Ultra-high energy cosmic rays (UHECRs, energies above roughly 101810^{18} eV) have defied source identification for decades. Gamma-ray bursts (GRBs), and in particular the population of nearby low-luminosity GRBs (LLGRBs) typified by GRB 980425/SN 1998bw, are longstanding candidate accelerators. Moore, Gendre, Orange & Panther (MNRAS 530, 555, 2024) showed from a rate calculation over an X-ray-selected sample of 41 LLGRBs that reconciling the theoretical LLGRB particle flux with the observed UHECR flux requires each burst to accelerate at most 10−13 M⊙10^{-13}\,M_\odot of UHECRs, and listed the uncertainties that keep this bound and the GRB–UHECR hypothesis untested: unsettled LLGRB origin and jet geometry (hence an unbounded beaming correction fbf_{\rm b}), poorly known intergalactic magnetic fields (IGMF) that decouple production epochs from present-day arrivals through deflections and century-scale delays, a rate normalization dominated by the single nearby event GRB 980425, and the absence of any confirmed GRB neutrino counterpart, leaving the baryonic (proton) loading of GRB jets unmeasured. As of 2024–2026 all of these threads remain open: neutrino nondetections (IceCube, Auger, KM3NeT constraints from KM3-230213A) tighten but do not close the baryonic-loading question; LLGRB geometry is still being actively remodelled; IGMF constraints remain lower limits with orders-of-magnitude uncertainty; and transient-source rate bounds from UHECR anisotropy bracket, but do not decide, the LLGRB contribution.

Background

Cosmic rays with energies above ∼1018\sim 10^{18} eV are called ultra-high energy cosmic rays (UHECRs). Because such particles cannot be magnetically confined to the Galaxy for long and lose energy over cosmological distances, their sources must be both extremely powerful and relatively nearby. Propagation through the cosmic microwave background (CMB) limits the distance from which a ∼1019.5\sim 10^{19.5} eV proton can reach us; this attenuation, the Greisen–Zatsepin–Kuzmin (GZK) effect, defines an effective GZK horizon of order tens to a few hundreds of Mpc, so only sources within that horizon contribute appreciably to the observed flux. Gamma-ray bursts (GRBs), the most luminous explosive transients known, were proposed early on as UHECR sources (Waxman 1995; Vietri 1995; Milgrom & Usov 1995). Attention has focused on the subpopulation of low-luminosity GRBs (LLGRBs), events with isotropic gamma-ray luminosities of roughly 104610^{46}–104910^{49} erg s−1^{-1} (versus ∼1051\sim 10^{51}–105310^{53} for classical long GRBs), associated with Type Ic supernovae, which are abundant in the local Universe precisely because they are faint enough to be detected only nearby. The prototype is GRB 980425/SN 1998bw at ∼40\sim 40 Mpc. The physical origin and geometry of LLGRBs remain unsettled: leading pictures are a relativistic shock breakout from the progenitor's extended envelope, a mildly relativistic collimated outflow, or an ordinary GRB viewed off-axis, and the choice fixes the jet opening angle and hence the beaming correction fbf_{\rm b}, the factor by which the true event rate exceeds the rate of events beamed toward the observer. Moore et al. (2024) computed the local LLGRB rate from an X-ray-selected sample of 41 events (afterglow properties being less plagued by instrumental selection effects than prompt gamma-ray properties), propagated it through the GZK horizon, and bracketed the per-burst particle luminosity between the quasi-spherical limit fb=1f_{\rm b}=1 and a deliberately nonphysical upper bound, concluding that consistency with the observed UHECR flux demands at most ∼10−13\sim 10^{-13} solar masses of UHECRs accelerated per LLGRB. Because only GRB 980425 lies within the GZK horizon, the derived rate and flux are statistically dominated by that single event. Two further ingredients remain poorly constrained. First, the strength, coherence length, and topology of the intergalactic magnetic field (IGMF), the weak field permeating cosmic voids, are unknown to within orders of magnitude; it should not suppress the total flux for an isotropic source population, but it delays sub-GZK particles by potentially hundreds of years, blurring the relation between when UHECRs were produced and when they arrive, and its turbulent structure sets the angular spread of bursts from transient sources. Second, the baryonic loading of GRB jets — the ratio of energy carried by protons (and nuclei) to energy radiated as photons — which determines the UHECR yield per unit gamma-ray energy, can be probed through high-energy neutrinos produced when accelerated hadrons photodisintegrate or interact with photons in the jet, and through comparison of the UHECR composition with the composition of GRB circum-burst and host media; no neutrino has ever been associated with a GRB, and models show the expected neutrino fluence depends strongly on jet composition and Lorentz factor, so nondetections constrain but have not settled the hadronic content.

Problem Statement

Determine whether the low-luminosity gamma-ray burst population can supply an appreciable fraction of the ultra-high-energy cosmic rays observed at Earth, and with what per-burst yield — Moore et al. (2024) find consistency with the observed flux only if each LLGRB accelerates at most ∼10−13 M⊙\sim 10^{-13}\,M_\odot of UHECRs. Four linked uncertainties currently bound this question from both sides: (i) the emission geometry and origin of LLGRBs (shock breakout versus mildly relativistic outflow versus off-axis viewing), which fixes the beaming correction fbf_{\rm b} entering the true rate and per-burst luminosity; (ii) the intergalactic magnetic field strength, coherence length, and topology, which set the deflections and century-to-kiloyear delays connecting production epochs to present-day arrival flux and timing; (iii) the statistical and selection uncertainties of the LLGRB rate normalization, which is dominated by the single nearby event GRB 980425 within the GZK horizon; and (iv) the baryonic loading of GRB jets, which is currently unmeasured.

References

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