Constraining Low-luminosity Gamma-Ray Bursts as Ultra-high-energy Cosmic Ray Sources Using GRB 060218 as a Proxy

Abstract

We study the connection between low-luminosity gamma-ray bursts (llGRBs) and ultra-high-energy cosmic rays (UHECRs) using the canonical low-luminosity GRB 060218 as a proxy. We focus on the consequential synchrotron emission from electrons that are co-accelerated in the UHECR acceleration region, comparing this emission to observations. Both the prompt and afterglow phases are considered. For the prompt phase, we find that bright optical-UV emission is inevitable if the co-accelerated electrons are instantaneously injected into a power-law distribution. To enable acceleration of UHECRs while accommodating the optical-UV emission, it is necessary to keep the electrons from fast cooling (e.g., via reheating). Yet, the energetics of such models are independently constrained from our analysis of the afterglow. For the afterglow phase, we consider mildly relativistic outflows with bulk Lorentz factor Γ 2. Using thermal synchrotron radiation, we show that the initial kinetic energy of the afterglow blast wave of GRB 060218 was 10 times lower than the minimum energy required to satisfy the observed flux of UHECRs. Indeed, a blast wave with sufficient energy and where electrons carry 10-20% of the energy as suggested by particle-in-cell simulations, would typically overshoot the available radio data at ∼ 3 days by more than an order of magnitude. If GRB 060218 is representative of the llGRB population as a whole, then our results show that their relativistic afterglows are unlikely to be the dominant sources of UHECRs. It also implies that for the prompt phase to be the main origin of UHECRs, a majority of the energy would need to escape as cosmic rays, neutrinos, or radiation before the onset of the afterglow, independent of the prompt emission mechanism. More generally, our study demonstrates that synchrotron emission from thermal electrons is a powerful diagnostic of the physics of mildly relativistic shocks.

The problematic connection between low-luminosity gamma-ray bursts and ultra-high-energy cosmic rays

“…As can be seen in the panel, if GRB 060218 hosted accelerated of cosmic-rays to observed energies of 10 20 eV, the optical synchrotron emission from the electrons co-accelerated with the UHECRs would be four orders of magnitude brighter than what was observed. We refer to Samuelsson et al [2] for details on how the optical flux is calculated and how the results varies with the parameters.…”

“…The way to break the degeneracy is to look at the emission from the population of thermal electron (1 − ξ a ), which will constitute the bulk number when ξ a is small. To correctly capture the emission and absorption from the non-thermal and the thermal electrons, we use the numerical simulation outlined in Pe'er & Waxman [16] with some necessary additions as explained in Samuelsson et al [2]. The code assumes spherically symmetry and one-zone emission, accounting for cyclo-synchrotron emission, inverse Compton cooling of the electrons with full Klein-Nishina corrections, and pair production and annihilation.…”

“…It also contains complementary information to other emitted messengers, such as neutrinos and photohadronic gamma-rays, and is therefore important to consider when conducting multi-messenger studies of UHECR sources. The methodology and results presented here are described in more detail in Samuelsson et al [1,2].…”

Particle Acceleration in Mildly Relativistic Outflows of Fast Energetic Transient Sources

“…The mildly relativistic magneto-hydrodynamic (MHD) flows were shown (see, e.g., [48,49]) to be the most efficient environment providing the maximum energies of the accelerated nuclei for a given magnetic/kinetic luminosity of the power engine. Recent models suggested a possibility of cosmic ray acceleration to ultra high energies in the low-luminosity GRBs associated with SNe (see, e.g., [50,51]) and in relativistic SNe [52]. Fast outflows from SNe with dense circumstellar shells could accelerate cosmic rays up to the high energy regime on a few weeks timescale (e.g., [53,54]).…”

UHECR from high- and low-luminosity Gamma-Ray Bursts

“…Several publications discuss Low-Luminosity GRBs (LL-GRBs) with isotropic luminosities of iso < 10 49 erg as a distinct source class which can power the observed UHECR and/or neutrino flux [6][7][8][9][10]. However, [11,12] argue that cosmic rays in these objects may not reach ultra-high energies . Multi-zone models may alleviate the tension between neutrino bounds and cosmic-ray fits by decoupling the production radii of the different particle species; see for example [13,14].…”