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