ISSN 1068-3356, Bulletin of the Lebedev Physics Institute, 2014, Vol. 41, No. 4, pp. 110–114. c© Allerton Press, Inc., 2014.Original Russian Text c© G.A. Gusev, Kyaw Maung, 2014, published in Kratkie Soobshcheniya po Fizike, 2014, Vol. 41, No. 4, pp. 37–43.

Is it Possible to Determine the Chemical Compositionof Cosmic Rays in the “LORD” Lunar Experiment?

G. A. Gusev and Kyaw MaungLebedev Physical Institute, Russian Academy of Sciences,

Leninskii pr. 53, Moscow, 119991 Russia; e-mail: gusevgag@mail.ruReceived November 13, 2013

Abstract—The results of the simulation of cascade radio emission from ultrahigh-energy cosmicrays in the LORD lunar experiment using circularly polarized antennas are presented. It is shownthat based on the characteristics of radio emission caused by cascades from protons and iron nucleiin lunar regolith and escaped into vacuum it is impossible to distinguish these cascades in theprimary energy region above 1020 eV.

DOI: 10.3103/S1068335614040058

Keywords: cascade, cosmic rays, chemical composition, Cherenkov radiation, ultrahigh energies,neutrino, lunar regolith.

Currently, the radio method for measuring ultrahigh-energy cosmic rays and neutrino (UHECR andUHEN) is rather actively developed (see, e.g., [1]). One of the interesting possibilities is to use the Moonas a target for detecting cosmic particles by a radio method using orbital radio wave telescopes [2, 3]. Inthe not distant future, the “LORD” (Lunar Orbital Radio Detector) experiment [2, 3] is planned, whichwill make it possible to estimate for the first time the capability of new space technologies in comparisonwith the capability of large ground-based installations. Currently, practical equipment for the “LORD”experiment is developed and designed, whose main parameters important for simulation are already fixedin the context of the complex “LUNA GLOBE” orbital project.

In [4], it was shown that the position of the extensive air shower (EAS) maximum can be determinedby radio signals with certain accuracy, so that to distinguish EASs produced by protons and heaviernuclei by this parameter. It is natural to pose this question under conditions of the “LORD” experimentas well, to which the present study is devoted. Certainly, in the first stage of this experiment we willhave too limited information about the cascade radio emission to confidently consider the possibilityof distinguishing cascades from protons and, e.g., iron nuclei; nevertheless, it seems interesting toestimate the possibility of this approach within simulation of the direct problem of cascade radio wavemeasurements.

Monte Carlo simulation of the “LORD” experiment was performed in [5, 6]. In particular, in [6], theformulas are presented which allow Monte Carlo simulation of particle detection, taking into accountactual directional patterns (DP), radio wave polarization and polarization of linearly polarized antennas,and galactic noise arrival at DP side lobes. This allows tracing the main features of the actual detectorresponse to Cherenkov radiation, without regard to which the solution of the multiparametric inverseproblem of the particle energy reconstruction will contain systematic errors. At the same time, this isnecessary for optimal choice of the equipment parameters under practical experimental conditions.

According to the considerations of [6], in this study, we perform new numerical simulation for abroadband circularly polarized log-periodic spiral antenna which will be actually used in the experiment.This became possible, since development and design of the “LORD” equipment are currently close tothe end. The choice of the circular, rather than linear, polarization of the antenna [6] is caused by thesignal triggering features, the requirement of radiation measurement stability, as well as by the designconstraints of the used spacecraft. One more advantage of such antennas is the independence of themeasured signal amplitude in both channels of its linear polarization. This is because the amplitudesof the left- and right-polarized components are

√2 times lower than the signal magnitude and are

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IS IT POSSIBLE TO DETERMINE THE CHEMICAL COMPOSITION 111

controlled only by the antenna DP. This does cause the trigger stability, in contrast to the trigger withlinearly polarized antennas.

