Non-parametric determination of H and He interstellar fluxes from cosmic-ray data

TL;DR

This paper develops a non-parametric method using MCMC to accurately determine interstellar H and He cosmic-ray fluxes from satellite data, accounting for uncertainties and testing the force-field approximation.

Contribution

It introduces a non-parametric, MCMC-based approach to extract interstellar fluxes and modulation levels from TOA cosmic-ray data, improving accuracy and uncertainty quantification.

Findings

Best-fit interstellar fluxes with 2-10% precision

Uncertainties in fluxes lead to ~30 MV uncertainty in modulation levels

Force-field approximation effectively models high-precision data

Abstract

Top-of-atmosphere (TOA) cosmic-ray (CR) fluxes from satellites and balloon-borne experiments are snapshots of the solar activity imprinted on the interstellar (IS) fluxes. Given a series of snapshots, the unknown IS flux shape and the level of modulation (for each snapshot) can be recovered. We wish (i) to provide the most accurate determination of the IS H and He fluxes from TOA data alone, (ii) to obtain the associated modulation levels (and uncertainties) while fully accounting for the correlations with the IS flux uncertainties, and (iii) to inspect whether the minimal force-field approximation is sufficient to explain all the data at hand. Using H and He TOA measurements, including the recent high-precision AMS, BESS-Polar, and PAMELA data, we performed a non-parametric fit of the IS fluxes $J^{\rm IS}_{\rm H,~He}$ and modulation level $\phi_i$ for each data-taking period. We relied on a Markov chain Monte Carlo (MCMC) engine to extract the probability density function and correlations (hence the credible intervals) of the sought parameters. Although H and He are the most abundant and best measured CR species, several datasets had to be excluded from the analysis because of inconsistencies with other measurements. From the subset of data passing our consistency cut, we provide ready-to-use best-fit and credible intervals for the H and He IS fluxes from MeV/n to PeV/n energy (with a relative precision in the range [2-10\%] at 1$\sigma$). Given the strong correlation between $J^{\rm IS}$ and $\phi_i$ parameters, the uncertainties on $J^{\rm IS}$ translate into $\Delta\phi\approx \pm 30$~MV (at 1$\sigma$) for all experiments. We also find that the presence of $^3$He in He data biases $\phi$ towards higher $\phi$ values by $\sim 30$~MV. The force-field approximation gives an excellent ($\chi^2/$dof$=1.02$) description of the recent high-precision TOA H and He fluxes.