependency
computation
Absorption length From Urick
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Pressure Field Plots _at_ 400m from Axis
e-
e-
e-
21
22
46
10 TeV
100 TeV
1 TeV
p
p
p
44
81
23
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Maximal Pressure _at_ 400m from Axis
e-
e-
e-
n0.98
Agreement with previous studies
1 TeV
10 TeV
100 TeV
p
p
p
n1.22
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Modelling of the Acoustic Signal

• Acoustic rays perpendicular to the core of the
  shower
• Group velocity close to sound velocity in water
• Wave front equation as
• Two parameters rmax, Leff

z
To shower

• Depends on
• nature energy of incident particle
• noise conditions

Dr
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Effective length of the shower

• Longitudinal shape of pressure field scales with
  maximum of longitudinal energy deposition

_at_400 m
little variations with S/N ratio
N/Pmax
P/Pmax

• Maximum of energy deposition scales as a log law

z/zemax
Dz/zemax
? LPM ?
31.7 MeV Critical energy
Maximum of energy deposition
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Maximal Propagation Range

• Amplitude model as

Long range - Absorption

• Calibration given by

60mPa signal _at_ 400m _at_ 10PeV
? LPM ?
Small range - Geometric spreading
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Guess on parameters
No LPM effect
With LPM effect ?
Energy (eV) Leff (m) rmax (km)
1018 10 (10) 1- (1)
1019 10-50? (20) 1-10? (2)
1020 10-100? (40) 3-15? (4)
Energy (eV) Leff (m) rmax (km)
1018 7.4 1
1019 8.1 3-10
1020 8.9 5-15
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Velocity Profile in Mediterranean Sea

• Linear at depth below 100 m
• Acoustic rays follow circular trajectories with
  curvature radius

Stable temperature 13.2 C
1.6 cm/s per m
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Deflection and Propagation Delays
B
DD
td
z
tr
f
z
x
A
f
DT td-tr
x
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Compact Array of Hydrophones Studies
Efficiency Angular resolution Triggering
Leff
Large sea bed arrays AUTEC TREMAIL
Compact array
Mix-array (cf Timo Karg -Erlangen University)
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Effective Volume of Detection

• Volume on which a shower of orientation is
  detected
• Single phone, infinite medium
• Compact arrays d Leff ltlt H

Hit function 0 or 1
Whole water space
rmax
Leff
Independent of direction
Bottom-surface term
Coincidence term
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Event Rates and Efficiency
density of events (L-3 T-1) Independent of
position

• Event rate as

? Astrophysical Flux ?
Target density 6.1029 m -3 for N in H2O
Single phone in ? medium
nN NCCC cross section from A. gazizov (2002)
Energy (eV) Effective volume (km3) Effective Section (km2)
1018 0.03 3.6 10-4
1019 0.06-16 1.8 10-3-0.5
1020 1-71 0.08-5.4
Relative quantity Efficiency
Number of phones
Single phone Non limited
Highly dependent on propagation range
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Single phone Statistics of Events

• Density of probability to be hit decreases with
  distance to shower as
• Uniform density of showers, radial density of
  showers increases as
• Most of detected events will come from long
  range

Radial density of events (km-1)
Distance (km)
75 of detected events are located at more than
rmax/2
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Single phone effect of Sea Bed and Surface
z
H 2500 m
Optimized at mid-depth
Efficiency ()
1019 eV
1020 eV
1018 eV
cos(q)
Bottom limitation
Surface limitation
Non limited phone
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2 Hydrophones in Coincidence
d/Leff 0,5
d/Leff 1
Efficiency ()
d/Leff 2
d/Leff 50
2 km spacing 2-3º aperture at 1020 eV
cos(q)
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TDoA Reconstruction Algorithm

• Quasi-planar approximation (3 Phones, NL)
• Point source of sound (4 Phones, NL)
• Line Source of sound (7 Phones, NL)

(4 Phones, L)
Direction
(5 Phones, L)
Position
Position, Orientation
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Monte-Carlo Studies of Arrays
Shower position orientation
Real position
Nominal position
Measured Position
Hydrophone random position
Hit function
Shower Random Generator
Leff rmax
Reconstruction Algorithm
Measured Arrival time
yes
no
Mean Efficiency
Trash
Propagation model
Random time origin
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About Measurements and Reconstruction

