Study of high energy cosmic rays by different components of back scattered radiation

generated in the lunar regolith

N. N. Kalmykov1, A. A. Konstantinov1, R. A. Mukhamedshin2, D. M. Podorozhnyi1, L. G. Sveshnikova1,

A. N. Turundaevskiy1, L. G. Tkachev3, A. P. Chubenko4

1Scobel’tsyn Research Institute of Nuclear Physics, Moscow State University, Moscow, Russia 2 Institute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia3Joint Institute for Nuclear Research, Dubna, Russia4Lebedev Physical Institute, Russian Academy of Sciences, Moscow, Russia

Possible experiments aimed at studying the primary cosmic rays on the Moon’s surface considered. Monte-Carlo simulation was used. Three components (secondary neutrons, gamma rays, and radio waves) of back scattered radiation can be simultaneously registered. These components of radiation are generated by showers developing in the lunar regolith. Primary particle parameters can be reconstructed.

The chemical composition of PCRs must be studied to discover the origin of peculiarities in the PCR energy spectrum, investigate the ratio of

secondary_to_primary nuclei in the high energy range, and search for exotic particles.

The Moon surface

We analyze using three components to measure the parameters of PCR particles incident on the lunar surface: secondary neutrons, gamma quanta (particles of back current), and radio waves. The signals for each component are evaluated using a Monte Carlo (MC) simulation of showers.

Neutron albedo

Neutron background is for 600 μs. 100 (solid) and 8 (dashed) m2 registration area.

It was found during simulations that for PCR particles incident at angles of ~ 50° to the vertical, the total number of neutrons reaching the surface is ~104 at 100 TeV, or approximately 10% of the total number of neutrons generated in the regolith.

Neutron energy spectra (protons, helium, iron)

We considered energy spectra (in figure), fluctuations and spatial characteristics of a neutron spot on the Moon’s surface. It was found that at PCR energies E0 ~ 1014 eV, the fluctuations in the neutron flux of primary nuclei are ~20% for the case of iron and ~30% for carbon, while for protons they are ~70%. The last effect is due to the higher penetrability of protons.

Albedo of gamma-rays

• Many secondary particles are generated by showers in matter. The part of these particles is emitted at big angles relative to the primary particle direction. The gamma quanta contribution into back current is sufficient due to decay of low energy secondary neutral pions.

• We considered primary protons with energies of 1012 to 1015 eV to estimate the albedo gamma ray yield. By means of MC simulation (using the GEANTcode) we studied some characteristics of back scattered particles (with energies >15 keV) included the total number of albedo gamma quanta ng and their spatial distribution.

• The main part of albedo gamma quanta is concentrated is some meters area near the track of the primary particle.

Gamma albedo spatial distribution (all trajectories). The background is shown for 100

(solid) and 10 (dashed) μs registration

Albedo gamma quanta energy spectra

Gamma albedo energy dependence. The background is shown for 100 (solid) and 10

(dashed) μs registration

The total back current depends on the angle of the cascade axis’s inclination θ, which can be determined using the asymmetry of the back scattered particles spatial

distribution. This distribution is more asymmetrical for large inclination angles. We used as asymmetry parameter the ratio of spatial distribution dispersions Rct=σ2(Xl)/σ2(Xt) .

Here Xl , Xt are longitudinal and transverse axes of dispersion ellipse. The cosθ asymmetry dependence is close to logarithmical cosθ=0.505 log(7.25/Rct). The RMS

errors of cosθ are equal 0.16 at 1013 eV and 0.12 at 1015 eV.

We used total number of back scattered gamma quanta and asymmetry data to reconstruct primary particles energies. As energy E increases, the error of its

determination decreases from ~200% (at E~1012 eV) to ~100% (at E~1014 –1015 eV).

Albedo of radio emission

MC simulations were conducted for different showers (using the GEANT code). The field of radio emission was calculated from every particle of the shower. The radio wave absorption and refraction in the regolith were taken into account. Refraction factor n was set at 1.7 for density ρ=1.7 g/cm3, and was scaled for other values according to the Clausius–Mossotti formula.

Frequency spectrum of the field intensity of radio waves (total field) (proton, 1013 eV) at different angles of observation θ (θ=60° corresponds to the

Cherenkov angle).

As can be seen, frequencies ≈1–10 GHz are the best for

observations. These frequencies can be used for energy

measurements.

Spatial distribution of radio emission

We took into account the absorption and refraction of radio waves and their reflection from regolith layers of different densities. Only in inclined showers the emission from a Cherenkov peak can emerge from the regolith into the vacuum of space. For vertical showers total reflection diminishes radio emission. At the top layer of regolith the total reflection angle is equal to θR=35°. The Cherenkov angle is equal to θC=55°. Thus a Cherenkov peak registration can be used only for showers with zenith angle θ> θC- θR=20°.

The reconstructed energy distribution (proton, 1013 eV)For a Cherenkov peak the energy dependence of the intensity of the

radio emission field is close to linear:

Eνmax9·10–5(E0/1 TeV)1.03

μV/m·MHz (at 45°). This dependence can be used to

reconstruct primary energy. The RMS errors are equal to 30% (at

1012 eV), 20% (at 1013 eV), 15% (at 1014 eV).

If we assume that the noise level is 1 μV m–1 MHz–1 at 1 GHz, then the lower threshold of radio emission

field recording is ~1016-1017 eV; it is more efficient to arrange the receiving antennas above the ionization neutron calorimeter.

Conclusion

Our simulations demonstrate the feasibility to registrate PCR particles in three components (neutrons, gamma rays, and radio waves) of the back current from showers developing in the lunar regolith. The lower thresholds for recording the PCR particles is ~1014 eV (for gamma albedo), ~1016 eV (for radio emission), and the error of primary energy determination is sufficiently low to reconstruct primary energy spectra.