1. 27-30 June 2006V. Bertin, V. Niess- ARENA 2006 - Newcastle1 Acoustic Signal Computations in the Mediterranean Sea ARENA 2006, Newcastle V. Bertin, V. Niess CPPM - IN2P3/CNRS - U. Méditerranée – France

2. 27-30 June 2006V. Bertin, V. Niess- ARENA 2006 - Newcastle2 General Context This Presentation Focuses on Acoustic Signal Computations PhD work at CPPM ( September 2002- September 2005 )PhD work at CPPM ( September 2002- September 2005 ) Dedicated Acoustic ‘team’ at CPPM ( 2002-2005 ) With Engineers & Physicists, mostly involved in ANTARES See i.e. : Stanford Workshop 2003Stanford Workshop 2003 ICRC 2005, PuneICRC 2005, Pune http://marwww.in2p3.fr/~niess/these.pdf (in French) astro-ph/0511617 ( to be published in Astroparticle Physics )

3. 27-30 June 2006V. Bertin, V. Niess- ARENA 2006 - Newcastle3 A Brief Reminding Thermo-acoustic coupling mechanism ( Askaryian, 1957 ; Sulak et al., 1978 ) 2) Propagation : Vertically stratified medium ( Refraction ) 3) Output : Pressure signal ( Transduction … ) 1) Input : Energy density ( UHE Particle showers ) Thermodynamic factor Constant here ( Mediterranean Sea, 1 km depth )

4. 27-30 June 2006V. Bertin, V. Niess- ARENA 2006 - Newcastle4 Modelling Energy Deposition Cross sections from : Gandhi et al. Phys. Rev. D58, 093009 (1998) hadronic and electromagnetic showers N, l W,Z hadrons Deep Inelastic Scattering hadrons Thermo-Acoustic emission : Efficiency increases with energy density Showers required Focus on 2 limit cases : e charged current ( CC ) : because 100 % of e energy goes into showers but strong LPM spread …  dedicated Monte carlo L neutral current ( NC ) : because it is presumed giving compact showers but only ~20 % of the L energy  Parametrisation ( GEANT 4/ EAS data ) Considering : J. Alvarez-Muniz, E. Zas Phys. Lett. B 441 (1997) 218 Phys. Lett. B 434 (1998) 396

5. 27-30 June 2006V. Bertin, V. Niess- ARENA 2006 - Newcastle5 GEANT4 : Longitudinal Profile GEANT 4, QGSP In a water box Extensive Air Showers, from M. Nagano and A. Watson Rev. Mod. Phys., Vol 72, No. 3, July 2000 Geant 4,   GEANT 4 results are consistent with Extensive Air Showers But LPM is a Matter effect … Depth of maximum ( X 0 ) Depth of maximum ( g/cm 2 ) LPM ?? E LPM ‘PDG Parameterisation’ : Good agreement

6. 27-30 June 2006V. Bertin, V. Niess- ARENA 2006 - Newcastle6 GEANT 4 : Lateral Distribution Sustained by Microscopic observation of ~ 100 GeV e-showers in Lead plate/Emulsion N. Hotta et al. Phys. Rev. D, Vol 22, No. 1, July 1980 Power law behaviour 5·10 -4 r m GEANT 4 Exponents vary mostly with depth little with primary nature and energy ( @ 50+ TeV ) Core exponent ( ~10 % agreement with EAS) z/z max Lateral exponents E  50 TeV  /r m

7. 27-30 June 2006V. Bertin, V. Niess- ARENA 2006 - Newcastle7 Electromagnetic LPM : Scheme 1D 2D Use a dedicated 2 steps scheme : 1.Randomize the high energy part of shower ( LPM fluctuations ) 2. Reconstruct : Filter with average parametrisations for secondary showers Monte-Carlo (Metropolis) (FIR algorithms) primary Migdal’s cross sections for LPM : Not constrained experimentally in the strong suppression regime we are concerned with

