30TH INTERNATIONAL COSMIC RAY CONFERENCE

The Lunar Cherenkov Technique: From Parkes Onwards

C. W. JAMES1, R. D. EKERS2, R. MCFADDEN3, R. J. PROTHEROE1

1 School of Chemistry & Physics, Univ. of Adelaide, SA, Australia2Australia Telescope National Facility, Epping, NSW, Australia3 University of Melbourne, Vic., Australiaclancy.james@adelaide.edu.au

Abstract: The lunar Cherenkov technique, which aims to detect the coherent Cherenkov radiation pro-duced when UHE particles interact in the lunar regolith, wasfirst attempted with the Parkes radio-telescope in 1995, though the theory was not sufficiently developed at this time to calculate a limit onthe UHE neutrino flux from the non-observation. Since then, the technique has evolved to include ex-periments utilising lower frequencies, wider bandwidths,and entire arrays of antenna. We develop asimulation to analyse the full range of experiments, and calculate the UHE neutrino flux limit from theParkes experiment, including the directional dependence.Our results suggest a methodology for planningfuture observations, and demonstrate how to utilise all available information on the nature of radio pulsesfrom the Moon for the detection of UHE particles.

Introduction

The lunar Cherenkov technique aims to detectultra-high energy (UHE:>EeV) cosmic rays andneutrinos via the coherent Cherenkov radiationemitted in the radio regime by their interactionsin the outer layers of the Moon. The radiationis detected via ground-based radio-telescopes, asfirst proposed by Dagkesamanskii & Zheleznykh[1] and attempted at Parkes [2], with an experimentat Goldstone calculating the first limits on an UHEparticle flux [3].

The use of existing radio-telescopes means thatthe choice of observational parameters such as fre-quency, bandwidth, and length of run has beenlimited. A ‘next-generation’ radio-array, the SKA(Square Kilometre Array, [4]), is currently in theplanning stages, providing a unique opportunityto optimise a powerful instrument for this techn-qiue. While current efforts aim to detect a singleCherenkov pulse, the ultimate goal is to determinethe source and flux of the highest energy cosmicrays and neutrinos. Here, we propose how obser-vations might be tailored to achieve this, by exam-ining the frequency- and directional-dependenceof

the sensitivity of these experiments to UHE neutri-nos.

The first attempts at the technique all observedat frequencies above1 GHz, with large anten-nas using beam sizes with FWHM equal to orsmaller than the Moon’s apparent diameter of0.5◦.The SKA and other future experiments will likelyutilise smaller antennas observing over lower fre-quencies for which the entire Moon will be covereduniformly by each individual beam. Frequency andbeam-size determine much of the phenomenology,and we use results for Parkes and the SKA as repre-sentative of prior and planned experiments respec-tively.

Simulations

The program used to simulate the lunar Cherenkovtechnique was a Monte Carlo code described in[5]. This code, like previous simulations, only in-cluded a single layer in which detectable UHE par-ticle interactions were allowed. However, as the re-golith properties are expected to reflect that of theunderlying material, we modified the code to al-low UHE neutrino interactions in the sub-regolithlayer, modelled with density3 g/cm3. This layer

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was treated simply as denser regolith, with refrac-tive indexn and absorption lengthℓ scaled by den-sity as per [6] ton = 2.5 andℓ = 29 λ.

The effect of including only the classical regolithwas to artificially limit the aperture to neutrinos ofenergies sufficiently large that interactions at thebase of this (typically10 m deep) layer were be-ing readily detected, especially at low frequencies,where attenuation within the regolith is minimal.Including two layers is more appropriate than ex-tending a single layer to greater depths, since someradiation losses are to be expected during the trans-mission of radio-waves from the underlying ma-terial (be it lava flows in the mare or ungardenedmegaregolith in the highlands) to the regolith.

The parameters used to simulate the Parkes exper-iment are described in [5]. For the SKA, we use aneffective collecting area ofAeff = 1km2, and sys-tem temperatureTsys = 50◦ K, and assume uniformcoverage of the Moon over all frequencies. Detec-tion required an integrated signal strength in V/mover the full bandwidth of8 times the RMS noisevoltage.

