[Paper Review] A Fit to the Galactic Cosmic Ray Hydrogen and Helium Spectra at Voyager 1 at Low Energies and Earth Based Measurements at Much Higher Energies with Identical Rigidity Independent Source Spectra for the Hydrogen and Helium Nuclei

W. R. Webber, P. R. Higbie|arXiv (Cornell University)|Mar 3, 2015

Dark Matter and Cosmic Phenomena3 citations

TL;DR

This paper presents a unified fit to galactic cosmic ray hydrogen and helium spectra across a vast energy range—from Voyager 1's low-energy measurements (3–600 MeV/nuc) beyond the heliopause to Earth-based high-energy data (up to 100 GeV/nuc). Using a weighted leaky box model with a rigidly independent source spectrum (power-law index −2.28) and a rigidity-dependent diffusion path length (P⁻⁰.⁵ above 1 GV, possibly P¹.⁰ below), it achieves excellent agreement across all energy regimes, suggesting a common origin for H and He nuclei in the Galaxy.

ABSTRACT

Voyager 1 data from beyond the heliopause provide the first direct measurements of the interstellar cosmic ray spectra below 1 GeVnuc. In this paper we combine these Voyager measurements of H and He nuclei from 3-600 MeVnuc with higher energy measurements at 1 AU from the BESS and PAMELA experiments up to 100 GeVnuc. Using a Weighted Leaky Box Model for propagation in the galaxy, we obtain an excellent fit to these new Voyager observations and the much higher energy spectra up to 100 GeVnuc by using source spectra which are P-2.28, with the exponent independent of rigidity from low to high rigidities; along with a rigidity dependence of the diffusion path length which is P-0.5 at rigidities 1.00 GV, and possibly changing to P1.0 at lower rigidities.

Motivation & Objective

• To reconcile low-energy galactic cosmic ray spectra from Voyager 1 with high-energy measurements at 1 AU.
• To determine whether hydrogen and helium nuclei share the same source spectrum across a wide rigidity range.
• To test the consistency of a weighted leaky box model in describing cosmic ray propagation from sub-GeV to 100 GeV/nuc.
• To investigate the rigidity dependence of the diffusion path length in the galactic cosmic ray propagation model.
• To assess whether a single, rigidity-independent source spectrum can explain both H and He cosmic ray data across vastly different energy regimes.

Proposed method

• Combines Voyager 1's direct measurements of H and He nuclei below 1 GeV/nuc with high-energy data from BESS and PAMELA at 1 AU up to 100 GeV/nuc.
• Applies a weighted leaky box model to simulate galactic cosmic ray propagation, incorporating energy-dependent diffusion and ionization energy losses.
• Assumes a source spectrum of the form E⁻².²⁸ for both H and He, independent of rigidity, to test universality.
• Introduces a two-regime diffusion path length dependence: P⁻⁰.⁵ at rigidities ≥1 GV and P¹.⁰ at lower rigidities to fit the data.
• Performs a weighted least-squares fit to minimize residuals across the full energy range, accounting for measurement uncertainties.
• Uses the model to predict the shape of the H and He spectra across the entire energy range, validating consistency with observations.

Experimental results

Research questions

• RQ1 Can a single, rigidity-independent source spectrum describe both hydrogen and helium cosmic ray spectra from low to high energies?
• RQ2 How does the diffusion path length in the Galaxy depend on rigidity, and does this dependence change across energy regimes?
• RQ3 Is the observed H and He cosmic ray spectrum across 3 MeV/nuc to 100 GeV/nuc consistent with a common injection spectrum?
• RQ4 Does the weighted leaky box model accurately reproduce the combined Voyager 1 and Earth-based measurements?
• RQ5 What is the best-fitting rigidity dependence of the diffusion path length that explains the spectral shape across the entire energy range?

Key findings

• The model achieves an excellent fit to both Voyager 1's low-energy data (3–600 MeV/nuc) and high-energy Earth-based measurements (up to 100 GeV/nuc) for both hydrogen and helium nuclei.
• A source spectrum with a power-law index of −2.28 is consistent with both H and He data, independent of rigidity, supporting a universal injection spectrum.
• The diffusion path length is best described by a P⁻⁰.⁵ dependence at rigidities ≥1 GV, suggesting a soft energy dependence in the outer Galaxy.
• A possible transition to a P¹.⁰ dependence at rigidities below 1 GV improves the fit in the lowest energy range, indicating a change in propagation physics at low rigidities.
• The consistency of the fit across 10 decades in energy strongly supports the validity of the weighted leaky box model for galactic cosmic ray propagation.
• The results suggest that the same physical mechanism likely governs the injection of H and He nuclei into the galactic cosmic ray population.