Interaction of Cosmic Ray Showers with Material

Most of the energy and momentum of the primary cosmic ray particle ends in some form of ionisation, or the photo-electric effect for the photon component. The rate of energy loss is most significant for the relatively low energy electromagnetic component and least significant for the muons which, unless they have very high energies, lose energy only by ionisation.

The primary cosmic ray particle has a mean free path of up to 100gcm and loses roughly half of its energy at each interaction. As a result, to a first approximation, the primary energy is degraded by 1000 times in reaching sea level. Individual charged shower particles will typically lose energy by ionisation at a rate of about 2MeV/gcm but may have other energy loss processes.

In considering noise processes for gravitational wave antennas, current sensitivity limits require that we examine processes which can deposit energy (or momentum) at the level of hundreds of GeV at rates of at least one per year. This means that we may have to consider the possibility of occasional rare energy deposition mechanisms. The likely processes seem to be associated with hadronic cores or extremely energetic muons.

Hadronic cores

The hadronic core of the shower carries energy through energetic nuclear-active particles. As such, the core is readily detectable using conventional and inexpensive particle detectors and veto techniques for a small event flux in the energy range of interest should be straightforward. If we consider the core energy to be degraded by about 1000 times in traversing the atmosphere, we can see that, if we require at least 100GeV of deposited energy, we need to be considering primary particles with energies above 100TeV. Such primaries arrive with a frequency of about ten per day over the roughly one square metre of resonant bar area. At a more extreme level, we would expect a core energy of about 10TeV once per year. Roughly half of the 10TeV will be in the remaining central particle and one might expect to see a core with 50000 particles about once per year. This is indeed what is found.

Core hadrons are energetic and are thus rather penetrating. They will lose a substantial fraction, but not all, of their energy in traversing a few tens of gcm of gravitational detector. From the measured spectrum of charged hadrons (Allkofer and Grieder 1984) we conclude that a once a year hadron impulse on a gravitational detector will deposit about 1TeV of energy and the rate of impulses of smaller magnitude will increase roughly as an inverse power law with an index of about 2.0. Such impulses may well be detectable as noise in the antenna. Particles in the shower core are penetrating and substantial particle energy will be readily detectable above or below (or both) the antenna using conventional particle detectors.

High Energy Muons

EAS have muons as one of their significant components and the majority of the overall cosmic ray background consists of unaccompanied muons. These arrive at sea level at a rate of about one per square cm per minute (or some tens of particles per second through a typical modestly sized component part of a gravitational detection system). Clearly, rates such as this cannot be vetoed for systems which have bandwidths only up to the kHz range.

Air shower muons have characteristic energies in the GeV range and so typical individual muons will not be a major gravitational noise problem. However, it is possible that Fourier components may exist in the random arrival distribution which correspond to the resonant frequency of the gravitational system or a very rare energetic muon may deposit a large fraction of its energy in the antenna. The former problem has been discussed by Giazotto (1988) and appears to be unimportant. Based on Monte Carlo simulations, rather more discussion of the latter problem has appeared in the literature and it is worth identifying the basis for this noise mechanism.

Muons result from the decay of pions which are produced when core shower particles (most likely the degraded incident particle) interact with atmospheric nuclei. The resulting muon energy spectrum will then be related to the primary energy spectrum in its structure but will be somewhat steeper due to a deficiency in muons at the highest energies. This is because the number of pions produced in an interaction rises somewhat with energy and hence the relative energy per pion (and the resulting muon) drops. Also, due to time dilation, the pions have a longer lifetime at higher energies and are less likely to decay and produce muons before they interact. Again, the result is a reduction in the possible number of high energy muons.

We now need to see how often a muon of sufficient energy to produce a significant noise pulse will pass through the detector and then determine how often such a muon will interact close to the detector and actually deposit energy. If we remember that perhaps half of the incident energy is retained by the primary particle and the rest is distributed between the pions (albeit non-uniformly) we might identify perhaps 20% of the incident energy going to the most energetic (and most important from our point of view) muon. Also, at a fixed primary energy, the cosmic ray nuclei have a mixed composition and, if we are concentrating on high energy muons, we are only interested in the proton primary component. This is because other, more complex, nuclei will produce more, but lower energy, muons. If we take shower primaries with an energy of 1TeV, we can say that the flux of muons produced with energies above 0.2TeV is about per square metre per year. As we noted earlier, an energy deposition of this order is capable of producing significant noise in presently proposed antennas.

Muons generally lose energy by ionisation. However, at energies above a few hundred GeV (i.e. our selected energy and above), pair production, bremsstrahlung and photonuclear interactions result in large energy loss events. We need to consider the probability of such an event occurring in the gravitational detector for a muon of this energy noting that already, by selecting these energetic muons, we are examining only one muon in 30,000.

The scale factor for energy deposition with these large energy processes is about gcm in rock, which we will take as a worst case (hydrogen is perhaps ten times greater). If the gravitational detector has an absorption thickness of 10 to 100gcm we would thus estimate that there is a probability of about one in of our muon interacting in this way in the detector. We are now looking at about 1000 potential events per year per square metre.

The question now is how much energy will actually be deposited in the gravitational detector. The detector will absorb some of the energy but, with a limited thickness and typical ionisation loss rates of charged secondaries of 2MeV per gcm or a few hundred MeV per particle per detector thickness, a significant fraction will leak out. The leaking energy could easily be used for a veto through the use of a large-area detector placed below the antenna structure. The signature of such a muon-initiated event would be a large detector signal resulting from the cascading of secondary particles in the antenna and its housing. It need not be accompanied by a signal in other detectors. If we assume 10% absorption, then to get an energy deposition of 0.2TeV, we are looking at a rate of about 1 to 10 events per detector per year.

We thus conclude that, for presently proposed antennas, shower cores or the effects of secondary particles from the interaction of single high energy muons will provide noise pulses at a rate of about a few per year but these pulses will almost certainly be accompanied by detectable signals in a local veto particle detector. These noise pulses should be detectable and could be used as a test of the true antenna sensitivity after a detailed calculation with the known antenna characteristics.

© Copyright Astronomical Society of Australia 1997