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The acceleration site for ultra-high energy cosmic rays (UHECR) is still an open question despite extended research. In this paper, we reconsider the prompt phase of gamma-ray bursts (GRBs) as a possible candidate for this acceleration and constrain the maximum proton energy in optically thin synchrotron and photospheric models, using properties of the prompt photon spectra. We find that neither of the models favour acceleration of protons to $10^{20}$ eV in high-luminosity bursts. We repeat the calculations for low-luminosity GRBs (llGRBs) considering both protons and completely stripped iron and find that the highest obtainable energies are $< 10^{19}$ eV and $< 10^{20}$ eV for protons and iron respectively, regardless of the model. We conclude therefore that for our fiducial parameters, GRBs, including low-luminosity bursts, contribute little to none to the UHECR observed. We further constrain the conditions necessary for an association between UHECR and llGRBs and find that iron can be accelerated to $10^{20}$ eV in photospheric models, given very efficiency acceleration and/or a small fractional energy given to a small fraction of accelerated electrons. This will necessarily result in high prompt optical fluxes, and the detection of such a signal could therefore be an indication of successful UHECR acceleration at the source.
We reconsider the possibility that gamma-ray bursts (GRBs) are the sources of the ultra-high energy cosmic rays (UHECRs) within the internal shock model, assuming a pure proton composition of the UHECRs. For the first time, we combine the information from gamma-rays, cosmic rays, prompt neutrinos, and cosmogenic neutrinos quantitatively in a joint cosmic ray production and propagation model, and we show that the information on the cosmic energy budget can be obtained as a consequence. In addition to the neutron model, we consider alternative scenarios for the cosmic ray escape from the GRBs, i.e., that cosmic rays can leak from the sources. We find that the dip model, which describes the ankle in UHECR observations by the pair production dip, is strongly disfavored in combination with the internal shock model because a) unrealistically high baryonic loadings (energy in protons versus energy in electrons/gamma-rays) are needed for the individual GRBs and b) the prompt neutrino flux easily overshoots the corresponding neutrino bound. On the other hand, GRBs may account for the UHECRs in the ankle transition model if cosmic rays leak out from the source at the highest energies. In that case, we demonstrate that future neutrino observations can efficiently test most of the parameter space -- unless the baryonic loading is much larger than previously anticipated.
We investigate the production of ultra-high-energy cosmic ray (UHECR) in relativistic jets from low-luminosity active galactic nuclei (LLAGN). We start by proposing a model for the UHECR contribution from the black holes (BHs) in LLAGN, which present a jet power $P_{mathrm{j}} leqslant 10^{46}$ erg s$^{-1}$. This is in contrast to the opinion that only high-luminosity AGN can accelerate particles to energies $ geqslant 50$ EeV. We rewrite the equations which describe the synchrotron self-absorbed emission of a non-thermal particle distribution to obtain the observed radio flux density from sources with a flat-spectrum core and its relationship to the jet power. We find that the UHECR flux is dependent on the {it observed radio flux density, the distance to the AGN, and the BH mass}, where the particle acceleration regions can be sustained by the magnetic energy extraction from the BH at the center of the AGN. We use a complete sample of 29 radio sources with a total flux density at 5 GHz greater than 0.5 Jy to make predictions for the maximum particle energy, luminosity, and flux of the UHECRs from nearby AGN. These predictions are then used in a semi-analytical code developed in Mathematica (SAM code) as inputs for the Monte-Carlo simulations to obtain the distribution of the arrival direction at the Earth and the energy spectrum of the UHECRs, taking into account their deflection in the intergalactic magnetic fields. For comparison, we also use the CRPropa code with the same initial conditions as for the SAM code. Importantly, to calculate the energy spectrum we also include the weighting of the UHECR flux per each UHECR source. Next, we compare the energy spectrum of the UHECRs with that obtained by the Pierre Auger Observatory.
The origin of the ultra high energy cosmic rays (UHECR) with energies above E > 1017eV, is still unknown. The discovery of their sources will reveal the engines of the most energetic astrophysical accelerators in the universe. This is a written version of a series of lectures devoted to UHECR at the 2013 CERN-Latin-American School of High-Energy Physics. We present an introduction to acceleration mechanisms of charged particles to the highest energies in astrophysical objects, their propagation from the sources to Earth, and the experimental techniques for their detection. We also discuss some of the relevant observational results from Telescope Array and Pierre Auger Observatory. These experiments deal with particle interactions at energies orders of magnitude higher than achieved in terrestrial accelerators.
Ultra-high-energy (UHE) cosmic rays (CRs) interact with cosmic background radiation through hadronic processes, and the Universe would become `opaque to UHE CRs of energies $sim$($10^{18}$- $10^{20}$) eV over about several tens of Mpc, setting the Greisen-Zatsepin-Kuzmin (GZK) horizon. We demonstrate that a non-negligible fraction of the UHE CRs arriving on Earth could originate from beyond the GZK horizon when heavy nuclear CRs, and the population and evolution of UHE CR sources are taken into account. We show how the multi-particle CR horizon is modified by different source populations, and discuss how this leads to the natural emergence of an isotropic flux component in the observed UHE CR background. This component would coexist with an anisotropic foreground component contributed by nearby sources within the GZK horizon.
While there is some level of consensus on a Galactic origin of cosmic rays up to the knee ($E_{k}sim 3times 10^{15}$ eV) and on an extragalactic origin of cosmic rays with energy above $sim 10^{19}$ eV, the debate on the genesis of cosmic rays in the intermediate energy region has received much less attention, mainly because of the ambiguity intrinsic in defining such a region. The energy range between $10^{17}$ eV and $sim 10^{19}$ eV is likely to be the place where the transition from Galactic to extragalactic cosmic rays takes place. Hence the origin of these particles, though being of the highest importance from the physics point of view, it is also one of the most difficult aspects to investigate. Here I will illustrate some ideas concerning the sites of acceleration of these particles and the questions that their investigation may help answer, including the origin of underline{ultra} high energy cosmic rays.