Volume 497, Number 3, April III 2009
|Page(s)||991 - 1007|
|Section||Numerical methods and codes|
|Published online||09 February 2009|
A Markov Chain Monte Carlo technique to sample transport and source parameters of Galactic cosmic rays
I. Method and results for the Leaky-Box model
Laboratoire de Physique Subatomique et de Cosmologie , 53 avenue des Martyrs, 38026 Grenoble, France e-mail: email@example.com
2 Laboratoire de Physique Nucléaire et des Hautes Énergies , Tour 33, Jussieu, 75005 Paris, France
3 Laboratoire de l'accélérateur linéaire , Université Paris-Sud 11, Bâtiment 200, BP 34, 91898 Orsay Cedex, France
4 Laboratoire de Physique Théorique , Chemin de Bellevue BP 110, 74941 Annecy-le-Vieux, France
5 Université de Savoie, 73011 Chambéry, France
Accepted: 7 December 2008
Context. Propagation of charged cosmic-rays in the Galaxy depends on the transport parameters, whose number can be large depending on the propagation model under scrutiny. A standard approach for determining these parameters is a manual scan, leading to an inefficient and incomplete coverage of the parameter space.
Aims. In analyzing the data from forthcoming experiments, a more sophisticated strategy is required. An automated statistical tool is used, which enables a full coverage of the parameter space and provides a sound determination of the transport and source parameters. The uncertainties in these parameters are also derived.
Methods. We implement a Markov Chain Monte Carlo (MCMC), which is well suited to multi-parameter determination. Its specificities (burn-in length, acceptance, and correlation length) are discussed in the context of cosmic-ray physics. Its capabilities and performances are explored in the phenomenologically well-understood Leaky-Box Model.
Results. From a technical point of view, a trial function based on binary-space partitioning is found to be extremely efficient, allowing a simultaneous determination of up to nine parameters, including transport and source parameters, such as slope and abundances. Our best-fit model includes both a low energy cut-off and reacceleration, whose values are consistent with those found in diffusion models. A Kolmogorov spectrum for the diffusion slope (δ = 1/3) is excluded. The marginalised probability-density function for δ and α (the slope of the source spectra) are δ ≈ 0.55-0.60 and α ≈ 2.14-2.17, depending on the dataset used and the number of free parameters in the fit. All source-spectrum parameters (slope and abundances) are positively correlated among themselves and with the reacceleration strength, but are negatively correlated with the other propagation parameters.
Conclusions. The MCMC is a practical and powerful tool for cosmic-ray physic analyses. It can be used to confirm hypotheses concerning source spectra (e.g., whether ) and/or determine whether different datasets are compatible. A forthcoming study will extend our analysis to more physical diffusion models.
Key words: diffusion / methods: statistical / ISM: cosmic rays
© ESO, 2009
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.