# Systematic uncertainties on the cosmic-ray transport parameters Is it possible to reconcile B/C data with δ = 1 / 3 or δ = 1 / 2 ? 

1 Laboratoire de Physique Nucl´ eaire et des Hautes Energies ( lpnhe ), Universit´ es Paris VI et Paris VII, CNRS/IN2P3, Tour 33, Jussieu, Paris, 75005, France 2 

Dept. of Physics and Astronomy, University of Leicester, Leicester, LE17RH, UK 3 iap 

Institut d’Astrophysique de Paris ( ), UMR7095 CNRS, Universit´ e Pierre et Marie Curie, 98 bis bd Arago, 75014 Paris, France 4 lpsc 

Laboratoire de Physique Subatomique et de Cosmologie ( ), Universit´ e Joseph Fourier Grenoble 1, CNRS/IN2P3, Institut Polytechnique de Grenoble, 53 avenue des Martyrs, Grenoble, 38026, France 5 

The Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, AlbaNova, SE- 10691 Stockholm, Sweden 

Received / Accepted 

D. Maurin 1 , 2 , $^{3}$, A. Putze4 , $^{5}$, and L. Derome4 

## ABSTRACT 

Context. The B/C ratio is used in cosmic-ray physics to constrain the transport parameters. However, from the same set of data, the various published values show a puzzling large scatter of these parameters. Aims. 

We investigate the impact of using different inputs (gas density and hydrogen fraction in the Galactic disc, source spectral shape, low-energy dependence of the diffusion coefficient, and nuclear fragmentation cross-sections) on the best-fit values of the transport parameters. We quantify the systematics produced when varying these inputs, and compare them to statistical uncertainties. We discuss the consequences for the slope of the diffusion coefficient δ . Methods. The analysis relies on the propagation code USINE interfaced with the Minuit minimisation routines. Results. 

We find the typical systematic uncertainties to be greater than the statistical ones. The several published values of δ (from 0.3 to 0.8) can be recovered when varying the low-energy shape of the diffusion coefficient and the convective wind strength. Models including a convective wind are characterised by δ ≳ 0 . 6, which cannot be reconciled with the expected theoretical values (1 / 3 and 1 / 2). However, from a statistical point of view ( χ 2 analysis), models with both reacceleration and convection—hence large δ —are favoured. The next favoured models in line yield δ , which can be accommodated with 1 / 3 and 1 / 2, but require a strong upturn of the diffusion coefficient at low energy (and no convection). Conclusions. 

To date, using the best statistical tools, the transport parameter determination is still plagued by many unknowns at low energy ( ∼ GeV/n). To disentangle all these configurations, measurements of the B/C ratio at TeV/n energies and/or combination with other secondary-to-primary ratios is necessary. 

Key words. Methods: statistical – ISM: cosmic rays 

## 1. Introduction 

A central question in Galactic cosmic ray (GCR) physics lies in the determination of the transport parameters. The standard procedure consists in fitting a secondary-to- primary ratio, e.g. B/C. In general, the parameters derived in different studies provide inconsistent values, especially for the slope δ of the diffusion coefficient. It is important to understand the origin of these differences. 

The first attempts to get the best-fit value of the trans- port parameters, as well as their statistical uncertainties, were carried in Maurin et al. (2001) and Lionetto et al. (2005). Recently, we implemented a Markov chain Monte Carlo (MCMC) to estimate the probability-density function (PDF) of the transport and source parameters for Galactic cosmic rays (Putze et al. 2009, 2010, hereafter Papers I and II). This sound statistical technique applied to current B/C data allowed us to estimate the statistical uncertainties on various parameters. We found typical uncertainties of 

∼ 10 − 20%. Although such precision is expected given the accuracy of the data, one may wonder whether these re- sults are not dominated by systematic uncertainties from the input ingredients and assumptions made to do the cal- culation. 

This is an important issue since in our pre- vious studies, the best-fit slope observed in a diffusion/constant-convection/reacceleration propagation model (Maurin et al. 2001, 2002)—confirmed by our recent MCMC analysis (Paper II)—points to δ ≈ 0 . 75 − 0 . 85. This is at variance with the result of the GALPROP code (Strong & Moskalenko 1998), where the best-fit models correspond to smaller δ ≈ 0 . 3 − 0 . 4 (Lionetto et al. 2005) in either a diffusion/linear-convection or a diffu- sion/reacceleration model. Moreover, none of these results agree with the best-fit slopes from leaky-box models (with rigidity cut-off), where δ ≈ 0 . 5 − 0 . 6 (e.g., Webber et al. 2003—no reacceleration—, or Paper I—with reaccelera- tion). Such a scatter in δ was also observed in Jones et al. (2001). 

