The production of acoustic signals from the interactions of ultra-high energy (UHE) cosmic ray neutrinos in water and ice has been studied. A new computationally fast and efficient method of deriving the signal is presented. This method allows the implementation of up to date parameterisations of acoustic attenuation in sea water and ice that now includes the effects of complex attenuation, where appropriate. The methods presented here have been used to compute and study the properties of the acoustic signals which would be expected from such interactions. A matrix method of parameterising the signals, which includes the expected fluctuations, is also presented. These methods are used to generate the expected signals that would be detected in acoustic UHE neutrino telescopes.
Deep Dive into Study of the acoustic signature of UHE neutrino interactions in water and ice.
The production of acoustic signals from the interactions of ultra-high energy (UHE) cosmic ray neutrinos in water and ice has been studied. A new computationally fast and efficient method of deriving the signal is presented. This method allows the implementation of up to date parameterisations of acoustic attenuation in sea water and ice that now includes the effects of complex attenuation, where appropriate. The methods presented here have been used to compute and study the properties of the acoustic signals which would be expected from such interactions. A matrix method of parameterising the signals, which includes the expected fluctuations, is also presented. These methods are used to generate the expected signals that would be detected in acoustic UHE neutrino telescopes.
In recent years interest has grown in the detection of very high energy cosmic ray neutrinos which offer an unexplored window on the Universe [1]. Such particles may be produced in the cosmic particle accelerators which make the charged primaries or they could be produced by the interactions of the primaries with the Cosmic Microwave Background, the so called GZK effect [2]. The flux of neutrinos expected from these two sources has been calculated [3,4]. This is found to be very low so that large targets are needed for a measurable detection rate. It is interesting to measure this neutrino flux to see if it is compatible with the values expected from these sources, with any incompatibility implying new physics.
Searches for cosmic ray neutrinos are ongoing in AMANDA [5], IceCube [6], ANTARES [7], NESTOR [8], NEMO [9], KM3NeT [10] and at Lake Baikal [11] detecting upward going muons from the Cherenkov light in either ice or water. In general, these experiments are sensitive to lower energies than discussed here since the Earth becomes opaque to neutrinos at very high energies. The experiments could detect almost horizontal higher energy neutrinos but have limited target volume due to the attenuation of the light signal in the media. The Pierre Auger collaboration,using an extended air shower array detector, are searching for upward and almost horizontal showers from neutrino interactions [12]. In addition to these detectors there are ongoing experiments to detect the neutrino interactions by either radio or acoustic emissions from the resulting particle showers [1]. These latter techniques, with much longer attenuation lengths, allow very large target volumes utilising either large ice fields or dry salt domes for radio or ice fields and the oceans for the acoustic technique.
In order to test the feasibility of detecting such neutrinos by the acoustic technique it is necessary to understand the production, propagation and detection of the acoustic signal from the shower induced by an interacting neutrino in a medium. This has been treated in some detail in [13], however, in this treatment it is difficult to incorporate the true attenuation of the sound which has been found to be complex in nature [14] in media such as sea water. Such complex attenuation causes dispersion of the acoustic signal and complicates both the propagation of the sound through the water and the signal shape at the detectors. This paper is organised as follows. In section 2 the new approach to calculating the acoustic signal pressure is described and section 3 describes the methods used to model the attenuation of the sound as it propagates through the medium. Section 4 describes the detailed calculations of the sound signal in water and in ice as it arrives at the detector starting from the shower simulations described in [15]. Finally a new method of simulating signals incorporating shower-to-shower fluctuations is described in Section 5.
The standard equations used to determine the thermo-acoustic integrals are outlined in [13]. In this paper we use a complementary approach.
For the thermo-acoustic mechanism even though it is the pressure, p, that is detected it is the volume change, Q s , which couples to the velocity potential, Φ, which in turn creates the sound wave. 2 Interestingly, the velocity potential as a concept precedes the magnetic vector potential by over 100 years and was introduced by Euler in 1752 [17].
Three of the most important variables in acoustics are the pressure change from equilibrium, p, the particle velocity, v, and the velocity potential, Φ. Assuming zero curl these three variables are related by:
where ρ is the density. For sources of acoustic energy this velocity potential has a function in acoustics equivalent to the magnetic vector potential in electromagnetism. We are trying to solced the wave equation to get the pressure pulse at the location of an observer placed at |r|. This can be dome by integrating all the contributions of infinitessimally small sources at locations |r |.
For an observer at r and a shower event at r separated by a distance r = |r -r |:
where q s is the time rate of change of an infinitesimal volume and c the velocity of sound. In our case we are interested in integrating q s over the cascade volume where this volume change is caused by the injection of an energy density E (in J.m -3 .s -1 ) over this cascade volume. For an infinitesimal volume the volume change starting at time t = 0, is given by:
where β the thermal expansion coefficient, C p the specific heat capacity, ρ the density and τ the thermal time constant. The integral term is caused by cooling as the deposited energy, within the volume, conducts or convects away into the surrounding fluid. However as the time constant for this thermal cooling mechanism is of the order of tens of milliseconds [19], and as we are primarily interested in the case where the energy is injected nearly instantaneously in acoustic
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