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

Abstract

Context. Ongoing measurements of the cosmic radiation (nuclear, electronic, and γ-ray) are providing additional insight into cosmicray 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 = 0.86 +0.04 −0.04 for diffusion, convection, and reacceleration, or δ = 0.234 +0.006 −0.005 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 ( 10 Be/ 9 Be, 26 Al/ 27 Al, 36 Cl/Cl) leads to L = 8 +8 −7 kpc and r h = 120 +20 −20 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 = 4 +1 −1 kpc and r h = 3 +70 −3 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 O(0) to O(2) if r h is forced to be 0, but it otherwise varies from O(0) to O(1) (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.

Cosmic ray anomalies from the MSSM?

“…Experimentally, there are measurements of B/C and various phenomenological propagation models that are used to constrain δ given the measured data. These works have found ranges of values for δ that provide consistency with B/C measurements, some favoring lower values δ = 0.3 − 0.5 [68][69][70] and others finding that larger values δ = 0.5 − 0.8 are preferred [71][72][73]. In this work we use only propagation models that have δ = 0.33.…”

“…As δ describes the spectrum of turbulent features in the bulk magnetic field, there has been a large industry devoted to theoretical and experimental considerations of what its value should be [68][69][70][71][72][73]. Particularly well-motivated theoretical values include δ = 0.33 (Kolmogorov turbulence) and δ = 0.5 (Kraichnan turbulence).…”

The GeV-TeV Galactic gamma-ray diffuse emission

“…As shown in Donato et al (2004), these propagation models correspond respectively to minimal, medium, and maximal fluxes of primary antiprotons whose exotic dark matter species would produce everywhere inside the DH, if they exist. The more recent analysis by Putze et al (2010) makes use of Monte Carlo techniques and gives similar results. That analysis confirms in particular that the half thickness L of the DH is not determined and may vary between 1 and 16 kpc.…”

A new look at the cosmic ray positron fraction

“…These parameter sets result from a secondaryto-primary ratio analysis (Maurin et al 2001) where 26 data points of the boron-to-carbon (B/C) ratio were fitted over the energy range from 0.1 to 35 GeV/n leading to a χ 2 less than 40. The advantage of choosing this study over more recent studies (Putze et al 2010;Coste et al 2012;Trotta et al 2011) J1745 − 3040…”