Results – Frequency Dependence

The first lunar Cherenkov experiments observed atfrequencies in the> 1 GHz range, as the powerradiated at the Cherenkov angle scales withν2 un-til the turnover frequency (2.3 GHz in the regolith[7]), above which decoherence effects from withinthe particle cascade become important. Recently,focus has been on observations at lower frequen-cies, as proposed by [8]. At low frequencies, theCherenkov cone is broader, and the radiation suf-fers less attenuation in propagating to the surface,allowing signals from a wider range of interactiongeometries at greater depths in the regolith to bedetected. For a simulated experiment with LO-FAR, assuming a bandwidth of20 MHz, [8] foundan optimum frequency range in the115−240 MHzband, below which (in the30 − 80 MHz band) theeffect of increasing sky temperature on sensitivitybecame significant.

High-frequency experiments have a lower energydetection threshold, since the signal from geomet-rically favourable events peaks in the GHz regime.How this impacts upon event rates depends on theshape of the UHE particle spectrum, and the aper-

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Figure 1: SpectraE(ν) of four different particle in-teractions as viewed from Earth. The three parameters(E, d, θ) give interaction energy, depth (m), and view-ing angle from the Cherenkov angle respectively.

ture at these energies. A better argument to notlimit observations to low frequencies only is thatto perform true UHE particle astronomy, the type,energy, and arrival direction of any detected parti-cles will need to be determined. The sensitivity ofthe high frequency component to interaction geom-etry means it could be used to resolve ambiguitiesbetween interaction energy, interaction depth, andorientation of the shower axis with respect to theobserver, which would likely remain unresolved inan experiment with a low frequency range.

The range of spectra plotted in Fig. 1 shows thedilemma. To detect the full range of events, it willbe essential to observe across the entire frequencyrange. However, any single choice of bandwidthover which to trigger results in reduced sensitivityto some fraction of events, since noise from the fre-quency range over which the signal is weakest willforce a higher detection threshold.

We run our simulation for the range of frequenciesfrom 100 MHz to 2 GHz, using bandwidths set ata fixed fraction (30%) of the central frequency, re-flecting that instruments designed to observed athigher frequencies tend to have a higher availablebandwidth. The results, together with the recalcu-lated Parkes aperture, is shown in Fig. 2.

Our results are in agreement with that of [8]. Wefind that for neutrino energies> 1021 eV (i.e.well above threshold), and frequencies between140 MHz and 1 GHz, the total effective aper-ture varies approximately asν−3. For neutrinos

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Figure 2:Calculated aperture to UHE neutrinos of theSKA observing at various frequencies. Also shown isthe Parkes aperture both with (this paper) and without([5]) sub-regolith layers included.

of energy less than an order of magnitude abovethe detection threshold, high frequency observa-tions have the greatest sensitivity, though above500 MHz the apertures are almost identical.

Results – Directional Sensitivity

Including geometrical tags in the simulation allowsthe sensitivity to be determined as a function ofparticle arrival direction, relative to the lunar cen-ter and beam pointing position . Fig. 3 shows theinstantaneous aperture of the Parkes experiment inlimb-pointing configuration. Note that the Moonshadows an area much larger than its apparent sizeof 0.5◦, and the total fraction of the sky seen at anyone instant is small. We calculate the directional-ity, defined here to be the peak aperture (of84 km2)over the mean integrated aperture (38 km2 sr/4π sr= 3 km2), to be28; should a point-like neutrino-source be suspected/discovered, a careful choiceof observation times and beam pointing positionswould enable a much stronger limit to be placed.

When applied to experiments such as LOFAR andthe SKA, with the Moon illuminated uniformly, thesensitivity forms an annulus around the Moon, asshown in Fig. 4. Similar results would be obtainedby placing multiple smaller beams around the limbof the Moon, as might be achieved with a focalplane array. Unlike the total aperture, the direc-tional properties vary slowly with observation fre-quency, with the annular sensitivity increasing inwidth with reduced frequency. An important re-

Figure 3: Directional sensitivity of the Parkes experi-ment to1022 eV neutrinos in limb-pointing mode. TheMoon is at(0, 0), beam centre at(0.5◦, 0).

