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

Abstract

The AMS-02 and HELIX experiments should soon provide ${}^{10}\mathrm{Be}{/}^9\mathrm{Be}$ 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 ${}^{10}\mathrm{Be}{/}^9\mathrm{Be}$, 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, $L=3.8_{-1.6}^{+2.8}$ kpc (data and cross-section uncertainties), and from the analysis of ${}^{10}\mathrm{Be}{/}^9\mathrm{Be}$ data with the simplified formula, $L=4.7\pm 0.6$ (data uncertainties) $\pm 2$ (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 ${}^{10}\mathrm{Be}{/}^9\mathrm{Be}$ measurements are extended up to several tens of GeV/n, or nuclear data for the production of ${}^{10}\mathrm{Be}$ and ${}^9\mathrm{Be}$ are improved; new data for the production cross-section of ${}^{16}\mathrm{O}$ into Be isotopes above a few GeV/n are especially desired.

9 pages, 2 tables, 5 figures (matches accepted A&A version): comparison to [De21] moved to appendix (also highlight impact of reacceleration)