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

Abstract

Context. 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. Aims. 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. Methods. 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 IS H, He and modulation level φ 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. Results. 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 readyto-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 1σ). Given the strong correlation between J IS and φ i parameters, the uncertainties on J IS translate into ∆φ ≈ ±30 MV (at 1σ) for all experiments. We also find that the presence of 3 He in He data biases φ towards higher φ values by ∼30 MV. The force-field approximation, despite its limitation, gives an excellent (χ 2 /d.o.f. = 1.02) description of the recent high-precision TOA H and He fluxes. Conclusions. The analysis must be extended to different charge species and more realistic modulation models. It would benefit from the AMS-02 unique capability of providing frequent high-precision snapshots of the TOA fluxes over a full solar cycle.

Solar Modulation of the Local Interstellar Spectrum With Voyager 1, Ams-02, Pamela, and Bess

“…During the completion of this work, we became aware of related studies by Ghelfi et al (2016) and by Cholis et al (2016). The data sets and methods used differ from those of our study, making the three analyses complementary.…”

“…The data sets and methods used differ from those of our study, making the three analyses complementary. Ghelfi et al (2016) focus on the determination of the interstellar proton and helium flux with splines. A comparison of their proton LIS (obtained with the force-field approximation) and ours (obtained with the rigidity-dependent solar modulation parameter) shows a very good agreement in the range 4 GV-1 TeV, but with different uncertainties.…”

Solution of Heliospheric Propagation: Unveiling the Local Interstellar Spectra of Cosmic-ray Species

“…The Voyager 1 data combined with recent AMS-02, PAMELA, and earlier BESS-Polar measurements, triggered a series of papers (Cholis et al 2016;Corti et al 2016;Ghelfi et al 2016) aiming at the derivation of the LIS for protons and He, and producing a generalization of the modulation potential that depends on time, charge sign, and rigidity, using the force-field approximation (Gleeson & Axford 1968) as a baseline. The parameterizations proposed in these papers and the correlations with the neutron monitor rate, the tilt angle of the heliospheric current sheet, and the polarity and strength of the heliospheric magnetic field they found is certainly a large step forward over the use of the simple force-field approximation in a not-so-distant past.…”

Cosmic Ray Modulation Observed by the Princess Sirindhorn Neutron Monitor at High Rigidity Cutoff

“…For three NM stations, we derived the time series of the spectra of proton and helium at the top of the atmosphere from time series of the solar modulation parameter as seen by a single NM 2 [10,11,12], Φ NM . We then applied the simulated yield functions from [18] to determine the count rates expected at DI.…”

“…These results are compatible with a spectral crossover at 5-6 GV. Comparison of the count rate at Doi Inthanon with simulated count rates estimated using the Local Interstellar Spectrum from [10,11] with the force-field approximation. The solar modulation parameters were estimated from NMs with different rigidity cutoffs, i.e., Almaty, McMurdo, and Newark with the method presented in [12].…”