Constraints on the spatially dependent cosmic-ray propagation model from Bayesian Analysis

TL;DR

This paper uses Bayesian analysis to constrain a spatially dependent cosmic-ray propagation model, revealing the size of the slow-diffusion disk and comparing model predictions with observations.

Contribution

It introduces a Bayesian parameter estimation approach to tightly constrain the spatially dependent cosmic-ray propagation model parameters, especially the thickness of the slow-diffusion disk.

Findings

The SDD thickness is constrained to 0.4-0.5 kpc.

Model predictions for $ar{p}/p$ ratio and CR anisotropy align with observations.

Electron and positron fluxes are underpredicted, suggesting additional sources.

Abstract

The energy spectra of primary and secondary cosmic rays (CR) generally harden at several hundreds of GeV, which can be naturally interpreted by propagation effects. We adopt a spatially dependent CR propagation model to fit the spectral hardening, where a slow-diffusion disk (SDD) is assumed near the Galactic plane. We aim to constrain the propagation parameters with the Bayesian parameter estimation based on a Markov chain Monte Carlo sampling algorithm. The latest precise measurements of carbon spectrum and B/C ratio are adopted in the Bayesian analysis. The $\rm{^{10}Be/^{9}Be}$ and Be/B ratios are also included to break parameter degeneracies. The fitting result shows that all the parameters are well constrained. Especially, the thickness of the SDD is limited to 0.4-0.5 kpc above and below the Galactic plane, which could be the best constraint for the slow-diffusion region among similar works. The $\bar{p}/p$ ratio and amplitude of CR anisotropy predicted by the SDD model are consistent with the observations, while the predicted high-energy electron and positron fluxes are slightly and significantly lower than the observations, respectively, indicating the necessity of extra sources.