Detection thresholds for the radiation field are chosen at the level of 4σ, where σ is the root-mean-square amplitude of the total thermal noise of the system, which includes receiver temperature Tr (mostlythe antenna preamplifier noise) and the effective antenna temperature Tan (taking into account its DP)which, in turn, includes thermal emission of the lunar surface, galactic noise [7], and solar radio emission[8]. For the galactic noise, we chose two versions, i.e., the high and low noises according to [6].

According to the Monte Carlo calculations of radio emission of electromagnetic and hadron cascades[2, 3, 5, 6], the frequency-angular dependence of the Fourier component of the radiation field strengthEf in a dense medium near the Cherenkov angle θC (where the most part of radiation is concentrated)can be approximated by the expression

Ef (θs, ϕn, θn,W ) = 0.5NormWf

f0

exp[−α(W )(cos θC − cos θ)2][1 + (f/f0)1.44]

Ts

Rs

sin θ

sin θC, μV/m/MHz, (1)

where

Norm ≈ 0.232(μV/TeV/MHz), f0 ≈ 3.3GHz, α(W ) = f2(GHz) × [70 + 3.3 ln(W (TeV))].

Ts(θs) =2 cos θt

n cos θt + cos θi; Rs(θs) = (RM ± h)

√(1 + cos2 θM − 2 cos θM cos θs),

sin θt = sin θs(RM + h)/Rs(θs); sin θt = n sin θi; cos θ = − cos θn cos θi + sin θn sin θi cos ϕn. (2)

Here W is the primary particle energy, Rs(θs) is the distance from the detector (at the height h) tothe surface point, Ts(θs) is the radiation transmittance during surface crossing, and θi and θt are theincidence and refraction angles of radio waves on the surface. The angles θi, θt, θ are expressed in termsof θs, ϕn, θn using relations (2), where θ is the angle between the normal from the satellite onto the lunarsurface and the radius directed from the Moon center to the cascade point, θn is the angle between thenormal to the lunar surface and the primary particle velocity, and ϕn is the cascade azimuth.

In the “LORD” experiment, the measurement frequency band of 200–400 MHz is chosen. For log-periodic spirals, the DP is only approximately independent of frequency in this band; therefore, we tookthe DP of the front lobe averaged over several frequencies and approximated it by the least-squaresmethod, having found it in the form of the following simple analytical function (in the case at hand of theantenna orientation along the local vertical) of the nadir angle θnad

f(θnad) = cos3.4(θnad). (3)

Further, to obtain the total signal field in the measurement band, expression (1) should be integratedover the registration frequency f , taking into account the main exponential frequency dependence ofthe integrand expression and taking, according to the mean value theorem, for the weak frequencydependence of the denominator in formula (1), the average frequency in the frequency range.Then theintegration can be performed analytically.

Using the obtained expression for the electric field, the electric field of Cherenkov radio emission forfour energies 1020, 3 · 1020, 6 · 1020, and 1021 eV for protons and iron nuclei is calculated. We believethat the cascade from iron nuclei can be considered as a set of 56 cascades from nucleons with anenergy lower by a factor of 56 than the energy of the primary proton cascade. First, we calculate thesignal amplitude in the case of protons and iron nuclei for fixed angles of particle incidence, the tilt angleθn = 90◦ and the azimuth angle ϕn = 0◦, as a function of the angle θs, when the signal amplitude ismaximum. Then, at each of the above cascade energies, for a given orbit altitude, and a chosen detectionthreshold of 100 μV, we find such an angle θs at which the difference between proton and iron nucleussignal amplitudes is maximum (under the condition that the detection threshold is exceeded). Usingthese values, we construct the dependences of the signal amplitude on the incident particle (cascade)energy for the proton and iron in the indicated energy range. The calculation is performed for lunarsatellite orbit altitudes of 500 and 1000 km from the lunar surface.

The result is shown in Fig. 1, where we can see that the difference between electric fields for cascadesfrom protons and iron in magnitudes increases with energy, whereas the relative difference decreases.

