The Small Contribution of Molecular Bremsstrahlung Radiation to the Air-Fluorescence Yield of Cosmic Ray Shower Particles

A small contribution of molecular Bremsstrahlung radiation to the air-fluorescence yield in the UV range is estimated based on an approach previously developed in the framework of the radio-detection of showers in the gigahertz frequency range. First, this approach is shown to provide an estimate of the main contribution of the fluorescence yield due to the de-excitation of the C $^3\Pi_{\mathrm{u}}$ electronic level of nitrogen molecules to the B $^3\Pi_{\mathrm{g}}$ one amounting to $Y_{[337]}=(6.05\pm 1.50)~$ MeV$^{-1}$ at 800 hPa pressure and 293 K temperature conditions, which compares well to previous dedicated works and to experimental results. Then, under the same pressure and temperature conditions, the fluorescence yield induced by molecular Bremsstrahlung radiation is found to be $Y_{[330-400]}^{\mathrm{MBR}}=0.10~$ MeV$^{-1}$ in the wavelength range of interest for the air-fluorescence detectors used to detect extensive air showers induced in the atmosphere by ultra-high energy cosmic rays. This means that out of $\simeq 175~$ photons with wavelength between 330 and 400 nm detected by fluorescence detectors, one of them has been produced by molecular Bremsstrahlung radiation. Although small, this contribution is not negligible in regards to the total budget of systematic uncertainties when considering the absolute energy scale of fluorescence detectors.Comment: 9 pages, 2 figures, accepted for publication in Astropart. Phys. arXiv admin note: text overlap with arXiv:1601.0055

An Estimate of the Spectral Intensity Expected from the Molecular Bremsstrahlung Radiation in Extensive Air Showers

A detection technique of ultra-high energy cosmic rays, complementary to the fluorescence technique, would be the use of the molecular Bremsstrahlung radiation emitted by low-energy electrons left after the passage of the showers in the atmosphere. The emission mechanism is expected from quasi-elastic collisions of electrons produced in the shower by the ionisation of the molecules in the atmosphere. In this article, a detailed calculation of the spectral intensity of photons at ground level originating from the transitions between unquantised energy states of free ionisation electrons is presented. In the absence of absorption of the emitted photons in the plasma, the obtained spectral intensity is shown to be 5 10^{-26} W m^{-2}Hz^{-1} at 10 km from the shower core for a vertical shower induced by a proton of 10^{17.5} eV.Comment: 16 pages, 6 figures, accepted in Astroparticle Physics. Compared to v1 version: 1. Inclusion of ro-vibrational processes. 2. Use of more accurate ionization potential values and energy distribution of the secondary electron

Molecular Bremsstrahlung Radiation at GHz Frequencies in Air

A detection technique for ultra-high energy cosmic rays, complementary to the fluorescence technique, would be the use of the molecular Bremsstrahlung radiation emitted by low-energy ionization electrons left after the passage of the showers in the atmosphere. In this article, a detailed estimate of the spectral intensity of photons at ground level originating from this radiation is presented. The spectral intensity expected from the passage of the high-energy electrons of the cascade is also estimated. The absorption of the photons in the plasma of electrons/neutral molecules is shown to be negligible. The obtained spectral intensity is shown to be $2\times10^{-21}$W cm$^{-2}$ GHz$^{-1}$ at 10 km from the shower core for a vertical shower induced by a proton of $10^{17.5}$ eV. In addition, a recent measurement of Bremsstrahlung radiation in air at gigahertz frequencies from a beam of electrons produced at 95 keV by an electron gun is also discussed and reasonably reproduced by the model.Comment: 20 pages, 9 figures, figures (2,4,7) improved in v2, accepted by Phys. Rev.

Angular Power Spectrum Estimation of Cosmic Ray Anisotropies with Full or Partial Sky Coverage

We study the angular power spectrum estimate in order to search for large scale anisotropies in the arrival directions distribution of the highest-energy cosmic rays. We show that this estimate can be performed even in the case of partial sky coverage and validated over the full sky under the assumption that the observed fluctuations are statistically spatial stationary. If this hypothesis - which can be tested directly on the data - is not satisfied, it would prove, of course, that the cosmic ray sky is non isotropic but also that the power spectrum is not an appropriate tool to represent its anisotropies, whatever the sky coverage available. We apply the method to simulations of the Pierre Auger Observatory, reconstructing an input power spectrum with the Southern site only and with both Northern and Southern ones. Finally, we show the improvement that a full-sky observatory brings to test an isotropic distribution, and we discuss the sensitivity of the Pierre Auger Observatory to large scale anisotropies.Comment: 16 pages, 6 figures, version accepted for publication by JCA