Transcript f - IceCube
PBP, 2003 SAUND (ocean) ACOUSTIC 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 ≥ 102 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 ≥ 1018 eV. For acoustic arrays I will make the case that absorption and scattering lengths are orders of magnitude larger than for optical arrays. em cascade pancake-shaped pressure wave Peak frequency contours for a 1019 eV hadronic cascade in ice, in kHz (J. Vandenbroucke) Peak pressure contours for a 1019eV hadronic cascade at 10 kHz in ice 2 4 x [km] Conversion of ionization energy into acoustic energy T [ºC) <vL> [m s-1] [m3 m-3 K-1] CP [J kg-1 K-1] Peak frequency <vL>2/CP ocean 15º 1530 25.5x10-5 3900 7.7 kHz 0.153 S.P. ice -51º 3920 12.5x10-5 1720 20 kHz 1.12 NaCl 30º 4560 11.6x10-5 839 42 kHz 2.87 Conversion efficiency is highest for salt and lowest for ocean. glacial ice at South Pole Acoustic waves are scattered at grain boundaries, not at bubbles. 10-2 1 km 10-4 10-6 Scattering depends on grain size, d, and frequency, f, not on temperature: 103 km s d -3 f -4 10-8 energy concentrated here 10-10 103 104 frequency [Hz] in Rayleigh regime 105 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: [m-1] f2 (1 + 4π2 f 2 2)v v = acoustic speed = relaxation time between two possible configurations = 0 exp (U/kT) and U ≈ 0.58 eV Consider two regimes: • SPATS (South Pole) T = -51 ºC, f >10 kHz, a ≈ 8.6 km or energy concentrated here • Ross Ice Shelf T ≈ -28 ºC, f < 1 kHz, a ≈ 500 m 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 <1 kHz have a > 500 m, and very little energy goes into such low-frequency waves. Site for ARIANNA? Ross Ice Shelf Temperature at 10-m depth Thickness Contours -28ºC -27º -27ºC <300m , Ross Sea Ross Sea 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 Cascade-induced acoustic pancakes are warped upward in firn (from Justin Vandenbroucke) = 20º = 10º = 30º = 40º Absorption in ice and salt 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. Scattering and absorption in NaCl 2 cm Scattering from grain boundaries s 0.1 km 1 km 10 km a 103 km 104 km 105 km phonon-phonon absorption (f) f 2 South Pole ice vs ideal salt domes Ice NaCl scatt abs grain size 10 kHz 30 kHz 10 kHz 30 kHz 0.2 cm 0.75 cm 1650 km 120 km 20 km 1.4 km 8-12 km 3x104 km 8-12 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.