We present a new design for the water Cherenkov detectors that are in use in various cosmic ray observatories. This novel design can provide a significant improvement in the independent measurement of the muonic and electromagnetic component of exten
sive air showers. From such multi-component data an event by event classification of the primary cosmic ray mass becomes possible. According to popular hadronic interaction models, such as EPOS-LHC or QGSJetII-04, the discriminating power between iron and hydrogen primaries reaches Fisher values of $sim$ 2 or above for energies in excess of $10^{19}$ eV with a detector array layout similar to that of the Pierre Auger Observatory.
Ultra-high energy cosmic rays generate extensive air showers in Earths atmosphere. A standard approach to reconstruct the energy of an ultra-high energy cosmic rays is to sample the lateral profile of the particle density on the ground of the air sho
wer with an array of surface detectors. For cosmic rays with large inclinations, this reconstruction is based on a model of the lateral profile of the muon density observed on the ground, which is fitted to the observed muon densities in individual surface detectors. The best models for this task are derived from detailed Monte-Carlo simulations of the air shower development. We present a phenomenological parametrization scheme which allows to derive a model of the average lateral profile of the muon density directly from a fit to a set of individual Monte-Carlo simulated air showers. The model reproduces the detailed simulations with a high precision. As an example, we generate a muon density model which is valid in the energy range 1e18 eV < E < 1e20 eV and the zenith angle range 60 deg < theta < 90 deg. We will further demonstrate a way to speed up the simulation of such muon profiles by three orders of magnitude, if only the muons in the shower are of interest.
We study the possibility to extract the multipolar moments of an underlying distribution from a set of cosmic rays observed with non-uniform or even partial sky coverage. We show that if the degree is assumed to be upper bounded by $L$, each multipol
ar moment can be recovered whatever the coverage, but with a variance increasing exponentially with the bound $L$ if the coverage is zero somewhere. Despite this limitation, we show the possibility to test predictions of a model without any assumption on $L$ by building an estimate of the covariance matrix seen through the exposure function.
The arrival time distribution of cosmic ray events is well suited to extract information regarding sky anisotropies. For an experiment with nearly constant exposure, the frequency resolution one can achieve is given by the inverse of the time $T$ dur
ing which the data was recorded. For $T$ larger than one calendar year the resolution becomes sufficient to resolve the sidereal and diurnal frequencies. Using a Fourier expansion on a modified time parameter, we show in this note that one can accurately extract sidereal modulations without knowledge of the experimental coverage. This procedure also gives the full frequency pattern of the event sample under studies which contains important information about possible systematics entering in the sidereal analysis. We also show how this method allows to correct for those systematics. Finally, we show that a two dimensional analysis, in the form of the spherical harmonic ($Y_l^m$) decomposition, can be performed under the same conditions for all $m e 0$.
