SAUND (ocean)

ACOUSTIC

PBP, 2003

Propagation of ultrahigh-energy neutrino-producedacoustic 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.

42x [km]

em cascade pancake-shapedpressure wave

Peak pressure contours for a 1019eV hadronic cascade at 10 kHz in ice

Peak frequency contours for a 1019 eV hadronic cascade in ice, in kHz (J. Vandenbroucke)

Conversion of ionization energy into acoustic energy

ocean S.P. ice NaClT [ºC) 15º -51º 30º

<vL> [m s-1] 1530 3920 4560

[m3 m-3 K-1] 25.5x10-5 12.5x10-5 11.6x10-5

CP [J kg-1 K-1] 3900 1720 839

Peak frequency 7.7 kHz 20 kHz 42 kHz

<vL>2/CP 0.153 1.12 2.87

Conversion efficiency is highest for salt and lowest for ocean.

0.4

cmd ≈

0.2

cm

b =

( s

c at)-1

= s

c att

erin

g co

e ff ic

iein

t [m

-1]

glacial ice at South Pole

d =

1 cm

10-2

10-4

10-6

10-8

10-10

103 104 105

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

103 km

energyconcentrated

here

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 + 4π2 f 2 2)v

v = acoustic speed

= relaxation time between two possible configurations

= 0 exp (U/kT) and U ≈ 0.58 eV

[m-1]

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

energyconcentrated

here

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.

Ross Ice Shelf

>500

m

<300m ,

Ross Sea Ross Sea

Thickness ContoursTemperature at 10-m depth

Site forARIANNA?

-27ºC

-27º-28ºC

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

= 40º = 30º

= 20º

= 10º

Cascade-induced acoustic pancakes are warped upward in firn(from Justin Vandenbroucke)

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

phonon-phononabsorption (f) f 2

105 km

103 km

s

a

104 km

Scattering from grainboundaries

2 cm

0.1 km

1 km

10 km

Scattering and absorption in NaCl

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 3x104 km 3300

km

• In typical salt domes, scattering is worse than in South Pole ice because grain size is larger.

• 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.

grainsize