• Hydrophones Positions Fixed on Lines
• Arrival time Sampling
• Energy estimation

Phones are moving
ANTARES structure 1m free rotation around line
axis line deformation
Acoustic positioning system Accuracy sp 3 cm
t0 measurements errors
Noise
At 500 kHz sampling rate 2 ms
Model Acoustic wave front is not a perfect line
st 5 ms
Less than 5 ms curvature, but at 400m from shower
From signal Amplitude Distance estimation
Z-dependant
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Alignment 3 Phones in Coincidence
30
60
45
1020 eV
z-axis
D
Sea bed surface damping
Efficiency ()
Coincidence Cut-off
cos(q)
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Alignment 3 Phones in Coincidence
Low range over-populated
10 kHz absorption length
10 kHz absorption length
! Low Statistics !
Max. Error on Distance (95 CL)
Max. Error on Distance (95 CL)
Max. Error on Energy (95 CL)
Max. Error on Energy (95 CL)
Generation Threshold
D 0 cm
D 100 cm
Cut on Distance 0.1ltDlt6 km
95 CL
95 CL
70
Probability ()
Probability ()
Rejection ()
Rejection ()
Distance (km)
Distance (km)
Max. error on Distance
Max. error on Distance
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3D-Antenna 4 Phones in Coincidence
60
45
30
1019 eV
z
q
Sea bed surface damping
Local Interferences ?!
Coincidence damping
Solid frame
Accurate Phone Positions
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3D-Antenna 4 Phones in Coincidence
Accurate reconstruction !
95 CL
Max. error on Direction (95 CL)
Max. error on Direction (95 CL)
Probability ()
2
2
2
cos(fz)
cos(fx)
cos(fy)
Max. error on Direction
Distance (km)
Quasi planar-approximation Non valid at short
range
Accuracy is independent on direction
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Rectangular Array 5 Phones in Coincidence
Cut on reconstructed distance 0.1 lt D lt 6 km
1020 eV
Sea bed surface damping
Coincidence cut-off
30 º
45 º
30
Rectangular Array 5 Phones in Coincidence
95 CL
Low range over-populated with miss-reconstructed
events
Probability ()
Probability ()
Max. error on Energy
Max. error on Distance
Generation Threshold
95 CL
Max. error on Direction (95 CL)
Probability ()
2º
Max. error on Direction
Distance estimation (km)
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Rectangular Array 8 Phones in Coincidence
Cut on reconstructed distance 0.1 lt D lt 6
km and on residuals
15
30
Coincidence cut-off
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Rectangular Array 8 Phones in Coincidence
95 CL
Low range over-populated with miss-reconstructed
events
Probability ()
Probability ()
10 kHz absorption length
Max. error ratio on Distance (95 CL)
Max. error on Distance
Max. error on Energy
Max. error ratio on Energy (95 CL)
95 CL
Generation Threshold
2
Probability ()
Max. error on Direction (95 CL)
1
Distance estimation (km)
Distance estimation (km)
Distance Estimation (km)
Max. error on Direction
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Conclusions on Compact Arrays

• TDoA Location Algorithms No Precise
  reconstruction from CA
• Allow for rough (within factor 2-3) estimation
  of shower-to-hydrophone distance
• TDoA Direction Algorithm Precise estimation of
  local sound direction (1º) can be achieved

Great Sensitivity to measurements errors for
outside-events
due to events statistics
Short range estimation(lt1km) not reliable
But
Long range accuracy estimation biased by
generator-cut range
Short range events(lt300 m) not reliable (few
events)
But
Due to events radial distribution, on CA most of
events are locally seen as planar sound waves
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Association of 3D-Antenna
60
30
45
Better than Rectangular 8-Phone Array
Efficiency ()
Reconstruction from incidence directions
Shower Distance Orientation
cos(q)
35
Statistical Methods
1 angular resolution (95 CL) on sound incidence
direction No sound-ray refraction No relative
motion of sources
q (?)
10 isotropic background 310 sources