1. SAUND (ocean) ACOUSTIC PBP, 2003

2. Propagation of ultrahigh-energy neutrino-produced acoustic waves in ice and salt The only affordable way to expand the collecting power of a future neutrino observatory by a factor ≥ 10 2 seems to be with radio and/or acoustic arrays. Their much lower sensitivity to neutrino-induced cascades is an advantage when the goal is to detect neutrinos with energy ≥ 10 18 eV. For acoustic arrays I will make the case that absorption and scattering lengths are orders of magnitude larger than for optical arrays.

3. 4 2 x [km] em cascade  pancake-shaped pressure wave Peak pressure contours for a 10 19 eV hadronic cascade at 10 kHz in ice Peak frequency contours for a 10 19 eV hadronic cascade in ice, in kHz (J. Vandenbroucke)

4. Conversion of ionization energy into acoustic energy ocean S.P. iceNaCl T [ºC) 15º -51º 30º [m s -1 ] 1530 39204560  [m 3 m -3 K -1 ] 25.5x10 -5 12.5x10 -5 11.6x10 -5 C P [J kg -1 K -1 ] 3900 1720839 Peak frequency 7.7 kHz20 kHz42 kHz   2  /C P 0.153 1.12 2.87 Conversion efficiency is highest for salt and lowest for ocean.

5. 0.4 cm  d  ≈ 0.2 cm b = ( scat ) -1 = scattering coefficieint [m -1 ] glacial ice at South Pole d = 1 cm 10 -2 10 -4 10 -6 10 -8 10 -10 10 3 10 4 10 5 frequency [Hz] Acoustic waves are scattered at grain boundaries, not at bubbles. Scattering depends on grain size, d, and frequency, f, not on temperature: s  d -3 f -4 in Rayleigh regime 0.1 cm 1 km 10 3 km energy concentrated here

6. Acoustic absorptivity,  [m -1 ], depends on T, not on d Dominant energy loss mechanism for acoustic waves in cold ice (T < -10ºC) is due to proton reorientation. Absorptivity: f 2  (1 + 4π 2 f 2  2 )v v = acoustic speed  = relaxation time between two possible configurations  =  0 exp (U/kT) and U ≈ 0.58 eV  [m -1 ] 

7. Consider two regimes: SPATS (South Pole) T = -51 ºC, f >10 kHz, a ≈ 8.6 km or Ross Ice Shelf T ≈ -28 ºC, f < 1 kHz, a ≈ 500 m energy concentrated here

8. Acoustic array on Ross Ice Shelf for GZK neutrinos? Advantages: Flatness: acoustic waves can propagate by hopping along firn-air interface. Cheap: deploy at the surface; no drilling required Close to McMurdo; more accessible than South Pole Disadvantages: At T ≥ -28ºC, only waves with f 500 m, and very little energy goes into such low-frequency waves.

9. Ross Ice Shelf >500 m <300m, Ross Sea Thickness Contours Temperature at 10-m depth Site for ARIANNA? -27ºC -27º -28ºC

11. Propagation in firn is analogous to propagation in lunar soil. Due to density gradient of firn, body waves follow curved paths and propagate in 2D if surface is flat. = hydrophones buried at ~1 m

12.  = 40º  = 30º  = 20º  = 10º Cascade-induced acoustic pancakes are warped upward in firn (from Justin Vandenbroucke)

13. D L In ice, acoustic waves lose energy by pulling protons (black dots) back and forth between bond sites. In NaCl acoustic waves lose energy by interactions of acoustic phonons with the thermal phonon background. Absorption in ice and salt

14. phonon-phonon absorption   (f)  f 2 10 5 km 10 3 km s a 10 4 km Scattering from grain boundaries 2 cm 0.1 km 1 km 10 km Scattering and absorption in NaCl

15. South Pole ice vs ideal salt domes scatt abs 10 kHz 30 kHz 10 kHz 30 kHz Ice 0.2 cm 1650 km 20 km 8-12 km 8-12 km NaCl 0.75 cm 120 km 1.4 km 3x10 4 km 3300 km 1.In typical salt domes, scattering is worse than in South Pole ice because grain size is larger. 2.In salt domes, both scattering and absorption are dominated by impurities: clay, other minerals, and liquid inclusions. 3. Calculations of scatt and abs must be checked with measurements at proposed sites. 4. Available volume of South Pole ice >> volume of any salt dome. 5. Drilling into ice is far cheaper than into salt domes. grain size