Figure 4: Normalised instantaneous aperture (relativeunits) of a nominal SKA (see text) observing from100−150 MHz to 1021 eV neutrinos. The plot is over theentire sky, with the Moon at the centre.

sult is that for energies well above threshold, theaperture to all arrival directions is greater at lowfrequencies.

Fig. 5 compares the directional sensitivity to1022 eV neutrinos of the SKA (bandwidth from300 MHz to 1 GHz) and ANITA, for which99% ofthe neutrino aperture over the duration of one po-lar orbit is contained within declinations between−10◦ and +15◦ [9]. To account for improvedsensitivity of ANITA with time, we normalise theSKA aperture to give the same isotropic sensitiv-ity as ANITA. Evidently, there exists a significantoverlap between the nominal ANITA and SKA

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Figure 5:Combined directional sensitivity to1022 eVneutrinos in celestial coordinates of a0.3− 1 GHz SKAand ANITA, scaled to have equal isotropic apertures. Weassume a uniform ANITA aperture between−10◦ <δ < +15◦. Also shown is the galactic plane (thin blackline), supergalactic plane (thin white line), lunar orbit(thick black line), and the positions of some AGN, usedas proxies for point-like UHE neutrino sources.

apertures, and large regions to which neither ex-periment is sensitive.

Discussion

The highly directional sensitivity of the Parkes ex-periments suggests that current limits on the UHEneutrino flux are a strong function of celestialcoordinates. The current strongest limits on anisotropic flux below1023 eV come from ANITA-lite [10], which had little sensitivity beyond15◦

from zero declination. Limits from other lunarCherenkov experiments observing at higher fre-quencies at Goldstone [3] and Kalyazin [11] willbe more directional than those at Parkes, and thuslarge areas of the sky would still be left unprobed.This leaves ample scope for experiments with dif-ferent directional sensitivities to make useful ob-servations to further constrain the UHE neutrinoflux.

The future of the lunar Cherenkov technique as ameans to determine the flux of the highest energycosmic rays and neutrinos hinges on the ability toturn positive detections into useful information onparticle energy and arrival direction. This requirestaking full advantage of the wide frequency rangeavailable to instruments such as the SKA, and willlikely require multiple detection algorithms, opti-mised for various pulse spectra, to be used in par-

allel. The optimisation must take into account thesteepness and degree of anisotropy in the (knownor expected) UHE particle flux, as well as the sen-sitivites of other experiments. The already highsignal processing requirements of de-dispersionand sub-nanosecond time resolution over a largearray will make further innovation in pulse detec-tion technology a necessity.

Conclusion

We have found the lunar Cherenkov technique tobe highly directionally sensitive, especially at highfrequencies. We have also demonstrated that ob-servations over a broad frequency range with theSKA will be a very powerful technique for UHEparticle astronomy. With further improvementsin simulation methods, and knowledge of the lu-nar near-surface, it will be possible to devise ad-vanced pulse detection and reconstruction algo-rithms, based on the methodology presented here.

Acknowledgements

This research was supported under the AustralianResearch Council’s Discovery funding scheme(project # DP0559991). Professor R. D. Ekers isthe recipient of an Australian Research CouncilFederation Fellowship (project # FF0345330).

References

[1] R. D. Dagkesamanskii, & I. M. Zheleznykh, Sov.Phys. JETP Let., 50, 233, 1989.

[2] T. H. Hankins, R. D. Ekers, J. D. O’Sullivan MN-RAS, 283, 1027, 1996.

[3] Gorham P. W. et al., Phys. Rev. Lett., 93, 041101,2004

[4] Y. Terzian and J. Lazio. In L. M. Stepp, ed,Ground-based and Airborne Telescopes. Proc. ofthe SPIE, 6267, 2006.

[5] C. W. James et al. astro-ph/0702619, 2007.[6] G. R. Olhoeft & D. W. Strangway.

Earth and Planetary Sci. Lett. , 24, 394, 1975.[7] J. Alvarez-Muniz, Phys. Rev. D, 74, 2, 023007,

2006[8] O. Scholten et al. Astropart. Phys. , 26, 219, 2006.[9] P. Miocinovic et al., astro-ph/0503304 v1, 2005

[10] S. Barwick et al., Phys. Rev. Lett., 96, 171101,2006

[11] A. R. Beresnyak et al., Astronomy Reports, 49,127, 2005

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