Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
A Monte Carlo exploration of methods to determine the UHECR composition with the Pierre Auger Observatory HE. 1.4 D.D’Urso for the Pierre Auger Collaboration http://www.auger.org/auger-authors-ICRC2009.pdf Composition analysis with the moments of Xmax distribution (MM) Mass composition is derived from the best choice of primary fractions that reproduce observed mean and variance of Xmax distribution using their expectation values (method of moments, MM). Modelling a data set of cosmic rays as a mixture of three primary masses (a, b and c) with relative abundances Pa, Pb and Pc = 1 - Pa – Pb, the expected mean shower maximum is X exp Pa X a Pb X b Pc X c where < Xi> is the mean Xmax for simulated data set of the i-th species.The same applies to estimate the expected variance (ΔXexp)2. Assuming that the data set is so large that <Xmax> and Δ Xmax are statistically independent, in each energy bin, data could be fitted obtaining Pa and Pb. Mass Composition from a logarithmic likelihood fit to Xmax distribution (LLF) The measured Xmax distribution is reproduced weighting the distributions of different primary particles.The method assumes that the observed events Ndata are a mixture of Nm pure mass samples with unknown fractions pj. The expected number of showers with Xmax into i-th bin is i N data aij pj MC i 1, , N j 1 Nj Nm aij = MC events from primary j into the i-th bin; NjMC = total number of MC events from primary j. The probability to observe ni events into the i-th bin is given by the product of Poisson distributions of mean νi Nm ni i i P( ) ni N data i 1 e ni ! Primary fractions are determined maximizing the logarithm of P(ni) with respect to pj Multiparametric Analysis for the primary composition Reconstructed primary fractions are corrected for the mixing probabilities Pi→j that an event of mass i is identified as primary j, and for the trigger-reconstruction-selection efficiency for each primary mass A set of observables define a parameter space populated with simulated cascades produced by different primaries. In each cell (h1, …, hn), the fraction of the population of primary i define the probability for a real shower falling into the cell to be initiated by a nucleus of species i. ( h1.. hn) i p N ( h1.. hn) i N ( h1.. hn) tot The primary fractions for a data set of Ndata showers is then given by the mean classification probability over the sample M pj p m 1 ( h1.. hn ) j M Performances Data reported by the Auger Collaboration at the ICRC 2007 have been analyzed in terms of proton and iron primaries and the measured Elongation Rate curve has been compared with that estimated considering, in each energy bin, the mean Xmax corresponding to the reconstructed mixture of LLF and MTA. Auger results have been confirmed with independent Monte Carlo techniques which can be corrected for the bias introduced by the analysis cuts applied and exploit a larger statistics avoiding very strong cuts. For different proton-iron mixing, N events have been randomly selected from proton and iron Monte Carlo data and the resulting samples have been analyzed. The whole procedure have been repeated many times. The input abundances are well reproduced by the methods in all cases, with a root mean square of the distribution of the reconstructed input fractions of less than 5%.