A. Putze et al.: An MCMC technique to sample transport and source parameters of Galactic cosmic rays. II. 2008; Gaps , Fuke et al. 2008). A complementary view of cosmic-ray propagation is given by anisotropy mea- surements from ground experiments of high energy (e.g., the Tibet Air Shower Arrays, Amenomori et al. 2006; Super-Kamiokande-I detector, Guillian et al. 2007; Eas- top , Aglietta et al. 2009). This multi-messenger and multi- energy picture will soon be completed: neutrino detectors are still in development (e.g., Icecube , Km3n e t ), but iden- tifying the sources of the GCRs should be within reach a few years after data collection (Halzen et al. 2008). All these measurements are probes to understand- ing and uncovering the sources of cosmic rays, the mechanisms of propagation, and the interaction of CRs with the gas and the radiation field of the Galaxy (Strong et al. 2007). It is important to determine the propagation parameters, because their value can be compared to theoretical predictions for the transport in turbulent magnetic fields (e.g., Casse et al. 2002; Ptuskin et al. 2006; Minnie et al. 2007; Tautz et al. 2008, Yan & Lazarian 2008 and references therein), or related to the source spectra predicted in acceleration models (e.g., Marcowith et al. 2006; Uchiyama et al. 2007; Plaga 2008; Reville et al. 2008, Reynolds 2008 and references therein). The transport and source parameters are also related to Galactic astrophysics (e.g., nuclear abundances and stellar nucleosynthesis—Silberberg & Tsao 1990; Webber 1997), and to dark matter indirect detection (e.g., Donato et al. 2004; Delahaye et al. 2008b). In the first paper of this series (Putze et al. 2009, here- after Paper I), we implemented a Markov Chain Monte Carlo (MCMC) to estimate the probability density func- tion (PDF) of the transport and source parameters. This allowed us to constrain these parameters with a sound sta- tistical method, to assess the goodness of fit of the models, and as a by-product, to provide 68% and 95% confidence level (CL) envelopes for any quantity we are interested in (e.g., B/C ratio, anti-proton flux). In Paper I, the analysis was performed for the simple Leaky Box Model (LBM) to validate the approach. We extend the analysis for the more realistic diffusion model, by considering constraints set by radioactive nuclei. The model is the minimal reaccelera- tion one, with a constant Galactic wind perpendicular to the disc plane (e.g., Jones et al. 2001; Maurin et al. 2001), allowing for a central underdensity of gas (of a few hun- dreds of pc) around the solar neighbourhood (Donato et al. 2002). The paper is organised as follows. In Sect. 2, we recall the main ingredients of the diffusion model, in particular the so-called local bubble feature. We briefly describe the MCMC technique in Sect. 3 (the full description was given in Paper I). We then estimate the transport parameters in the 1D and 2D geometry. In Sect. 4, this is performed at fixed L (halo size of the Galaxy), using the B/C ratio only. The analysis is extended in Sect. 5 by taking advantage of the radioactive nuclei to break the well-known degener- acy between the parameters K$_{0}$ (normalisation of the dif- fusion coefficient) and L . We then present our conclusions in Sect. 6. The set of j = 1 . . . n equations governing the prop- agation of n CR nuclei in the Galaxy is described in Berezinskii et al. (1990). It is a generic diffusion/convection In Eq. (3), the ionisation and Coulomb energy losses are taken from Mannheim & Schlickeiser (1994) and Strong & Moskalenko (1998). The divergence of the Galactic wind V gives rise to an energy loss term re- lated to the adiabatic expansion of cosmic rays. The last term is a first order contribution in energy from reacceler- ation. Equation (4) corresponds to a diffusion in momen- tum space, leading to an energy gain. The associated dif- fusion coefficient K$_{pp}$ (in momentum space) is taken from the model of minimal reacceleration by the interstellar tur- bulence (Osborne & Ptuskin 1988; Seo & Ptuskin 1994). It is related to the spatial diffusion coefficient K by The coefficients b and c in Eq. (1) are respectively first and second order gains/losses in energy, with The operator L (we omit the superscript j ) describes the diffusion K ( r , E ) and the convection V ( r ) in the Galaxy, but also the decay rate Γ$_{rad}$( E ) = 1 / ( γτ$_{0}$ ) if the nu- cleus is radioactive, and the destruction rate Γ$_{inel}$( r , E ) = ∑ ISM n$_{ISM}$ ( r ) vσ$_{inel}$ ( E ) for collisions with the interstellar matter (ISM), in the form The differential density N j of the nucleus j is a function of the total energy E and the position r in the Galaxy. Assuming a steady state, the transport equation can be written in a compact form as Below, we reiterate the assumptions of the model, and describe the free parameters that we constrain in this study (Sect. 2.4). Several diffusion models are considered in the lit- erature (Webber et al. 1992; Bloemen et al. 1993; Strong & Moskalenko 1998; Jones et al. 2001; Maurin et al. 2001; Berezhko et al. 2003; Shibata et al. 2006; Evoli et al. 2008; Farahat et al. 2008). We use a popular two-zone diffusion model with minimal reacceleration, where the Galactic wind is constant and perpendicular to the Galactic plane. The 1D and 2D version of this model are discussed, e.g., in Jones et al. (2001) and Maurin et al. (2001). For the sake of legibility, the solutions are given in Appendix A. equation with energy gains and losses. Depending on the as- sumptions made about the spatial and energy dependence of the transport coefficients, semi-analytical or fully nu- merical procedures are necessary to solve this set of equa- tions. The solution also depends on the boundary condi- tions, hence on the geometry of the model for the Galaxy. 2.1. Transport equation 2. Propagation model K$_{pp}$ × K = 4 3 V 2 a p 2 δ (4 − δ $^{2}$) (4 − δ ) , (5) b ( r , E ) = 〈 dE dt 〉 ion , coul . − ∇ . V 3 E$_{k}$ ( 2 m + E$_{k}$ m + E$_{k}$ ) (3) + (1 + β $^{2}$) E × K$_{pp}$, c ( r , E ) = β 2 × K$_{pp}$. (4) L ( r , E ) = − ∇ · ( K ∇ ) + ∇ · V + Γ$_{rad}$ + Γ$_{inel}$ . (2) L $^{j}$Nj + ∂ ∂E ( b $^{j}$Nj − c $_{j}$∂N j ∂E ) = S j . (1) 2