Theoretical uncertainties in extracting cosmic-ray diffusion parameters: the boron-to-carbon ratio
Résumé
Context. PAMELA and, more recently, AMS-02, are ushering us into a new era of greatly reduced statistical uncertainties in experimental measurements of cosmic-ray fluxes. In particular, new determinations of traditional diagnostic tools such as the boron-to-carbon ratio (B/C) are expected to significantly reduce errors on cosmic-ray diffusion parameters, with important implications for astroparticle physics, ranging from inferring primary source spectra to indirect dark matter searches.
Aims. It is timely to stress, however, that the conclusions obtained crucially depend on the framework in which the data are interpreted as well as on some nuclear input parameters. We aim at assessing the theoretical uncertainties affecting the outcome, with models as simple as possible while still retaining the key dependencies.
Methods. We compared different semi-analytical, two-zone model descriptions of cosmic-ray transport in the Galaxy: infinite slab(1D), cylindrical symmetry (2D) with homogeneous sources, cylindrical symmetry (2D) with inhomogeneous source distribution. We tested for the effect of a primary source contamination in the boron flux by parametrically altering its flux. We also tested for nuclear cross-section uncertainties. All hypotheses were compared by chi(2) minimisation techniques to preliminary results from AMS-02.
Results. We find that the main theoretical bias on the determination of the diffusion coefficient index delta (up to a factor two) is represented by the assumption that no injection of boron takes place at the source. The next most important uncertainty is represented by cross-section uncertainties, which reach +/- 20% in delta. As a comparison, nuclear uncertainties are more important than the shift in the best-fit when introducing a convective wind of velocity less than or similar to 30 km s(-1), with respect to a pure diffusive baseline model. Perhaps surprisingly, homogeneous 1D vs. 2D performances are similar in determining diffusion parameters. An inhomogeneous source distribution marginally alters the central value of the diffusion coefficient normalisation (at the 10%, 1 sigma level). However, the index of the diffusion coefficient delta is basically unaltered, as well as the goodness of fit.
Conclusions. Our study suggests that, differently for instance from the leptonic case, realistic modelling of the geometry of the Galaxy and of the source distribution are of minor importance to correctly reproduce B/C data at high energies and thus, to a large extent, for the extraction of diffusion parameters. The ansatz on the lack of primary injection of boron represents the most serious bias and requires multi-messenger studies to be addressed. If this uncertainty could be lifted, nuclear uncertainties would still represent a serious concern; they degrade the systematic error on the inferred parameters to the 20% level, or three times the estimated experimental sensitivity. To reduce this, a new nuclear cross-section measurement campaign might be required.