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Fig. 1. Dependences of the signal field amplitudes for the cascades from proton and iron nucleus on the primary nucleusenergy for incidence angles θn = 90◦, ϕn = 0◦, the satellite altitude of 500 km, and the reception frequency band of200–400 MHz.

Fig. 2. Dependences of the signal field amplitudes for the cascades from proton and iron nucleus on the primary nucleusenergy for incidence angles θn = 85◦, ϕn = 20◦, the satellite altitude of 500 km, and reception band of 200–400 MHz.

The same calculation was performed for the angles of primary particle incidence θn = 85◦, ϕn = 20◦;the result is shown in Fig. 2.

A comparison of the figures shows that the conditions for distinguishing protons and iron nuclei areimproved with decreasing the tilt θn and azimuth ϕn angles. The relative difference of proton and ironnucleus signal amplitude is ∼15% (Fig. 1) at an energy of 6 · 1020 eV; Fig. 2 for this energy shows a 45%increment of the iron nucleus signal amplitude in comparison with protons. At even larger deviations ofangles θn and ϕn from 90◦ and 0◦, the relative signal amplitude increment will be even larger. However,the signal itself significantly decreases in this case; hence, this unlikely can be used in practice, sincethis effect can be implemented only for the highest energies where statistics is small. As a result, wecan conclude that the case of particle incidence angles when the tilt angle is θn = 90◦ and the azimuthangle is ϕn = 0◦ is least favorable fir analyzing the UHECR chemical composition, although the signalamplitude for such directions of primary particle arrival is maximum.

To complete the picture, the dependence of these results on the measurement frequency band shouldbe considered. Precisely, we also consider the frequency band of 500–800 MHz for the case of particleincidence angles corresponding to the incidence angles in Fig. 1. In this frequency range, the DP of theantenna under study slightly differs from the DP in the frequency range of 200–400 MHz and can be

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Fig. 3. Dependences of the signal field amplitudes for the cascades from proton and iron nucleus on the primary nucleusenergy for incidence angles θn = 90◦, ϕn = 0◦, the satellite altitude of 500 km, and the reception frequency band of500–800 MHz.

approximately presented by the following simple function of the nadir angle θnad,

f(θnad) = cos2.5(θnad). (4)

The DP defined by formula (4) in the frequency band of 500–800 MHz is somewhat wider than theDP in the band of 200–400 MHz, which slightly increases the angular aperture of measurements. Theresult calculated for a slightly wider band of 500–800 MHz, in a higher-frequency range, for an orbitaltitude of 500 km and a detection threshold of 100 μV, is shown in Fig. 3. We can see that the resultfor this frequency range is almost the same, which is not a priori obvious. We note that the detectionsensitivity in this frequency range is higher, and the used threshold can be lower, since galactic and solarnoises in this range are lower.

Thus, the performed simulation shows that it is impossible to determine the UHECR chemicalcomposition in the “LORD” experiment, since the difference between the signal amplitudes for protonand iron nucleus cascades is very small and requires a high accuracy of determining the signal amplitude,unattainable for the planned “LORD” experiment. It should be noted that the solution of the inverseproblem of the energy reconstruction in the conditions of the “Lord” experiment with accuracy of 50–100% should be considered as quite successful, although hardly achievable under conditions of highfluctuations at low expected statistics. It is clear that such an accuracy is insufficient for determining theUHECR chemical composition by the proposed method. At the same time, it should be considered thatthe actual statistics of events in the case of the prevalence of iron nuclei in the UHECR spectrum shouldsubstantially exceed the statistics of events in the case of the prevalence of protons. This excess canreach 100%, which increases the detection probability of limiting detectable UHECR energies. Thus,the prevalence of heavy nuclei in the UHECR spectrum increases the chance of observation of primaryparticles with extremely high energies in comparison with the case of the prevalence of protons.

ACKNOWLEDGMENTS

This study was supported in part by the program of the Presidium of the Russian Academy ofSciences “Fundamental Properties of Matter and Astrophysics”.

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