β-radioactive cosmic rays in a diffusion model:: Test for a local bubble?

In a previous analysis, Maurin et al. (2001) have constrained several parameters of the cosmic ray diffusive propagation (the diffusion coefficient normalization K-0 and its spectral index delta, the halo half-thickness L, the Alfven velocity V-a, and the galactic wind V-c) using stable nuclei. In a second paper (Donato et al. 2002), these parameters were shown to reproduce the observed antiproton spectrum with no further adjustment. In the present paper, we extend the analysis to the 3-radioactive nuclei Be-101, Al-26 and Cl-36. These species will be shown to be particularly sensitive to the properties of the local interstellar medium (LISM). As studies of the LISM suggest that we live in an underdense bubble of extent r(hole) similar to 50-200 pc, this local feature must be taken into account. We present a modified version of our diffusion model which describes the underdensity as a hole in the galactic disc; we believe some of the formulae presented here are new. It is found that the presence of the bubble leads to a decrease in the radioactive fluxes which can be approximated by a simple factor exp(-r(hole)/l(rad)) where 1-d = rootK(gammatau0) is the typical distance travelled by a radioactive nucleus before it decays. We find that each of the radioactive nuclei independently points towards a bubble of radius : 100 pc. If these nuclei are considered simultaneously, only models with a bubble radius r(hole) similar to 60-100 pc are marginally consistent with data. In particular, the standard case r(hole) = 0 pc is disfavored. Our main concern is about the consistency of the currently available data, especially Al-26/Al-27.