Transcript poster0113_durso - Pierre Auger Observatory

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%.