How to Infer the Mass Composition from Eas Observations Demonstrated with Kascade Data

The KASCADE experiment detecting many observables of extensive air showers provides the possibility to handle data on event-by-event basis and to investigate details of the energy dependence of the primary cosmic ray flux in the energy range of 1014 1016 eV. We use Bayesian decision making and neural net approaches for data classification into multiple categories. A first attempt, approaching the spectra for the different elemental components of the primary flux is presented and discussed under methodical aspects. INTRODUCTION The ambiguities occurring in interpretations of cosmic ray experiments arise from insufficient knowledge about the characteristics of hadron-nuclear interactions above accelerator energies. Furthermore uncertainties in the primary cosmic ray composition, aggravated by strong fluctuations of all shower parameters observed in indirect experiments. In order to perform more detai led conclusions on the type of primary we develop a consistent theory of statistical inference, based on nonparametric models, in which various nonparametric procedures (density estimation, Bayesian decision making, error rate estimation, feature extraction, sample control during handling, neural net models, etc...) are implemented (Chilingarian et al.,1990; 1991). All statistical decisions and procedures are correct within the prechosen model. Thus a realistic simulation is the key problem of any physical inference in indirect experiments. Extensive air shower (EAS) investigations are a classical example of such a situation. An adequate consideration of detector response and an identical reconstruction of experimental and simulated data are necessary. The first simulation data base of the KASCADE experiment (Klages et al., 1997) fulfilling the above requirements is available since recently, and we use specific EAS parameters, like the truncated numbers of electrons/photons (Ne(truncated)) and muons (Nμ(truncated)) and the age (Age30) parameter (Weber et al.,1997) as input for our analysis. The physical meaning of these variables will not be discussed, we only mention that the procedures of their use are identical for experimental data and simulations. It is also very important to say that hypotheses about lateral distributions of muons and electrons at very small and large distances are not of influence. SELECTION OF THE BEST VARIABLE SUBSET To select signatures sensitive to the primary cosmic ray (PCR) composition, various characteristics of EAS initiated by different primaries (divided into five groups) were examined. A comparison of selected features for Proton Helium and Proton Iron pairs are presented in Table 1 , where P-quantiles of Student, Kolmogorov-Smirnov and Mann-Whitney pairwise statistical tests are given. From the relative values of this quantiles one can estimate the possibility of primary discrimination by the chosen EAS parameters. corresponding author: e-mail: [email protected] †A full list of authors and institutions of the KASCADE Collaboration is given at the end of this volume. primaries t Dn MW p Fe Ne(truncated) 13.62 6.79 9.23 p Fe Nμ(truncated) 3.28 1.67 5.76 p Fe Age30 21.13 8.71 16.54 p Fe NCD μ 0.17 3.37 6.69 p He Ne(truncated) 3.33 4.13 7.84 p He Nμ(truncated) 0.03 1.27 1.87 p He Age30 5.86 2.93 6.3 p He NCD μ 1.95 1.46 2.64 The three variables used provide the opportunity to distinguish with rather high accuracy between iron and protons, but, as expected, the proton helium discrimination is uncertain. In the present analysis we restrict ourselves to the three types of primaries: light, medium and heavy. MASS DISCRIMINATION OF PRIMARIES