8. 27-30 June 2006V. Bertin, V. Niess- ARENA 2006 - Newcastle8 Electromagnetic LPM : Results Parametrisation extends up to 10 17 eV LPM LPM cascades stochastic Longitudinal profiles of energy deposition Depth of the maximum log 10 ( E / 1 GeV ) z max ( X 0 ) Normalised longitudinal density Depth [ z ] (m) GEANT4 e ( 10 19 eV ) LPM ‘tail’ hadronic  ( 5·10 13 eV )

9. 27-30 June 2006V. Bertin, V. Niess- ARENA 2006 - Newcastle9 Acoustic Signal Computation Propagation time : Ray tracing model Approximate Green function : No (de)-focusing ( ~ few % ) Strength of signal = time/spatial coherence : This is where to play … Reduce integral to 1D with causality/symmetries : Sum over 2 acoustic rays Longitudinal density Transform of lateral distribution Observer point, Time & Ray structure

10. 27-30 June 2006V. Bertin, V. Niess- ARENA 2006 - Newcastle10 Propagation Loss Signal Strongly modelled by Absorption Phase dependent model Driven by : L. Liebermann Phys. Rev. 76(10), November 1949 With ‘modern’ input from : R.E. Francois and G.R. Garrison J. Acoust. Soc.Am. 72(6), 1982 Absorption length ( km ) Impulse response ( scaled ) Frequency ( kHz ) Time ( scaled ) MgSO 4 B(OH) 3 Viscosity 1/f 2 Transition from MgSO 4 Delayed Impulse response

11. 27-30 June 2006V. Bertin, V. Niess- ARENA 2006 - Newcastle11 Near Field/ Far Field Angular aperture ( NC compact cascades ) Pressure field ( mPa ) e CC, E = 125 EeV, 10 km distance LPM Spherical wave-front ( far field ) Fuzzy image Longitudinal density Cylindrical wave-front ( near field ) Compact cascades : Rigorous far field conditions achieved only at ~10 km Transition :

12. 27-30 June 2006V. Bertin, V. Niess- ARENA 2006 - Newcastle12 Signal Shape R/C versus  t diagram Signal characterised by : Duration :  t Symmetry ratio : R/C Get insight on source nature, extension ( R/C ), distance (  t ) Signal more asymmetric than previous studies

13. 27-30 June 2006V. Bertin, V. Niess- ARENA 2006 - Newcastle13 Mediterranean Sea Refraction Mediterranean Sea Linear sound velocity profile Below 100 m z ( m ) Amplitude (  Pa ) Time (  s ) Pressure field (  Pa ) @ 1 km from the source Amplitude is little affected Effect is mostly native : Local sound velocity variation on energy deposition area Not ray structure Global deflection given by a ray tracing model Deflection   Directivity only depends on 

14. 27-30 June 2006V. Bertin, V. Niess- ARENA 2006 - Newcastle14 Effective Volume Model driven extrapolation Near field, CC e Far field, NC L Signal amplitude ( dB ref 1  Pa ) Sonic Volume ( dB ref 1 km 3 ) Range ( dB ref 1 m ) 1 km 1 km 3 Amplitude ( dB ref 1  Pa ) Signal threshold levels : 1 to 10 mPa Energies : 10 18 to 10 20 eV Model Parameters : Range  max, Effective length L eff, effective angular aperture  eff

15. 27-30 June 2006V. Bertin, V. Niess- ARENA 2006 - Newcastle15 Boundary effects Shadowing from the sea bed ( Refraction ) Shadow Zone Source Shadow Factor : Efficiency = 1 - F H = 2500 m depth Receiver z i =448 m above sea bed Pure Monte-Carlo z i = H/2 Mean geometric efficiency ( % )  max /( H/2 ) Water extension is vertically limited Hypothesis : Direct detection At long range Detection limited Close to vertical cascades Analytical & Monte-Carlo

16. 27-30 June 2006V. Bertin, V. Niess- ARENA 2006 - Newcastle16 Benchmark Sensitivity Estimates Sea Noise 1-10 mPa in B = 100 khz ( Ceramic eq. ~ 2-6 mPa ) 10 18 eV 10 20 eV Mediterranean Sea 2500 m depth (ANTARES like) 1/E 2 Flux  1 an E 2  ~10 -6 GeV·cm -2 · sr -1 · s -1 1 evt/decade/year Flattening due to boundaries