The 'Forgotten' Neutrons: Implications for the Propagation of High-Energy Cosmic Rays in Magnetized Astrophysical and Cosmological Structures

Abstract

Cosmological filaments, galaxy clusters, and galaxies are magnetized reservoirs of cosmic rays (CRs). The exchange of CRs across these structures is usually modeled assuming that they remain charged and magnetically confined. At high energies, hadronic interactions can convert CR protons to neutrons. This physics is routinely included in air-shower and ultra-high-energy (UHE) CR propagation Monte Carlo simulations used for composition studies but is rarely treated explicitly in propagation models of CR transport and exchange between magnetized reservoirs. CR neutrons are not affected by magnetic fields and can propagate ballistically over kpc-Mpc distances before decaying back into protons, with relativistic time dilation extending their effective decay length. We show how such charged-neutral switching modifies CR confinement and escape in four representative environments: a Milky Way-like galaxy, a starburst galaxy, a galaxy cluster, and a cosmological filament. By solving the transport of a confined CR proton population in each structure using a diffusion/streaming propagation approach with hadronic pp and p$γ$ interactions, and treating neutron production and decay as a stochastic Poisson ''jump'' process, we find that neutron-mediated steps can allow additional CR escape from large-scale cosmological structures at energies where charged-particle transport alone would predict strong CR confinement and attenuation in ambient radiation fields. These effects imply a qualitative shift in how ultra-high-energy CRs are transferred from embedded sources into filaments and voids once intermediate neutron propagation is considered, with consequences for the partitioning of CRs across the large-scale structure of the Universe.

Figures (8)

• Figure S1: Energy-dependent escape fraction, $f_{\rm esc}(E)$, of injected CR protons from the four characteristic environments considered here: a galaxy cluster, a cosmological filament, a "normal" (Milky Way-like) galaxy, and a starburst galaxy. The black curves show the standard treatment in which hadronic (pp and p$\gamma$) interactions act only as sinks for the charged CR proton population ("without neutrons"). The red curves include charged--neutral switching: neutrons produced stochastically in hadronic interactions propagate ballistically and are counted as escaped if they cross the escape boundary before decaying ("with neutrons"). The escape fraction includes contributions from diffusive and ballistic escape of charged particles and, when active, neutron-mediated escape. Neutron production has a marked impact on high-energy CR escape in all four systems. In clusters and filaments, the neutron-mediated escape channel is dominated by p$\gamma$ interactions. In galaxies, particularly starbursts (where magnetic fields are stronger and interstellar gas density is typically higher), pp interactions drive neutron production at lower energies, but they decay before escaping. Thus the escape channel is only marginal at intermediate energies. In clusters, neutron production causes a modest increase in escape relative to the no-neutron case between $\sim$10$^{18}$ eV under present ($z=0$) conditions.
• Figure S2: Characteristic timescales governing CR confinement, hadronic interactions, and neutron-mediated escape in the four representative environments considered: a galaxy cluster, a cosmological filament, a normal (Milky Way-like) galaxy, and a starburst galaxy. In each panel we compare the charged-particle transport timescale, the pp and p$\gamma$ interaction timescales, the Lorentz-dilated free-neutron $\beta$-decay time, the ballistic crossing time to the relevant escape surface(s), and the fiducial snapshot age adopted for the escape calculations in Figure \ref{['fig:fesc_all_1']}. For the cylindrical systems, separate ballistic crossing times are shown for escape through the side boundary and through the end-caps/top--bottom surfaces. The shaded vertical bands indicate the approximate transition from magnetically confined charged-particle transport to the ballistic regime, based on the particle energy
• Figure S3: Escape factor per injected CR proton, $A(E)=N^{n}_{\rm esc}(E)/N_{\rm inj}^{\rm pri}(E)$, showing the mean number of CR nucleons that escape via the neutron-mediated channel per injected primary CR proton at a given energy $E$ for the illustrative model environments: galaxy cluster (black), cosmological filament (red), normal Milky Way-like galaxy (green), and starburst galaxy (blue). Values of $A\ll 1$ indicate that neutron production has little bearing on particle escape (few neutron-channel escapes per injected CR).
• Figure S4: Directional decomposition of CR escape from the Milky Way-like galaxy model, where charged--neutral switching is included. The total escape fraction $f_{\rm esc}(E)$ (black) is decomposed into contributions through the cylindrical side boundary at the edge of the galaxy ("side escape", dotted), and through the end-caps above and below the galaxy's plane ("end escape", dashed). In all cases, the effect of charged--neutral switching has no major bearing on the escape direction. This shows how the geometry of the system imprints an anisotropy on the emergent CR flux.
• Figure S5: Energy-dependent escape fraction, $f_{\rm esc}(E)$, of injected CR protons from the galaxy cluster model at higher redshift, shown for $z=0.5$ and $z=1$. Black curves show the standard treatment where hadronic interactions act only as sinks for the charged CR population ("without neutrons"), while red curves include charged--neutral switching and neutron-mediated escape ("with neutrons"). Compared with the current epoch results ($z=0$) shown in Figure \ref{['fig:fesc_all_1']}, the high-energy turnover shifts to lower energies at higher redshift because p$\gamma$ absorption and cooling losses are more effective. The neutron channel partially restores the escaping ultra-high-energy tail but does not eliminate the overall redshift-driven suppression in CR escape.