A Markov Chain Monte Carlo technique to sample transport and source parameters of Galactic cosmic rays

II. Results for the diffusion model combining B/C and radioactive nuclei

¹ The Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, AlbaNova, 10691 Stockholm, Sweden e-mail: antje@fysik.su.se
² Laboratoire de Physique Subatomique et de Cosmologie (LPSC), Université Joseph Fourier Grenoble 1, CNRS/IN2P3, Institut Polytechnique de Grenoble, 53 avenue des Martyrs, 38026 Grenoble, France
³ Laboratoire de Physique Nucléaire et des Hautes Energies (LPNHE), Universités Paris VI et Paris VII, CNRS/IN2P3, Tour 33, Jussieu, Paris, 75005, France
⁴ Dept. of Physics and Astronomy, University of Leicester, Leicester, LE17RH, UK
⁵ Institut d'Astrophysique de Paris (IAP), UMR 7095 CNRS, Université Pierre et Marie Curie, 98bis Bd Arago, 75014 Paris, France

Received: 7 January 2010
Accepted: 14 March 2010

Abstract

Context. Ongoing measurements of the cosmic radiation (nuclear, electronic, and γ-ray) are providing additional insight into cosmic-ray physics. A comprehensive picture of these data relies on an accurate determination of the transport and source parameters of propagation models.

Aims. A Markov Chain Monte Carlo method is used to obtain these parameters in a diffusion model. By measuring the B/C ratio and radioactive cosmic-ray clocks, we calculate their probability density functions, placing special emphasis on the halo size L of the Galaxy and the local underdense bubble of size r_h. We also derive the mean, best-fit model parameters and 68% confidence level for the various parameters, and the envelopes of other quantities.

Methods. The analysis relies on the USINE code for propagation and on a Markov Chain Monte Carlo technique previously developed by ourselves for the parameter determination.

Results. The B/C analysis leads to a most probable diffusion slope δ = for diffusion, convection, and reacceleration, or δ = for diffusion and reacceleration. As found in previous studies, the B/C best-fit model favours the first configuration, hence pointing to a high value for δ. These results do not depend on L, and we provide simple functions to rescale the value of the transport parameters to any L. A combined fit on B/C and the isotopic ratios (¹⁰Be/⁹Be, ²⁶Al/²⁷Al, ³⁶Cl/Cl) leads to L =  kpc and r_h =  pc for the best-fit model. This value for r_h is consistent with direct measurements of the local interstallar medium. For the model with diffusion and reacceleration, L =  kpc and r_h =  pc (consistent with zero). We vary δ, because its value is still disputed. For the model with Galactic winds, we find that between δ = 0.2 and 0.9, L varies from  to  if r_h is forced to be 0, but it otherwise varies from  to  (with r_h ~ 100 pc for all δ 0.3). The results from the elemental ratios Be/B, Al/Mg, and Cl/Ar do not allow independent checks of this picture because these data are not precise enough.

Conclusions. We showed the potential and usefulness of the Markov Chain Monte Carlo technique in the analysis of cosmic-ray measurements in diffusion models. The size of the diffusive halo depends crucially on the value of the diffusion slope δ, and also on the presence/absence of the local underdensity damping effect on radioactive nuclei. More precise data from ongoing experiments are expected to clarify this issue.