A simple determination of the halo size $L$ from $^{10}$Be/$^9$Be data

TL;DR

This paper introduces an analytical formula to determine the cosmic-ray halo size $L$ from $^{10}$Be/$^9$Be data, validated against detailed models, and discusses the impact of cross-section uncertainties on future measurements.

Contribution

The paper presents a simple, accurate analytical method to estimate $L$ from cosmic-ray data, validated against complex propagation models, and highlights the limitations imposed by nuclear cross-section uncertainties.

Findings

Best-fit $L$ from AMS-02 Be/B data is 3.8 kpc with updated cross-sections.

Consistent $L$ estimate of 4.7 kpc from $^{10}$Be/$^9$Be data using the formula.

Future improvements in $L$ measurement are limited by nuclear cross-section uncertainties.

Abstract

The AMS-02 and HELIX experiments should soon provide $\mathrm{^{10}Be/^9Be}$ cosmic-ray data of unprecedented precision. We propose an analytical formula to quickly and accurately determine $L$ from these data. Our formula is validated against the full calculation performed with the propagation code \usine{}. We compare the constraints on $L$ set by Be/B and $\mathrm{^{10}Be/^9Be}$, relying on updated sets of production cross-sections. The best-fit $L$ from AMS-02 Be/B data is shifted from 5 kpc to 3.8 kpc when using the updated cross-sections. We obtained consistent results from the Be/B analysis with USINE, $L=3.8^{+2.8}_{-1.6}$ kpc (data and cross-section uncertainties), and from the analysis of $\mathrm{^{10}Be/^9Be}$ data with the simplified formula, $L=4.7\pm0.6$ (data uncertainties) $\pm2$ (cross-section uncertainties) kpc. The analytical formula indicates that improvements on $L$ thanks to future data will be limited by production cross-section uncertainties, unless either $\mathrm{^{10}Be/^9Be}$ measurements are extended up to several tens of GeV/n, or nuclear data for the production of $\mathrm{^{10}Be}$ and $\mathrm{^9Be}$ are improved; new data for the production cross-section of $\mathrm{^{16}O}$ into Be isotopes above a few GeV/n are especially desired.